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A

SYSTEM OF LOGIC

EATIOCINATIVE AND INDUCTIVE

BEING A CONNECTED VIEW OF THE
PRINCIPLES OF EVIDENCE

AND THE

METHODS OF SCIENTIFIC INVESTIGATION

BY

JOHN STUART MILL

NEW IMPEESSION

LONGMANS, GREEN, AND CO.

39 PATEKNOSTER ROW, LONDON

FOURTH AVENUE & 30th STREET, NEW YORK

BOMBAY, CALCUTTA, AND MADRAS

1919

All rights reserved

Aq\S

Cop-

1006443

>

PEEFACE TO THE FIEST EDITION.

This book makes no pretence of giving to the Avorld a new theory
of the intellectual operations. Its claim to attention, if it possess
any, is grounded on the fact that it is an attempt not to supersede,
but to embody and systematise, the best ideas which have been
either promulgated on its subject by speculative writers, or con-
formed to by accurate thinkers in their scientific inquiries.

To cement together the detached fragmeuts of a subject never yet
treated as a whole ; to harmonise the true portions of discordant
theories, by supplying the links of thought necessary to connect
them, and by disentangling them from the errors with which they
are always more or less interwoven ; must necessarily require a con-
siderable amount of original specnlation. To other originality than
this, the present work lays no claim. In the existing state of the
cultivation of the sciences, there would be a very strong presumption
against any one who should imagine that he had eftected a revolution
in the theory of the investigation of truth, or added any funda-
mentally new process to the practice of it. The improvement which
remains to be etiected in the metliotls of philosophising (and tliQ
author believes that they have much need of improvement) can only
consist in performing more systematically and accurately operations;
with which, at least in their elementary form, the human intellect in
some one or other of its employments is already familiar.

In the portion of the work which treats of Ratiocination, the
author has not deemed it necessary to enter into technical details
which may be obtained in so perfect a shape from the existing
treatises on what is termed the Logic of the Schools. In the con-
tempt entertained by many modern philosophers for the syllogistic
art, it will be seen that he by no means participates ; though the
scientific theory on Avhich its defence is usually rested appears to him
erroneous : and the view which he has suggested of the nature and
functions of the Syllogism may, perhaps, afford the means of con-

iv PREFACE.

cUiating the principles of the art with as much as is well grounded
in the doctrines and objections of its assailants.

The same abstinence from details could not be observed in the
First Book, on Names and Propositions, because many useful prin-
ciples and distinctions which were contained in the old Logic have
been gradually omitted from the writings of its later teachers ; and
it appeared desirable both to revive these, and to reform and rationa
lise the philosophical foundation on which they stood. The earlier
chapters of this preliminary Book will consequently appear, to some
readers, needlessly elementary and scholastic. But those who knoAV
in what darkness the nature of our knowledge, and of the processes
by which it is obtained, is often involved by a confused apprehen-
sion of the import of the different classes of Words and Assertions,
will not regard these discussions as either frivolous or irrelevant to
the topics considered in the latter Books.

On the subject of Induction, the task to be performed was that of
generalising the modes of investigating truth and estimating evidence,
by which so many important and recondite laws of nature have, in the
various sciences, been aggregated to the stock of human knowledge.
That this is not a task free from difficulty may be presumed from
the fact, that even at a very recent period, eminent writers (among
whom it is sufficient to name Archbisliop Wluitely, and the author
of a celebrated article on Bacon in the Edinhiirgh Review) have not
scrupled to pronounce it impossible.* The author has endeavoured
to combat their theory in the manner in Avliich Diogenes confuted the
sceptical reasonings against the possibility of motion ; remembering
that Diogenes' argument would have been equally conclusive, thongh
his individual perambulations might not have extended beyond the
circuit of his own tub.

Whatever may be the value of what tlie author has succeeded in
effecting on this branch of his subject, it is a duty to acknowledge that
for much of it he has been indebted to several important treatises,
partly historical and partly philosophical, on the generalities and pro-
cesses of physical science, which have been published within the last
few years. To these treatises, and to their authors, he has endeavoured
to do justice in the body of the work. But as with one of these

* In the later editions of Archbishop Whately's Logic, he states his meaning' to be,
not that "rules" for the ascertainment of truths by inductive investigation cannot
be laid dow^n, or that tbey may not be " of eminent service," but that they "must
always be comparatively vague and general, and incapable of being built up into a
regular demonstrative theory like that of the Syllogism." (Book iv. ch. iv. § 3.)
And he observes, that to devise a system for this purpose, capable of being "brought
into a scientific form," would be an achievement which "he must be more sanguine
than scientific who expects." (Book iv. ch. ii. § 4.) To effect this, liowever, being
the express object of the portion of the present work which treats of Induction, the
words in the text are no overstatement of the difference of opinion between Arch-
bishop Whately and me on the subject.

t^REFACEJ. V

writers, Dr. Wliewell, he lias occasion frequently to express ditferences
of opinion, it is more particularly incumbent on him in this place
to declare, that without the aid derived from the facts and ideas
contained in that gentleman's History of the Inductive Sciences, the
corresponding portion of this work would probably not have been
written.

The concluding Book is an attempt to contribute towards the solu-
tion of a question, which the decay of old opinions, and the agitation
that disturbs Euiopean society to its inmost depths, render as impor-
tant in the present day to the practical interest of human life, as it
must at all times be to the completeness of our speculative know-
ledge : viz. Whether moral and social phenomena are really exceptions
to the general certainty and uniformity of the course of nature ; and
how far the methods, by which so many of the laws of the physical
world have been numbered among truths irrevocably acquired and
universally assented to, can be made instrumental to the formation
of a similar body of received doctrine in moral and political science.

PREFACE TO THE THIRD AND FOURTH
EDITIONS.

Several criticisms, of a more or less controversial character, on this
work, have appeared since the publication of the second edition ; and
Dr. Whewell has lately published a reply to those parts of it in which
some of his opinions were controverted.*

1 have carefully reconsidered all the points on an hieh my conclu-
sions have been assailed ; but, I have not to announce a change of
opinion on any matter of importance. Such minor oversights as have
been detected, either by myself or by my critics, I have, in general
silently, corrected ; but it is not to be inferred that I agree with the
objections which have been made to a passage in every instance in
which I have altered or cancelled it. I have often done so, merely
that it might not remain a stumbling-block, when the amount of dis-
cussion necessary to place the matter in its true light would have
exceeded what was suitable to the occasion.

To several of the arguments which have been urged against me, I
have thought it useful to reply with some degree of minuteness ; not

* Kow forming a cLajiter in his volume on The Philosophy of Di&covei~y.

VI PREFACE.

from any taste for controversy, but because the opportunity was
favourable for placing my own conclusions, and the grounds of them,
more clearly and completely before the reader. Truth on these sub-
jects is militant, and can only establish itself by means of conflict.
The most opposite opinions can make a plausible show of evidence
while each has the statement of its own case ; and it is only possible
to ascertain which of them is in the right after hearing and comparing
what each can say against the other, and what the other can urge in
its defence.

Even the criticisms from which I most dissent have been of great
service to me, by showing in what places the exposition most needed
to be improved or the argument strengthened. And I should have
been well pleased if the book had undergone a much greater amount
of attack, as in that case I should probably have been enabled to
improve it still more than I believe I have now done.

PREFACE TO THE EIGHTH EDITION.

In the subsequent editions, the attempt to improve the work by
additions and corrections, suggested by criticism or by thought, has
been continued. The additions and corrections in tlie present (eighth)
edition, which are not very considerable, are chiefly such as have
been suggested by Professor Bain's Logic, a book of great merit and
value. Mr. Bain's view of the science is essentially the same with
that taken in the present treatise, the differences of opinion being few
and unimportant compared with the agreements ; and he has not
only enriched the exposition by many applications and illustrative
details, but has appended to it a minute and very valuable discussion
of the logical principles specially applicable to each of the sciences ; a
task for which the encyclopedical character of his knowledge peculiarly
qualified him. I have in several instances made use of his exposition
to improve my ow^n, by adopting, and occasionally by controverting,
matter contained in his treatise.

The longest of tlie additions belongs to the chapter on Causation,
and is a discussion of the question, hoAV far, if at all, tlie ordinaiy
mode of stating the law of Cause and Effect requires modification to
adapt it to the new doctrine of the Conservation of Force : a point
still more fully and elaborately treated in Mr. Bain's work.

C 0 I^ T E N T S.

INTHODUCTIOK
c.

A definition at the commencement of a subject must be provisional
Is Logic the art and science of reasoning?
Or the art and science of the pursuit of truth ?
Logic is concerned with inferences, not with intuitive trutlis
Relation of Logic to the otlier sciences . .
Its utility, how shown
Uefinitiuu of Logic stated and illustrated

BOOK I.
OF NAMES AND PROPOSITIONS.

Chapter I. I

0/ the Necessity of commencing with an \
Analysis of Languaye.

BEC. PAGE

1. Theory of names, why a necessary |

part of Ix»«ic ii ;

2. First step in the analysis of Pro- I

positions . . .. . . . . 12 |

3. Names must be studied before i

things 13

Chapter II.
Of Names.

1. Names ore names of things, not of

our ideas

2. Words which are not names, but

pai ts of names

3. General and Singular names

4. Concrete and Abstract

5. Connotative and Non-counoiative

6. Positive and Negative

7. Relative and A b-olute

8. Univocal and ^Equivocal . .

Chapter III.
Of the Things denoted by Names.

1. Necessity of an enumeration of

Nameable Things. The Cate-
gories of Aristotle . . . . . . 29

2. Ambiguity of the most general

names . . . . 30

3. Feelings, or states of consciousness

4. Feelings must be distinguislied

from theii- physical antecedents.
Perceptions, what,

5. Volitions and Actions, what

6. Substance and Atti ibute . .

7. Body . .

8. Mind

9. Qualities
10. Relations

n. Resemblance..

12. Quantity

13. All attributes of bodies are

grounded on states of conscious-
ness

14. So also all attributes of mind . .

15. Recapitulation

PAGE
32

Chapter IV.

Of Propositions.

Nature and office of the copula . . 49
Affirmative and Negative proposi-
tions 51

Simple and Complex . . . . 52

Universal, Particular, and Singular 54

Chapter V.

Of the Import oj Propositions.

I. Doctrine that a Proposition is the
expression of a relation between
two ideas 55

viii

CONTENTS.

Doctrine that it is the expression
of a relation between the mean-
ings of two names

Doctrine that it consists in refer-
ring Ronietbing to, or excluding
something from, a class . .

What it really is

It asserts (or denies) a sequence, a
co-existence, a simple existence,
a causation

— or a resemblance

Propositions of which the terms
are abstract

68

Chapter VI.
Oj Propositions merely Verbal.

1. Essential and Accidental Proposi-

tions

2. All essential Propositions are

identical Propositions

3. Individuals have no essences

4. Real Propositions, how distin-

guished from verbal

5. Two modes of representing the

import of a real Proposition . . 7

Chapter VII.

Of the Nature of Classification, and

the Five Predicables.

1. Classification, how connected with

naming

74

76

SEC. PAGE

2. The Predicables, what .. .. 77

3. Genus and Species . . . . . . 77

4. Kinds have a real existence in

nature 79

5. Differentia , . 8i

6. Differentiai for general purposes,

and differentiae for special or

technical purposes . , . . 83

7. Proprium 84

8. Accidens 88

Chapter VIII.
Of Definition.

A definition, what 86

Every name can be defined whose
meaning is susceptible of analy-
sis 87

Complete, how distinguished from
incomplete definitions . . . . 88

— and from descriptions . . . . 89
What are called definitions of

Things, are definitions of Names
with an implied assumption of
tlie existence of Things corre-
sponding to them 92

— even when such things do not

in reality exist . . . . . . 97

Definitions, though of names only,
must be grounded on knowledge
of the corresponding things . . 98

BOOK II.
OF EEASONING.

Chapter I.
Of Inference, or Reasoning, in general.

1. Retrospect of the preceding Book 103

2. Inferences improperly so called . . 104

3. Inferences proper, distinguished

into inductions and ratiocina-
tions 107

Chapter II.
Of Batiocination, or Syllogism.

1. Analysis of the Syllogism .. .. 108

2. The dictum de omni not the foun-

dation of reasoning, but a mere
identical proposition .. .. 113

3. What is the really fundamental

axiom of Ratiocination .. .. 116

4. The other form of the axiom . . 117

Chapter III.

Of the Functions and Logical Value
of the Syllogism.

1. Is the Syllogism a petitio prin-

cipii? . . . . . . .... 119

2. InsufiBciency of the common

theory 120

3. All inference is from particulars.

to particulars 121

4. General Propositions are a record

of such inferences, and the rules
of the Syllogism are rules for the
interpretation of the record . . 126

5. The Syllogism not the type of

reasoning, but a test of it . . 128

6. The true type, what . . . . 131
7 Relation between Induction and

Deduction .. .. .. .. 133

8. Objections answered .. .. 134

9. Of Formal Logic, and its relation

to the Logic of Truth . . . . 136

CONTENTS.

ht

Chapter IV.

0/ Trains of Reasoning, and Deduc-
tive Sciences.

SEC PAGE

1. For what purpose trains of reason-

ing exist

2. A train of reasoning is a series of

inductive Inferences

3. — from particulars to particulars

through marks of marks . .

4. Why there are deductive sciences

5. Why otlier sciences still remain

expeiimental

6. Experimental sciences may become

deductive by the progress of
experiment

7. In what manner this usually takes

place

137

138

139
141

143

M5

145

Chapter V.

Of Demonstration, and Ifecessar^
Truths.

The Theorems of Geometry are
necessary truths i-uly in the
sense of necessarily following
from hypotheses

Those liypotheses are real facts
with some of their circumstances
exaggerated or omitted . .

Some of the first principles of
Geometry are axioms, and these
are not hypothetical

— but are experimental truths . .

An objection answered

SEC. PAGE

6. Dr. Whewell's opinions on axioms

examined . . 156

Chapter VI.
The same Subject continued.

1. All deductive sciences are induc-

tive 164

2. The propositions of the Science of

Number are not verbal, but gene-
ralisations from experience . . 166

3. In what sense hypothetical . . 169

4. The characteristic property of de-

monstrative science is to be
hypothetical .. .. .. 170

5. Definition of demonstrative evi-

dence 171

Chapter VII.

Examination of some Opinions op-
posed to the preceding doctrines.

172

173

Doctrine of the Universal Pos-
tulate . .

The test of inconceivability does
not represent the aggregate of
past experience

— nor is implied in every process
of thought 175

Objections answered .. .. 179

Sir W. Hamilton's opinion on the
Principles of Contradiction and
Excluded Middle 182

BOOK III.
OF INDUCTION.

Chapter I.

Preliminary Ohstrvations on Induc-
tion in General.

1. Importance of an Inductive Logic 185

2. The Logic of Science is also that of

business and life 185

Chapter II.
Of Inductions im,properly so called.

1. Inductions distinguished from ver-

bal transformations . . . . 18

2. — from inductions, falsely so

called, in mathem-atics . . . . 19

3. — and from descriptions . . . . 19

4. Examination of Dr. Whewell's

theory of Induction

5. Further illustration of the preced

ing remarks 198

192

Chapter III.
Od the G-round of Induction.

Axiom of the uniformity of the
course of Nature . . . . . . 200

Not true in every sense. Induc-
tion per enumerationem simplicem 203

The question of Inductive Logic
stated 20s

Chapter IV.
Of Laivs of Nature.

The general regularity in nature
is a tissue of partial regularities,
called laws ao6

Scientific induction must be
grounded on previous spon-
tanei 'US inductions .. .. 208

Ate there any inductions fitted to
be a test of all others ? . . . . 20Q

CONTENTS.

Chapter V.
0/ the Law of Univei'sal Causation.

SEC. PAGE

1. The universal law of successive

plieiioinena is the Law of
Causation 211

2. — i.e. the law that every con-

sequent has an invariable ante-
cedent 213

3. The cause of a phenomenon is the

assemblage of its conditions . . 214

4. The distinction of agent and

patient illusory 218

5. Case in which the effect consists

in giving a property to an object 220

6. Tlie c;iuse is not the invariai)le

antecedent, but the uncondi-
tional invavUMo antecedent .. 221

7. Can a cause be simultaneous with

its effect? . . .. .. . . 224

8. Idea of a permanent Cause, or

original natural agent . . . . 225

9. Uniformities of co-existence be-

tween effects of different per-
manent causes are not laws . . 227

10. Theory of the Conservation of

Force 228

11. Doctrine that volition is an eflfi-

cient cause, examined . . . . 232

Chapter VI.
Of the Composition of Causes.

1. Two modes of , the conjunct action

of causes, the mechanical and
the chemical . . . . . . 242

2. The composition of causes the

general rule, the other case ex-
ct-ptional 244

3. Are effects jji oportional to their

causes ? . . 246

Chapter VII.
bf Observation and Experiment.

1, The first step of inductive inquiry

is a mental analysis of conqolex
phenottiena into thuir elements 247

2. The next is an actual separation

249

of those elements . .
3. Advantages of experiment over
observation 1 '.

249

4. Advantages of observation over
experiment 25

Chapter VIII.

Of the Four Methods of Experimental
Inquiry.

1. Method of Agreement . . . . 253

2. M'-thod of Difference ,. .. 255

3. Mutual relation of these two me-

thods 256

SEC. PAGE

4. Joint Method of Agreement and

Difference . . . » . , . . 258

5. Method of Residues 259

6. Method of Concomitant Variations 260

7. Limitations of this last method . . 264

Chapter IX.

Miscellaneous Examples of the Four
Methods.

1. Liebig's theory of metallic poisons 267

2. Theory of induced electricity . . 269

3. Dr. Wells' theory of dew .. .. 271

4. Dr. Brown-Sequard's theory of

cadaveric rigidity 276

5. Examplesof the Method of Residues 279

6. Di-. Whewell's objections to the

Four Methods 282

Chapter X.

Of Plurality of Causes : and of the In-
termixture of Effects.

1. One effect may have several causes 285

2. — which is the source of a character-

istic imperfection of the Method

of Agreement 286

3. Plurality of Causes, how ascer-

tained 288

4. Concurrence of Causes which do

not compound their effects . . 289

5. Difficulties of the investigation

when causes compound their
effects . . . . . . . . . . 291

6. Three modes of investigating the

laws of complex effects . . . . 294

7. The method of simple observation

inapplicable 295

8. The purely experimental method

inapplicable 296

Chapter XI.
Of the Deductive Method.

1. First stage ; ascertainment of the

liiws of the separate causes by
direct inductijan 299

2. Sec! >nd stage ; ratiocination from

the simple laws of the complex
cases . . . . . . . . . . 302

3. Third stage ; verification by specific

experience 303

Chapter XII.
Of the Explanation of Laws of Nature.

1. Explanation defined . . . . 305

2. First mode of explanation ; by re-

solvinsr the law of a complex effect
into the laws of tlie concurrent
causes and the fact of their co-ex-
istence 305

CONTENTS.

TO.

BEC. PAGE

3. Second mode ; by the detection of

an intei-mediate link in the se-
quence 306

4. Liiws are always resolved into laws

more general than themselves .. 307

5. Third mode ; the subsiimption of

less general laws under a more
general one . . 308

6. What the explanation of a law of

nature amounts to 310

Chapter XIII.

Miscellaneous Examples of the Explana-
tion of Laics of Nature.

1. The general theories of the sciences 311

2. Examples from chemical specula-

tions 312

3. Example from Dr. Brown-Seqnard's

researches on the nervous systcTu 313

4. Examples of following newly-dis-

covered laws into their complex
mjinifestations 314

5. Examples of empirical generalisa-

tions, afterwards confirmed and
explained deductively .. .. 315

6. Example from mental science . . 316

7. Tendency of all the sciences to be-

come deductive 317

Chapter xrv.

Of the Limits to the Explanation of Laws
of Nature ; and of Hypotheses.

1. Can all the seqxiences in nature be

resolvable into one law? . . . . 318

2. Ultimate laws cannot be less numer-

ous than the distinguishable feel-
ings of o\ir nature 318

3. In what sense ultimate facts can

be explained .. 321

4. The proper use of scientific hypo-

theses . . . . 322

5. Tiieir indispensableness . . . . 326

6. The two degrees of legitimacy in

hypotheses 327

7. Some inquiries apparently hypo-

thetical are really inductive .. 332

Chapter XV.

Of Progressive Effects ; and of the Con-
tinued Action of Causes.

1. How a progressive effect results

from the simple continuance of
the cause 333

2. — and from the progressiveness of

the cause 336

3. Derivative laws generated from a

single ultimate law 337

Chapter XVI.

Of Empirical Laws.

1. Definition of an emi-irical law .. 338

SEC. PACK

2. Derivative laws commonly depend

on collocations 339

3. The collocations of the permanent

causes are not reducible to any
law 340

4. Hence empirical laws cannot be

relied on beyond the limits of
actual experience . . . . . . 340

5. Generalisations which rest only 011

the Method of Agreement can 01. ly

be received as empirical laws . . 341

6. Signs from which an observed uni-

fonnity of sequence may be pre-
sumed to be resolvable . . . . 342

7. Two kinds of empirical laws . . 343

Chapter XVII.
Of Chance and its Elimination.

1. The proof of empirical laws de-

pends on tiie theory of chance . . 344

2. Cliance defined and characterised 345

3. The elimination of chance . . . . 348

4. Discovery of residual phenomena

by eliminating chance .. .. 349

5. The doctrine of chances .. .. 350

Chapter XVIII.
Of the Calculation of Chances.

1. Foundation of the doctrine of

chances, as taught by mathe-
matics.. .•. ■.. .. .. 350

2. The doctrine tenable .. .. 352

3. On what foundation it really rests 352

4. Its tiltimate dependence on causa-

tion 355

5. Theorem of the doctrine of chances

which relates to the cause of a
given event 357

6. How applicable to the elimination

of chance 358

Chapter XIX.

Of the Extension of Derivative Laws to
Adjacent Cases.

1. Derivative laws, when not causal,

are almost always contingent on
collocations . . 360

2. On what grounds they can be ex-

tended to cases Ijej'ond the bounds

of actual experience . . . . 361

3. Those cases must be adjacent cases 362

Chapter XX.
Of Analogy.

1. Various senses of the word analogy 364

2. Nature of analogical evidence . . 365

3. On what circumstances its value

depends 367

3ui

CONTENTS.

Chapter XXI.

Of the Evidence of the Law of Universal
Causation.

SKC. PAGE

1. The law of causality does not rest

on an instinct 368

2. But on an induction by simple

enumeration 371

3. In what cases such induction is

allowable 373

4. The universal prevalence of the law

of causality, on what grounds ad-
missible 374

Chapter XXII.

Of Uniformities of Co-existence not de-
pendent on Causation.

377

379

380
381

382

382
383

384

1. Uniformities of co-existence which

result from laws of sequence

2. The pro()erties of Kinds are uni

formities of co-existence . .

3. Some are derivative, others ulti

mate

4. No universal axiom of co-existence

5. The evidence of uniformities of co-

existence, how measured . .

6. When derivative, their evidence is

that of empirical laws

7. So also when ultimate

8. Ttie evidence stronger in propor-

tion as tiie law is more general . .

9. Every distinct Kind must be exa-

mined 385

Chapter XXIII.

Of Approximate Genei'alisations, and
Probable Evidence.

1. The inferences called probable rest

on approximate generalisations. . 386

2. Approximate generalisations less

usef id in science than in life . . 387

3. In what cases they may be resoi-ted

to 388

4. In what manner proved . . . . 389

5. With what precautions employed 390

SEC. pagb

6. The two modes of combining pro-

babilities 391

7. How approximate generalisations

may be converted into accurate
generalisations equivalent to them 394

Chapter XXIV.
Of the Remaining Laws of Nature.

1. Propositions which assert mere ex-

istence 2,gs

2. Resemblance considered as a sub-

ject of science

3. The axioms and theorems of mathe-

matics comprise the principal laws
of resemblance

4. — and those of order in place, and

rest on induction by simple enu-
meration

5. The propositions of arithmetic

aflSrm the modes of formation of
some given number

6. Those of algebra affirm the equiva-

lence of different modes of forma-
tion of numbei's generally

7. The propositions of Geometry are

laws of outward nature . .

8. Why Geometry is almost entirely

deductive

9. Function of mathematical truths

in the other sciences, and limits
of that function

Chapter XXV.
Of the Grounds of Disbelief.

1. Improbability and impossibility . .

2. Examination of Hume's doctrine of

miracles

3. The degrees of improbability corre-

spond to differences in the nature
of the generalisation with which
an assertion conflicts

4. A fact is not incredible because the

chances are against it

5. Are coincidences less credible than

other facts?

6. An opinion of Laplace examined . .

396

397

398

405

406

407
408

413
415

BOOK IV.

OF OPERATIONS SUBSIDIARY TO INDUCTION.

Chapter I.
Of Observation and Description.

I. Observation, how far a subject of

Logic .. .. .. .. .. 419

a. A great part of what seems obser-
vation iti really inference . . . . 420

The description of an observation
affirms more than is contained in
the observation 422

— namely, an agreement among
phenomena ; and the comparison
of phenomena to ascertain such
agreements is a preliminary to
induction 423

CONTENTS.

Xlll

Chapter II.

Of Abstraction, or the Formation of
Conceptions.

SEC. PAGE

1. The comparison which is a prelimi-

nary to induction implies general
conceptions 424

2. — but these need not be pre-exis-

tent 425

3. A general conception, originally tho

result of a comparison, becomes
itself the type of comparison . . 427

4. What is meant by appropriate con-

ceptions . . . . . . , . 429

5. — and by clear conceptions . . 430

6. Further illustration of the subject 432

Chapter III.
Of Naming, as subsidiary to Induction.

1. The fundamental property of names

as an insiriiment of thought .. 433

2. Names are not indispensable to in-

duction 434

3. In what manner subservient to it 435

4. General names not a mere contriv-

ance to economise the use of lan-
guage 436

Chapter IV.

Of the Requisites of a Philosophical
Language, and the Principles of De-
finition.

1. First requisite of philosophical lan-

guage, a steady and determinate I

meaning for every general name 436

2. Names in common use have often

a loose connotation . . . . 436

3. — wliich the logician should fix,

with as little alteration as pes- j

sible 438 I

4. Vihy definition is often a question

not of words but of things . . 439

5. How the logician should deal with

the transitive applications of
WO! ds . . . . . . . . . . 441

6. Evil consequences of casting off any

portion of the customary connota-
tion of words

Chapter V.

444

On the Natural History of the VaHa-
tions in the Meaning of Terms.

I. How circumstances originally acci-
dental become incorporated into
the meaning of words . . . . 448

SEC. PAGE

2. — and sometimes become the whole

meaning .. 450

3. Tendency of words to become gene-

ralised .. .. 451

4. — and to become specialised . . 453

Chapter VI.

The Principles of Philosophical Lan-
guage further considered.

1. Second requisite of philosophical

language, a name far every im-
portant meaning 455

2. — viz. first, an accurate descrip-

tive terminology 456

3. — secondly, a name for each of the

more important results of scien-
tific abstraction 458

4. — thirdly, a nomenclature, or sys-

tem of the names of Kinds . . 459

5. Peculiar nature of the connotation

of names which belong to a nomen-
clature 461

6. In what cases language may, and

may not, be used lucchauically . . 462

Chapter VII.

Of Classification as Subsidiary to In-
duction.

1. Classification as here treated of,

wherein different from the classi-
fication implied in naming . . 465

2. Theory of natural groups . . . . 466

3. Are natural groups given by type

or by definition? 468

4. Kinds are natural groups .. .. 470

5. How the names of Kinds should be

constructed 473

Chapter VIII.
Of Classification by Series.

1. Natural groups should be arranged

in a natural series . . . . . . 475

2. The arrangement should follow the

degrees of the main phenome-
non 475

3. — which implies the assumption

of a type-species . . . . . . 476

4. How the divisions of the series

should be determined . . . . 477

5. Zoology affords the completest type

of scientific classification.. .. 478

XIV

CONTENTS.

BOOK V.
ON FALLACIES.

485

487

Chapter I.
Of Fallacies in General.

SEC. PAGE

1. Theory of fallacies a necessary part

of Logic 481

2. Casual mistakes are not fallacies. . 482

3. The moral sources of erroneous

opinion, how related to the intel-
lectual 482

Chapter II.
Classification of Fallacies.

1. On what criteria a classification of

fallacies should be grounded

2. The five classes of fallacies. .

3. The reference of a fallacy to one or

another class is sometimes arbi-
trary

Chapter III.

Fallacies of Simple Inspection, or a
priori Fallacies.

1. Character of this class of Fallacies 48!

2. Natural prejudice of mistaking

subjective laws for objective,
exemplified in popular supersti-
tions 48c

3. Natural prejudices that things

which we think of together must
exist together, and that what is
inconceivable must be false

4. Natural prejudice of ascribing

objective existence to abstrac-
tions

5. Fallacy of the Sufficient Reason . .

6. Natural prejudice that tiie differ-

ences in nature correspond to the
distinctions in language ..

7. Prejudice that a phenomenon can-

not liave more than one cause , .

8. Prejudice that the conditions of a
• phenomenon must resemble the

phenomenon

491

495
496

497

Chapter IV.
Fallacies of Observation.

SEC. PAGE

1. Non-observation and Mal-observa-

tion

2. Non-observation of instances, and

non-obseryation of circumstances

3. Examples of the former

4. — and of the latter . .

5. Mal-observation characterised and

exemplified

Chapter V.
Fallacies of Generalisation.

1. Character of the class

2. Certain kinds of generaHsation

must always be groundless

3. Attempts to resolve phenomena

radically different into the same

4. Fallacy of mistaking empirical for

causal laws . .

5. Post hoc, ergo propter hoc ; and the

deductive fallacy corresponding
to it

6. Fallacy of False Analogies . .

7. Function of metaphors in reason-

ing

8. How fallacies of generalisation

grow out of bad classification . .

Chapter VI.
Fallacies of Ratiocination,

1. Introductory Remarks

2. Fallacies in the conversion and
pequipollency of propositions

4-

Fallacies in the syllogistic process
Fallacy of changing the premises . .

Chapter VII.
Fallacies of Confusion.

1. Fallacy of Ambiguous Terms

2. Fallacy of Petitio Principii

3. Fallacy of Ignoratio EUnchi

506

506
507

509

512

S14

515
516

519
520

525

526

526
527
527

530
537
542

CONTENTS.

BOOK VI.

ON THE LOGIC OF THE MOEAL SCIENCES.

Chapter I.
Introductory Remarks,

SEG. PAGE

I. The backward sfcite of the Moial
Sciences can only be remedied
by applying to them the methods
of Physical Science, duly ex-
tended and genei-alisod . . . . 545

3. How far this can be attemi^ted in

the present work 546

Chapter II.
Of Liberty and Xecessity.

1. Are human actions subject to the

law of causality ? 547

2. The doctrine commonly called

Philosophical Necessity, in what
sense true 547

3. Inappropriateness and pernicious

effect of the term Necessity . . 549

4. A motive nob always the antici-

pation of a pleasure or u pain . . 551

Chapter III.

That there is, or may be, a Science of
Human Nature.

1. There may be sciences which are

not exact sciences 552

2. To what scientific type the Science

of Human Nature corresponds . . 553

Chapter IV.
Of the Laics of Mind.

What is meant by Laws of Mind. ,

Is there a Science of Psychology ?

The principal investigations of
Psychology characterised

Relation of nienttd facts to physi-
cal conditions

555
555

557

Chapter V.

Of Ethology, or the Science of the For-
mation of Character.

1. The Empirical Laws of Human

Nature 562

2. — are merely approximate genera-

lisations. The universal laws
are those of the formation of
character . , 563

3. The laws of the formation of char-

acter cannot be ascertained by

obNcrvation and experiment .. 564

4. — but must be studied deductively 567

5. The principles of Ethology are the

axiomata media of mental science 568

6. Ethology characterised . • . . 570

Chapter VI.

General Considerations on the Social
Science.

1. Are Social Phenomena a subject of

Science? .. 571

2. Of what nature the Social Science

must be

572

Chapter VII.

Of the Chemical, or Experimental
Method in the Social Science.

1. Characters of the mode of thinking

which deduces political doctrines
from specific experience . . , . 573

2. In ttie Social Science experiments

are impossible . . . . . . 574

3. — the Method of Difference in-

ajjplicable 575

4. — and the Methods of Agreement

and of Concomitant Variations
inconclusive .. .. ., 576

5. The Method of Residues also in-

conclusive, and presupposes De-
duction 577

Chapter VIII.
Of the Geometrical, or Abstract Method.
I. Characters of this mode of think-
of the Geometrical
the

ing

2. Examples

Method

3. The interest-philosoi^hy of

Bentham School . .

578
579
580

Chapter IX.

Of the Physical, or Concrete Deductive
Method.

1. The Direct and Inverse Deductive

Metlinds 583

2. Difficulties of the Direct Deductive

ilethod in the Social Science . . 585

3. To wliat extent the ditferent

branches of sociolo„dcal specu-

XVI

CONTENTS.

SIC. PAGE

lation can be studied apart.
Political Economy characterised 587

4. Political Ethology, or the science

of National Character , . . . 590

5. The Empirical Laws of the Social

Science . . 592

6. The Verification of the Social

Science 593

Chapter X.

Oj the Inverse Deductive, or His-
torical Method.

1. Distinction between the general

Science of Society and special
Sociological inquiries . . . . 594

2. What is meant by a State of

Society? 595

3. The Progressiveness of Man and

Society 595

4. The laws of the succession of states

of Society can only be ascei--
tained by the Inverse Deductive
Method 597

5. Social Statics, or the science of the

Co-existences of Social Pheno-
mena .. 598

6. Social Dynamics, or the science of

the Successions of Social Pheno-
mena . . 603

7. Outlines of the Historical Method 604

8. Fiiture prospects of Sociological

Inquiry .. 605

Chapter XL

Additional Elucidations of the Science
of History.

SKC. PAGE

1. The subjection of historical facts

to tuiiform laws is verified by
statistics 607

2. — does not imply the insignifi-

cance of moral causes . . . . 6og

3. — nor the inefficacy of the charac-

ters of individuals and of the
acts of governments .. .. 611

4. The historical importance of emi-

nent men and of the policy of
governments illustrated . . . . 613

Chapter XII.

Of the Logic of Practice, or Art ; in-
cluding Morality and Policy.

1. Morality not a science, but an Art 616

2. Relation between rules of Art and

the theorems of the correspond-
ing science 616

3. Wliat is the proper function of

rules of Art? 617

4. Art cannot be Deductive . . . . 618

5. Every Art consists of truths of

Science, arranged in the order
suitable for some practical use . . 619

6. Teleology, or the doctrine of Ends 619

7. Necessity of an ultimate standard,

or first principle of Teleology . . 620

8. Conclusion 622

INTRODUCTION

§ I. There is as great diversity
among authors in the modes which
they have adopted of defining logic, as
in their treatment of the details of
it. This is what might naturally be
expected on any subject on which
writers have availed themselves of
the same language as a means of de-
livering different ideas. Ethics and
jurisprudence are liable to the remark
in common with logic. Almost every
writer having taken a different view
of some of the particulars which these
branches of knowledge are usually
understood to include, each has so
framed his definition as to indicate
beforehand his own peculiar tenets,
and sometimes to beg the question in
their favour.

This diversity is not so much an
evil to be complained of, as an inevit-
able and in some degree a proper
result of the imperfect state of those
sciences. It is not to be expected
that there should be agreement about
the definition of anything, until there
is agreement about the thing itself.
To define, is to select from among all
the properties of a thing, those which
shall be understood to be designated
and declared by its name ; and the
properties must be well known to us
before we can be competent to deter-
mine which of them are fittest to be
chosen for this purpose. Accordingly,
in the case of so complex an aggrega-
tion of particulars as are compre-
hended in anything which can be
called a science, the definition we set
out with is seldom that which a more
extensive knowledge of the subject

' shows to be the most appropriate.
Until we know the particulars them-

I selves, we cannot fix upon the most
correct and compact mode of circum-
scribing them by a general descrip-
tion. It was not until after an ex-
tensive and accurate acquaintance
with the details of chemical pheno-
mena, that it was found possible to
frame a rational definition of chemis-
try ; and the definition of the science
of life and organization is still a
matter of dispute. So long as the
sciences are imperfect, the definitions
must partake of their imperfection ;
and if the former are progressive, the
latter ought to be so too. As much,
therefore, as is to be expected from a
definition placed at the commence-
ment of a subject, is that it should
define the scope of our inquiries : and
the definition which I am about to
offer of the science of logic, pretends
to nothing more, than to be a state-
ment of the question which I have
put to myself, and which this book
is an attempt to resolve. The reader
is at liberty to object to it as a defini-
tion of logic ; but it is at all events
a correct definition of the subject of
these volumes.

§ 2. Logic has often been called
the Art of Reasoning. A writer*
who has done more than any other
person to restore this study to the
rank from which it had fallen in the
estimation of the cultivated class in
our own country, has adopted the

* Archbishop Whately.
A

INTRODUCTION.

above definition with an amendment ;
he has defined Logic to be the Science,
as well as the Art, of reasoning ;
meaning by the former term, the
analysis of the mental process which
takes place whenever we reason, and
by the latter, the rules, grounded on
that analysis, for conducting the pro-
cess correctly. There can be no
doubt as to the propriety of the emen-
dation. A right understanding of
the mental process itself, of the con-
ditions it depends on, and the steps
of which it consists, is the only basis
on which a system of rules, fitted for
the direction of the process, can pos-
sibly be founded. Art necessarily
presupposes knowledge ; art, in any
but its infant state, presupposes scien-
tific knowledge : and if every art
does not bear the name of a science,
it is only because several sciences are
often necessary to form the ground-
work of a single art. So complicated
are the conditions which govern our
practical agency, that to enable one
thing to be done, it is often requisite
to know the nature and properties of
many things.

Logic, then, comprises the science of
reasoning, as well as an art, founded on
that science. But the word Reason-
ing, again, like most other scientific
terms in popular use, abounds in
ambiguities. In one of its accepta-
tions, it means syllogizing ; or the
mode of inference which may be
called (with sufficient accuracy for
the present purpose) concluding from
generals to particulars. In another
of its senses, to reason is simply to
infer any assertion, from assertions
already admitted : and in this sense
induction is as much entitled to be
called reasoning as the demonstra-
tions of geometry.

Writers on logic have generally
preferred the former acceptation of
the term : the latter, and more exten-
sive signification is that in which I
mean to use it. I do this by virtue
of the right I claim for every author,
to give whatever provisional definition
he pleases of his own subject. But

sufficient reasons will, I believe, un-
fold themselves as we advance, why
this should be not only the provisional
but the final definition. It involves,
at all events, no arbitrary change in
the meaning of the word ; for, with
the general usage of the English
language, the wider signification, I
believe, accords better than the more
restricted one.

§ 3. But Reasoning, even in the
widest sense of which the word is
susceptible, does not seem to compre-
hend all that is included, either in
the best, or even in the most current,
conception of the scope and province
of our science. The employment of
the word Logic to denote the theory
of Argumentation, is derived from the
Aristotelian, or, as they are commonly
termed, the scholastic, logicians. Yet
even with them, in their systematic
treatises. Argumentation was the sub-
ject only of the third part : the two
former treated of Terms, and of Pro-
positions ; under one or other of which
heads were also included Definition
and Division. By some, indeed, these
previous topics were professedly intro-
duced only on account of their con-
nexion with reasoning, and as a
preparation for the doctrine and rules
of the syllogism. Yet they were
treated with greater minuteness, and
dwelt on at greater length, than was
required for that purpose alone. More
recent writers on logic have generally
understood the term as it was em-
ployed by the able author of the Port
Royal Logic ; viz., as equivalent to
the Art of Thinking. Nor is this
acceptation confined to books, and
scientific inquiries. Even in ordinary
conversation, the ideas connected with
the word Logic include at least pre-
cision of language, and accuracy of
classification : and we perhaps oftener
hear persons speak of a logical ar-
rangement, or of expressions logically
defined, than of conclusions logically
deduced from premises. Again, a
man is often called a great logician,
or a man of powerful logic, not for

DEFINITION AND PROVINCE OF LOGIC.

the accuracy of his deductions, but
for the extent of his command over
premises ; because the general propo-
sitions required for explaining a difl&-
culty or refuting a sophism, copiously
and promptly occur to him : because,
in short, his knowledge, besides being
ample, is well under his command for
argumentative use. Whether, there-
fore, we conform to the practice of
those who have made the subject
their particular study, or to that of
popular writers and common dis-
course, the province of logic will
include several operations of the intel-
lect not usually considered to fall
within the meaning of the terms
Reasoning and Argumentation.

These various operations might be
brought within the compass of the
science, and the additional advantage
be obtained of a very simple defini-
tion, if, by an extension of the term,
sanctioned by high authorities, we
were to define logic as the science
which treats of the operations of the
human understanding in the pursuit
of truth. For to this ultimate end,
naming, classification, definition, and
all other operations over which logic
has ever claimed jurisdiction, are
essentially subsidiary. They may
all be regarded as contrivances for
enabling a person to know the truths
which are needful to him, and to
know them at the precise moment at
which they are needful. Other pur-
poses, indeed, are also served by these
operations ; for instance, that of im-
parting our knowledge to others.
But, viewed with regard to this pur-
pose, they have never been considered
as within the province of the logician.
The sole object of Logic is the guid-
ance of one's own thoughts : the
communication of those thoughts to
others falls under the consideration
of Rhetoric, in the large sense in
which that art was conceived by the
ancients ; or of the still more exten-
sive art of Education. Logic takes
cognizance of our intellectual opera-
tions, only as they conduce to our

over that knowledge for our own
uses. If there were but one rational
being in the universe, that being
might be a perfect logician ; and the
science and art of logic would be the
same for that one person as for the
whole human race.

§ 4. But, if the definition which
wo formerly examined included too
little, that which is now suggested
has the opposite fault of including
too much.

Truths are known to us in two
ways : some are known directly, and
of themselves ; some through the
medium of other truths. The former
are the subject of Intuition, or Con-
sciousness ; * the latter, of Inference.
The truths known by intuition are
the original premises from which all
others are inferred. Our assent to
the conclusion being grounded on the
truth of the premises, we never could
arrive at any knowledge by reason-
ing, unless something could be known
antecedently to all reasoning.

Examples of truths known to us by
immediate consciousness, are our own
bodily sensations and mental feelings.
I know directly, and of my own know-
ledge, that I was vexed yesterday,
or that I am hungry to-day. Ex-
amples of truths which we know only
by way of inference, are occurrences
which took place while we were
absent, the events recorded in history,
or the theorems of mathematics. The
two former we infer from the testi-
mony adduced, or from the traces of
those past occurrences which still
exist ; the latter, from the premises
laid down in books of geometry, under
the title of definitions and axioms.
Whatever we are capable of knowing
must belong to the one class or to

* I use these terms indiscriminately, be-
cause, for the purpose in view, there is no
need for making any distinction between
tliem. But metapliysicians usually re-
strict the name Intuition to the direct
knowledge we are supposed to have of
things external to our minds, and Con-
sciousness to our knowledge of our own
mental phenomena.

INTRODUCTION.

the other ; must be in the number of
the primitive data, or of the conclu-
sions which can be drawn from these.
With the original data, or ultimate
premises of our knowledge; with their
number or nature, the mode in which
they are obtained, or the tests by
which they may be distinguished ;
logic, in a direct way at least, has,
in the sense in which I conceive the
science, nothing to do. These ques-
tions are partly not a subject of
science at all, partly that of a very
different science.

Whatever is knovvTi to us by con-
sciousness, is known beyond possibility
of question. What one sees or feels,
whether bodily or mentally, one can-
not but be sure that one sees or feels.
No science is required for the purpose
of establishing such truths ; no rules
of art can render our knowledge of
them more certain than it is in itself.
There is no logic for this portion of
our knowledge.

But we may fancy that we see or
feel what we in reality infer. A
truth, or supposed truth, which is
really the result of a very rapid in-
ference, may seem to be apprehended
intuitively. It has long been agreed
by thinkers of the most opposite
schools, that this mistake is actually
made in so familiar an instance as
that of the eyesight. There is nothing
of which we appear to ourselves to
be more directly conscious, than the
distance of an object from us. Yet it
has long been ascertained, that what
is perceived by the eye, is at most
nothing more than a variously coloured
surface ; that when we fancy we see
distance, all we really see is certain
variations of apparent size, and de-
grees of faintness of colour ; that our
estimate of the object's distance from
us is the result partly of a rapid in-
ference from the muscular sensations
accompanying the adjustment of the
focal distance of the eye to objects
unequally remote from us, and partly
of a comparison (made with so much
rapidity that we are unconscious of
:piaking it) between the size and colour

of the object as they appear at the
time, and the size and colour of the
same or of similar objects as they ap-
peared when close at hand, or when
their degree of remoteness was known
by other evidence. The perception
of distance by the eye, which seems
so like intuition, is thus, in reality,
an inference grounded on experience ;
an inference, too, which we learn to
make ; and which we make with more
and more correctness as our experi-
ence increases ; though in familiar
cases it takes place so rapidly as to
appear exactly on a par with those
perceptions of sight which are really
intuitive, our pex'ceptions of colour.*

Of the science, therefore, which
expounds the operations of the human
understanding in the pursuit of truth,
one essential part is the inquiry :
What are the facts which are the
objects of intuition or consciousness,
and what are these which we merely
infer? But this inquiry has never
been considered a portion of logic.
Its place is in another and a perfectly
distinct department of science, to
which the name metaphysics more
particularly belongs : that portion of
mental philosophy which attempts to
determine what part of the furniture
of the mind belongs to it originally,
and what part is constructed out of
materials furnished to it from without.
To this science appertain the great
and much debated questions of the
existence of matter ; the existence of
spirit, and of a distinction between it
and matter ; the reality of time and
space, as things without the mind,
and distinguishable from the objects
which are said to exist in them. For
in the present state of the discussion

* This important theory has of late been
called in question by a writer of deserved
reputation, Mr. Samuel Bailey; but I do
not conceive that the grounds on which
it has been admitted as an established
doctrine for a century past, have been at
all shaken by that gentleman's objections.
I have elsewhere said what appeared to,
me necessary in reply to his arguments.
(Westminster Review for October 1842; re-
printed iu Dissertations and Discussions^

vol, a.)

t)EFINlTlON AND l^ROVINCE OF LOGIC.^

on these topics, it is almost univer-
sally allowed that the existence of
matter or of spirit, of space or of
time, is in its nature unsusceptible of
being proved ; and that if anything
is known of them, it must be by imme-
diate intuition. To the same science
belong the inquiiries into the nature
of Conception, Perception, Memory,
and Belief ; all of which are opera-
tions of the understanding in the
pursuit of truth ; but with which, as
phenomena of the mind, or with the
possibility which may or may not
exist of analysing any of them into
simpler phenomena, the logician as
such has no concern. To this science
must also be referred the following,
and all analogous questions : To what
extent our intellectual faculties and
our emotions are innate — to what
extent the result of association :
Whether God, and duty, are realities,
the existence of which is manifest to
us cl 2^riori by the constitution of our
rational faculty ; or whether our
ideas of them are acquired notions,
the origin of which we are able to
trace and explain ; and the reality of
the objects themselves a question not
of consciousness or intuition, but of
evidence and reasoning.

The province of logic must be re-
stricted to that portion of our know-
ledge which consists of inferences from
truths previously known ; whether
those antecedent data be general pro-
positions, or particular observations
and perceptions. Logic is not the
science of Belief, but the science of
Proof, or Evidence. In so far as
belief professes to be founded on proof,
the office of logic is to supply a test
for ascertaining whether or not the
belief is well grounded. With the
claims which any proposition has to
belief on the evidence of conscious-
ness, that is, without evidence in tlie
proper sense of the word, logic has
nothing to do.

§ 5. By far the greatest portion of
our knowledge, whether of general
truths or of particular facts, being

avowedly matter of inference, nearly
the whole, not only of science, but of
human conduct, is amenable to the
authority of logic. To draw infer-
ences has been said to be the great
business of life. Every one has daily,
hourly, and momentary need of ascer-
taining facts which he has not directly
observed ; not from any general pur-
pose of adding to his stock of know-
ledge, but because the facts them-
selves are of importance to his in-
terests or to his occupations. The
business of the magistrate, of the
military commander, of the navigator,
of the physician, of the agriculturist,
is merely to judge of evidence, and to
act accordingly. They all have to
ascertain certain facts, in order that
they may afterwards apply certain
rules, either devised by themselves,
or prescribed for their guidance by
others ; and as they do this well or
ill, so they discharge well or ill the
duties of their several callings. It is
the only occupation in which the
mind never ceases to be engaged ;
and is the subject, not of logic, but
of knowledge in general.

Logic, however, is not the same
thing with knowledge, though the
field of logic is coextensive with the
field of knowledge. Logic is the
common judge and arbiter of all par-
ticular investigations. It does not
undertake to find evidence, but to
determine whether it has been found.
Logic neither observes, nor invents,
nor discovers ; but judges. It is no
part of the business of logic to infox'm
the surgeon what appearances are
found to accompany a violent death.
This he must learn from his own
experience and observation, or from
that of others, his predecessors in his
peculiar pursuit. But logic sits in
judgment on the sufficiency of that
observation and experience to justify
his rules, and on the sufficiency of his
rules to justify his conduct. It does
not give him proofs, but teaches him
what makes them proofs, and how he
is to judge of them. It does not
teach that any particular fact proves

INTtlODtJCTION;

any other, but points out to what
conditions all facts must conform, in
order that they may prove other facts.
To decide whether any given fact
fulfils these conditions, or whether
facts can be found which fulfil them
in a given case, belongs exclusively to
the particular art or science, or to our
knowledge of the particular subject.

It is in this sense that logic is, what
it was so expressively called by the
schoolmen and by Bacon, ai's art mm ;
the science of science itself. All
science consists of data and conclu-
sions from those data, of proofs and
what they prove : now logic points
out what relations must subsist be-
tween data and whatever can be
concluded from them, between proof
and everything which it can prove.
If there be any such indispensable
relations, and if these can be precisely
determined, every particular branch
of science, as well as every individual
in the guidance of his conduct, is
bound to conform to those relations,
under the penalty of making false
inferences — of drawing conclusions
which are not grounded in the reali-
ties of things. Whatever has at any
time been concluded justly, whatever
knowledge has been acquired other-
wise than by immediate intuition,
depended on the observance of the
laws which it is the province of logic
to investigate. If the conclusions are
just, and the knowledge real, those
laws, whether known or not, have
been observed.

' § 6. We need not, therefore, seek
any farther for a solution of the
question, so often agitated, respecting
the utility of logic. If a science of
logic exists, or is capable of existing,
it must be useful. If there be rules
to which every mind consciously or
■Unconsciously conforms in every in-
stance in which it infers rightly, there
seems little necessity for discussing
whether a person is more likely to
observe those rules, when he knows
the rules, than when he is unac-
c^uainted with them.

A science inay undoulotedly bd
brought to a certain, not inconsider-
able, stage of advancement, without
the application of any other logic to
it than what all persons, who are
said to have a sound xinderstanding,
acquire empirically in the course of
their studies. Mankind judged of
evidence, and often correctly, before
logic was a science, or they never
could have made it one. And they
executed great mechanical works be-
fore they understood the laws of
mechanics. But there are limits both,
to what mechanicians can do without;
principles of mechanics, and to what
thinkers can do without principles of
logic. A few individuals, by extra-
ordinary genius, or by the accidental
acquisition of a good set of intellec-
tual habits, may work without prin-
ciples in the same way, or nearly the
same way, in which they would have
worked if they had been in possession
of principles. But the bulk of man-
kind require either to understand the
theory of what they are doing, or to
have rules laid down for them by
those who have understood the theory.
In the progress of science from its
easiest to its more difficult problems,
each great step in advance has usually
had either as its precursor, or as its
accompaniment and necessary condi-
tion, a corresponding improvement in
the notions and principles of logic
received among the most advanced
thinkers. And if several of the more
difficult sciences are still in so defec-
tive a state ; if not only so little is
proved, but disputation has not ter-
minated even about the little which
seemed to be so ; the reason perhaps
is, that men's logical notions have not
yet acquired the degree of extension,
or of accuracy, requisite for the esti-
mation of the evidence proper to those
particular departments of knowledge.

§ 7. Logic, then, is the science of
the operations of the understanding
which are subservient to the estima-
tion of evidence : both the process
itself of advancing from known truths

DEFINITION AND PROVINCE OF LOGIC.

to unknown, and all other intellectual
operations in so far as auxiliary to
this. It includes, therefore, the opera-
tion of Naming ; for language is an
instrument of thought, as well as a
means of communicating our thoughts.
It includes, also, Definition, and
Classification. For, the use of these
operations {putting all other minds
than one's own out of consideration)
is to serve not only for keeping our
evidences and the conclusions from
them permanent and readily acces-
sible in the memory, but for so mar-
shalling the facts which we may at
•any time be engaged in investigat-
ing, as to enable us to perceive more
•clearly what evidence there is, and
to judge with fewer chances of error
whether it be sufficient. These, there-
fore, are operations specially instru-
mental to the estimation of evidence,
and, as such, are within the province
of Logic. There are other more
elementary processes, concerned in all
thinking, such as Conception, Memory,
and the like ; but of these it is not
necessary that Logic should take any
peculiar cognizance, since they have
no special connexion with the problem
of Evidence, further than that, like
all other problems addressed to the
understanding, it presupposes them.

Our object, then, will be, to attempt
a correct analysis of the intellectual
process called Reasoning or Inference,
and of such other mental operations
as are intended to facilitate this : as
well as, on the foundation of this
analysis, and pari passu with it, to
bring together or frame a set of rules
or canons for testing the sufficiency
of any given evidence to prove any
given proposition.

With respect to the first part of
this undertaking, I do not attempt to
decompose the mental operations in
question into their ultimate elements.
It is enough if the analysis as far as
it goes is correct, and if it goes far
enough for the practical purposes of
logic considered as an art. The
separation of a complicated pheno-
menon into its component parts is not

like a connected and interdependent
chain of proof. If one link of an
argument breaks, the whole drops to
the ground ; but one step towards an
analysis holds good and has an inde-
pendent value, though we should
never be able to make a second. The
results which have been obtained by
analytical chemistry are not the less
valuable, though it should be dis-
covered that all which we now call
simple substances are really com-
pounds. All other things are at any
rate compounded of those elements :
whether the elements themselves ad-
mit of decomposition, is an important
inquiry, but does not affect the cer-
tainty of the science up to that point.
I shall, accordingly, attempt to
analyse the process of inference, and
the processes subordinate to inference,
so far only as may be requisite for as-
certaining the difference between a
correct and an incorrect performance
of those processes. The reason for
thus limiting our design, is evident.
It has been said by objectors to logic,
that we do not learn to use our
muscles by studying their anatomy.
The fact is not quite fairly stated ;
for if the action of any of our muscles
were vitiated by local weakness, or
other physical defect, a knowledge of
their anatomy might be very neces-
sary for effecting a cure. But we
should be justly liable to the criticism
involved in this objection, were we,
in a treatise on logic, to carry the
analysis of the reasoning process be-
yond the point at which any inac-
curacy which may have crept into it
must become visible. In learning
bodily exercises (to carry on the same
illustration) we do, and must, analyse
the bodily motions so far as is neces-
sary for distinguishing those which
ought to be performed from those
which ought not. To a similar extent,
and no further, it is necessary that
the logician should analyse the men-
tal processes with which logic is con-
cerned. Logic has no interest in
carrying the analysis beyond the point
at which it becomes apparent whether

8

INTRODUCTION.

the operations have in any individual
case been rightly or wrongly per-
formed : in the same manner as the
science of music teaches us to dis-
criminate between musical notes, and
to know the combinations of which
they are susceptible, but not what
number of vibrations in a second cor-
respond to each ; which, though use-
ful to be known, is useful for totally
different purposes. The extension of
Logic as a Science is determined by
its necessities as an Art : whatever it
does not need for its practical ends,
it leaves to the larger science which
may be said to correspond, not to
any particular art, but to art in gene-
ral ; the science which deals with the
constitution of the human faculties ;
and to which, in the part of our men-
tal nature which concerns Logic, as
well as in all other parts, it belongs
to decide what are ultimate facts, and
what are resolvable into other facts.
And I believe it will be found that
most of the conclusions arrived at in
"ihis work have no necessary connexion
with any particular views respecting
the ulterior analysis. Logic is com-
mon ground on which the partisans of
Hartley and of Reid, of Locke and of
Kant may meet and join hands.
Particular and detached opinions of
all these thinkers will no doubt occa-
sionally be controverted, since all of
them were logicians as well as meta-
physicians ; but the field on which
their principal battles have been
fought, lies beyond the boundaries of
our science.

It cannot, indeed, be pretended
that logical principles can be alto-
gether irrelevant to those more ab-
struse discussions ; nor is it possible
but that the view we are led to take
of the problem which logic proposes,
must have a tendency favourable to
the adoption of some one opinion, on
these controverted subjects, rather
than another. For metaphysics, in
endeavouring to solve its own peculiar
problem, must employ means, the
validity of which falls under the
cognizamce of logic. It proceeds, no

doubt, as far as possible, merely by
a closer and more attentive interroga-
tion of our consciousness, or more
properly speaking, of our memory ;
and so far is not amenable to logic.
But wherever this method is insuffi-
cient to attain the end of its inqiiiries,
it must proceed, like other sciences,
by means of evidence. Now, the
moment this science begins to draw
inferences from evidence, logic be-
comes the sovereign judge whether
its inferences are well grounded, or
what other inferences would be so.

This, however, constitutes no nearer
or other relation between logic and
metaphysics, than that which exists
between logic and every other science.
And I can conscientiously affirm, that
no one proposition laid down in this
work has been adopted for the sake
of establishing, or with any reference
to its fitness for being employed in
establishing, preconceived opinions in
any department of knowledge or of
inquiry on which the speculative
world is still undecided.*

* The view taken in the text, of the defi-
nition and purpose of Logic, stands ia
marked opposition to that of the scliool of
philosophy wliich, in this country, is re-
presented by the writings of Sir William
Hamilton and of his numerous pupils.
Logic, as this school conceives it, is " the
Science of the Formal Laws of Thought ;"
a definition framed for the express purpose
of excluding, as irrelevant to Logic, what-
ever relates to Belief and Disbelief, or to
the pursuit of truth as such, and restrict-
ing the science to that very limited portion
of its total province, which has reference
to the conditions, not of Truth, but of
Consistency. What I have thought it use-
ful to say in opposition to this limitation
of the field of Logic, has been said at some
length in a separate worl<, first published
in 1865, and entitled An Examination of
Sir William Hamilton's Philosophy, and of
the Principal Philosophical Questions dis-
cussed in his Writings. For the purposes of
the present Treatise, I am content that the
justification of the larger extension which
I gave to the domain of the science, should
rest on the sequel of the Treatise itself.
Some remarks on the relation which the
Logic of Consistency bears to the Logic of
Truth, and on the place wliich that par-
ticular part occupies in the whole to which
it belongs, will be found in the present
volume (J3ook II, chap. iii. § 9).

BOOK I.

OF NAMES AND PEOPOSITIONa

•' La scolastique, qui produisit dans la logique, comme dans la morale, et dans une
pai'tie de la metapliysiqiie, une subtilit6, une precision d'idees, dont I'habitude inconnue
aux anciens, a contribue plus qu'on ne croit au progres de la bonne pliilosophie."—
Co-NDORCET, Vie de Turgot.

" To the scboolmen the vulgar languages are principally indebted for what precision
and analytic subtlety they possess." — Sir W. Hamilton, Discussions in Philosophy/,'

OP NAMES AND PEOPOSITIONg.

CHAPTER I.

'OP THE NECESSITY OF COMMENCING
WITH AN ANALYSIS OF LANGUAGE.

§ I. It is so much the established
practice of Avriters on logic to com-
mence their treatises by a few general
observations (in most cases, it is true,
rather meagre) on Terms and their
varieties, that it will, perhaps, scarcely
be required from me in merely follow-
ing the common usage, to be as parti-
cular in assigning my reasons, as it is
usually expected that those should be
who deviate from it.

The practice, indeed, is recom-
mended by considerations far too
obvious to require a formal justifica-
tion. Logic is a portion of the Art
of Thinking : Language is evidently,
and by the admission of all philoso-
phers, one of the principal instruments
or helps of thought ; and any imper-
fection in the instrument, or in the
mode of employing it, is confessedly
liable, still more than in almost any
other art, to confuse and impede the
process, and destroy all ground of
confidence in the result. For a mind
not previously versed in the meaning
a,nd right use of the various kinds of
words, to attempt the study of methods
of philosophising, would be as if some
one should attempt to become an
astronomical observer, having never
learned to adjust the focal distance
of his optical instruments so as to see
distinctly.

Since Reasoning, or Inference, the
J)rincipal subject of logic, is an opera-

tion which usually takes place by
means of words, and in complicated
cases can take place in no other way ;
those who have not a thorough insight
into the signification and purposes of
words, will be under chances, amount-
ing almost to certainty, of reasoning
or inferring incorrectly. And logi-
cians have generally felt that unless,
in the very first stage, they removed
this source of error ; unless they taught
their pupil to put away the glasses
which distort the object, and to use
those which are adapted to his purpose
in such a manner as to assist, not per-
plex, his vision ; he would not be in
a condition to practise the remaining
part of their discipline with any pro-
spect of advantage. Therefore it is
that an inquiry into language, so far
as is needful to guard against the
errors to which it gives rise, has at all
times been deemed a necessary pre-
liminary to the study of logic.

But there is another reason, of a
still more fundamental nature, why
the import of words should be the
earliest subject of the logician's con-
sideration : because without it he can-
not examine into the import of Pro-
positions. Now this is a subject which
stands on the very threshold of the
science of logic.

The object of logic, as defined in
the Introductory Chapter, is to ascer-
tain how we come by that portion of
our knowledge (much the greatest
portion) which is not intuitive : and
by what criterion we can, in matters
not self-evident, distinguish between

t2

INAMES AND l>ROPOSlTlONg.

things proved and things not proved,
between what is worthy and what is
unworthy of belief. Of the various
questions which present themselves
to our inquiring faculties, some re-
ceive an answer from direct conscious-
ness, others, if resolved at all, can only
be resolved by means of evidence.
Logic is concerned with these last.
But before inquiring into the mode
of resolving questions, it is necessary
to inquire what are those which offer
themselves ; what questions are con-
ceivable ; what inquiries are there, to
which mankind have either obtained,
or been able to imagine it possible
that they should obtain, an answer.
This point is best ascertained by a
survey and analysis of Propositions.

§ 2. The answer to every question
which it is possible to frame, must be
contained in a Proposition, or Asser-
tion. Whatever can be an object of
belief, or even of disbelief, must, when
put into words, assume the form of a
proposition. All truth and all error
lie in propositions. What, by a con-
venient misapplication of an abstract
term, we call a Truth, means simply
a True Proposition ; and errors are
false propositions. To know the im-
port of all possible propositions, would
be to know all questions which can
be raised, all matters which are sus-
ceptible of being either believed or
disbelieved. How many kinds of in-
quiries can be propounded ; how many
kinds of judgments can be made ; and
how many kinds of propositions is it
possible to frame with a meaning ;
are but different forms of one and the
same question. Since, then, the ob-
jects of all Belief and of all Inquiry
express themselves in propositions ; a
sufficient scrutiny of Propositions and
of their varieties will apprize us what
questions mankind have actually asked
of themselves, and what, in the nature
of answers to those questions, they
have actually thought they had
grounds to believe.

Now the first glance at a proposi-
tion shows that it is formed by put-

ting together two names. A proposi-
tion, according to the common simple
definition, which is sufficient for our
purpose, is, discourse, in ichich some-
thing is affirmed or denied of some-
thing. Thus, in the proposition, Gold
is yellow, the quality yelloiu is affirmed
of the substance gold. In the pro-
position, Franklin was not born in
England, the fact expressed by the
words horn in England is denied of
the man Pranklin.

Every proposition consists of three
parts : the Subject, the Predicate, and
the Copula. The predicate is the
name denoting that which is affirmed
or denied. The subject is the name
denoting the person or thing which
something is affirmed or denied of.
The copula is the sign denoting that
there is an affirmation or denial ; and
thereby enabling the hearer or reader
to distinguish a proposition from any
other kind of discourse. Thus, in
the proposition, the earth is round,
the Predicate is the word round,
which denotes the quality affirmed,
or (as the phrase is) predicated : the
earth, words denoting the object which
that quality is affirmed of, compose
the Subject ; the word is, which serves
as the connecting mark between the
subject and predicate, to show that
one of them is affirmed of the other,
is called the Copula.

Dismissing, for the present, the
copula, of which more will be said
hereafter, every proposition, then,
consists of at least two names ; brings
together two names, in a particular
manner. This is already a first step
towards what we are in quest of. It
appears from this, that for an act of
belief, one object is not sufficient ;
the simplest act of belief supposes,
and has something to do with, two
objects : two names, to say the least ;
and (since the names must be names
of something) two nameable things.
A large class of thinkers would cut
the matter short by saying, two ideas.
They would say, that the subject and
predicate are both of them names of
ideas, the idea of gold, for instance,

NECESSITY OF AN ANALYSIS OF LANGUAGE.

13

and the idea of yellow ; and that
what takes place (or part of what
takes place) in the act of belief, con-
sists in bringing (as it is often ex-
pressed) one of these ideas under the
other. Eut this we are not yet in a
condition to say : whether such be
the correct mode of describing the
phenomenon, is an after considera-
tion. The result with which for the
present we must be contented, is,
that in every act of belief tico objects
are in some manner taken cognizance
of ; that there can be no belief
claimed, or question propounded,
which does not embrace two distinct
(either material or intellectual) sub-
jects of thought ; each of them cap-
able, or not, of being conceived by
itself, but incapable of being believed
bj'- itself.

I may say, for instance, " the sun."
The word has a meaning, and suggests
that meaning to the mind of any one
who is listening to me. But suppose
I ask him. Whether it is true :
whether he believes it ? He can give
no answer. There is as yet nothing
to believe, or to disbelieve. Now,
however, let me make, of all possible
assertions respecting the sun, the one
which involves the least of reference
to any object besides itself ; let me
say, " the sun exists." Here, at once,
is something which a person can say
he believes. But here instead of only
one, we find two distinct objects of
conception : the sun is one object ;
existence is another. Let it not be
said that this second conception,
existence, is involved in the first ;
for the sun may be conceived as no
longer existing. " 'J'he sun " does
not convey all the meaning that is
conveyed by " the sun exists : " " my
father " does not include all the
meaning of "my father exists," for
he may be dead ; " a round square "
does not include the meaning of '* a
round souare exists," for it does not
and cannot exist. When I say " the
sun," " my father," or " a round
square," I do not call upon the hearer
for any belief or disbelief, nor can

either the one or the other be afforded
me ; but if I say, "the sun exists,"
" my father exists," or a " round
square exists," I call for belief ; and
should, in the first of the three in-
stances, meet with it ; in the second,
with belief or disbelief, as the case
might be ; in the third, with dis-
belief.

§ 3, This first step in the analysis
of the object of belief, which, though
so obvious, will be found to be not
unimportant, is the only one which
we shall find it practicable to make
without a preliminary survey of lan-
guage. If we attempt to proceed
further in the same path, that is, to
analyse any further the import of
Propositions, we find forced upon us,
as a subject of previous consideration,
the import of Names. For every pro-
position consists of two names ; and
every proposition affirms or denies
one of these names, of the other.
Now what we do, what passes in our
mind, when we affirm or deny two
names of one another, must depend
on what they are names of ; since it
is with reference to that, and not to
the mere names themselves, that we
make the affirmation or denial. Here,
therefore, we find a new reason why
the signification of names, and the
relation generally between names and
the things signified by them, must
occupy the preliminary stage of the
inquiry we are engaged in.

It may be objected that the mean-
ing of names can guide us at most
only to the opinions, possibly the
foolish and groundless opinions, which
mankind have formed concerning
things, and that as the object of
philosophy is truth, not opinion, the
philosopher should dismiss words and
look into things themselves, to ascer-
tain what questions can be asked and
answered in regard to them. This
advice (which no one has it in his
power to follow) is in reality an ex-
hortation to discard the whole fruits
of the labours of his predecessors,
and conduct himself as if he were the

14

NAMES AND PROPOSITIONS.

first person who had ever turned an
inquiring eye upon nature. What
does any one's personal knowledge of
Things amount to, after subtracting
all which he has acquired by means
of the words of other people ? Even
after he has learned as much as people
usually do learn from others, will the
notions of things contained in his
individual mind afford as sufficient a
basis for a catalogue raisonne as the
notions which are in the minds of all
mankind ?

In any enumeration and classifica-
tion of Things, which does not set
out from their names, no varieties of
things will of course be comprehended
but those recognised by the particular
inquirer ; and it will still remain to
be established, by a subsequent exami-
nation of names, that the enumeration
has omitted nothing which ought to
have been included. But if we begin
with names, and use them as our clue
to the things, we bring at once before
us all the distinctions which have
been recognised, not by a single
inquirer, but by all inquirers taken
together. It doubtless may, and I
believe it will, be found, that man-
kind have multiplied the varieties
unnecessarily, and have imagined dis-
tinctions among things, where there
were only distinctions in the manner
of naming them. But we are not
entitled to assume this in the com-
mencement. We must begin by re-
cognising the distinctions made by
ordinary language. If some of these
appear, on a close examination, not to
be fundamental, the enumeration of
the different kinds of realities may be
abridged accordingly. But to impose
upon the facts in the first instance
the yoke of a theory, while the
grounds of the theory are reserved for
discussion in a subsequent stage, is
not a course which a logician can
reasonably adopt.

CHAPTER II.

OF NAMES.

§ I. "A NAME," says Hobbes,* ** is
a word taken at pleasure to serve for
a mark which may raise in our mind
a thought like to some thought we
had before, and which being pro-
nounced to others, may be to them
a sign of what thought the speaker
had f before in his mind." This
simple definition of a name, as a word
(or set of words) serving the double
purpose of a mark to recall to our-
selves the likeness of a former thought,
and a sign to make it known to others,
appears unexceptionable. Names,
indeed, do much more than this ; but
whatever else they do, grows out of,
and is the result of this : as will
appear in its proper place.

Are names more properly said to
be the names of things, or of our
ideas of things ? The first is the ex-
pression in common use ; the last is
that of some metaphysicians, who con-
ceived that in adopting it they were
introducing a highly important dis-
tinction. The eminent thinker, just
quoted, seems to countenance the
latter opinion. " But seeing," he con-
tinues, " names ordered in speech (as
is defined) are signs of our concep-
tions, it is manifest they are not signs
of the things themselves ; for that
the sound of this word stone should
be the sign of a stone, cannot be
understood in any sense but this, that
he that hears it collects that he that
pronounces it thinks of a stone."

If it be merely meant that the con-
ception alone, and not the thing itself,.
is recalled by the name, or imparted
to the hearer, this of course cannot,
be denied. Nevertheless, there seems,
good reason for adhering to the.
common usage, and calling (as indeed
Hobbes himself does in other places),
the word sun the name of the sun^

* Computation or Logic, chap. ii.

t In the original "had, or had not."-
These last words, as involving a subtlety-
foreign to onr present purpose, I have for-,
borne to quote...

NAMES.

15

and not the name of our idea of the
sun. For names are not intended
only to make the hearer conceive
what we conceive, but also to inform
him what we believe. Now, when I
use a name for the purpose of express-
ing a belief, it is a belief concerning
the thing itself, not concerning my
idea of it. When I say, "the sun is
the cause of day," I do not mean that
my idea of the sun causes or excites
in me the idea of day : or in other
words, that thinking of the sun makes
me think of day. I mean, that a
certain physical fact, which is called
the sun's presence (and which, in the
ultimate analysis, resolves itself into
sensations, not ideas) causes another
physical fact, which is called day.
It seems proper to consider a word
as the name of that which we intend
to be understood by it when we use
it ; of that which any fact that we
assert of it is to be understood of ;
that, in short, concerning which, when
we employ the word, we intend to give
information. Names, therefore, shall
always be spoken of in this work as
the names of things themselves, and
not merely of our ideas of things.

But the question now arises, of what
things ? and to answer this it is neces-
sary to take into consideration the
different kinds of names.

§ 2. It is usual, before examining
the various classes into which names
are commonly divided, to begin by
distinguishing from names of every
description, those words which are
not names, but only parts of names.
Among such are reckoned particles,
as of, to, trull/, often; the inflected
cases of nouns substantive, as me, him,
Johns ; and even adjectives, as large,
heavy. These words do not express
things of which anything can be
afiii'med or denied. We cannot say.
Heavy fell, or A heavy fell ; Truly,
or A truly, was asserted ; Of, or An
of, was in the room. Unless, indeed,
we are speaking of the mere words
themselves, as when we say, Truly is
an English word, or, Heavy is an

adjective. In that case they are com-
plete names, viz. names of those parti-
cular sounds, or of those particular
collections of written characters. This
employment of a word to denote the
mere letters and syllables of which it
is composed, was termed by the school-
men the suppositio materialis of the
word. In any other sense we cannot
introduce one of these words into the
subject of a proposition, unless in
combination with other words ; as,
A heavy body fell, A truly important
fact was asserted, A member of parlia-
ment was in the room.

An adjective, however, is capable
of standing by itself as the predicate
of a proposition ; as when we say.
Snow is white j and occasionally even
as the subject, for we may say. White
is an agreeable colour. The adjective
is often said to be so used by a gram-
matical ellipsis : Snow is white, in-
stead of Snow is a white object :
White is an agreeable colour, instead
of, A white colour, or, The colour
white, is agreeable. The Greeks and
Romans were allowed, by the rules of
their language, to employ this ellipsis
universally in the subject as well as
in the predicate of a proposition. In
English this cannot, generally speak-
ing, be done. We may say, The
earth is round ; but we cannot say,
Round is easily moved ; we must say,
A round object. This distinction,
however, is rather grammatical than
logical. Since there is no difference
of meaning between round, and a
round object, it is only custom which
prescribes that on any given occasion
one shall be used, and not the other.
We shall, therefore, without scruple,
speak of adjectives as names, whether
in their own right, or as representa-
tive of the more circuitous forms of
expression above exemplified. The
other classes of subsidiary words have
no title whatever to be considered as
names. An adverb, or an accusative
case, cannot under any circumstances
(except when their mere letters and
syllables are spoken of) figure as one
of the terms of a proposition,

i6

NAMES AND PROPOSITIONS.

Words which are not capable of
bemg used as names, but only as
parts of names, were called by some
of the schoolmen Syncategorematio
terms : from citv, with, and KaTrjyop^oj,
to predicate, because it was only with
some other word that they could be
predicated. A word which could be
used either as the subject or predicate
of a proposition without being accom-
panied by any other word, was termed
by the same authorities a Categore-
matic term. A combination of one
or more Categorematic, and one or
more Syncategorematiq words, as A
heavy body, or A court of justice,
they sometimes called a mixed term ;
but this seems a needless multiplica-
tion of technical expressions. A
mixed term is, in the only useful
sense of the word, Categorematic.
It belongs to the class of what have
been called many- worded names.

Tor, as one word is frequently not
a name, but only part of a name, so
a number of words often compose one
single name, and no more. These
words, " The place which the wisdom
or policy of antiquity had destined
for the residence of the Abyssinian
princes," form in the estimation of
the logician only one name ; one
Categorematic term. A mode of de-
termining whether any set of words
makes only one name, or more than
one, is by predicating something of it,
and observing whether, by this pre-
dication, we make only one assertion
or several. Thus, when we say, John
Nokes, who was the mayor of the
town, died yesterday — by this predi-
cation we make but one assertion ;
whence it appears that " John Nokes,
who was the mayor of the town," is no
more than one name. It is true that
in this proposition, besides the asser-
tion that John Nokes died yesterday,
there is included another insertion,
namely, that John Nokes was mayor
of the town. But this last assertion
was already made : we did not make
it by adding the predicate, "died
yesterday." Suppose, however, that
thQ words had been, John Nokes and

the mayor of the town, they would
have formed two names instead of
one. For when we say, John Nokes
and the mayor of the town died yes-
terday, we make two assertions : one,
that John Nokes died yesterday ; the
other, that the mayor of the town
died yesterday.

It being needless to illustrate at
any greater length the subject of
many-worded names, we proceed to
the distinctions which have been
established among names, not accord-
ing to the words they are composed
of, but according to their significa-
tion.

§ 3. All names are names of some-
thing, real or imaginary ; but all
things have not names appropriated
to them individually. Tor some in-
dividual objects we require, and con-
sequently have, separate distinguish-
ing names ; there is a name for every
person, and for every remarkable
place. Other objects, of which we
have not occasion to speak so fre-
quently, we do not designate by a
name of their own ; but when the
necessity arises for naming them, we
do so by putting together several
words, each of which, by itself, might
be and is used for an indefinite num-
ber of other objects ; as when I say,
this stone : " this " and " stone " being,
each of them, names that may be used
of many other objects besides the par-
ticular one meant, though the only
object of which they can both be used
at the given moment, consistently
with their signification, may be the
one of which I wish to speak.

Were this the sole purpose for
which names, that are common to
more things than one, could be em-
ployed ; if they only served, by
mutually limiting each other, to afford
a designation for such individual ob-
jects as have no names of their own ;
they could only be ranked among
contrivances for economizing the use
of language. But it is evident that
this is not their sole function. It is
by their means that we are enabled

NAMES.

17

to assert general propositions ; to
affirm or deny any predicate of an
indefinite number of things at once.
The distinction, therefore, between
general names, and individual or singu-
lar names, is fundamental ; and may
be considered as the first grand divi-

y sion of names.

^ A general name is familiarly de-

fined, a name which is capable of
being truly affirmed, in the same
sense, of each of an indefinite number
of things. An individual or singular
name is a name which is only capable
of being truly affirmed, in the same
sense, of one thing.

Thus, man is capable of being
truly affirmed of John, George, Mary,
and other persons without assignable
limit ; and it is affirmed of all of
them in the same sense ; for the word
man expresses certain qualities, and
when we predicate it of those persons,
we assert that they all possess those
qualities. But John is only capable
of being truly affirmed of one single
person, at least in the same sense.
Tor, though there are many persons
who bear that name, it is not con-
ferred upon them to indicate any
qualities, or anything which belongs
to them in common ; and cannot be
said to be aifirmed of them in any
sense at all, consequently not in the
same sense. "The king who suc-
ceeded William the Conqueror," is
also an individual name. For, that
there cannot be more than one person
of whom it can be truly aflSrmed, is
implied in the meaning of the words.
Even "<Ae king," when the occasion or
the context defines the individual of
whom it is to be understood, may justly
be regarded as an individual name.

It is not unusual, by way of ex-
plaining what is meant by a general
name, to say that it is the name of a
class. But this, though a convenient
mode of expression for some purposes,
is objectionable as a definition, since
it explains the clearer of two things
by the more obscure. It would be
more logical to reverse the proposi-
tion, and turn it into a definition of

the word class : " A class is the inde-
finite multitude of individuals denoted
by a general name."

It is necessary to distinguish general
from collective names. A general name
is one which can be predicated of each
individual of a multitude ; a collec-
tive name cannot be predicated of
each separately, but only of all taken
together. "The 76th regiment of
foot in the British army," which is
a collective name, is not a general
but an individual name ; for though
it can be predicated of a multitude of
individual soldiers taken jointly, it
cannot be predicated of them severally.
We may say, Jones is a soldier, and
Thompson is a soldier, and Smith is
a soldier, but we cannot say, Jones
is the 76th regiment, and Thompson
is the 76th regiment, and Smith is
the 76th regiment. We can only say,
Jones, and Thompson, and Smith, and
Brown, and so forth (enumerating all
the soldiers), are the 76th regiment.

" The 76th regiment " is a collec-
tive name, but not a general one : " a
regiment " is both a collective and a
general name. General with respect
to all individual regiments, of each of
which separately it can be affirmed :
collective with respect to the indi-
vidual soldiers of whom any regiment
is composed.

§ 4. The second general division of
names is into concrete and abstract.
A concrete name is a name which
stands for a thing ; an abstract name
is a name which stands for an attri-
bute of a thing. Thus John, the sea,
this table, are names of things. White,
also, is the name of a thing, or rather
of things. Whiteness, again, is the
name of a quality or attribute of
those things. Man is a name of
many things ; humanity is a name of
an attribute of those things. Old is
a name of things ; old age is a name
of one of their attributes.

I have used the words concrete and
abstract in the sense annexed to them
by the schoolmen, who, notwithstand-
ing the imperfections of their philo-

i8

NAMES AND PROPOSITIONS.

sophy, were unrivalled in the con-
struction of technical language, and
whose definitions, in logic at least,
though they never went more than a
little way into the subject, have
seldom, I think, been altered but to
be spoiled. A practice, however, has
grown up in more modem times,
which, if not introduced by Locke,
has gained currency chiefly from his
example, of applying the expression
" abstract name " to all names which
are the result of abstraction or gene-
ralisation, and consequently to all
general names, instead of confining it
to the names of attributes. The meta-
physicians of the Condillac school, —
whose admiration of Locke, passing
over the profoundest speculations of
that truly original genius, usually
fastens with peculiar eagerness upon
his weakest points, — have gone on
imitating him in this abuse of lan-
guage, until there is now some diffi-
culty in restoring the word to its
original signification. A more wanton
alteration in the meaning of a word
is rarely to be met with ; for the
expression general name, the exact
equivalent of which exists in all lan-
guages I am acquainted with, was
already available for the purpose to
which abstract has been misappro-
priated, while the misappropriation
leaves that important class of words,
the names of attributes, without any
compact distinctive appellation. The
old acceptation, however, has not
gone so completely out of use, as to
deprive those who still adhere to it of
all chance of being understood. By
abstract, then, I shall always, in Logic
proper, mean the opposite of concrete ;
by an abstract name, the name of an
attribute ; by a concrete name, the
name of an object.

Do abstract names belong to the
class of general, or to that of singular
names ? Some of them are certainly
general. I mean those which are
names not of one single and definite
attribute, but of a class of attributes.
Such is the word colour, which is a
common to whiteness, redness

&c. Such is even the word white-
ness, in respect of the different shades
of whiteness to which it is applied in
common : the word magnitude, in
respect of the various degrees of mag-
nitude and the various dimensions of
space ; the word weight, in respect of
the various degrees of weight. Such
also is the word attribute itself, the
common name of all particular attri-
butes. But when only one attribute,
neither variable in degree nor in kind,
is designated by the name ; as visible-
ness ; tangibleness ; equality ; square-
ness ; milkwhiteness ; then the name
can hardly be considered general ; for
though it denotes an attribute of
many different objects, the attribute
itself is always conceived as one, not
many.* To avoid needless logo-
machies, the best course would pro-
bably be to consider these names as
neither general nor individual, and to
place them in a class apart.

It may be objected to our definition
of an abstract name, that not only the
names which we have called abstract,
but adjectives, which we have placed
in the concrete class, are names of
attributes ; that white, for example,
is as much the name of the colour as
whiteness is. But (as before remarked)
a word ought to be considered as the
name of that which we intend to be
understood by it when we put it to
its principal use, that is, when we
employ it in predication. When we
say snow is white, milk is white,
linen is white, we do not mean it to
be understood that snow, or linen, or
milk, is a colour. We mean that they
are things having the colour. The
reverse is the case with the word
whiteness ; what we affirm to he
whiteness is not snow, but the colour
of snow. Whiteness, therefore, is
the name of the colour exclusively :
white is a name of all things what-
ever having the colour ; a name, not
of the quality of whiteness, but of
every white object. It is true, this
name was given to all those various

* Vide infra, note at the end of § 3, book
11. chap. ii.

NAMES.

19

objects on account of the quality ; and
we may therefore say, without impro-
priety, that the quality forms part of
its signification ; but a name can
only be said to stand for, or to be a
name of, the things of which it can
be predicated. We shall presently
see that all names which can be said
to have any signification, all names
by applying which to an individual
we give any information respecting
that individual, may be said to imply
an attribute of some sort ; but they
are not names of the attribute ; it
has its own proper abstract name.

§ 5. This leads to the consideration
of a third great division of names,
into connotative and non-connotative,
the latter sometimes, but improperly,
called absolute. This is one of the
most important distinctions which we
shall have occasion te point out, and
one of those which go deepest into
the nature of language.

A non-connotative term is one
which signifies a subject only, or an
attribute only. A connotative term
is one which denotes a subject, and
implies an attribute. By a subject is
here meant anything which possesses
attributes. Thus John, or London,
or England, are names which signify
a subject only. Whiteness, length,
virtue, signify an attribute only.
None of these names, therefore, are
connotative. Butw/tiie, lung, virtuous,
are connotative. The word white de-
notes all white things, as snow, paper,
the foam of the sea, &c., and implies,
or in the language of the schoolmen,
connotes* the attribute wkdeness.
The word white is not predicated of
the attribute, but of the subjects,
snow, &c. ; but when we predicate it
of them, we convey the meaning that
the attribute whiteness belongs to
them. The same may be said of the
other words above cited. Virtuous,
for example, is the name of a class,
which includes Socrates, Howard, the

* Notare, to mark ; Connotare, to mark
along with ; to mark one thing with or in
addition to another.

Man of Ross, and an undefinable
number of other individuals, past,
present, and to come. These indi-
viduals, collectively and severally, can
alone be said with propriety to be
denoted by the word : of them alone
can it properly be said to be a name.
But it is a name applied to all of
them in consequence of an attribute
which they are supposed to possess in
common, the attribute which has re-
ceived the name of virtue. It is
applied to all beings that are con-
sidered to possess this attribute ; and
to none which are not so considered.

All concrete general names are con-
notative. The word man, for example,
denotes Peter, Jane, John, and an in-
definite number of other individuals,
of whom, taken as a class, it is the
name. But it is applied to them,
because they possess, and to signify
that they possess, certain attributes.
These seem to be, corporeity, animal
life, rationality, and a certain external
form, which for distinction we call
the human. Every existing thing,
which possessed all these attributes,
would be called a man ; and anything
which possessed none of them, or
only one, or two, or even three of
them without the fourth, would not
be so called. For example, if in the
interior of Africa there were to be
discovered a race of animals possess-
ing reason equal to that of human
beings, but with the form of an ele-
phant, they would not be called men.
Swift's Houyhnhnms would not be so
called. Or if such newly -discovered
beings possessed the form of man
without any vestige of reason, it is
probable that some other name than
that of man would be found for them.
How it happens that there can be
any doubt about the matter, will
appear hereafter. The word man,
therefore, signifies all these attributes,
and all subjects which possess these
attributes. But it can be predicated
only of the subjects. What we call
men, are the subjects, the individual
Stiles and Nokes ; not the qualities
by which their humanity is consti-

NAMES AND PROPOSITIONS.

tuted. The name, therefore, is said
to signify the subjects directly^ the
attributes indirectly ; it denotes the
subjects, and iiriplies, or involves, or
indicates, or as we shall say hence-
forth connotes, the attributes. It is
a connotative name.

Connotative * names have hence
been also called denominative, because
the subject which they denote is de-
nominated by, or receives a name
from, the attribute which they con-
note. Snow, and other objects, re-
ceive the name white, because they
possess the attribute which is called
whiteness ; Peter, James, and others
receive the name man because they
possess the attributes which are con-
sidered to constitute humanity. The
attribute, or attributes, may therefore
be said to denominate those objects,
or to give them a common name.

It has been seen that all concrete
general names are connotative. Even
abstract names, though the names
only of attributes, may in some in-
stances be justly considered as con-
notative ; for attributes themselves
may have attributes ascribed to them ;
and a word which denotes attributes
may connote an attribute of those
attributes. Of this description, for
example, is such a word as fault;
equivalent to hud or hurtful quality.
This word is a name common to many
attributes, and connotes hurtfulness,
an attribute of those various attri-
butes. When, for example, we say
that slowness, in a horse, is a fault,
we do not mean that the slow move-
ment, the actual change of place of
the slow horse, is a bad thing, but
that the property or peculiarity of
the horse, from which it derives that

* Archbishop Whately, who, in the later
editions of iiis Elements of Logic, aided in
reviving the important di-tinc ion tieiit- d
of in the text, proposes Lheteim ''Attribu-
tive" as a subsiitute for " Connutaiive "
(p. 22, 9th ed.). The expression is, in itself,
appropriate; but as it has not the advan-
tage of being connected with an}' vetb, of
so markedly distinctive a character as "to
connote," it is not, I think, fitted to supply
the place of the word Connotative in scien-
tific use.

name, the quality of being a slow
mover, is an undesirable peculiarity.

In regard to those concrete names
which are not general but individual,
a distinction must be made.

Proper names are not connotative :
they denote the individuals who are
called by them ; but they do not
indicate or imply any attributes as
belonging to those individuals. When
we name a child by the name of Paul,
or a dog by the name Caesar, these
names are simply marks used to en-
able those individuals to be made
subjects of discourse. It may be
said, indeed, that we must have had
some reason for giving them those
names rather than any others ; and
this is true ; but the name, once
given, is independent of the reason.
A man may have been named John,
because that was the name of his
father ; a town may have been named
Dartmouth, because it is situated at
the mouth of the Dart. But it is no
part of the signification of the word
John, that the father of the person
so called bore the same name ; nor
even of the word Dartmouth, to be
situated at the mouth of the Dart,
If sand should choke up the mouth of
the river, or an earthquake change its
course, and remove it to a distance
from the town, the name of the town
would not necessarily be changed.
That fact, therefore, can form no
part of the signification of the word ;
for otherwise, when the fact c«m-
fessedly ceased to be true, no one
would any longer think of applying
the name. Proper names are attached
to the objects themselves, and are not
dependent on the continuance of any
attribute of the object.

But there is another kind of names,

which, although they are individual

names, that is, predicable only of one

object, are really connotative. For,

though we may give to an individual

a name utterly unmeaning, which we

I call a proper name, — a word which

I answers the purpose of showing what

thing it is we are talking about, but

1 not of telling anything about it ; yet

NAMES.

31

ft name peculiar to an individual is
not necessarily of this description. It
may be significant of some attribute,
or some union of attributes, which,
being possessed by no object but one,
determines the name exclusively to
that individual. " The sun " is a
name of this description; "God,"
when used by a monotheist, is another.
These, however, are scarcely examples
of what we are now attempting to
illustrate, being, in strictness of lan-
guage, general, not individual names :
for, however they may be in fact pre-
dicable only of one object, there is
nothing in the meaning of the words
themselves which implies this : and,
accordingly, when we are imagining
and not affirming, we may speak of
many suns ; and the majority of man-
kind have believed, and still believe,
that there are many gods. But it is
easy to produce words which are real
instances of connotative individual
names. It may be part of tlie mean-
ing of the connotative name itself,
that there can exist but one individual
possessing the attribute which it con-
notes : as for instance, " the only son
of John Stiles ; " " the first emperor
of Rome." Or the attribute connoted
may be a connexion with some deter-
minate event, and the connexion may
be of such a kind as only one indi-
vidual could have ; or may at least be
such as only one individual actually
had ; and this may be implied in the
form of the expression. " The father
of Socrates" is an example of the
one kind (since Socrates could not
have had two fathers) ; " the author
of the Iliad," " the murderer of Henri
Quatre," of the second. For, though
it is conceivable that more persons
than one might have participated in
the authorship of the Iliad, or in the
murder of Henri Quatre, the employ-
ment of the article the implies that,
in fact, this was not the case. What
is here done by the word the, is done
in other cases by the context : thus,
" Caesar's army " is an individual
name, if it appears from the context
that the army meant is that which

Caesar commanded in a particular

battle. The still more general ex-
pressions, "the Roman army," or
" the Christian army," may be indi-
vidualised in a similar manner. An-
other case of frequent occurrence has
already been noticed ; it is the follow-
ing. The name, being a many- worded,
one, may consist, in the first place, of
a general name, capable therefore in
itself of being affirmed of more things
than one, but which is, in the second
place, so limited by other words joined
with it, that the entire expression can
only be predicated of one object, con-
sistently with the meaning of the
general term. This is exemplified in
such an instance as the following :
" the present Prime Minister of Eng-
land." Prime Minister of England
is a general name ; the attributes
which it connotes may be possessed
by an indefinite number of persons :
in succession however, not simul-
taneously ; since the meaning of the
name itself imports (among other
things) that there can be only one
such person at a time. This being
the case, and the application of the
name being afterwards limited by
the article and the word present, to
such individuals as possess the attri-
butes at one indivisible point of time,
it becomes applicable only to one in-
dividual. And as this appears from
the meaning of the name, without
any extrinsic proof, it is strictly an
individual name.

From the preceding observations it
will easily be collected, that whenever
the names given to objects convey any
information, that is, whenever they
have properly any meaning, the mean-
ing resides not in what they denote,
but in what they connote. The only
names of objects which connote no-
thing arepropernames; and these have,
strictly speaking, no signification.*

"^ A writer who entitles his book Philo-
sophy : or, The Science of Truth, charges me
in his veiy first page (referring .at the fnot
of it to this passage) with asserting that
general names have properly no significa-
tion. And he repeats thi.s statement many
times in the course of hi* volume, with

u

NAMES AND PROPOSITIONS.

If, like the robber in the Arabian
Nights, we make a mark with chalk
on a house to enable us to know it
again, the mark has a purpose, but it
has not properly any meaning. The
chalk does not declare anything about
the house ; it does not mean, This is
such a person's house, or This is a house
which contains booty. The object of
making the mark is merely distinc-
tion. I say to myself, All these houses
are so nearly alike that if I lose sight
of them I shall not again be able to
distinguish that which I am now look-
ing at, from any of the others ; I must
therefore contrive to make the appear-
ance of this one house unlike that of
the others, that I may hereafter know
when I see the mark — not indeed any
attribute of the house — but simply
that it is the same house which I am
now looking at. Morgiana chalked
all the other houses in a similar
manner, and defeated the scheme :
how ? simply by obliterating the dif-
ference of appearance between that
house and the others. The chalk
was still there, but it no longer
served the purpose of a distinctive
mark.

When we impose a proper name,
we perform an operation in some de-
gree analogous to what tlie robber
intended in chalking th« house. We
put a mark, not indeed upon the ob-
ject itself, but, so to speak, upon the
idea of the object. A proper name
is but an unmeaning mark which we
connect in our minds with the idea
of the object, in order that whenever
the mark meets our eyes or occurs to
our thoughts, we may think of that
individual object. Not being attached
to the thing itself, it does not, like

comments, not at all flattering', thereon.
It is well to be now and then reminded to
liow gieat a length perverse misquotation
(for, strange hs it appears, I <io not believe
that the writer is dishonest) can snmetimes
go. It is a warning to readers when they
see an author accused, with volume and
page referred to, and the apparent gtia-
ranree of inverted commas, of maintaining
something more than commonly absurd,
not to give implicit credence to the asser-
tion without verifying the reference.

the chalk, enable tis to distinguish
the object when we see it ; but it
enables us to distinguish it when it
is spoken of, either in the records of
our own experience, or in the dis-
course of others ; to know that what
we find asserted in any proposition
of which it is the subject, is asserted
of the individual thing with which
we were previously acquainted.

When we predicate of anything its
proper name ; when we say, pointing
to a man, this is Brown or Smith, or
pointing to a city, that it is York, we
do not, merely by so doing, convey
to the reader any information about
them, except that those are their
names. By enabling him to identify
the individuals, we may connect them
with information previously possessed
by him ; by saying, This is York, w^e
may tell him that it contains the
Minster. But this is in virtue of
what he has previously heard concern-
ing York ; not by anything implied
in the name. It is otherwise when
objects are spoken of by connotative
names. When we say. The town is
built of marble, we give the hearer
what may be entirely new informa-
tion, and this merely by the significa-
tion of the many- worded connotative
name, "built of marble." Such names
are not signs of the mere objects, in-
vented because we have occasion to
think and speak of those objects in-
dividually ; but signs which accom-
pany an attribute : a kind of livery
in which the attribute clothes all
objects which are recognised as pos-
sessing it. They are not mere marks,
but more, that is to say, significant
marks ; and the connotation is what
constitutes their significance.

As a proper name is said to be the
name of the one individual which it
is predicated of, so (as well from the
importance of adhering to analogy,
as for the other reasons formerly as-
signed) a connotative name ought to
be considered a name of all the various
individuals which it is predicable of,
or in other words denotes, and not of
what it connotes. But by learning

XAMBS.

n

what things it is a name of, we do
not learn the meaning of the name :
for to the same thing we may, with
equal propriety, apply many names,
not equivalent in meaning. Thus, I
call a certain man by the name
Sophroniscus : I call him by another
name, The father of Socrates. Both
these are names of the same indi-
vidual, but their meaning is altogether
different ; they are applied to that
individual for two different purposes :
the one, merely to distinguish him
from other persons who are spoken
of ; the other to indicate a fact relat-
ing to him, the fact that Socrates was
his son. I further apply to him these
other expressions : a man, a Greek,
an Athenian, a sculptor, an old man,
an honest man, a brave man. All
these are, or may be, names of So-
phroniscus, not indeed of him alone,
but of him and each of an indefinite
number of other human beings. Each
of these names is applied to Sophro-
niscus for a different reason, and by
each whoever understands its mean-
ing is apprised of a distinct fact or
number of facts concerning him ; but
those who knew nothing about the
names except that they were applic-
able to Sophroniscus, would be alto-
gether ignorant of their meaning. It
is even possible that I might know
every single individual of whom a
given name could be with truth
affirmed, and yet could not be said
to know the meaning of the name.
A child knows who are its brothers
and sisters, long before it has any
definite conception of the nature of
the facts which are involved in the
signification of those words.

In some cases it is not easy to decide
precisely how much a particular word
does or does not connote ; that is, we
do not exactly know (the case not
having arisen) what degree of differ-
ence in the object would occasion a
difference in the name. Thus, it is
clear that the word man, besides
animal life and rationality, connotes
also a certain external form ; but it
would be impossible to say precisely

what form ; that is, to decide hoW
great a deviation from the form ordi-
narily found in the beings whom we
are accustomed to call men, would
suffice in a newly-discovered race to
make us refuse them the name of man.
Rationality, also, being a quality which
admits of degrees, it has never been
settled what is the lowest degree of
that quality which would entitle any
creature to be considered a human
being. In all such cases, the meaning
of the general name is so far unsettled
and vague ; mankind have not come
to any positive agreement about the
matter. When we come to treat of
Classification, we shall have occasion
to show under what conditions this
vagueness may exist without practical
inconvenience ; and cases will appear
in which the ends of language are
better promoted by it than by com-
plete precision ; in order that, in
natural history for instance, indivi-
duals or species of no very marked
character may be ranged with those
more strongly characterised indivi-
duals or species, to which, in all their
properties taken together, they bear
the nearest resemblance.

But this partial uncertainty in the
connotation of names can only be free
from mischief when guarded by strict
precautions. One of the chief sources,
indeed, of lax habits of thought, is the
custom of using connotative terms
without a distinctly ascertained conno-
tation, and with no more precise
notion of their meaning than can be
loosely collected from observing what
objects they are used to denote. It is
in this manner that we all acquire,
and inevitably so, our first knowledge
of our vernacular language. A child
learns the meaning of the words man,
or white, by hearing them applied to
a variety of individual objects, and
finding out, by a process of generali-
zation and analysis which he could
not himself describe, what those dif-
ferent objects have in common. In
the case of these two words the pro-
cess is so easy as to require no assist-
ance from culture ; the objects called

24

NAMES AND PROPOSITIONS.

human beings, and the objects called
white, differing from all others by
qualities of a peculiarly definite and
obvious character. But in many
other cases, objects bear a general
resemblance to one another, which
leads to their being familiarly classed
together under a common name,
while, without more analytic habits
than the generality of mankind pos-
sess, it is not immediately apparent
what are the particular attributes,
upon the possession of which in com-
mon by them all, their general resem-
blance depends. When this is the
case, people use the name without any
recognised connotation, that is, with-
out any precise meaning ; they talk,
and consequently think, vaguely, and
remain contented to attach only the
same degree of significance to their
own words, which a child three years
old attaches to the words brother and
sister. The child at least is seldom
puzzled by the starting up of new
individuals, on whom he is ignorant
whether or not to confer the title ;
because there is usually an authority
close at hand competent to solve all
doubts. But a similar resource does
not exist in the generality of cases ;
and new objects are continually pre-
senting themselves to men, women,
and children, which they are called
upon to class propria motu. They,
accordingly, do this on no other prin-
ciple than that of superficial simi-
larity, giving to each new object the
name of that familiar object, the
idea of which it most readily recalls,
or which, on a cursory inspection, it
seems to them most to resemble :
as an unknown substance found in
the ground will be called, according
to its texture, earth, sand, or a stone.
In this manner, names creep on from
subject to subject, until all traces of
a common meaning sometimes dis-
appear, and the word comes to denote
a, number of things not only indepen-
dently of any common attribute, but
which have actually no attribute in
common ; or none but what is shared
by other things to which the name is

capriciously refused.* Even scientific
writers have aided in this perversion
of general language from its purpose ;
sometimes because, like the vulgar,
they knew no better ; and sometimes
in deference to that aversion to admit
new words, which induces mankind,
on all subjects not considered tech-
nical to attempt to make the original
stock of names serve with but little
augmentation to express a constantly
increasing number of objects and
distinctions, and, consequently, to
express them in a manner progres-
sively more and more imperfect.

To what a degree this loose mode
of classing and denominating objects
has rendered the vocabulary of mental
and moral philosophy unfit for the
purposes of accurate thinking, is best
known to whoever has most medi-
tated on the present condition of
those branches of knowledge. Since,
however, the introduction of a new
technical language as the vehicle of
speculations on subjects belonging to
the domain of daily discussion, is
extremely diflBcult to effect, and would
not be free from inconvenience even
if effected, the problem for the philo-
sopher, and one of the most difficult
which he has to resolve, is, in retain-
ing the existing phraseology, how
best to alleviate its imperfections.
This can only be accomplished by

* " Take the familiar term Stone. It is
applied to mineral and rocky materials, to
the kernels of fruit, to the accumulations
in the gall-bladder and in the kidney;
while it is refused to polished minerals
(called gems), to rocks that have the
cleavage suited for roofing (slates), and to.
baked clay (bricks). It occurs in the
designation of the magnetic oxide of iron
(loadstone), and not in speaking of other
metallic ores. Such a term is wholly
unfit for accurate reasoning, unless hedged
round on every occasion by other phrases ;
as building stone, precious stone, gall
stone, (fee. Moreover, the methods of defi-
nition are baffled for want of sufficient
community to ground upon. There is no
quality uniformly present in the cases
where it is applied, and uniformly absent
whei-e it ia not applied ; hence the definer
would have to employ largely the licence
of striking off existing applications, and
taking in new ones."— Bain, Logic, ii. lya.

NAMES.

25

giving to every general concrete name
which there is frequent occasion to
predicate, a definite and fixed conno-
tation ; in order that it may be known
what attributes, when we call an
object by that name, we really mean
to predicate of the object. And the
question of most nicety is, how to
give this fixed connotation to a name,
with the least possible change in the
objects which the name is habitually
employed to denote ; with the least
possible disarrangement, either by
adding or substraction, of the group
of objects which, in however imper-
fect a manner, it serves to circum-
scribe and hold together ; and with
the least vitiation of the truth of any
propositions which are commonly re-
ceived as true.

This desirable purpose, of giving
a fixed connotation where it is want-
ing, is the end aimed at whenever
any one attempts to give a definition
of a general name already in use ;
every definition of a connotative name
being an attempt either merely to
declare, or to declare and analyse, the
connotation of the name. And the
fact, that no questions which have
arisen in the moral sciences have been
subjects of keener controversy than
the definitions of almost all the lead-
ing expressions, is a proof how great
an extent the evil to which we have
adverted has attained.

Names with indeterminate conno-
tation are not to be confounded with
names which have more than one
connotation, that is to say, ambiguous
words. A word may have several
meanings, but all of them fixed and
recognised ones ; as the word post,
for example, or the word box, the
various senses of which it would be
endless to enumerate. And the pau-
city of existing names, in comparison
with the demand for them, may often
render it advisable and even neces-
sary to retain a name in this multi-
plicity of acceptations, distinguishing
these so clearly as to prevent their
being confounded with one another.
Such a word may be considered as

two or more names, accidentally
written and spoken alike. *

* Before quitting the subject of conno-
tative names, it is proper to observe, that
the first writer who, iu our times, has
adopted from the schoolmen the word to
connote, Mr. James Mill, iu his Analysis of
the Phenomena of the Human Mind, employs
it in a signification difTeicut from that in
which it is liere used. He uses the word
in a sense coextensive with its etymology,
applying it to every case in which a name,
while pointing directly to one thing (which
is cousequently termed its signification),
includes also a tacit reference to some other
thing. In the case considered in the text,
that of concrete general names, his lan-
guage and mine are the converse of one
another. Considering (very justly) the
signification of the name to lie in the attri-
bute, he speaks of the word as noting the
attribute, and connoting the things possess-
ing the attribute. And he describes ab-
stract names as being properly concrete
names with their connotation dropped :
whereas, in my view, it is the denotation
which would be said to be dropped, what
was previously connoted becoming the
whole signification.

In adopting a phraseology at variance
with that which so high an authority, and
one which I am less likely than any other
person to undervalue, has deliberately
sanctioned, I have been influenced by the
urgent necessity for a term exclusively
appropriated to express the manner in
wliich a concrete general name serves to
mark the attributes which are involved
in its signification. Ihis necessity can
scarcely be felt in its full force by any one
who has not found by experience how vain
is the attempt to communicate clear ideas
on the philosophy of language without
such a word. It is hardly an exaggeration
to say, that some of the most prevalent of
the errors with which Logic has been in-
fected and a large part of the cloudiness
and confusion of ideas which have en-
veloped it, would, in all probability, liave
been avoided, if a term had been in common
use to express exactly what I have signified
by the term to connote. And the school-
men to whom we are indebted for the
greater part of our logical language, gave
us this also, and in this very sense. For
though some of their general expressions
countenance the use of the word in the
more extensive and vague acceptation in
which it is taken by Mr. Mill, yet when
they had to define it specifically as a tech-
nical term, and to fix its meaning as such,
with that admirable precision which always
characterises their definitions, they clearly
explained that nothing was said to be con-
noted except /orm«, which word may gene-
rally, in their writings, be understood as
synonymous with attributes.

Now, if the word to connote, so well

^

NAMES AlfD PBOPOSmONS.

§ 6. The fourth principal division of
names is into positive and negative.
Positive, as mariy tree, good ; negative,
as Twt-man, not-tree, not-good. To
every positive concrete name, a cor-
responding negative one might be
framed. After giving a name to any
one thing, or to any plurality of things,
we might create a second name which
should be a name of all things what-
ever, except that particular thing or
things. These negative names are
employed whenever we have occasion
to speak collectively of all things other
than some thing or class of things.
When the positive name is connota-
tive, the corresponding negative name
is connotative likewise ; but in a
peculiar way, connoting not the pre-
sence but the absence of an attribute.
Thus, not-white denotes all things
whatever except white things ; and
connotes the attribute of not possess-
ing whiteness. For the non-posses-
sion of any given attribute is also an
attribute, and may receive a name as
such ; and thus negative concrete
names may obtain negative abstract
names to correspond to them.*

suited to the purpose to which they applied
it, be diverted from that purpose by being
taken to fulfil another, for which it does
not seem to me to be at all required ; I am
unable to find any expression to replace it,
but such as are commonly employed in a
sense so much more general, that it would
be useless attempting to associate them
peculiarly with this precise idea. Such
are the words, to involve, to imply, &c.
By employing these, I should fail of attain-
ing the object for which alone the name is
needed, namely, to distinguish this par-
ticular kind of involving and implying
from all other kinds, and to assure to it
the degree of habitual attention which its
importance demands.

* Professor Bain (Logic, 1. 56) thinks that
negative names are not names of all things
whatever except those denoted by the
corielative p'isitive name, but only for all
things of some particular class : not-white,
for instance, he deems not to be a name
for everything in nature except white
things, but only for every coloured thing
other than white. In this case, however,
as in all others, the test of what a name
denotes is what, it can be predicated of :
and we can cert duly predicate of a sound,
or a smell, that it is not white. The aflQrma-
tion and the negation of the same attribute

Names which are positive in form
are often negative in reality, and
others are really positive though their
form is negative. The word incon-
venient, for example, does not express
the mere absence of convenience ; it
expresses a positive attribute, that of
being the cause of discomfort or
annoyance. So the word unpleasant,
notwithstanding its negative form,
does not connote the mere absence
of pleasantness, but a less degree of
what is signified by the word painfid,
which, it is hardly necessary to say,
is positive. Idle, on the other hand,
is a word which, though positive in
form, expresses nothing but what
would be signified either by the
phrase not working, or by the phrase
not disposed to work ; and sober, either
by not drunk or by not drunken.

There is a class of names called
privative. A privative name is equi-
valent in its signification to a positive
and a negative name taken together ;
being the name of something which
has once had a particular attribute,
or for some other reason might have
been expected to have it, but which
has it not. Such is the word blind,
which is not equivalent to not seeing,
or to not capable of seeing, for it would
not, except by a poetical or rhetorical
figure, be applied to stocks and stones.
A thing is not usually said to be blind,
unless the class to which it is most
familiarly referred, or to which it is
referred on the particular occasion,
be chiefly composed of things which
can see, as in the case of a blind man,
or a blind horse ; or unless it is sup-
posed for any reason that it ought to
see ; as in saying of a man, that he
rushed blindly into an abyss, or of
philosophers or the clergy that the
greater part of them are blind guides.
The names called privative, therefore,
connote two things ; the absence of
certain attributes, and the presence
of others, from which the presence
also of the former might naturally
have been expected.

cannot but divide the whole field of predi-
cation between them.

NAMM.

27

§ 7. The fifth leading division of
names is into relative and absolute, or
let us rather say, relative and non-
relative; for the word absolute is put
upon much too hard duty in meta-
physics, not to be willingly sp&red
when its services can be dispensed
with. It resembles the word civil in
the language of jurisprudence, which
stands for the opposite of criminal,
the opposite of ecclesiastical, the
opposite of military, the opposite of
political — in short, the opposite of
any positive word which wants a
negative.

Relative names are such as father,
son ; ruler, subject ; like, equal ; un-
like, unequal ; longer, shorter ; cause,
effect. Their characteristic property
is, that they are always given in pairs.
Every relative name which is predi-
cated of an object, supposes another
object (or objects), of which we may
predicate either that same name or
another relative name which is said
to be the correlative of the former.
Thus, when we call any person a son,
we suppose other persons who must
be called parents. When we call
any event a cause, we suppose another
event which is an effect. When we
say of any distance that it is longer,
we suppose another distance which is
shorter. When we say of any object
that it is like, we mean that it is like
some other object, which is also said
to be like the first. In this last case
both objects receive the same name ;
the relative term is its own correlative.

It is evident that these words,
when concrete, are, like other con-
crete general names, connotative ;
they denote a subject, and connote
an attribute ; and each of them has
or might have a corresponding ab-
stract name, to denote the attribute
connoted by the concrete. Thus the
concrete like has its abstract likeness ;
the concretes, father and son, have,
or might have, the abstracts, pater-
nity, and filiety, or sonship. The
concrete name connotes an attribute,
and the abstract name which answers
to it denotes that attribute. But of

what nature is the attribute ? Where-
in consists the peculiarity in the con-
notation of a relative name?

The attribute signified by a relatiT«
name, say some, is a relation ; and
this they give, rf not as a sufficient
explanation, at least as the only one
attainable. If they are asked. What,
then, is a relation ? they do not pro-
fess to be able to tell. It is generally
I regarded as something peculiarly re-
! condite and mysterious. I cannot,
however, perceive in what respect it
is more so than any other attribute ;
indeed, it appears to me to be so in a
somewhat less degree. I conceive
rather, that it is by examining into
the signification of relative names, or,
in other words, into the nature of the
attribute which they connote, that a
clear insight may best be obtained
into the nature of all attributes : of
all that is meant by an attribute.

It is obvious, in fact, that if we
take any two correlative names,
father and son for instance, though
the objects rfe-noted by the names
are different, they both, in a certain
sense, connote the same thing. They
cannot, indeed, be said to connote the
same attribute : to be a father, is not
the same thing as to be a son. But
when we call one man a father,
another a son, what we mean to
affirm is a set of facts, which are
exactly the same in both cases. To
predicate of A that he is the father
of B, and of B that he is the son of
A, is to assert one and the same fact
in different words. The two pro-
positions are exactly equivalent :
neither of them asserts more or
asserts less than the other. The
paternity of A and the filiety of B
are not two facts, but two modes of
expressing the same fact. That fact,
when analysed, consists of a series of
physical events or phenomena, in
which both A and B are parties con-
cerned, and from which they both
derive names. What those names
really connote, is this series of events :
that is the meaning, and the whole
meaning, which either of them is

2S

NAMES AND PROPOSITIONS.

intended to convey. The series of
events may be said to constitute the
relation ; the schoolmen called it the
foundation of the relation, funda- 1
mentum relationis. ^ ^ |

In this manner any fact, or series •
of facts, in which two different |
objects are implicated, and which is j
therefore predicable of both of them, I
may be either considered as consti- ;
tuting an attribute of the one, or an I
attribute of the other. According as !
we consider it in the former, or in |
the latter aspect, it is connoted by j
the one or the other of the two corre-
lative names. Father connotes the
fact, regarded as constituting an
attribute of A; son connotes the
same fact, as constituting an attri-
bute of B. It may evidently be
regarded with equal propriety in
either light. And all that appears
necessary to account for the exist-
ence of relative names, is, that when-
ever there is a fact in which two in-
dividuals are concerned, an attribute
grounded on that fact may be ascribed
to either of these individuals.

A name, therefore, is said to be
relative, when, over and above the ob-
ject which it denotes, it implies in its
signification the existence of another
object, also deriving a denomination
from the same fact which is the ground
of the first name. Or (to express the
same meaning in other words) a name
is relative, when, being the name of
one thing, its signification cannot be
explained but by mentioning another.
Or we may state it thus — when the
name cannot be employed in discourse
so as to have a meaning, unless the
name of some other thing than what
it is itself the name of, be either
expressed or understood. These de-
finitions are all, at bottom, equivalent,
being modes of variously expressing
this one distinctive circumstance —
that every other attribute of an object
might, without any contradiction, be
conceived still to exist if no object
besides that one had ever existed ; *

• Or rather, all objects except itself and
the percipient mind ; for, as we snail see

but those of its attributes which are
expressed by relative names, would
on that supposition be swept away.

§ 8. Names have been further dis-
tinguished into univocal and cequi-
vocal: these, however, are not two
kinds of names, but two different
modes of employing names. A name
is univocal, or applied univocally, with
respect to all things of which it can
be predicated in the same sense ; it is
sequivocal, or applied sequivocally, as
respects those things of which it is
predicated in different senses. It is
scarcely necessary to give instances
I of a fact so familiar as the double
meaning of a word. In reality, as
has been already observed, an sequi-
vocal or ambiguous word is not one
name, but two names, accidentally
coinciding in sound. File meaning a
steel instrument, and file meaning a
line of soldiers, have no more title to
be considered one word, because
written alike, than grease and Greece
have, because they are pronounced
alike. They are one sound, appro
priated to form two different words.

An intermediate case is that of a
name used analogically or metaphori-
cally ; that is, a name which is pre-
dicated of two things, not univocally,
or exactly in the same signification,
but in significations somewhat similar,
and which being derived one from the
other, one of them may be considered
the primary, and the other a secondary
signification. As when we speak of a
brilliant light and a brilliant achieve-
ment. The word is not applied in the
same sense to the light and to the
achievement ; but having been applied
to the light in its original sense, that
of brightness to the eye, it is trans-
hereafter, to ascribe any attiibute to an
object, necessarily implies a mind to per-
ceive it.

The simple and clear explanation given
in tiie text, of relation and relative names,
a subject so long the opprobrium of meta-
phypics, was given (as far as I know) for
tbe first time, by Mr. James Mill, in his
Analysis of the Ph«*.tiomena of the Human
Mind:

THINGS DENOTED BY NAMES.

29

ferred to the achievement in a deriva-
tive signification, supposed to be
somewhat like the primitive one.
The word, however, is just as properly
two names instead of one, in this
case, as in that of the most perfect
ambiguity. And one of tlie com-
monest forms of fallacious reasoning
arising from ambiguity, is that of
arguing from a metaphorical expres-
sion as if it were literal ; that is. as if
a word, when applied metaphorically,
were the same name as when taken
in its original sense : which will be
seen more particularly in its place.

CHAPTER III.

OP THE THINGS DENOTED BY NAMES.

§ I. Looking back now to the com-
mencement of our inquiry, let us
attempt to measure how far it has
advanced. Logic, we found, is the
Theory of Proof. But proof supposes
something provable, which must be a
Proposition or Assertion ; since no-
thing but a Proposition can be an
object of belief, or therefore of proof.
A Proposition is, discourse which
affirms or denies something of some
other thing. This is one step : there
must, it seems, be two things con-
cerned in every act of belief. But
what are these Things? They can
be no other than those signified by
the two names, which being joined
together by a copula constitute the
Proposition. If, therefore, we knew
what all names signify, we should
know everything which, in the exist-
ing state of human knowledge, is cap-
able either of being made a subject
of affirmation or denial, or of being
itself affirmed or denied of a subject.
We have accordingly, in the preced-
ing chapter, reviewed the various
kinds of Names, in order to ascertain
what is signified by each of them.
And we have now carried this survey
far enough to be able to take an
account of its results, and to exhibit

an enumeration of all kinds of Things
I which are capable of being made pre-
I dicates, or of having anything predi-
cated of them : after which to determine
the import of Predication, that is, of
Propositions, can be no arduous task.
! The necessity of an enumeration of
Existence, as the basis of Logic, did
not escape the attention of the school-
men, and of their master Aristotle,
the most comprehensive, if not also
the most sagacious, of the ancient
philosophers. The Categories, or Pre-
dicaments— the former a Greek word,
the latter its literal translation in the
Latin language — were believed to be
an enumeration of all things capable
of being named ; an enumeration by
the summa genera, i.e., the most ex-
tensive classes into which things
could be distributed ; which, there-
fore, were so many highest Predicates,
one or other of which was supposed
capable of being affirmed with truth
! of every nameable thing whatsoever.
The following are the classes into
which, according to this school of
philosophy. Things in general might
be reduced : —

OixTia,

Substantia.

noabi/,

Quantitas.

Iloid./,

Qiialitas.

IIpOS^ Tl,

Relatio.

Xloteiv,

Actio.

IId<rxfiv,

Passio.

Uov,

Ubi.

ndre,

Quando.

Keiaflai,

Situs.

'Exei,',

Habitus.

The imperfections of this classifica-
tion are too obvious to require, and
its merits are not sufficient to reward,
a minute examination. It is a mere
catalogue of the distinctions rudely
marked out by the language of familiar
life, with little or no attempt to pene-
trate, by philosophic analysis, to the
rationale even of those common dis-
tinctions. Such an analysis, however
superficially conducted, would have
shown the enumeration to be both
redundant and defective. Some ob-
jects are omitted, and others repeated
several times under different heads.
It is like a division of animals into

30

NAMES AND PROPOSITIONS.

men, quadrupeds, horses, asses, and
ponies. That, for instance, could not
be a very comprehensive view of the
nature of Relation which could ex-
clude action, passivity, and local
situation from that category. The
same observation applies to the cate-
gories Quando (or position in time),
and Ubi (or position in space) ; while
the distinction between the latter
and Situs is merely verbal. The in-
congruity of erecting into a summum
genus the class which forms the tenth
category is manifest. On the other
hand, the enumeration takes no notice
of anything besides substances and
attributes. In what category are we
to place sensations, or any other feel-
ings and states of mind ; as hope,
joy, fear ; sound, smell, taste ; pain,
pleasure ; thought, judgment, concep-
tion, and the like? Probably all
these would have been placed by the
Aristotelian school in the categories
of actio and passio ; and the relation
of such of them as are active, to their
objects, and of such of them as are
passive, to their causes, would rightly
be so placed ; but the things them-
selves, the feelings or states of mind,
wrongly. Feelings, or states of con-
sciousness, are assuredly to be ac-
counted among realities, but they
cannot be reckoned either among
substances or attributes.*

* On the preceding passage Professor
Bain remarks {Logic, i. 265): "The Cate-
gories d< > not seem to have been intended
as a classification of Nameable Things, in
the sense of ' an enumeration of all kinds
of Things which are capable of being made
predicates, or of haviiiganythiug predicated
of them.' I hey seem to iiave been rather
intended as a generalization of predicates;
an analysis of the final import of predica-
tion. Viewed in tins light, they are not
open to tht^ objections offered by Mr. Mill.
The proper question to ask is not — In what
Category are we to place sensations or other
feelings or states of mind? but. Under
what Categories can we predicate regard-
ing states of mind? Take, for example,
Hope. When we say tiiat it is a state of
mind, we predicate Substance : we may
also describe liow great it is (Quantity),
what is tiie quality of it, pleasurable or
painful (Quality), what it has reference to
(Relation). Aristotle seems to hare framed

§ 2. Before recommencing, under
better auspices, the attempt made
with such imperfect success by the
early logicians, we must take notice
of an unfortunate ambiguity in all the
concrete names which correspond to
the most general of all abstract terms,
the word Existence. When we have
occasion for a name which shall be
capable of denoting whatever exists,
as contradistinguished from non-
entity or Nothing, there is hardly a
word applicable to the purpose which
is not also, and even more familiarly,
taken in a sense in which it denotes
only substances. But substances are
not all that exists ; attributes, if
such things are to be spoken of, must
be said to exist ; feelings certainly
exist. Yet when we speak of an
object, or of a thing, we are almost
always supposed to mean a substance.
There seems a kind of contradiction
in using such an expression as that
one thing is merely an attribute of
another thing. And the announce-
ment of a Classification of Things
would, I believe, prepare most readers
the Categories on the plan— Here is an in-
dividual ; wtiat is the final analysis of all
tliat we can predicate about him? "

This is doubtless a true statement of the
leading idea in the classification. The
Category Ovaia was certainly understood
by Aristotle to be a general name for all
possible answers to the questions Quid sit ?
w lien asked rei^pecting a concrete indi-
vidual ; as the other Categories are names
comprehending all possilile answers to the
questions Quantum sit? Quale sit? &c. In
Aristotle's conception, tiierefore, the Cate-
gories may not have been a classification of
Thintrs ; but they were soon converted into
one by his scholastic followers, who cer-
tainly regarded and treated them as a
classification of Things, and carried them
out as such, dividing down the Category
Substance us a naturalist mignt do, into
the different classes of physical or meta-
physical objects as distinguished from
attributes, and the other Categories into
the principal varieties of quantity, quality,
relation, &c. It is, therefore, a just sub-
ject of complaint against them, that they
had no Category of Feeling. Feeling is
assu'cdly predicable as. a summum genus,
of every particular kind of feeling, for in-
stance, as in Mr. Bain's example, of Hope :
but it cannot be brought within any of the
Categories as interpreted either by Aristotle
or by his followers.

THINGS DENOTED BY NAMES.

31

for an enumeration like those in
natural history, beginning with the
great divisions of animal, vegetable,
and mineral, and subdividing them
into classes and orders. If, rejecting
the word Thing, we endeavour to find
another of a more general import, or
at least more exclusively confined to
that general import, a word denoting
all that exists, and connoting only
simple existence ; no word might be
presumed fitter for such a purpose
than being : originally the present
participle of a verb which in one of
its meanings is exactly equivalent to
the verb exists; and therefore suitable,
even by its grammatical formation, to
be the concrete of the abstract exist-
ence. But this word, strange as the
fact may appear, is still more com-
pletely spoiled for the purpose which
it seemed expressly made for, than
the word Thing. Being is, by custom,
exactly synonymous with substance ;
except that it is free from a slight
taint of a second ambiguity ; being
applied impartially to matter and to
mind, while substance, though ori-
ginally and in strictness applicable to
both, is apt to suggest in preference
the idea of matter. Attributes are
never called Beings ; nor are feelings.
A being is that which excites feelings,
and which possesses attributes. The
soul is called a Being ; God and
angels are called Beings ; but if we
were to say, extension, colour, wis-
dom, virtue, are beings, we should
perhaps be suspected of thinking with
some of the ancients, that the cardinal
virtues are animals ; or, at the least.
of holding with the Platonic school
the doctrine of self-existent Ideas, or
with the followers of Epicurus that of
Sensible Forms, which detach them-
selves in every direction from bodies,
and by coming in contact with our
organs, cause our perceptions. We
should be supposed, in short, to be-
lieve that Attributes are Substances.
In consequence of this perversion
of the word Being, philosophers
looking about for something to supply
its place, laid their hands upon the

word Entity, a piece of barbarous
Latin, invented by the schoolmen to
be used as an abstract name, in
which class its grammatical form
would seem to place it ; but being
seized by logicians in distress to stop
a leak in their terminology, it has
ever since been used as a concrete
name. The kindred word essence,
bom at the same time and of the
same parents, scarcely underwent a
more complete transformation when,
from being the abstract of the verb
to he, it came to denote something
sufficiently concrete to be enclosed
in a glass bottle. The word Entity,
since it settled down into a concrete
name, has retained its universality
of signification somewhat less im-
paired than any of the names before
mentioned. Yet the same gradual
decay to which, after a certain age,
all the language of psychology seems
liable, has been at work even here.
If you call virtue an entity, you are
indeed somewhat less strongly sus-
pected of believing it to be a sub-
stance than if you called it a being ;
but you are by no means free from
the suspicion. Every word which
was originally intended to connote
mere existence, seems, after a time,
to enlarge its connotation to separate
existence, or existence freed from the
condition of belonging to a substance ;
which condition being precisely what
constitutes an attribute, attributes
are gradually shut out; and along
with them feelings, which in ninety -
nine cases out of a hundred have no
other name than that of the attribute
which is grounded on them. Strange
that when the greatest embarrassment
felt by all who have any considerable
number of thoughts to express, is to
find a sufficient variety of precise
words fitted to express them, there
should be no practice to which even
scientific thinkers are more addicted
than that of taking valuable words to
express ideas which are sufficiently
expressed by other words already
appropriated to them.
When it is impossible to obtain good

32

NAMES AND PROPOSITIONS.

tools, the next best thing is to under-
stand thoroughly the defects of those
we have. I have therefore warned
the reader of the ambiguity of the
names which, for want of better, I am
necessitated to employ. It must now
be the writer's endeavour so to employ
them as in no case to leave the mean-
ing doubtful or obscure. No one of
the above terms being altogether un-
ambiguous, I shall not confine myself
to any one, but shall employ on each
occasion the word which seems least
likely in the particular case to lead to
misunderstanding ; nor do I pretend
to use either these or any other words
with a rigorous adherence to one single
sense. To do so would often leave us
without a word to express what is
signified by a known word in some one
or other of its senses : unless authors
had an unlimited licence to coin new
words, together with (what it would
be more difficult to assume) unlimited
power of making readers understand
them. Nor would it be wise in a
writer, on a subject involving so much
of abstraction, to deny himself the
advantage derived from even an im-
proper use of a term, when, by means
of it, some familiar association is called
up which brings the meaning home to
the mind, as it were by a flash.

The difficulty both to the writer and
reader, of the attempt which must be
made to use vague words so as to
convey a precise meaning, is not
wholly a matter of regret. It is not
unfitting that logical treatises should
afford an example of that, to facilitate
which is among the most important
uses of logic. Philosophical language
will for a long time, and popular
language still longer, retain so much
of vagueness and ambiguity, that
logic would be of little value if it did
not, among its other advantages,
exercise the understanding in doing
its work neatly and correctly with
these imperfect tools.

After this preamble it is time to
proceed to our enumeration. We
shall commence with Feelings, the
simplest class of nameable things ; the

term Feeling being of course under-
stood in its most enlarged sense.

I. Feelings, or States of Con-
sciousness.

§ 3. A Feeling and a State of Con-
sciousness are, in the language of
philosophy, equivalent expressions :
everything is a feeling of which the
mind is conscious ; everything which
it feels, or, in other words, which
forms a part of its own sentient exist-
ence. In popular language Feeling
is not always synonymous with State
of Consciousness ; being often taken
more peculiarly for those states which
are conceived as belonging to the
sensitive, or to the emotional, phasis
of our nature, and sometimes, with a
still narrower restriction, to the emo-
tional alone, as distinguished from
what are conceived as belonging to
the percipient or to the intellectual
phasis. But this is an admitted
departure from correctness of lan-
guage ; just as, by a popular perver-
sion the exact converse of this, the
word Mind is withdrawn from its
rightful generality of signification,
and restricted to the intellect. The
still greater perversion by which
Feeling is sometimes confined not
only to bodily sensations, but to the
sensations of a single sense, that of
touch, needs not to be more particu-
larly adverted to.

Feeling, in the proper sense of the
term, is a genus, of which Sensation,
Emotion, and Thought, are subordi-
nate species. Un der the word Thought
is here to be included whatever we
are internally conscious of when we
are said to think ; from the conscious-
ness we have when we think of a red
colour without having it before our
eyes, to the most recondite thoughts
of a philosopher or poet. Be it re-
membered, however, that by a thought
is to be understood what passes in
the mind itself, and not any object
external to the mind, which the person
is commonly said to be thinking of.
He may be thinking of the sun, or of

THINGS DENOTED BY NAMES.

33

God, but the sun and God are not
thoughts ; his mental image, however,
of the sun, and his idea of God, are
thoughts ; states of his mind, not of
the objects themselves ; and so also
is his belief of the existence of the
sun, or of God ; or his disbelief, if the
case be so. Even imaginary objects
(which are said to exist only in our
ideas) are to be distinguished from
our ideas of them. I may think of a
hobgoblin, as I may think of the loaf
which was eaten yesterday, or of the
flower which will bloom to-morrow.
But the hobgoblin which never existed
is not the same thing with my idea
of a hobgoblin, any more than the
loaf which once existed is the same
thing with my idea of a loaf, or the
flower which does not yet exist, but
which will exist, is the same with my
idea of a flower. They are all, not
thoughts, but objects of thought ;
though at the present time all the
objects are alike non-existent.

In like manner, a Sensation is to
be carefully distinguished from the
object which causes the sensation ;
our sensation of white from a white
object: nor is it less to be distinguished
from the attribute whiteness, which
we ascribe to the object in consequence
of its exciting the sensation. Unfor-
tunately for clearness and due dis-
crimination in considering these sub-
jects, our sensations seldom receive
separate names. "We have a name
for the objects which produce in us
a certain sensation : the word white.
We have a name for the quality in
those objects, to which we ascribe
the sensation : the name whiteness.
But when we speak of the sensation
itself (as we have not occasion to do
this often except in our scientific
speculations), language, which adapts
itself for the most part only to the
common uses of life, has provided us
with no single-worded or immediate
designation ; we must employ a cir-
cumlocution, and say, The sensation
of white, or The sensation of white-
ness ; we must denominate the sensa-
tion either from the object, or from

the attribute, by which it is excited.
Yet the sensation, though it never
does, might very well be conceived to
exist, without anything whatever to
excite it. We can conceive it as
arising spontaneously in the mind.
But if it so arose, we should have
no name to denote it which would
not be a misnomer. In the case of
our sensations of hearing we are
better provided ; we have the word
Sound, and a whole vocabulary of
words to denote the various kinds of
sounds. For as we are often conscious
of these sensations in the absence of
any perceptible object, we can more
easily conceive having them in the
absence of any object whatever. We
need only shut our eyes and listen to
music, to have a conception of an uni-
verse with nothing in it except sounds,
and ourselves hearing them : and what
is easily conceived separately, easily
obtains a separate name. But in gene-
ral our names of sensations denote in-
discriminately the sensation and the
attribute. Thus, colour stands for the
sensations of white, red, &c., but also
for the quality in the coloured object.
We talk of the colours of things as
among their properties.

§ 4. In the case of sensations,
another distinction has also to be
kept in view, which is often con-
founded, and never without mis-
chievous consequences. This is, the
distinction between the sensation it-
self, and the state of the bodily organs
which precedes the sensation, and
which constitutes the physical agency
by which it is produced. One of the
sources of confusion on this subject is
the division commonly made of feel-
ings into Bodily and Mental. Philoso-
phically speaking, there is no founda-
tion at all for this distinction ; even
sensations are states of the sentient
mind, not states of the body, as dis-
tinguished from it. What I am con-
scious of when I see the colour blue,
is B^ feeling of blue colour, which is
one thing ; the picture on my retina,
or the phenomenon of hitherto mys-

34

NAMES AND PROPOSITIONS.

terious nature which takes place in
my optic nerve or in my brain, is
another thing, of which I am not at
all conscious, and which scientific in-
vestigation alone could have apprised
me of. These are states of my body :
but the sensation of blue, which is
the consequence of these states of
body, is not a state of body : that
which perceives and is conscious is
called Mind. When sensations are
called bodily feelings, it is only as
being the class of feelings which are
immediately occasioned by bodily
btates ; whereas the other kinds of
feelings, thoughts, for instance, or
emotions, are immediately excited
not by anything acting upon the
bodily organs, but by sensations, or
by previous thoughts. This, however,
is a distinction not in our feelings,
but in the agency which produces our
feelings : all of them when actually
produced are states of mind.

Besides the affection of our bodily
organs from without, and the sensa-
tion thereby produced in our minds,
many writers admit a third link in
the chain of phenomena, which they
call a Perception, and which consists
in the recognition of an external
object as the exciting cause of the
sensation. This perception, they say,
is an act of the mind, proceeding
from its own spontaneous activity ;
while in a sensation the mind is pas-
sive, being merely acted upon by the
outward object. And according to
some metaphysicians, it is by an act
of the mind, similar to perception,
except in not being preceded by any
sensation, that the existence of God,
the soul, and other hyperphysical
objects is recognised.

These acts of what is termed per-
ception, whatever be the conclusion
xiltimately come to respecting their
nature, must, I conceive, take their
place among the varieties of feelings
or states of mind. In so classing
them, I have not the smallest inten-
tion of declaring or insinuating any
theory as to the law of mind in which
these mental processes may be sup-

posed to originate, or the conditions
under which they may be legitimate
or the reverse. Far less do I mean
(as Dr. Whewell seems to suppose
must be meant in an analogous case*)
to indicate that as they are " merely
states of mind," it is superfluous to
inquire into their distinguishing pecu-
liarities. I abstain from the inquiry
as irrelevant to the science of logic.
In these so-called perceptions, or
direct recognitions by the mind, of
objects, whether physical or spiritual,
which are external to itself, I can see
only cases of belief ; but of belief
which claims to be intuitive, or inde-
pendent of external evidence. "When
a stone lies before me, I am conscious
of certain sensations which I receive
from it ; but if I say that these sen-
sations come to me from an external
object which I perceive, the meaning
of these words is, that receiving the
sensations, I intuitively believe that an
external cause of those sensations
exists. The laws of intuitive belief,
and the conditions under which it is
legitimate, are a subject which, as we
have already so often remarked, be-
longs not t'> logic, but to the science of
the ultimate laws of the human mind.
To the same region of speculation
belongs all that can be said respecting
the distinction which the German
metaphysicians and their French and
English followers so elaborately draw
between the acts of the mind and its
merely passive states; between what
it receives from, and what it gives to,
the crude materials of its experience.
I am aware that with reference to the
view which those writers take of the
primary elements of thought and
knowledge, this distinction is funda-
mental. But for the present purpose,
which is to examine, not the original
groundwork of our knowledge, but
how we come by that portion of it
which is not original ; the difference
between active and passive states of
mind is of secondary importance.
For us, they all are states of mindj

* Philosophy 0/ the Jndwtive Sciences,
voL i. p. 40.

THINGS DENOTED BY NAMES.

35

they all are feelings ; by which, let it
be said once more, I mean to imply
nothing of passivity, but simply that
they are psychological facts, facts
which take place in the mind, and are
to be carefully distinguished from the
external or physical facts with which
they may be connected either as
effects or as causes.

§ 5. Among active states of mind,
there is, however, one species which
merits particular attention, because
it forms a principal part of the con-
notation of some important classes of
names. I mean volitions, or acts of
the will. When we speak of sentient
beings by relative names, a large
portion of the connotation of the
name usually consists of the actions
of those beings ; actions past, present,
and possible or probable future. Take,
for instance, the words Sovereign and
Subject. What meaning do these
words convey, but that of innumerable
actions, done or to be done by the
sovereign and the subjects, to or in
regard to one another reciprocally ?
So with the words physician and
patient, leader and follower, tutor and
pupil. In many cases the words also
connote actions which would be done
under certain contingencies by persons
other than those denoted : as the
words mortgagor and mortgagee, ob-
ligor and obligee, and many other
words expressive of legal relation,
which connote what a court of justice
would do to enforce the legal obligation
if not fulfilled. There are also words
which connote actions previously done
by persons other than those denoted
either by the name itself or by its
correlative ; as the word brother.
From those instances, it may be seen
how large a portion of the connota-
tion of names consists of actions.
Now what is an action ? Not one
thing, but a series of two things ; the
state of mind called a volition, fol-
lowed by an effect. The volition or
intention to produce the effect, is one
thing ; the effect produced in conse-
quepce of the iptei^tion, is another

thing ; the two together constitute the
action. I f onn the purpose of instantly
moving nay arm ; that is a state of my
mind : my arm (not being tied or
paralytic) moves in obedience to my
purpose ; that is a physical fact, con-
sequent on a state of mind. The inten-
tion, followed by the fact, or (if we
prefer the expression) the fact when
preceded and caused by the intention,
is called the action of moving my arm.

§ 6. Of the first leading division of
nameable things, viz., Feelings or
States of Consciousness, we began by
recognising three sub-divisions ; Sen-
sations, Thoughts, and Emotions.
The first two of these we have illus-
trated at considerable length ; the
third. Emotions, not being perplexed
by similar ambiguities, does not re-
quire similar exemplification. And,
finally, we have found it necessary to
add to these three a fourth species,
commonly known by the name Voli-
tions. We shall now proceed to the
two remaining classes of nameable
things ; all things which are regarded
as external to the mind being con-
sidered as belonging either to the class
of Substances or to that of Attributes.

II. Substances.

Logicians have endeavoured to de-
fine Substance and Attribute ; but
their definitions are not so much
attempts to draw a distinction between
the things themselves, as instructions
what difference it is customary to
make in the grammatical structure of
the sentence, according as we are
speaking of substances or of attributes.
Such definitions are rather lessons of
English, or of Greek, Latin, or Ger-
man, than of mental philosophy. An
attribute, say the school logicians,
must be the attribute of something :
colour, for example, nmst be the colour
of something ; goodness must be the
goodness of something ; and if this
something should cease to exist, or
should cease to be connected with the
ftttribiite, the existence of th^ J^Hri-

36

NAMES AND PROPOSITIONS.

bute would be at an end, A substance,
on the contrary, is self-existent ; in
speaking about it, we need not put of
after its name. A stone is not the
stone of anything ; the moon is not
the moon of anything, but simply the
moon. Unless, indeed, the name
which we choose to give to the sub-
stance be a relative name ; if so, it
must be followed either by of, or by
some other particle, implying, as that
proposition does, a reference to some-
thing else : but then the other char-
acteristic peculiarity of an attribute
would fail ; the something might be
destroyed, and the substance might
still subsist. Thus, a father must be
the father of something, and so far
resembles an attribute, in being re-
ferred to something besides himself :
if there were no child, there would be
no father : but this, when we look
into the matter, only means that we
should not call him father. The man
called father might still exist though
there were no child, as he existed be-
fore there was a child : and there
would be no contradiction in suppos-
ing him to exist, though the whole uni-
verse except himself were destroyed.
But destroy all white substances, and
where would be the attribute white-
ness ? Whiteness, without any white
thing, is a contradiction in terms.

This is the nearest approach to a
solution of the difficulty, that will be
found in the common treatises on
logic. It will scarcely be thought to
be a satisfactory one. If an attribute
is distinguished from a substance by
being the attribute of something, it
seems highly necessary to understand
what is meant by of ; a particle which
needs explanation too much itself, to
be placed in front of the explanation
of anything else. And as for the
self -existence of substance, it is very
true that a substance may be con-
ceived to exist without any other sub-
stance, but so also may an attribute
without any other attribute ; and we
can no more imagine a substance with-
out attributes than we can imagine
attributes withput a sub^taijce.

Metaphysicians, however, have
probed the question deeper, and given
an account of Substance considerably
more satisfactory than this. Substances
are usually distinguished as Bodies or
Minds. Of each of these, philosophers
have at length provided us with a defi-
nition which seems unexceptionable.

§ 7. A body, according to the re-
ceived doctrine of modem metaphysi-
cians, may be defined, the external
cause to which we ascribe our sensa-
tions. When I see and touch a piece of
gold, I am conscious of a sensation of
yellow colour, and sensations of hard-
ness and weight ; and by varying the
mode of handling, I may add to these
sensations many others completely
distinct from them. The sensations
are all of which I am directly con-
scious ; but I consider them as pro-
duced by something not only existing
independently of my will, but externa]
to my bodily organs and to my mind.
This external something I call a body.

It may be asked, how come we to
ascribe our sensations to any external
cause ? And is there sufficient ground
for so ascribing them ? It is known,
that there are metaphysicians who
have raised a controversy on the
point ; maintaining that we are not
warranted in referring our sensations
to a cause such as we understand by
the word Body, or to any external
cause whatever. Though we have
no concern here with this controversy,
nor with the metaphysical niceties
on which it turns, one of the best
ways of showing what is meant by Sub-
stance is, to consider what position it is
necessary to take up, in order to main-
tain its existence against opponents.

It is certain, then, that a part of
our notion of a body consists of the
notion of a number of sensations of
our own, or of other sentient beings,
habitually occurring simultaneously.
My conception of the table at which
I am writing is compounded of its
visible form and size, which are com-
plex sensations of sight ; its tangible
form and size, which a,XQ comple^f

THINGS DENOTED BY NAMES.

37

sensations of our organs of touch and
of our muscles ; its weight, which is
also a sensation of touch and of the
muscles ; its colour, which is a sensa-
tion of sight ; its hardness, which is
a sensation of the muscles ; its com-
position, which is another word for all
the varieties of sensation which we
receive under various circumstances
from the wood of which it is made,
and so forth. All or most of these
various sensations frequently are, and,
as we learn by experience, always
might be, experienced simultaneously,
or in many different orders of succes-
sion at our own choice : and hence
the thought of any one of them makes
us think of the others, and the whole
becomes mentally amalgamated into
one mixed state of consciousness,
which, in the language of the school
of Locke and Hartley, is termed a
Complex Idea.

Now, there are philosophers who
have argued as follows. If we con-
ceive an orange to be divested of its
natural colour without acquiring any
new one ; to lose its softness without
becoming hard, its roundness without
becoming square or pentagonal, or of
any other regular or irregular figure
whatever ; to be deprived of size, of
weight, of taste, of smell ; to lose all
its mechanical and all its chemical
properties, and acquire no new ones ;
to become in short, invisible, intan-
gible, imperceptible not only by all our
senses, but by the senses of all other
sentient beings, real or possible ; no-
thing, say these thinkers, would re-
main. For of what nature, they ask,
could be the residuum ? and by what
token could it manifest its presence ?
To the unreflecting its existence seems
to rest on the evidence of the senses.
But to the senses nothing is appa-
rent except the sensations. We know,
indeed, that these sensations are bound
together by some law ; they do not
come together at random, but accord-
ing to a systematic order, which is
part of the order established in the
universe. When we experience one
of these sensations, we usually experi-

ence the others also, or know that we
have it in our power to experience
them. But a fixed law of connection,
making the sensations occur together,
does not, say these philosophers,
necessarily require what is called a
substratum to support them. The
conception of a substratum is but one
of many possible forms in which that
connection presents itself to our imagi-
nation ; a mode of, as it were, re-
alizing the idea. If there be such a
substratum, suppose it at this instant
miraculously annihilated, and let the
sensations continue to occur in the
same order, and how would the sub-
stratum be missed ? By what signs

j should we be able to discover that its
existence had terminated ? Should
we not have as much reason to believe

: that it still existed as we now have ?
And if we should not then be war-
ranted in believing it, how can we be
so now ? A body, therefore, according,
to these metaphysicians, is not any-
thing intrinsically different from the
sensations which the body is said to
produce in us ; it is, in short, a set of
sensations, or rather, of possibilities
of sensation, joined together according
to a fixed law.

j The controversies to which these
speculations have given rise, and the
doctrines which have been developed
in the attempt to find a conclusive

I answer to them, have been fruitful of
important consequences to the Science

j of Mind. The sensations (it was an-
swered) which we are conscious of,
and which we receive, not at random,
but joined togetherin a certain uniform
manner, imply not only a law or laws

, of connection, but a cause external to
our mind, which cause, by its own

I laws, determines the laws according

j to which the sensations are connected

I and experienced. The schoolmen
used to call this external cause by the
name we have already employed, a *m6-
stratuni ; and its attributes (as they
expressed themselves) inherent, liter-
ally stuck, in it. To this substratum
the name Matter is usually given
in philosophical discussions. It was

38

NAMES AKD PROPOSITIONS.

soon, however, acknowledged by all
who reflected on the subject, that the
existence of matter cannot be proved
by extrinsic evidence. The answer,
therefore, now usually made to Berke-
ley and his followers, is, that the belief
is intuitive ; that mankind, in all ages,
have felt themselves compelled, by a
necessity of their nature, to refer their
sensations to an external cause : that
even those who deny it in theory,
yield to the necessity in practice, and
both in speech, thought, and feeling,
do, equally with the vulgar, acknow-
ledge their sensations to be the effects
of something external to them : this
knowledge, therefore, it is affirmed, is
as evidently intuitive as our know-
ledge of our sensations themselves is
intuitive. And here the question
merges in the fundamental problem
of metaphysics properly so called : to
which science we leave it.

But although the extreme doctrine
of the Idealist metaphysicians, that
objects are nothing but our sensations
and the laws which connect them, has
not been generally adopted by subse-
quent thinkers ; the point of most
real importance is one on which those
metaphysicians are now very generally
considered to have made out their
case : viz., that all we knoiooi objects,
is the sensations which they give us,
and the order of the occurrence of
those sensations. Kant himself, on
this point, is as explicit as Berkeley
or Locke. However firmly convinced
that there exists an universeof "Things
in themselves," totally distinct from
the universe of phenomena, or of things
as they appear to our senses ; and
even when bringing into use a tech-
nical expression [Noumenon) to denote
what the thing is in itself, as con-
trasted with the representation of it in
our minds ; he allows that this repre-
sentation (the matter of which, he
says, consists of our sensations, though
the form is given by the laws of the
mind itself) is all we know of the
object : and that the real nature of
the Thing is, and by the constitution
of our faculties ever must remain, at

least in the present state of existence,
an impenetrable mystery to us. " Of
things absolutely or in themselves,"
says Sir William Hamilton,* " be they
external, be they internal, we know
nothing, or know them only as incog-
nisable ; and become aware of their
incomprehensible existence, only as
this is indirectly and accidentally
revealed to us, through certain quali-
ties related to our faculties of know-
ledge, and which qualities, again, we
cannot think as unconditioned, irre-
lative, existent in and of themselves.
All that we know is therefore phaeno-
menal, — phsenomenal of the un-
known." t The same doctrine is laid
down in the clearest and strongest
terms by M. Cousin, whose observa-
tions on the subject are the more
worthy of attention, as, in consequence
of the ultra-German and ontological
character of his philosophy in other
respects, they may be regarded as the
admissions of an opponent.^

* Discussions on Philosophy, &c. Appen-
dix I. pp. 643-4.

t It is to be regretted that Sir William
Hamilton, though he often strenuously in-
sists ou this doctrine, and though, in the
passage quoted, he states it with a compre-
hensiveness and force which leave nothing
to be desired, did not consistently adhere
to his own doctrine, but maintained along
with it opinions with which it is utterly
irreconcilable. See the third and other
chapters of ^n Examination of Sir William
Hamilton's Philosophy.

t "Nous savons qu'il existe quelque
chose hors de nous, parceque nous ne pou-
vons expliquer nos perceptions sans lea
rattacber k des causes distinctes de nous-
mfimes ; n<ius savons de plus que ces causes,
dont nous ne connaissons pas d'ailleura
I'essence, produisent les effets les plus vari-
ables, les plus divers, et meme les plus con-
traires, selon qu'elles rencontrent telle
nature ou telle disposition du sujet. Mais
savons-nous quelque chose de plus? et
meme, vu le caractfere ind6termine des
causes que nous concevons dans les corps,
y a-t-il quelque chose de plus k savoir? Y
a-t-il lieu de nous enquerir si nous perce-
vons les choses telles qu'elles sont? Non
evidemment. . . . Je ne dispas que lepro-
blfeme est insoluble, jedts qu'il est absurde et
enferme une contradiction. Nous ne savons
pas ce que ces causes sont en elles-mf,mes, et
la raison nous defend de chercher a le con-
naitre : mais il est bien Evident a priori,
qvi'elles ne sont pas en elles-memes ce qu'elUt

THINGS DENOTED BY NAMES.

39

There is not the slightest reason for
believing that what we call the sen-
sible qualities of the object are a type
of anything inherent in itself, or bear
any affinity to its own nature. A
cause does not, as such, resemble its
effects ; an east wind is not like the
feeling of cold, nor heat like the steam
of boiling water. Why then should
matter resemble our sensations ?
Why should the inmost nature of fire
and water resemble the impressions
made by those objects upon our
? * Or on what principle are

$<mt par rapport a nout, puisque la presence
du sujet modifie necessairement leur action.
Supprimez tout sujet sentant, il est certain
que ces causes agiraient encore puisqu'elles
continueraient d'exister; mais elles agi-
raient autrement ; elles seraient encore des
qualit^s et des propri^t^s, mais qui ne
ressembleraient k rien de ce que nous con-
naissons. Le feu ne maniiestetait plus
aucTine des propri^t^s que nous lui con-
naissons : que serait-il? C'est ce que nous
ne saurons jamais. C'ett d'ailleurs pent-
Stre un probleme qui ne repugnepas seulement
a la nature de notre esprit, mais n I'essence
ndme des chones. Quand mfime en effet on
Bupprimerait par le pens^e tous les svijets
sentants, il faudrait encore admettre que
nul corps ne manifesterait ses propri^t^s
autrement qu'en relation avec un sujet
quelcoiique, et dans ce cas ses proprietis ne
seraient encore que relatives : en sorte qu'il
me parait fort raisonnable d'admettre que
les proprieties d^terminees des corps n'exis-
tent pas indepeudamment d'un sujot quel-
coiique, et que quand on demande si les
proprietds de la mati^re sont telles que
nous les porcevons, il faudrait voir aupara-
vant si elles sont en tant qtie determin6ea>,
et dans quel sens il est vrai de dire qu'elles
sont." — Cours d'Hittoire de la Fhilosophie
Morale au iSme siecle, 8me leqon.

* An attempt, indeed, has been made by
Reid and others, to establish that although
some of the properties we ascribe to objects
exist only in our sensations, others exist
in the things themselves, being such as
cannot possibly be copies of any impression
upon the senses ; and they ask, from what
sensations our notions of extension and
figure have been derived? The gauntlet
thrown down by Reid was taken up by
Brown, who, applying greater powers of
analysis than had previously been applied
to tiie notions of extension and figure,
pointed out that the sensations from which
those notions are derived, are -ensations
of touch, combined with sensations of a
class previously too little adverted to by
metaphysicians, those which have their
seat in our muscular frame. His analysis,

we authorized to deduce from the
effects, an)rthing concerning the cause,
except that it is a cause adequate to
produce those effects ? It may, there-
fore, safely be laid down as a truth
both obvious in itself, and admitted
by all whom it is at present necessary
to take into consideration, that, of the
outward world, we know and can know
absolutely nothing, except the sensa-
tions which we experience from it.f

§ 8. Body having now been defined
the external cause, and (according to

which was adopted and followed up by
James Mill, has been further and greatly
improved upon in Professor Bain's pro-
found work. The Senses and the Intellect,
and in the chapters on " Perception " o£
a work of eminent analytic power, Mr.
Herbert Spencer's Principles of P»ycho-

On this point M. Cousin may again be
cited in favour of the better df.ctiine. M.
Cousin recognises, in opposition to Reid,
the essential subjectivity of our concep-
tions of what are called the primary quaU-
ties of matter, as extension, solidity, &c.,
equally with those of colour, heat, and the
remainder of the so-called secondary quali-
ties.—Cowri, ut supra, gme IcQon.

t This doctrine, which is the most com.
plete form of the philosophical theory
known as the Relativity of Human Know-
ledge, has, since the recent revival in this
country of an active interest in metaphy-
sical speculation, been the subject of a
greatly increased amount of discussion and
controversy ; and dissentients have mani-
fested themselves in considt-rably gieater
number than I had any knowledge of when
the passage in the text was written. The
doctrine has been attacked from two sides.
Some thinkers, among whom are the late
Professor Ferrier, in his Institutes of Meta-
physic, and Professor John Grote, in his
Erploratio Philosophica, appear to deny
altogether the reality of Noumena, or
Things in themselves — of an unknowable
substratum or support for the sensations
which we experience, and which, according
to the theory, constitute all our knowledge
of an external -world. It seems to me,
however, that in Professor Grote's case at
least, the denial of Noumena is only ap-
parent, and that he does not essentially
differ from the other class of objectors, in-
cluding Mr. Bailey in his valuable Letters
on the Philosophy of the Human Mind, and
(in spite ot the striking passage quoted in
the text) also Sir William Hamilton, who
contend for a direct knowledge by the
human mind of more than the sensations
— of certain attributes or properties as they

40

NAMES AND PROPOSITIONS.

the more reasonable opinion) the un-
known external cause, to which we re-
fer our sensations ; it remains to frame
a definition of Mind. Nor, after the
preceding observations, will this be
difficult. For, as our conception of a
body is that of an unknown exciting
cause of sensations, so our conception
of a mind is that of an unknown
recipient, or percipient, of them ; and
not of them alone, but of all our
other feelings. As body is under-
stood to be the mysterious something
which excites the mind to feel, so
mind is the mysterious something
which feels and thinks. It is un-
necessary to give in the case of mind,
as we gave in the case of matter, a
particular statement of the sceptical
system by which its existence as a
Thing in itself, distinct from the series
of what are denominated its states, is
called in question. But it is necessary
to remark, that on the inmost nature
(whatever be meant by inmost nature)
of the thinking principle, as well as
on the inmost nature of matter, we
are, and with our faculties must
always remain, entirely in the dark.
All which we are aware of, even in
our own minds, is (in the words of

exist not in us, but in the Things them-
selves.

With the first of these opinions, that
which denies Noumena, I have, as a meta-
physician, no quarrel ; but whether it be
true or false, it is irrelevant to Logic. And
since all the forms of language are in con-
tradiction to it, nothing but confusion
could result from its unnecessary intro-
duction into a treatise, every essential doc-
trine of which could stand equally well
with the opposite and accredited opinion.
The other and rival doctrine, that of a
direct perception or intuitive knowledge
of the outward object as it is in itself, con-
sidered as distinct from the sensations we
receive from it, is of far greater practical
moment. But even this question, depend-
ing on the nature and laws of Intuitive
Knowledge, is not within the province of
Logic. For the grounds of my own opinion
concerning it, I must content myself with
referring to a work already mentioned —
An Examination of Sir William Hamilton's
Philosophy: several chapters of which are
devoted to a full discussion of the questions
and theories relating to the supposed direct
perception of external objects.

James Mill) a certain "thread of
consciousness ; " a series of feelings,
that is, of sensations, thoughts, emo-
tions, and volitions, more or less
numerous and complicated. There is
something I call Myself, or, by
another form of expression, my mind,
which I consider as distinct from
these sensations, thoughts, &c. ; a
something which I conceive to be not
the thoughts, but the being that has
the thoughts, and which I can con-
ceive as existing for ever in a state of
quiescence, without any thoughts at
all. But what this being is, though
it is myself, I have no knowledge,
other than the series of its states of
consciousness. As bodies manifest
themselves to me only through the
sensations of which I regard them as
the causes, so the thinking principle,
or mind, in my own nature, makes
itself known to me only by the feel-
ings of which it is conscious. I
know nothing about myself, save my
capacities of feeling or being conscious
(including, of course, thinking and
willing) : and were I to learn any-
thing new concerning my own nature,
I cannot with my present faculties
conceive this new information to be
anything else, than that I have some
additional capacities, as yet unknown
to me, of feeling, thinking, or willing.
Thus, then, as body is the unsen-
tient cause to which we are naturally
prompted to refer a certain portion of
our feelings, so mind may be described
as the sentient subject (in the scholastic
sense of the term) of all feelings ; that
which has or feels them. But of the
nature of either body or mind, further
than the feelings which the former
excites, and which the latter experi-
ences, we do not, according to the
best existing doctrine, know any-
thing ; and if anything, logic has
nothing to do with it, or with the
manner in which the knowledge is
acquired. "With this result we may
conclude this portion of our subject,
and pass to the third and only re-
maining class or division of Nameable
Things.

THINGS DENOTED BY NAMES

41

III. Attributes, and, first,
Qualities.

§ 9. From what has already been
said of Substance, what is to be said
of Attribute is easily deducible. For
if we know not, and cannot know,
anything of bodies but the sensa-
tions which they excite in us or in
others, those sensations must be all
that we can, at bottom, mean by
their attributes ; and the distinction
which we verbally make between the
properties of things and the sensations
we receive from them, must originate
in the convenience of discourse rather
than in the nature of what is signified
by the terms.

Attributes are usually distributed
under the three heads of Quality,
Quantity, and Relation. We shall
come to the two latter presently : in
the first place we shall confine our-
selves to the former.

Let us take, then, as our example,
one of what are termed the sensible
qualities of objects, and let that
example be whiteness. When we
ascribe whiteness to any substance,
as, for instance, snow ; when we say
that snow has the quality whiteness,
what do we really assert ? Simply,
that when snow is present to our
organs, we have a particular sensa-
tion, which we are accustomed to call
the sensation of white. But how do
I know that snow is present ? Obvi-
ously by the sensations which I derive
from it, and not otherwise. I infer
that the object is present, because it
gives me a certain assemblage or
series of sensations. And when I
ascribe to it the attribute whiteness,
my meaning is only, that, of the
sensations composing this group or
series, that which I call the sensation
of white colour is one.

This is one view which may be
taken of the subject. But there is
also another and a different view.
It may be said, that it is true we
know nothing of sensible objects,
except the sensations they excite in
us; that the fact of our receiving
from snow the particular sensation

which is called a sensation of white,
is the ground on which we ascribe to
that substance the quality whiteness ;
the sole proof of its possessing that
quality. But because one thing may
be the sole evidence of the existence
of another thing, it does not follow
that the two are one and the same.
The attribute whiteness (it may be
said) is not the fact of receiving the
sensation, but something in the object
itself ; a power inherent in it ; some-
thing in virtue of which the object
produces the sensation. And when
we affirm that snow possesses the
attribute whiteness, we do not merely
assert that the presence of snow pro-
duces in us that sensation, but that it
does so through, and by reason of,
that power or quality.

For the purposes of logic it is not
of material importance which of these
opinions we adopt. The full discus-
sion of the subject belongs to the
other department of scientific en-
quiry, so often alluded to under the
name of metaphysics ; but it may be
said here, that for the doctrine of the
existence of a peculiar species of
entities called qualities, I can see no
foundation except in a tendency of
the human mind which is the cause
of many delusions. I mean, the dis-
position, wherever we meet with two
names which are not precisely synony-
mous, to suppose that they must be
the names of two different things ;
whereas in reality they may be names
of the same thing viewed in two dif-
ferent lights, or under different sup-
positions as to surrounding circum-
stances. Because quality and sensation
cannot be put indiscriminately one
for the other, it is supposed that they
cannot both signify the same thing,
namely, the impression or feeling with
which we are affected through our
senses by the presence of an object ;
though there is at least no absurdity
in supposing that this identical im-
pression or feeling may be called a
sensation when considered merely in
itself, and a quality when looked at
in relation to any one of the numerous

42

NAMES AND PROPOSITIONS.

objects, the presence of which to our
organs excites in our minds that
among various other sensations or
feelings. And if this be admissible as
a supposition, it rests with those who
contend for an entity per se called a
quality, to show that their opinion is
preferable, or is anything in fact but
a lingering remnant of the old doctrine
of occult causes : the very absurdity
which Moliere so happily ridiculed
when he made one of his pedantic
physicians account for the fact that
opium produces sleep by the maxim,
Because it has a soporific virtue.

It is evident that when the physician
stated that opium has a soporific
virtue, he did not account for, but
merely asserted over again, the fact
that it produces sleep. In like
manner, when we say that snow is
white because it has the quality of
whiteness, we are only re-asserting in
more technical language the fact that
it excites in us the sensation of white.
If it be said that the sensation must
have some cause, I answer, its cause
is the presence of the assemblage of
phenomena which is termed the
object. When we have asserted that
as often as the object is present, and
our organs in their normal state, the
sensation takes place, we have stated
all that we know about the matter.
There is no need, after assigning a
certain and intelligible cause, to
suppose an occult cause besides, for
the purpose of enabling the real cause
to produce its effect. If I am asked,
why does the presence of the object
cause this sensation in me, I cannot
tell : I can only say that such is my
nature, and the nature of the object ;
that the fact forms a part of the con-
stitution of things. And to this we
must at last come, even after inter-
polating the imaginary entity. What-
ever number of links the chain of
causes and effects may consist of, how
any one link pBoduces the one which
is next to it, remains equally inex-
plicable to us. It is as easy to com-
prehend that the object should pro-
duce the sensation directly and at.

once, as that it should produce the
same sensation by the aid of some-
thing else called the power of produc-
ing it.

But, as the difficulties which may
be felt in adopting this view of the
subject cannot be removed without
discussions transcending the bounds
of our science, I content myself with
a passing indication, and shall, for
the purposes of logic, adopt a language
compatible with either view of the
nature of qualities. I shall say, —
what at least admits of no dispute, —
that the quality of whiteness ascribed
to the object snow, is grounded on its
exciting in us the sensation of white ;
and adopting the language already
used by the school logicians in the
case of the kind of attributes called
Relations, I shall term the sensation
of white the foundation of the quality
whiteness. For logical purposes the
sensation is the only essential part of
what is meant by the word ; the only
part which we ever can be concerned
in proving. When that is proved, the
quality is proved ; if an object ex-
cites a sensation, it has, of course,
the power of exciting it.

rv. Relahons.

§ 10. The qualities of a body, we
have said, are the attributes grounded
on the sensations which the presence
of that particular body to our organs
excites in our minds. But when we
ascribe to any object the kind of
attribute called a Relation, the founda-
tion of the attribute must be something
in which other objects are concerned
besides itself and the percipient.

As there may with propriety be
said to be a relation between any
two things to which two correlative
names are or may be given, we may
expect to discover what constitutes a
relation in general, if we enumerate
the principal cases in which mankind
have imposed correlative names, and
observe what these cases have in
common.

What, then, is the character which

THINGS DENOTED BY NAMES.

43

is possessed in common by states of
circumstances so heterogeneous and
discordant as these : one thing like
another ; one thing unlike ant)ther ;
one thing near another ; one thing far
from another ; one thing before, after,
along with another ; one thing greater,
equaJ, less, than another ; one thing
the cause of another, the effect of
another ; one person the master, ser-
vant, child, parent, debtor, creditor,
sovereign, subject, attorney, client, of
another, and so on ?

Omitting, for the present, the case
of Resemblance, (a relation which
requires to be considered separately,)
there seems to be one thing common
to all these cases, and only one ; that
in each of them there exists or occurs,
or has existed or occurred, or may be
expected to exist or occur, some fact
or phenomenon, into which the two
things which are said to be related to
each other, both enter as parties con-
cerned. This fact, or phenomenon,
is what the Aristotelian logicians
called the fundamentum relationis.
Thus in the relation of greater and
less between two magnitudes, the
fundamentum relationis is the fact
that one of the two magnitudes could,
under certain conditions, be included
in, without entirely filling, the space
occupied by the other magnitude. In
the relation of master and servant,
the fundamentum relationis is the fact
that the one has undertaken, or is
compelled, to perform certain services
for the benefit and at the bidding of
the other. Examples might be inde-
finitely multiplied ; but it is already
obvious that whenever two things are
said to be related, there is some fact,
or series of facts, into which they
both enter : and that whenever any
two things are involved in some one
fact, or series of facts, we may ascribe
to those two things a mutual relation
grounded on the fact. Even if they
have nothing in common but what
is common to all things, that they
are members of the universe, we call
that a relation, and denominate them
fellow-creatures, fellow-beings, or fel-

low-denizens of the universe. But
in proportion as the fact into which
the two objects enter as parts is of a
more special and peculiar, or of a more
complicated nature, so also is the rela-
tion grounded upon it. And there are
as many conceivable relations as there
are conceivable kinds of facts in which
two things can be jointly concerned.

In the same manner, therefore, as
a quality is an attribute grounded on
the fact that a certain sensation or
sensations are produced in us by the
object, so an attribute grounded on
some fact into which the object enters
jointly with another object, is a rela-
tion between it and that other object.
But the fact in the latter case consists
of the very same kind of elements as
the fact in the former ; namely, states
of consciousness. In the case, for
example, of any legal relation, as
debtor and creditor, principal and
agent, guardian and ward, the fun-
damentum relationis consists entirely
of thoughts, feelings, and volitions
(actual or contingent), either of the
persons themselves or of other persons
concerned in the same series of trans-
actions ; as, for instance, the inten-
tions which would be formed by a
judge, in case a complaint were made
to his tribunal of the infringement of
any of the legal obligations imposed by
the relation ; and the acts which the
judge would perform in consequence ;
acts being (as we have already seen)
another word for intentions followed
by an effect, and that effect being but
another word for sensations, or some
other feelings, occasioned either to the
agent himself or to somebody else.
There is no part of what the names
expressive of the relation imply, that
is not resolvable into states of con-
sciousness ; outward objects being, no
doubt, supposed throughout as the
causes by which some of those states
of consciousness are excited, and
minds as the subjects by which all of
them are experienced, but neither the
external objects nor the minds making
their existence known otherwise than
by the states of consciousness.

44

NAMES AND PROPOSITIONS.

Oases of relation are not always so
complicated as those to which we last
alluded. The simplest of all cases of
relation are those expressed by the
words antecedent and consequent,
and by the word simultaneous. If
we say, for instance, that dawn pre-
ceded sunrise, the fact in which the
two things, dawn and sunrise, were
jointly concerned, consisted only of
the two things themselves ; no third
thing entered into the fact or pheno-
menon at all. Unless, indeed, we
choose to call the succession of the
two objects a third thing ; but their
succession is not something added to
the things themselves ; it is something
involved in them. Dawn and sunrise
announce themselves to our conscious-
ness by two successive sensations.
Our consciousness of the succession
of these sensations is not a third sen-
sation or feeling added to them ; we
have not first the two feelings, and
then a feeling of their succession. To
have two feelings at all, implies hav-
ing them either successively, or else
simultaneously. Sensations, or other
feelings, being given, succession and
simultaneousness are the two condi-
tions, to the alternative of which they
are subjected by the nature of our
faculties ; and no one has been able,
or needs expect, to analyse the matter
any farther.

§ II. In a somewhat similar posi-
tion are two other sorts of relations,
Likeness and TJnlikeness. I have
two sensations ; we will suppose them
to be simple ones ; two sensations of
white, or one sensation of white and
another of black. I call the first two
sensations like ; the last two unlike.
What is the fact or phenomenon con-
stituting the fundamentum of this
relation ? The two sensations first,
and then what we call a feeling of
resemblance, or of want of resem-
blance. Let us confine ourselves to
the former case. Resemblance is evi-
dently a feeling ; a state of the con-
sciousness of the observer. Whether
the feeling of the resemblance of the

two colours be a third state of con-
sciousness, which I have after having
the two sensations of colour, or whether
(like the feeling of their succession)
it is involved in the sensations them-
selves, may be a matter of discussion.
But in either case, these feelings of
resemblance, and of its opposite dis-
similarity, are parts of our nature ;
and parts so far from being capable of
analysis, that they are pre-supposed
in every attempt to analyse any of our
other feelings. Likeness and unlike-
ness, therefore, as well as antecedence,
sequence, and simultaneousness, must
stand apart among relations, as things
sui generis. They are attributes
grounded on facts, that is, on states
of consciousness, but on states which
are peculiar, unresolvable, and inex-
plicable.

But, though likeness or unlikeness
cannot be resolved into anything else,
complex cases of likeness or unlikeness
can be resolved into simpler ones.
When we say of two things which
consist of parts, that they are like one
another, the likeness of the wholes
does admit of analysis ; it is com-
pounded of likenesses between the
various parts respectively, and of like-
ness in their arrangement. Of how
vast a variety of resemblances of parts
must that resemblance be composed,
which induces us to say that a portrait,
or a landscape, is like its original. If
one person mimics another with any
success, of how many simple like-
nesses must the general or complex
likeness be compounded : likeness in
a succession of bodily postures ; like-
ness in voice, or in the accents and
intonations of the voice ; likeness in
the choice of words, and in the
thoughts or sentiments expressed,
whether by word, countenance, or
gesture.

All likeness and unlikeness of which
we have any cognizance, resolve them-
selves into likeness and unlikeness
between states of our own, or some
other, mind. When we say that one
body is like another, (since we know
nothing of bodies but the sensations

THINGS DENOTED BY NAMES.

45

which they excite,) we mean really
that there is a resemblance between
the sensations excited by the two
bodies, or between some portions at
least of those sensations. If we say
that two attributes are like one another,
(since we know nothing of attributes
except the sensations or states of feel-
ing on which they are grounded,) we
mean really that those sensations, or
states of feeling, resemble each other.
We may also say that two relations
are alike. The fact of resemblance
between relations is sometimes called
analogy, forming one of the numerous
meanings of that word. The relation
in which Priam stood to Hector,
namely, that of father and son, re-
sembles the relation in which Philip
stood to Alexander ; resembles it so
closely that they are called the same
relati(m. The relation in which
Cromwell stood to England resembles
the relation in which Napoleon stood
to France, though not so closely as to
be called the same relation. The
meaning in both these instances must
be, that a resemblance existed between
the facts which constituted the funda-
mentum relationis.

This resemblance may exist in all
conceivable gradations, from perfect
undistinguishableness to something
extremely slight. When we say, that
a thought suggested to the mind of a
person of genius is like a seed cast into
the ground because the former pro-
duces a multitude of other thoughts,
and the latter a multitude of other
seeds, this is saying that between the
relation of an inventive mind to a
thought contained in it, and the rela-
tion of a fertile soil to a seed contained
in it, there exists a resemblance : the
real resemblance being in the two
fundamerda relationis, in each of which
there occurs a germ, producing by its
development a multitude of other
things similar to itself. And as,
whenever two objects are jointly con-
cerned in a phenomenon, this consti-
tutes a relation between those objects,
so, if we suppose a second pair of
objects concerned in a second pheno-

menon, the slightest resemblance be-
tween the two phenomena is suflBcient
to admit of its being said that the
two relations resemble ; provided, of
course, the points of resemblance are
found in those portions of the two
phenomena respectively which are
connoted by the relative names.

While speaking of resem.blance, it
is necessary to take notice of an
ambiguity of language, against which
scarcely any one is sufficiently on his
guard. Resemblance, when it exists
in the highest degree of all, amounting
to'undistinguishableness, is often called
identity, and the two similar things
are said to be the same. I say often,
not always ; for we do not say that two
visible objects, two persons for in-
stance, are the same, because they are
so much alike that one might be mis-
taken for the other : but we constantly
use this mode of expression when
speaking of feeling ; as when I say
that the sight of any object gives me
the same sensation or emotion to- day
that it did yesterday, or the same
which it gives to some other person.
This is evidently an incorrect appli-
cation of the word same; for the
feeling which I had yesterday is
gone, never to return ; what I have
to-day is another feeling, exactly like
the former perhaps, but distinct from
it ; and it is evident that two different
persons cannot be experiencing the
same feeling, in the sense in which
we say that they are both sitting at
the same table. By a similar am-
biguity we say, that two persons are
ill of the same disease ; that two
persons hold the same ofBce ; not in
the sense in which we say that they
are engaged in the same adventure,
or sailing in the same ship, but in the
sense that they fill offices exactly
similar, though, perhaps, in distant
places. Great confusion of ideas is
often produced, and many fallacies
engendered, in otherwise enlightened
understandings, by not being suffi-
ciently alive to the fact, (in itself not
always to be avoided,) that they use
the same name to express ideas sq

46

NAMES AND PROPOSITIONS.

different as those' of identity and un-
distinguishable resemblance. Among
modern writers, Archbishop Whately
stands almost alone in having drawn
attention to this distinction, and to
the ambiguity connected with it.

Several relations, generally called
by other names, are really cases of re-
semblance. As, for example, equality ;
which is but another word for the
exact resemblance commonly called
identity, considered as subsisting be-
tween things in respect of their
quantity. And this example forms a
suitable transition to the third and
last of the three heads under which,
as already remarked, Attributes are
commonly arranged.

V. QUANTITT.

§ 12. Let us imagine two things,
between which there is no difference,
(that is, no dissimilarity,) except in
quantity alone : for instance, a gallon
of water, and more than a gallon of
water. A gallon of water, like any
other external object, makes its pre-
sence known to us by a set of sensa-
tions which it excites. Ten gallons
of water are also an external object,
making its presence known to us in a
similar manner ; and as we do not
mistake ten gallons of water for a
gallon of water, it is plain that the
set of sensations is more or less dif-
ferent in the two cases. In like
manner, a gallon of water, and a
gallon of wine, are two external
objects, making their presence known
by two sets of sensations, which sensa-
tions are different from each other. In
the first case, however, we say that the
difference is in quantity ; in the last
there is a difference in quality, while
the quantity of the water and of the
wine is the same. What is the real
distinction between the two cases ? It
is not within the province of Logic to
analyse it ; nor to decide whether it
is susceptible of analysis or not. For
us the following considerations are
sufficient. It is evident that the
geusations I receive from the gallon of

water, and those I received from the
gallon of wine, are not the same, that
is, not precisely alike ; neither are
they altogether unlike : they are
partly similar, partly dissimilar ; and
that in which they resemble is pre-
cisely that in which alone the gallon
of water and the ten gallons do not
resemble. That in which the gallon
of water and the gallon of wine are
like each other, and in which the
gallon and the ten gallons of water
are unlike each other, is called their
quantity. This likeness and unlike-
ness I do not pretend to explain, no
more than any other kind of likeness
or unlikeness. But my object is to
show, that when we say of two things
that they differ in quantity, just as
when we say that they differ in
quality, the assertion is always
grounded on a difference in the sen-
sations which they excite. Nobody,
I presume, will say, that to see, or to
lift, or to drink, ten gallons of water,
does not include in itself a different
set of sensations from those of seeing,
lifting, or drinking one gallon ; or
that to see or handle a foot-rule, and
to see or handle a yard-measure made
exactly like it, are the same sensations.
I do not undertake to say what the
difference in the sensations is. Every-
body knows, and nobody can tell ; no
more than any one could tell what
white is to a person who had never
had the sensation. But the differ-
ence, so far as cognizable by our
faculties, lies in the sensations.
Whatever difference we say there is
in the things themselves, is in this,
as in all other cases, grounded, and
grounded exclusively, on a difference
in the sensations excited by them.

YI. Attributes Concluded.

§ 13. Thus, then, all the attri-
butes of bodies which are classed
under Quality or Quantity, are
grounded on the sensations which we
received from those bodies, and may
be defined, the powers which the
boclies have of exciting those scR'

THINGS DENOTED BY NAMES.

47

sations. And the same general ex-
planation has been found to apply to
most of the attributes usually classed
under the head of Relation. They,
too, are grounded on some fact or
phenomenon into which the related
objects enter as parts ; that fact or
phenomenon having no meaning and
no existence to us, except the series of
sensations or other states of conscious-
ness by which it makes itself known ;
and the relation being simply the
power or capacity which the object
posgesses of taking part along with
the correlated object in the production
of that series of sensations or states
of consciousness. We have been
obliged indeed, to recognise a some-
what different character in certain
peculiar relations, those of succession
and simultaneity, of likeness and un-
likeness. These, not being grounded
on any fact or phenomenon distinct
from the related objects themselves,
do not admit of the same kind of
analysis. But these relations, though
not, like other relations, grounded on
states of consciousness, are themselves
states of consciousness : resemblance
is nothing but our feeling of resem-
blance ; succession is nothing but our
feeling of succession. Or, if this be
disputed, (and we cannot, without
transgressing the bounds of our
science, discuss it here,) at least our
knowledge of these relations, and even
our possibility of knowledge, is con-
fined to those which subsist between
sensations, or other states of con-
sciousness ; for, though we ascribe
resemblance, or succession, or simul-
taneity, to objects and to attributes,
it is always in virtue of resemblance
or succession or simultaneity in the
sensations or states of consciousness
which those objects excite, and on
which those attributes are grounded.

§ 14. In the preceding investigation
we have, for the sake of simplicity,
considered bodies only, and omitted
minds. But what we have said is
applicable, mutatis mutandis, to the
latter. The attributes of minds, as

well as those of bodies, are grounded
on states of feeling or consciousness.
But in the case of a miiid, we have to
consider its own states, as well as
those which it produces in other
minds. Every attribute of a mind
consists either in being itself affected
in a certain way, or affecting other
minds in a certain way. Considered
in itself, we can predicate nothing of
it but the series of its own feelings.
When we say of any mind, that it is
devout, or superstitious, or meditative,
or cheerful, we mean that the ideas,
emotions, or volitions implied in those
words, form a frequently recurring
part of the series of feelings, or states
of consciousness, which fill up the
sentient existence of that mind.

In addition, however, to those attri-
butes of a mind which are grounded
on its own states of feeling, attributes
may also be ascribed to it, in the same
manner as to a body, grounded on the
feelings which it excites in other
minds. A mind does not, indeed,
like a body, excite sensations, but it
may excite thoughts or emotions.
The most important example of attri-
butes ascribed on this ground, is the
employment of terms expressive of
approbation or blame. When, for
example, we say of any character, or
(in other words) of any mind, that it
is admirable, we mean that the con-
templation of it excites the sentiment
of admiration ; and indeed somewhat
more, for the word implies that we
not only feel admiration, but approve
that sentiment in ourselves. In some
cases, under the semblance of a single
attribute, two are really predicated :
one of them, a state of the mind it-
self; the other, a state with which
other minds are affected by thinking
of it. As when we say of any one
that he is generous. The word gene-
rosity expresses a certain state of mind,
but being a term of praise, it also ex-
presses that this state of mind excites
in us another mental state, called
approbation. The assertion made,
therefore, is twofold, and of the fol-
lowing purport : Certain feelings form

48

NAMES AND PROPOSITIONS.

habitually a part of this person's
sentient existence ; and the idea of
those feelings of his, excites the senti-
ment of approbation in ourselves or
others.

As we thus ascribe attributes to
minds on the ground of ideas and
emotions, so may we to bodies on
similar grounds, and not solely on the
ground of sensations : as in speaking
of the beauty of a statue ; since this
attribute is grounded on the peculiar
feeling of pleasure which the statue
produces in our minds ; which is not
a sensation, but an emotion.

YTT. Geneeal Kesults.

§ 15. Our survey of the varieties of
Things which have been, or which are
capable of being, named — which have
been, or are capable of being, either
predicated of other Things, or them-
selves made the subject of predica-
tions— is now concluded.

Our enumeration commenced with
Feelings. These we scrupulously dis-
tinguished from the objects which
excite them, and from the organs by
which they are, or may be supposed
to be, conveyed. Feelings are of
four sorts : Sensations, Thoughts,
Emotions, and Volitions. What are
called Perceptions are merely a par-
ticular case of Belief, and belief is a
kind of thought. Actions are merely
volitions followed by an effect.

After Feelings we proceeded to
Substances. These are either Bodies
or Minds. Without entering into
the grounds of the metaphysical
doubts which have been raised con-
cerning the existence of Matter and
Mind as objective realities, we stated
as sufficient for us the conclusion in
which the best thinkers are now for
the most part agreed, that all we can
know of Matter is the sensations
which it gives us, and the order of
occurrence of those sensations ; and
that while the substance Body is the
unknown cause of our sensations, the
substance Mind is the unknown re-
cipient.

The only remaining class of Name-
able Things is attributes ; and these
are of three kinds, Quality, Relation,
and Quantity. Qualities, like sub-
stances, are known to us no otherwise
than by the sensations or other states
of consciousness which they excite :
and while, in compliance with com-
mon usage, we have continued to
speak of them as a distinct class of
Things, we showed that in predicating
them no one means to predicate any-
thing but those sensations or states
of consciousness, on which they may
be said to be grounded, and by which
alone they can be defined or described.
Relations, except the simple cases of
likeness and unlikeness, succession and
simultaneity, are similarly grounded
on some fact or phenomenon, that
is, on some series of sensations
or states of consciousness, more or
less complicated. The third species
of Attribute, Quantity, is also mani-
festly grounded on something in our
sensations or states of feeling, since
there is an indubitable difference in
the sensations excited by a larger and
a smaller bulk, or by a greater or a
less degree of intensity, in any object
of sense or of consciousness. All
attributes, therefore, are to us nothing
but either our sensations and other
states of feeling, or something inex-
tricably involved therein ; and to this
even the peculiar and simple relations
just adverted to are not exceptions.
Those peculiar relations, however, are
so important, and, even if they might
in strictness be classed among states
of consciousness, are so fundamentally
distinct from any other of those
states, that it would be a vain subtlety
to bring them under that common
description, and it is necessary that
they should be classed apart.*

* Professor Bain {Logic, i. 45) defines
attributes as "points of community among
classes." This definition expresses well
one point of view, but is liable to the
objection that it applies only to the attri-
butes of classes ; though an object, unique
in its kind, may be said to have attributes.
Moreover, the definition is not ultimate,
since the points of community themselves

PROPOSITIONS.

49

As the result, therefore, of our
analysis, we obtain the following as
an enumeration and classification of
all Nameable Things : —

1st. Feelings, or States of Con-
sciousness.

2nd. The Minds which experience
those feelings.

3rd. The Bodies, or external objects
which excite certain of those feelings,
together with the powers or properties
whereby they excite them ; these
latter (at least) being included rather
in compliance with common opinion,
and because their existence is taken
for granted in the common language
from which I cannot prudently deviate,
than because the recognition of such
powers or properties as real existences
appears to be warranted by a sound
philosoph}'.

4th, and last. The Successions and
Co-existences, the Likenesses and Un-
likenesses, between feelings or states
of consciousness. Those relations,
when considered as subsisting be-
tween other things, exist in reality only
between the states of consciousness
which those things, if bodies, excite,
if minds, either excite or experience.

This, until a better can be sug-
gested, may serve as a substitute for
the Categories of Aristotle considered
as a Classification of Existences.
The practical application of it will
appear when we commence the in-
quiry into the Import of Proposi-
tions ; in other words, when we in-
quire what it is which the mind
actually believes when it gives what
is called its assent to a proposition.

These four classes comprising, if
the classification be correct, all
Nameable Things, these or some of
them must of course compose the
signification of all names ; and of
these, or some of them, is made up
whatever we call a fact.

For distinction's sake, every fact
which is solely composed of feelings

admit of, and require, further analysis;
and Mr. Bain does analyse them into re-
semblance in the sensations, or other states
of consciousness excited by the object.

or states of consciousness considered
as such, is often called a Psychological
or Subjective fact ; while every fact
which is composed, either wholly or
in part, of something dififerent from
these, that is, of substances and
attributes, is called an Objective fact.
We may say, then, that every ob-
jective fact is grounded on a corre-
sponding siibjective one ; and has no
meaning to us, (apart from the sub-
jective fact which corresponds to it,)
except as a name for the unknown
and inscrutable process by which
that subjective or psychological fact
is brought to pass.

CHAPTER IV.

OP PROPOSITIONS.

§ I. In treating of Propositions, as
already in treating of Names, some
considerations of a comparatively
elementary nature respecting their
form and varieties must be premised,
before entering upon that analysis of
the import conveyed by them, which
is the real subject and purpose of this
preliminary book.

A proposition, we have before said,
is a portion of discourse in which a
predicate is aflBrmed or denied of a sub-
ject. A predicate and a subject are all
that is necessarily required to make up
a proposition : but as we cannot con-
clude from merely seeing two names
put together, that they are a pre-
dicate and a subject, that is, that one
of them is intended to be affirmed or
denied of the other, it is necessary
that there should be some mode or
form of indicating that such is the
intention ; some sign to distinguish
a predication from any other kind of
discourse. This is sometimes done
by a slight alteration of one of the
words, called an ivflection; as when
we say. Fire burns ; the change of
the second word from hum to hums
showing that we mean to affirm the
predicate burn of the subject fire.
But this function is more commonly

so

NAMES AND PROPOSITIONS.

fulfilled by the word is, when an
affirmation is intended, is not, when
a negation ; or by some other part of
the verb to be. The word which thus
serves the purpose of a sign of predica-
tion is called, as we formerly observed,
the copula. It is important that there
should be no indistinctness in our
conception of the nature and office
of the copula ; for confused notions
respecting it are among the causes
which have spread mysticism over
the field of logic, and perverted its
speculations into logomachies.

It is apt to be supposed that the
copula is something more than a
mere sign of predication ; that it also
signifies existence. In the proposi-
tion, Socrates is just, it may seem to
be implied not only that the quality
just can be affirmed of Socrates, but
moreover that Socrates is, that is to
say, exists. This, however, only shows
that there is an ambiguity in the word
is ; a word which not only performs
the function of the copula in affirma-
tions, but has also a meaning of its
own, in virtue of which it may itself
be made the predicate of a proposi-
tion. That the employment of it as
a copula does not necessarily include
the affirmation of existence, appears
from such a proposition as this : A
centaur is a fiction of the poets ; where
it cannot possibly be implied that a
centaur exists, since the proposition
itself expressly asserts that the thing
has no real existence.

Many volumes might be filled with
the frivolous speculations concerning
the nature of Being, (tto 6v, ovaia.
Ens, Entitas, Essentia, and the like,)
which have arisen from overlooking
this double meaning of the word to
he; from supposing that when it
signifies to exist, and when it signifies
to he some specified thing, as to he a
man, to he Socrates, to he seen or
spoken of, io he a phantom, even to
he a nonentity, it must still, at bottom,
answer to the same idea ; and that a
meaning must be found for it which
shall suit all these cases. The fog
'\yhich rose from this narrow spot

diffused itself at an early period over
the whole surface of metaphysics.
Yet it becomes us nOt to triumph
over the great intellects of Plato and
Aristotle because we are now able to
preserve ourselves from many errors
into which they, perhaps inevitably,
fell. The fire-teazer of a modem
steam-engine produces by his exer-
tions far greater effects than Milo
of Crotona could, but he is not there-
fore a stronger man. The Greeks
seldom knew .any language but their
own. This rendered it far more
difficult for them than it is for us, to
acquire a readiness in detecting
ambiguities. One of the advantages
of having accurately studied a plurality
of languages, especially of those
languages which eminent thinkers
have used as the vehicle of their
thoughts, is the practical lesson we
learn respecting the ambiguities of
words, by finding that the same word
in one language corresponds, on dif-
ferent occasions, to different words in
another. When not thus exercised,
even the strongest understandings find
it difficult to believe that things which
have a common name have not in
some respect or other a common
nature ; and often expend much
labour very unprofitably (as was
frequently done by the two philo-
sophers just mentioned) in vain
attempts to discover in what this
common nature consists. But, the
habit once formed, intellects much
inferior are capable of detecting even
ambiguities which are common to
many languages : and it is surprising
that the one now under consideration,
though it exists in the modern lan-
guages as well as in the ancient,
should have been overlooked by
almost all authors. The quantity of
futile speculation which had been
caused by a misapprehension of the
nature of the copula was hinted at by
Hobbes ; but Mr. James Mill * was,
I believe, the first who distinctly
characterized the ambiguity, and

* Analysis of the Human Mind, i. 126 et
seq.

PROPOSITIONS.

51

pointed out how many errors in the
received systems of philosophy it has
had to answer for. It has indeed
misled the modems scarcely less than
the ancients, though their mistakes,
because our understandings are not
yet so completely emancipated from
their influence, do not appear equally
irrational.

We shall now briefly review the
principal distinctions which exist
among propositions, and the technical
terms most commonly in use to ex-
press those distinctions.

§ 2. A proposition being a portion
of discourse in which something is
affirmed or denied of something, the
first division of propositions is into
affirmative and negative. An affir-
mative proposition is that in which
the predicate is affirmed of the subject ;
as, Caesar is dead. A negative pro-
position is that in which the predicate
is denied of the subject ; as, Caesar is
not dead. The copula, in this last
species of proposition, consists of the
words is not, which are the sign of
negation ; is being the sign of affir-
mation.

Some logicians, among whom may
be mentioned Hobbes, state this dis-
tinction differently ; they recognise
only one form of copula, is, and attach
the negative sign to the predicate.
" Caesar is dead," and " Caesar is not
dead," according to these writers, are
propositions agreeing not in the sub-
ject and predicate, but in the subject
only. They do not consider " dead,"
but " not dead," to be the predicate of
the second proposition, and they ac-
cordingly define a negative proposition
to be one in which the predicate is a
negative name. The point, though
not of much practical moment, de-
serves notice as an example (not un-
frequent in logic) where by means of
an apparent simplification, but which
is merely verbal, matters are made
more complex than before. The notion
of these writers was, that they could
get rid of the distinction between
affirming and denying, by treating

every case of denying as the affirming
of a negative name. But what is
meant by a negative name ? A name
expressive of the absence of an attri-
bute. So that when we affirm a nega-
tive name, what we are really predi-
cating is absence and not presence ;
we are asserting not that anything is,
but that something is not ; to express
which operation no word seems so
proper as the word denying. The
fundamental distinction is between a
fact and the non-existence of that
fact ; between seeing something and
not seeing it, between Caesar's being
dead and his not being dead ; and if
this were a merely verbal distinction,
the generalization which brings both
within the same form of assertion
would be a real simplification : the
distinction, however, being real, and
in the facts, it is the generalization
confounding the distinction that is
merely verbal ; and tends to obscure
the subject, by treating the difference
between two kinds of truths as if it
were only a difference between two
kinds of words. To put things to-
gether, and to put them or keep them
asunder, will remain different opera-
tions, whatever tricks we may play
with language.

A remark of a similar nature may
be applied to most of those distinc-
tions among propositions which are
said to have reference to their mo-
dality; as, difference of tense or time ;
the sun did rise, the sun is rising, the
sun will rise. These differences, like
that between affirmation and nega-
tion, might be glossed over by con-
sidering the incident of time as a mere
modification of the predicate : thus,
The sun is an object having risen, The
sun is an object now rising, The sun is
an object to rise Tiei'eafter. But the
simplification would be merely verbal.
Past, present, and futiire, do not con-
stitute so many different kinds of
rising ; they are designations belong-
ing to the event asserted, to the sun's
rising to day. They affect, not the
predicate, but the applicability of the
predicate to the particular subject.

s»

NAMES AND PROPOSITIONS.

That which we affirm to be past,
present, or future, is not what the
subject signifies, nor what the predi-
cate signifies, but specifically and ex-
pressly what the predication signifies ;
what is expressed only by the proposi-
tion as such, and not by either or
both of the terms. Therefore the
circumstance of time is properly con-
sidered as attaching to the copula,
which is the sign of predication, and
not to the predicate. If the same
cannot be said of such modifications
as these, Caesar may be dead ; Caesar
is perhaps dead ; it is possible that
Caesar is dead ; it is only because
these fall altogether under another
head, being properly assertions not of
anything relating to the fact itself,
but of the state of our own mind in
regard to it ; namely, our absence of
disbelief of it. Thus " Caesar may
be dead " means '* I am not sure that
Caesar is alive."

§ 3. The next division of proposi-
tions is into Simple and Complex ;
more aptly (by Professor Bain *)
termed Compound. A simple pro-
position is that in which one predicate
is affirmed or denied of one subject.
A compound proposition is that in
which there is more than one predicate,
or more than one subject, or both.

At first sight this division has the
air of an absurdity ; a solemn distinc-
tion of things into one and more than
one ; as if we were to divide horses
into single horses and teams of horses.
And it is true that what is called a
complex (or compound) proposition is
often not a proposition at all, but
several propositions, held together by
a conjunction. Such, for example, is
this : Caesar is dead, and Brutus is
alive : or even this, Caesar is dead,
hut Brutus is alive. There are here
two distinct assertions ; and we might
as well call a street a complex house,
as these two propositions a complex
proposition. It is true that the syn-
categorematic words arid and hut have

* Logic, i. 8s.

a meaning ; but that meaning is so
far from making the two propositions
one, that it adds a third proposition
to them. All particles are abbrevia-
tions, and generally abbreviations of
propositions ; a kind of shorthand,
whereby something which, to be ex-
pressed fully, would have required a
proposition or a series of propositions,
is suggested to the mind at once.
Thus the words, Cassar is dead and
Brutus is alive, are equivalent to
these : Caesar is dead ; Brutus is
alive ; it is desired that the two pre-
ceding propositions should be thought
of together. If the words were,
Caesar is dead, hut Brutus is alive, the
sense would be equivalent to the same
three propositions together with a
fourth ; " between the two preceding
propositions there exists a contrast : "
viz. either between the two facts them«
selves, or between the feelings with
which it is desired that they should be
regarded.

In the instances cited the two pro*
positions are kept visibly distinct, each
subject having its separate predicate,
and each predicate its separate sub-
ject. For brevity, however, and to
avoid repetition, the propositions are
often blended together : as in this,
" Peter and James preached at Jeru-
salem and in Galilee," which contains
four propositions : Peter preached at
Jerusalem, Peter preached in Galilee,
James preached at Jerusalem, James
preached in Galilee.

We have seen that when the two or
more propositions comprised in what
is called a complex proposition are
stated absolutely and not under any
condition or proviso, it is not a pro-
position at all, but a plurality of pro-
positions ; since what it expresses is
not a single assertion, but several
assertions, which, if true when joined,
are true also when separated. But
there is a kind of proposition which,
though it contains a plurality of sub-
jects and of predicates, and may be
said in one sense of the word to con-
sist of several propositions, contains
but one assertion ; and its truth does

PROPOSITIONS.

55

not at all imply that of the simple
propositions which compose it. An
example of this is, when the simple
propositions are connected by the
particle or ; as, either A is B or C is
D ; or by the particle if ; as, A is B
if C is D. In the former case, the
proposition is called disjunctive, in the
latter, conditional: the name hypo-
thetical was originally common to
both. As has been well remarked by
Archbishop Whately and others, the
disjunctive form is resolvable into the
conditional ; every disjunctive pro-
position being equivalent to two or
more conditional ones. " Either A is
B or C is D," means, " if A is not B,
C is D ; and if C is not D, A is B."
A-11 hypothetical propositions, there-
fore, though disjunctive in form, are
conditional in meaning ; and the
words hypothetical and conditional
may be, as indeed they generally are,
used synonymously. Propositions in
which the assertion is not dependent
on a condition, are said, in the lan-
guage of logicians, to be categorical.

An hypothetical proposition is not,
like the pretended complex proposi-
tions which we previously considered,
a niere aggregation of simple proposi-
tions. The simple propositions which
form part of the words in which it is
couched, form no part of the assertion
which it conveys. When we say. If
the Koran comes from God, Mahomet
is the prophet of God, we do not in-
tend to affirm either that the Koran
does come from God, or that Mahomet
is really His prophet. Neither of
these simple propositions may be true,
and yet the truth of the hypotheti-
cal proposition may be indisputable.
What is asserted is not the truth of
either of the propositions, but the
inferribility of the one from the other.
What, then, is the subject, and what
the predicate of the hypothetical pro-
position ? " The Koran " is not the
subject of it, nor is "Mahomet: " for
nothing is affirmed or denied either of
the Koran or of Mahomet. The real
subject of the predication is the entire
proposition, *' Mahomet is the prophet

of God ; " and the affirmation is, that
this is a legitimate inference from the
proposition, *' the Koran comes from
God." The subject and predicate,
therefore, of an hypothetical proposi-
tion are names of propositions. The
Bvibject is some one proposition. The
predicate is a general relative name
applicable to propositions of this form
— "an inference from so and so." A
fresh instance is here afforded of the
remark, that particles are abbrevia-
tions ; since " /f A is B, C is D," is
found to be an abbreviation of the
following : " The proposition C is D,
is a legitimate inference from the
proposition A is B."

The distinction, therefore, between
hypothetical and categorical proposi-
tions, is not so great as it at first
appears. In the conditional, as well
as in the categorical form, one predi-
cate is aflBrmed of one subject, and no
more : but a conditional proposition
is a proposition concerning a proposi-
tion ; the subject of the assertion is
itself an assertion. Nor is this a
property peculiar to hypothetical pro-
positions. There are other classes of
assertions concerning propositions.
Like other things, a proposition has
attributes which may be predicated
of it. The attribute predicated of it
in an hypothetical proposition, is that
of being an inference from a certain
other proposition. But this is only
one of many attributes that might be
predicated. We may say. That the
whole is greater than its part, is an
axiom in mathematics : That the
Holy Ghost proceeds from the Father
alone, is a tenet of the Greek Church :
The doctrine of the divine right of
kings was renounced by Parliament
at the Revolution : The infallibility
of the Pope has no countenance from
Scripture. In all these cases the
subject of the predication is an entire
proposition. That which these differ-
ent predicates are affirmed of is the
proposition, "the whole is greater
than its part ; " the proposition, "the
Holy Ghost proceeds from the Father
alone ; " the proposition, kings have a

54

NAMES AND PHOPOSITIONS.

divine right ; " the proposition, " the
Pope is infallible."

Seeing, then, that there is much
less difference between hypothetical
propositions and any others, than one
might be led to imagine from their
form, we should be at a loss to account
for the conspicuous position which
they have been selected to fill in
treatises on logic, if he did not re-
member that what they predicate of a
proposition, namely, its being an in-
ference from something else, is precisely
that one of its attributes with which
most of all a logician is concerned.

§ 4. The next of the common
divisions of Propositions is into Uni-
versal, Particular, Indefinite, and
Singular : a distinction founded on
the degree of generality in which the
name, which is the subject of the
proposition, is to be understood. The
following are examples :

AU men are mortal — Universal.

Some men are mortal — Particular.

Man is mortal — Indefinite.

Julim Ccesar is mortal — Singular.

The proposition is Singular when
the subject is an individual name.
The individual name needs not be
a proper name. "The Founder of
Christianity was crucified," is as much
a singular proposition as " Christ was
crucified."

When the name which is the sub-
ject of the proposition is a general
name, we may intend to affirm or
deny the predicate, either of all the
things that the subject denotes, or
only of some. When the predicate
is affirmed or denied of all and each
of the things denoted by the siibject,
the proposition is universal ; when of
some undefined portion of them only,
it is particular. Thus, All men are
mortal ; Every man is mortal ; are
universal propositions. No man is
immortal, is also an universal propo-
sition, since the predicate, immortal,
is denied of each and every individual
denoted by the term man ; the nega-
tive proposition being exactly equiva-

lent to the following. Every man is
not-immortal. But "some men are
wise," "some men are not wise," are
particular propositions ; the predicate
tdse being in the one case affirmed
and in the other denied not of each
and every individual denoted by the
term man, but only of each and every
one of some portion of those indivi-
duals, without specifying what por-
tion ; for if this were specified, the
proposition would be changed either
into a singular proposition, or into an
universal proposition with a different
subject ; as, for instance, '^ all properly
instructed men are wise, " There are
other forms of particular propositions ;
as, ^^ Most men are imperfectly edu-
cated : " it being immaterial how large
a portion of the subject the predicate
is asserted of, as long as it is left un-
certain how that portion is to be dis-
tinguished from the rest.*

When the form of expression does
not clearly show whether the general
name which is the subject of the pro-
position is meant to stand for all the
individuals denoted by it, or only for
some of them, the proposition is, by
some logicians, called Indefinite ;
but this, as Archbishop Whately
observes, is a solecism, of the same
nature as that committed by some
grammarians when in their list of
genders they enumerate the doubtful

* Instead of Universal and Particular, as
applied to propositions, Professor Bain pro-
poses (Logic, i. 81) the terms Total and
Partial ; reserving the former pair of terms
for their inductive meaninpr, " the contrast
between a general proposition and the par-
ticulars or iTidividuals that we derive it
from." This change in nomenclature would
be attended with the further advantage,
that Singular propositions, which in tiie
Syllogism follow the same rules as Uni-
versal, would be included along with them
in the same class, that of Total predica-
tions. It is not the Subject's denoting
many things or only one, that is of im-
portance in reasoning, it is that tlu^ asser-
tion is made of the whole or a part only of
what the Subject denotes. The words
Universal and Particular, however, are so
familiar and so well understood in both
the senses mentioned by Mr. Bain, that
the double meaning does not produce any
material inconvenience.

IMPORT OF PROPOSITIONS.

55

gender. The speaker must mean to
assert the proposition either as an
universal or as a particular proposi-
tion, though he has failed to declare
which : and it often happens that
though the words do not show which
of the two he intends, the context, or
the custom of speech, supplies the
deficiency. Thus, when it is affirmed
that " Man is mortal," nobody doubts
that the assertion is intended of all
human beings ; and the word indi-
cative of universality is commonly
emitted, only because the meaning is
evident without it. In the proposition,
"Wine is good," it is understood with
«qual readiness, though for somewhat
different reasons, that the assertion ia
not intended to be universal, but
particular.* As is observed by Pro-
fessor Bain,t the chief examples of
Indefinite propositions occur "with
names of material, which are the sub-
jects sometimes of universal, and at
other times of particular predication.
'Fcod is chemically constituted by
carbon, oxygen, &c.,' is a proposition
of universal quantity ; the meaning
is all food — all kinds of food. * Food
is necessary to animal life ' is a case
of particular quantity ; the meaning
is some sort of food, not necessarily
all sorts. * Metal is requisite in order
to strength ' does not mean all kinds
of metal. 'Gold will make a way,'
means a portion of gold."

When a general name stands for
each and every individual which it is
a name of, or in other words, which
it denotes, it is said by logicians to
be distHbuted, or taken distributively.
Thus, in the proposition. All men
are mortal, the subject, Man, is dis-
tributed, because mortality is aflBrmed
of each and every man. The predi-
cate. Mortal, is not distributed,
because the only mortals who are
spoken of in the proposition are those

* It may, however, be considered as
equivalent to an universal proposition with
a different predicate, viz. "All wine is
good qiid wine," or " is good in respect of
the qualities which consti*iute it wine."

t Logic, i. 82.

who happen to be men ; while the
word may, for aught that appears,
and in fact does, comprehend within
it an indefinite number of objects
besides men. In the proposition,
Some men are mortal, both the pre-
dicate and the subject are undis-
tributed. In the following, No men
have wings, both the predicate and
the subject are distributed. Not only
is the attribute of having wings
denied of the entire class Man, but
that class is severed and cast out
from the whole of the class Winged,
and not merely from some part of
that class.

This phraseology, which is of great
service in stating and demonstrating
the rules of the syllogism, enables us
to express very concisely the defini-
tions of an universal and a particular
proposition. An universal proposi-
tion is that of which the subject is
distributed ; a particular proposition
is that of which the subject is un-
distributed.

There are many more distinctions
among propositions than those we
have here stated, some of them of
considerable importance. But, for
explaining and illustrating these, more
suitable opportunities will occur in
the sequel.

CHAPTER V.

OF THE IMPORT OF PROPOSITIONS.

§ I. An inquiry into the nature of
propositions must have one of two
objects : to analyse the state of mind
called Belief, or to analyse what is
believed. All language recognises a
difference between a doctrine or
opinion, and the fact of entertaining
the opinion ; between assent, and
what is assented to.

Logic, according to the conception
here formed of it, has no concern
with the nature of the act of judging
or believing; the consideration of
that act, as a phenomenon of the
mind, belongs to another science.

56

NAMES AND PROPOSITIONS.

Philosophers, however, from Descartes
downwards, and especially from the
era of Leibnitz and Locke, have by
no means observed this distinction ;
and would have treated with great
disrespect any attempt to analyse the
import of Propositions, unless founded
on an analysis of the act of Judgment.
A proposition, they would have said,
is but the expression in words of a
Judgment. The thing expressed, not
the mere verbal expression, is the
important matter. When the mind
assents to a proposition, it judges.
Let us find out what the mind does
when it judges, and we shall know
what propositions mean, and not
otherwise.

Conformably to these views, almost
all the writers on Logic in the last
two centuries, whether English, Ger-
man, or French, have made their
theory of Propositions, from one end
to the other, a theory of Judgments.
They considered a Proposition, or a
Judgment, for they used the two
words indiscriminately, to consist in
affirming or denying one idea of
another. To judge, was to put two
ideas together, or to bring one idea
under another, or to compare two
ideas, or to perceive the agreement
or disagreement between two ideas :
and the whole doctrine of Proposi-
tions, together with the theory of
Reasoning,(alwaysnecessarilyfounded
on the theory of Propositions,) was
stated as if Ideas, or Conceptions, or
whatever other term the writer pre-
ferred as a name for mental represen-
tations generally, constituted essen-
tially the subject-matter and substance
of those operations.

It is, of course, true, that in any
case of judgment, as for instance when
we judge that gold is yellow, a process
takes place in our minds, of which
some one or other of these theories
is a partially correct account. We
must have the idea of gold and the
idea of yellow, and these two ideas
must be brought together in our mind.
But in the first place, it is evident
that this is only a part of what takes

place ; for we may put two ideas to-
gether without any act of belief ; as
when we merely imagine something,
such as a golden mountain ; or when
we actually disbelieve : for in order
even to disbelieve that Mahomet was
an apostle of God, we must put the
idea of Mahomet and that of an apos-
tle of God together. To determine
what it is that happens in the case of
assent or dissent besides putting two
ideas together, is one of the most in-
tricate of metaphysical problems. But
whatever the solution may be, we may
venture to assert that it can hav-e
nothing whatever to do with the iai-
port of propositions ; for this reason,
that propositions (except sometines
when the mind itself is the sulqject
treated of) are not assertions respect-
ing our ideas of things, but assertions
respecting the things themselves. In
order to believe that gold is yellow,
I must, indeed, have the idea of gold,
and the idea of yellow, and something
having reference to those ideas must
take place in my mind ; but my belief
has not reference to the ideas, it has
reference to the things. What I be-
lieve, is a fact relating to the out^v■ard
thing, gold, and to the impressiott
made by that outward thing upon the
human organs ; not a fact relating to
my conception of gold, which would
be a fact in my mental history, not a
fact of external nature. It is true,
that in order to believe this fact in
external nature, another fact must
take place in my mind, a process must
be performed upon my ideas ; but so
it must in everything else that I do.
I cannot dig the ground unless I have
the idea of the ground, and of a spade,
and of all the other things I am ope-
rating upon, and unless I put those
ideas together.* But it would be a

* Dr. Whewell (Philosophi/ of Discovery,
p. 242) questions this statement, and asks,
"Are we to say that a mole cannot dig
the ground, except he has an idea of the
ground, and of the snout and paws with
which he digs it ? " I do not know what
passes in a mole's mind, nor what amount
of mental apprehension may or may not
accompany his instinctive actions. But

IMPORT OF PROPOSITIONS.

57

very ridiculous description of digging
the ground to say that it is putting
one idea into another. Digging is an
operation which is performed upon the
things themselves, though it cannot
be performed unless I have in my mind
the ideas of them. And in like man-
ner, believing is an act which has for
its subject thefacts themselves, though
a previous mental conception of the
facts is an indispensable condition.
When I say that fire causes heat, do
I mean that my idea of fire causes my
idea of heat ? No : I mean that the
natural phenomenon, fire, causes the
natural phenomenon, heat. When I
mean to assert anything respecting
the ideas, I give them their proper
name ; I call them ideas ; as when I
say that a child's idea of a battle is
unlike the reality, or that the ideas
entertained of the Deity have a great
effect on the characters of mankind.

The notion that what is of primary
importance to the logician in a pro-
position, is the relation between the
two ideas corresponding to the subject
and predicate, (instead of the relation
between the two phenomena which
they respectively express,) seems to
me one of the most fatal errors ever
introduced into the philosophy of
Logic ; and the principal cause why
the theory of the science has made
Buch inconsiderable progress during
the last two centuries. The treatises
on Logic, and on the branches of
Mental Philosophy connected with
Logic, which have been produced
since the intrusion of this cardinal
error, though sometimes written by
men of extraordinary abilities and
attainments, almost always tacitly
imply a theory that the investigation
of truth consists in contemplating and
handling our ideas, or conceptions of
things, instead of the things them-
selves : a doctrine tantamount to the
assertion, that the only mode of ac-
quiring knowledge of nature is to

a human being does not use a spade by
instinct ; and he certainly could not use it
unless he had knowledge of a spade, and
of the earth which he uses it upon.

I study it at second-hand, as represented
in our own minds. Meanwhile, in-
quiries into every kind of natural
phenomena were incessantly establish-
ing great and fruitful truths on most
important subjects, by processes upon
I which these views of the nature of
Judgment and Reasoning threw no
\ light, and in which they afforded no
i assistance whatever. No wonder that
those who knew by practical experi-
ence how truths are arrived at, should
deem a science futile, which consisted
chiefly of such speculations. What
has been done for the advancement
of Logic since these doctrines came
into vogue, has been done not by pro-
fessed logicians, but by discoverers in
the other sciences ; in whose methods
of investigation many principles of
logic, not previously thought of, have
successively come forth into light, but
who have generally committed the
error of supposing that nothing what-
ever was known of the art of philoso-
phizing by the old logicians, because
theirmodern interpreters have written
to so little purpose respecting it.

We have to inquire, then, on the
present occasion, not into Judgment,
but judgments ; not into the act of
believing, but into the thing believed.
What is the immediate object of belief
in a Proposition ? What is the matter
of fact signified by it ? What is it to
which, when I assert the proposition,
I give my assent, and call upon others
to give theirs ? What is that which
is expressed by the form of discourse
called a Proposition, and the confor-
mity of which to fact constitutes the
truth of the proposition ?

§ 2. One of the clearest and most
consecutive thinkers whom this coun-
try or the world has produced, I
mean Hobbes, has given the following
answer to this question. In every
proposition (says he) what is signified
is, the belief of the speaker that the
predicate is a name of the same thing
of which the subject is a name ; and
if it really is so, the proposition is
true. Thus the proposition, All men

NAMES AND PROPOSITIONS.

are living beings (he would say) is
true, because living being is a name of
everything of which man is a name.
All men are six feet high, is not true,
because six feet high is riot a name of
everything (though it is of some
things) of which man is a name.

What is stated in this theory as the
definition of a true proposition, must
be allowed to be a property which all
true propositions possess. The subject
and predicate being both of them
names of things, if they were names
of quite different things the one name
could not, consistently with its signi-
fication, be predicated of the other.
If it be true that some men are copper-
coloured, it must be true — and the
proposition does really assert — that
among the individuals denoted by the
name man, there are some who are
also among those denoted by the name
copper-coloured. If it be true that
all oxen ruminate, it must be true
that all the individuals denoted by
the name ox are also among those
denoted by the name ruminating ;
and whoever asserts that all oxen
ruminate, undoubtedly does assert
that this relation subsists between
the two names.

The assertion, therefore, which,
according to Hobbes, is the only one
made in any proposition, really is
made in every proposition : and his
analysis has consequently one of the
requisites for being the true one. We
may go a step farther ; it is the only
analysis that is rigorously true of all
propositions without exception. What
he gives as the meaning of proposi-
tions, is part of the meaning of all
propositions, and the whole meaning
of some. This, however, only shows
what an extremely minute fragment
of meaning it is quite possible to in-
clude within the logical formula of a
proposition. It does not show that
no proposition means more. To war-
rant us in putting together two words
with a copula between them, it is
really enough that the thing or things
denoted by one of the names should
be capable, without violation of usage.

of being called by the other name also.
If, then, this be all the meaning
necessarily implied in the form of
discourse called a Proposition, why
do I object to it as the scientific defi-
nition of what a proposition means?
Because, though the mere collocation
which makes the proposition a propo-
sition, conveys no more than this
scanty amount of meaning, that same
collocation combined with other cir-
cumstances, that form combined with
other mutter, does convey more, and
the proposition in those other circum-
stances does assert more, than merely
that relation between the two names.

The only propositions of which
Hobbes' principle is a sufficient
account, are that limited and unim-
portant class in which both the pre-
dicate and the subject are proper
names. For, as has already been
remarked, proper names have strictly
no meaning ; they are mere marks for
individual objects : and when a pro-
per name is predicated of another
proper name, all the signification con-
veyed is, that both the names are
marks for the same object. But this
is precisely what Hobbes produces as
a theory of predication in general.
His doctrine is a full explanation of
such predications as these : Hyde
was Clarendon, or, TuUy is Cicero.
It exhausts the meaning of those pro-
positions. But it is a sadly inadequate
theory of any others. That it should
ever have been thought of as such,
can be accounted for only by the fact,
that Hobbes, in common with the
other Nominalists, bestowed little or
no attention upon the connotation of
words ; and sought for their meaning
exclusively in what they denote : as if
all names had been (what none but
proper names really are) marks put
upon individuals ; and as if there
were no difference between a proper
and a general name, except that the
first denotes only one individual, and
the last a greater number.

It has been seen, however, that the
meaning of all names, except proper
names and that portion of the cUss

IMPORT OF PROPOSITIONS.

59

of abstract names which are not con-
notative, resides in the connotation.
When, therefore, we are analysing the
meaning of any proposition in which
the predicate and the subject, or
either of them, are connotative names,
it is to the connotation of those terms
that we must exclusively look, and not
to what they denote, or, in the language
of Hobbes, (language so far correct,)
are names of.

In asserting that the truth of a
proposition depends on the conformity
of import between its terms, as, for
instance, that the proposition, Socrates
is wise, is a true proposition, because
Socrates and wise are names applicable
to, or, as he expresses it, names of,
the same person ; it is very remark-
able that so powerful a thinker
should not have asked himself the
question, But how came they to be
names of the same person ? Surely
not because such was the intention of
those who invented the words. When
mankind fixed the meaning of the
word wise, they were not thinking of
Socrates, nor, when his parents gave
him the name of Socrates, were they
thinking of wisdom. The names
huppen to fit the same person because
of a certain fact, which fact was not
known, nor in being, when the names
were invented. If we want to know
what the fact is, we shall find the
clue to it in the connotation of the
names.

A bird or a stone, a man or a wise
man, means simply an object having
such and such attributes. The real
meaning of the word man, is those
attributes, and not Smith, Brown,
and the remainder of the individuals.
The word mortal, in like manner, con-
notes a certain attribute or attri-
butes ; and when we say, All men are
mortal, the meaning of the proposi-
tion is, that all beings which possess
the one set of attributes possess also
the other. If, in our experience, the
attributes connoted by man are always
accompanied by the attribute connoted
by mortal, it will follow as a conse-
quence, that the class man will be

wholly included in the class mortal,
and that mortal will be a name of all
things of which man is a name : but
why ? Those objects are brought
under the name by possessing the
attributes connoted by it : but their
possession of the attributes is the real
condition on which the truth of the
proposition depends ; not their being
called by the name. Connotative
names do not precede, but follow, the
attributes which they connote. If
one attribute happens to be always
found in conjunction with another
attribute, the concrete names which
answer to those attributes will of
course be predicable of the same
subjects, and may be said, in Hobbes'
language, (in the propriety of which
on this occasion I fully concur,) to be
two names for the same things. But
the possibility of a concurrent applica-
tion of the two names, is a mere con-
sequence of the conjunction between
the two attributes, and was, in most
cases, never thought of when the
names were introduced and their
signification fixed. That the diamond
is combustible, was a proposition
certainly not dreamt of when the
words Diamond and Combustible first
received their meaning ; and could
not have been discovered by the most
ingenious and refined analysis of the
signification of those words. It was
found out by a very different process,
namely, by exerting the senses, and
learning from them, that the attri-
bute of combustibility existed in the
diamonds upon which the experiment
was tried ; the number or character
of the experiments being such, that
what was true of those individuals
might be concluded to be true of all
substances "called by the name,"
that is, of all substances possessing
the attributes which the name con-
notes. The assertion, therefore, when
analysed, is, that wherever we find
certain attributes, there will be found
a certain other attribute : which is
not a question of the signification of
names, but of laws of nature ; the
order existing among phenomena.

NAMES AND PROPOSITIONS.

§ 3. Although Hobbes' theory of
Predication has not, in the terms in
which he stated it, met with a very
favourable reception from subsequent
thinkers, a theory virtually identical
with it, and not by any means so
perspicuously expressed, may almost
be said to have taken the rank of an
established opinion. The most gener-
ally received notion of Predication
decidedly is that it consists in refer-
ring something to a class, i.e., either
placing an individual under a class,
or placing one class under another
class. Thus, the proposition, Man is
mortal, asserts, according to this
view of it, that the class man is in-
cluded in the class mortal. "Plato
is a philosopher," asserts that the
individual Plato is one of those who
compose the class philosophers. If
the proposition is negative, then,
instead of placing something in a
class, it is said to exclude something
from a class. Thus, if the following
be the proposition. The elephant is
not carnivorous ; what is asserted
(according to this theory) is, that the
elephant is excluded from the class
carnivorous, or is not numbered among
the things comprising that class.
There is no real difference, except in
language, between this theory of Pre-
dication and the theory of Hobbes.
For a class ia absolutely nothing but
an indefinite number of individuals
denoted by a general name. The
name given to them in common, is
what makes them a class. To refer
anything to a class, therefore, is to
look upon it as one of the things
which are to be called by that common
name. To exclude it from a class,
is to say that the common name is
not applicable to it.

How widely these views of predi-
cation have prevailed, is evident from
this, that they are the basis of the
celebrated dictum de omni et nvllo.
When the syllogism is resolved, by
all who treat of it, into an inference
that what is true of a class is true of
all things whatever that belong to
the claes ; and when this is laid down

by almost all professed logicians as
the ultimate principle to which all
reasoning owes its validity ; it is clear
that in the general estimation of
logicians, the propositions of which
reasonings are composed can be the
expression of nothing but the process
of dividing things into classes, and
referring everything to its proper

This theory appears to me a signal
example of a logical error very often
committed in logic, that of Harepov
trp&repov, or explaining a thing by
something which presupposes it,
When I say that snow is white, I
may and ought to be thinking of snow
as a class, because I am asserting a
proposition as true of all snow : but
I am certainly not thinking of white
objects as a class ; I am thinking of
no white object whatever except
snow, but only of that, and of the
sensation of white which it gives me.
When, indeed. I have judged, or
assented to the propositions, that
snow is white, and that several other
things are also white, I gradually
begin to think of white objects as a
class, including snow and those other
things. But this is a conception
which followed, not preceded, those
judgments, and therefore cannot be
given as an explanation of them
Instead of explaining the effect by
the cause, this doctrine explains the
cause by the effect, and is, I conceive,
founded on a latent misconception of
the nature of classification.

There is a sort of language very
generally prevalent in these discus-
sions, which seems to suppose that
classification is an arrangement and
grouping of definite and known indi-
viduals : that when names were im-
posed, mankind took into considera-
tion all the individual objects in the
imiverse, distributed them into parcels
or lists, and gave to the objects of
each list a common name, repeating
this operation toties quoties until they
had invented all the general names
of which language consists ; which
having been once done, if a question

IMPORT OF PROPOSITIONS.

6i

■ubsequently arises, whether a certain
general name can be truly predicated
of a certain particular object, we have
only (as it were) to read the roll of
the objects upon which that name
was conferred, and see whether the
object about which the question arises
is to be found among them. The
framers of language (it would seem to
be supposed) have predetermined all
the objects that are to compose each
class, and we have only to refer to
the record of an antecedent decision.

So absurd a doctrine will be owned
by nobody when thus nakedly stated ;
but if the commonly received explana-
tions of classification and naming do
not imply this theory, it requires to
be shown how they admit of being
reconciled with any other.

General names are not marks put
upon definite objects ; classes are not
made by drawing a line round a given
number of assignable individuals.
The objects which compose any given
class are perpetually fluctuating. We
may frame a class without knowing
the individuals, or even any of the
individuals, of which it may be com-
posed ; we may do so while believing
that no such individuals exist. If by
the meaning of a general name are to
be understood the things which it is
the name of, no general name, except
by accident, has a fixed meaning at
all, or ever long retains the same
meaning. The only mode in which
any general name has a definite mean-
ing, is by being a name of an indefinite
variety of things ; namely, of all
things, known or unknown, past,
present, or future, which possess cer-
tain definite attributes. When, by
studpng not the meaning of words,
but the phenomena of nature, we dis-
cover that these attributes are pos-
sessed by some object not previously
known to possess them (as when
chemists found that the diamond was
combustible), we include this new
object in the class ; but it did not
already belong to the class. We place
the individual in the class because
the proposition is true ; the proposi-

tion is not true because the object ia
placed in the class.*

It will appear hereafter, in treating
of reasoning, how much the theory of
that intellectual process has been
vitiated by the influence of these
erroneous notions, and by the habit
which they exemplify of assimilating
all the operations of the human under-
standing which have truth for their
object, to processes of mere classifi-
cation and naming. Unfortunately,
the minds which have been entangled
in this net are precisely those which
have escaped the other cardinal error
commented upon in the beginning of
the present chapter. Since the revo-
lution which dislodged Aristotle from
the schools, logicians may almost be
divided into those who have looked
upon reasoning as essentially an affair
of Ideas, and those who have looked
upon it as essentially an affair of
Names.

Although, however, Hobbes' theory
of Predication, according to the well-
known remark of Leibnitz, and the
avowal of Hobbes himself,t renders

* Professor Bain remarks, in qualifica-
tion of the statement in the text (Logic, i.
fO). tliat the word Class h;is two meanings ;
"the class definite, and the class indefinite.
The class definite is an enumeration of
actual individuals, as the peers of the
realm, the oceans of the globe, the known
planets. . . . The class indefinite is un-
emimerated. Such classes are stars, planets,
gold-bearing rocks, men, poets, virtuous.
. . . In this last acceptation of the word,
class name and general name are identicaL
The class name denotes an indefinite
number of individuals, and connotes the
points of community or likeness."

The theory controverted in the text,
tacitly supposes all classes to be definite.
I have assumed them to be indefinite;
because for the pixrposes of Logic, definite
classes, as such, are almost useless ; though
often serviceable as means of abiidged ex-
pression. (Vide infra, book iii. ch. ii.)

t " From hence also this may be de-
duced, that the first truths were arbitrarily
made by those that first of all imposed
names upon things, or received them from
the imposition of others. For it is true
(for example) that man is a living creature,
but it is for this reason, tnat it pleased
men to impose both these names on the
same thing."— Computation or Logic, ch.
iii. sect. 8.

62

NAMES AND PROPOSITIONS.

truth and falsity completely arbitrary,
with no standard but the will of men,
it must not be concluded that either
Hobbes, or any of the other thinkers
who have in the main agreed with
him, did in fact consider the distinc-
tion between truth and error as less
real, or attached less importance to it,
than other people. To suppose that
they did so would argue total unac-
quaintance with their other specula-
tions. But this shows how little hold
their doctrine possessed over their
own minds. No person, at bottom,
even imagined that there was nothing
more in truth than propriety of ex-
pression ; than using language in
conformity to a previous convention.
When the inquiry was brought down
from generals to a particular case, it
has always been acknowledged that
there is a distinction between verbal
and real questions ; that some false
propositions are uttered from ignor-
ance of the meaning of words, but
that in others the source of the error
is a misapprehension of things ; that
a person who has not the use of
language at all may form propositions
mentally, and that they may be
untrue, that is, he may believe as
matters of fact what are not really
so. This last admission cannot be
made in stronger terms than it is by
Hobbes himself,* though he will not
allow such erroneous belief to be called
falsity, but only error. And he has
himself laid down, in other places,

* "Men are subject to err not only in
affirming and denying, but also in percep-
tion, and in silent cogitation. . . . Tacit
errors, or the errors of sense and cogita-
tion, are made by passing from one imagi-
nation to the imagination of another dif-
ferent thing ; or by feigning that to be
past, or future, which never was, nor ever
shall be ; as when by seeing the image of
the sun in water, we imagine tiie sun itself
to be there ; or by seeing swords, that
there has been, or shall be, fighting, be-
cause it uses to be so for the most part ; or
when from promises we feign the mind of
the promiser to be such and such ; or,
lastly, when from any sign we vainly
imagine something to be signified which
is not. And errors of this sort are com-
mon to all things that have sense."— C<m»-
putaticn or Logic, ch. v. sect i.

doctrines in which the true theory of
predication is by implication con-
tained. He distinctly says that general
names are given to things on account
of their attributes, and that abstract
names are the names of those attri-
butes. "Abstract is that which in
any subject denotes the cause of the
concrete name. . . . And these causes
of names are the same with the causes
of our conceptions, namely, some
power of action, or affection, of the
thing conceived, which some call the
manner by which anything works
upon our senses, but by most men
they are called accidents."* It is
strange that having gone so far, he
should not have gone one step farther,
and seen that what he calls the cause
of the concrete name, is in reality the
meaning of it ; and that when we
predicate of any subject a name which
is given because of an attribute, (or, as
he calls it, an accident,) our object is
not to affirm the name, but, by means
of the name, to affirm the attribute.

§ 4. Let the predicate be, as we
have said, a connotative term ; and
to take the simplest case first, let the
subject be a proper name : "The
summit of Chimborazo is white."
The word white connotes an attribute
which is possessed by the individual
object designated by the words "sum-
mit of Chimborazo ; " which attribute
consists in the physical fact of its
exciting in human beings the sensa-
tion which we call a sensation of
white. It will be admitted that, by
asserting the proposition, we wish to
communicate information of that phy-
sical fact, and are not thinking of the
names, except as the necessary means
of making that communication. The
meaning of the proposition, therefore,
is, that the individual thing denoted
by the subject, has the attributes con-
noted by the predicate.

If we now suppose the subject also
to be a connotative name, the mean-
ing expressed by the proposition has

* Ch. iii. sect. 3.

IMPORT OF PROPOSITIONS.

63

advanced a step farther in complica-
tion. Let us first suppose the pro-
position to be universal, as well as
affirmative: "All men are mortal."
In this case, as in the last, what the
proposition asserts (or expresses a be-
lief of) is, of course, that the objects
denoted by the subject (man) possess
the attributes connoted by the predi-
cate (mortal). But the characteristic
of this case is, that the objects are no
longer individually designated. They
are pointed out only by some of their
attributes : they are the objects called
men, that is, possessing the attributes
connoted by the name man ; and the
only thing known of them may be
those attributes : indeed, as the pro-
position is general, and the objects
denoted by the subject are therefore
indefinite in number, most of them
are not known individually at all.
The assertion, therefore, is not, as
before, that the attributes which the
predicate connotes are possessed by
any given individual, or by any num-
ber of individuals previously known
as John, Thomas, &c., but that those
attributes are possessed by each and
every individual possessing certain
other attributes ; that whatever has
the attributes connoted by the sub-
ject, has also those connoted by the
predicate ; that the latter set of attri-
butes comtantly accompany the former
set. Whatever has the attributes of
man has the attribute of mortality ;
mortality constantly accompanies the
attributes of man.*

* To the preceding statement it has been
objected, that " we naturally construe the
subject of a proposition in its extension,
and the predicate (which therefore may be
an adjective) in its intension, (connota-
tion) : and that consequently co-existence
of attributes does not, any more than the
opposite theory of equation of groups, cor-
respond with the living piocesses of thought
and language." I acknowledge the dis-
tinction lure dniwn, which, indeed, I had
myself laid down and exemplified a few
pages back (p. 60). But though it is true
that we naturally " construe the subject
of a proposition in its extension," this ex-
tension, or, in other words, the extent of
the class denoted by the name, is not ap-
Vrehend^d or indicated directly. It is both

If it be remembered that every
attribute is grounded on some fact or
phenomenon, either of outward sense
or of inward consciousness, and that
to possess an attribute is another
phrase for being the cause of, or form-
ing part of, the fact or phenomenon
upon which the attribute is grounded;
we may add one more step to com-
plete the analysis. The proposition
which asserts that one attribute al-
ways accompanies another attribute,
really asserts thereby no other thing
than this, that one phenomenon al-
ways accompanies another phenome-
non ; insomuch that where we find
the latter, we have assurance of the
existence of the former. Thus, in
the proposition, All men are mortal,
the word man connotes the attributes
which we ascribe to a certain kind of
living creatures, on the ground of
certain phenomena which they ex-
hibit, and which are partly physical
phenomena, namely, the impressions
made on our senses by their bodily
form and structure, and partly men-
tal phenomena, namely, the sentient
and intellectual life which they have
of their own. All this is understood
when we utter the word man, by any
one to whom the meaning of the word
is known. Now, when we say, Man
is mortal, we mean that wherever
these various physical and mental
phenomena are all found, there we
have assurance that the other physi-
cal and mental phenomenon, called
death, will not fail to take place. The
proposition does not affirm when ; for
the connotation of the word mortal
goes no farther than to the occurrence
of the phenomenon at some time or
other, leaving the particular time un-
decided.

apprehended and indicated solely through
the attributes. In the "living processes
of thought and langnage " the extension,
tiiough in this case rea ly thought of, (which
in the case of the preaicate it is not,) is
thought of only through tiie medium of
what my acute and courteous critic terms
the " intension "

For further illustrations of this subject,
see Examination of Sir William Hamilton'M
Philosophy, ch. xxiL

64

NAMES AND PROPOSITIONS.

§ 5. We have already proceeded
far enough, not only to demonstrate
the error of Hobbes, but to ascertain
the real import of by far the most
numerous class of propositions. The
object of belief in a proposition, when
it asserts anything more than the
meaning of words, is generally, as in
the cases which we have examined,
either the co-existence or the sequence
of two phenomena. At the very com-
mencement of our inquiry, we found
that every act of belief implied two
Things : we have now ascertained
what, in the most frequent case, these
two things are, namely, two Pheno-
mena, in other words, two states of
consciousness ; and what it is which
the proposition affirms (or denies) to
subsist between them, namely, either
succession or co-existence. And this
case includes innumerable instances
which no one, previous to reflection,
would think of referring to it. Take
the following example : A generous
person is worthy of honour. Who
would expect to recognise here a case
of co-existence between phenomena ?
But so it is. The attribute which
causes a person to be termed generous,
is ascribed to him on the ground of
states of his mind and particulars of
his conduct ; both are phenomena :
the former are facts of internal con-
sciousness ; the latter, so far as dis-
tinct from the former, are phj'sical
facts, or perceptions of the senses.
Worthy of honour admits of a similar
analysis. Honour, as here used,
means a state of approving and
admiring emotion, followed on occa-
sion by corresponding outward acts.
" Worthy of honour " connotes all
this, together with our approval of
the act of showing honour. All these
are phenomena; states of internal con-
sciousness, accompanied or followed
by physical facts. When we say, A
generous person is worthy of honour,
we affirm co existence between the
two complicated phenomena connoted
by the two terms respectively. We
affirm, that wherever and whenever
the inward feelings and outward facts

implied in the word generosity have
place, then and there the existence
and manifestation of an inward feel-
ing, honour, would be followed in our
minds by another inward feeling,
approval.

After the analysis, in a former
chapter, of the import of names,
many examples are not needed to
illustrate the import of propositions.
When there is any obscurity or dif-
ficulty, it does not lie in the mean-
ing of the proposition, but in the
meaning of the names which compose
it ; in the extremely complicated con-
notation of many words ; the immense
multitude and prolonged series of
facts which often constitute the phe-
nomenon connoted by a name. But
where it is seen what the phenome-
non is, there is seldom any difficulty
in seeing that the assertion conveyed
by the proposition is, the co-existence
of one such phenomenon with another ;
or the succession of one such pheno-
menon to another : so that where the
one is found, we may calculate on
finding the other, though perhaps not
conversely.

This, however, though the most
common, is not the only meaning
which propositions are ever intended
to convey. In the first place,
sequences and co-existences are not
only asserted respecting Phenomena ;
we make propositions also respecting
those hidden causes of phenomena,
which are named substances and
attributes. A substance, however,
being to us nothing but either that
which causes, or that which is con-
scious of, phenomena ; and the same
being true, mutatis mutandis, of attri-
butes ; no assertion can be made,
at least with a meaning, concern-
ing these unknown and unknowable
entities, except in virtue of the
Phenomena by which alone they
manifest themselves to our faculties.
When we say, Socrates was contem-
porary with the Peloponnesian war,
the foundation of this assertion, as of
all assertions concerning substances,
is an assertion concerning the pheno-

IMPORT OF PROPOSITIONS.

65

mena which they exhibit, — namely,
that the series of facts by which
Socrates manifested himself to man-
kind, and the series of mental states
which constituted his sentient ex-
istence, went on simultaneously with
the series of facts known by the
name of the Peloponnesian war.
Still, the proposition as commonly
understood does not assert that alone ;
it asserts that the Thing in itself,
the nouvienon Socrates, was existing,
and doing or experiencing those
various facts during the same time.
Co- existence and sequence, therefore,
may be affirmed or denied not only
between phenomena, but between
noumena, or between a noumenon
and phenomena. And both of nou-
mena and of phenomena we may
affirm simple existence. But what
is a noumenon ? An unknown cause.
In affirming, therefore, the existence
of a noumenon, we affirm causation.
Here, therefore, are two additional
kinds of fact, capable of being
asserted in a proposition. Besides
the propositions which assert Sequence
or Co-existence, there are some which
assert simple Existence ; * and others
assert Causation, which, subject to

* Professor Bain, in his logic (i. 256),
excludes Existence from the list, consider-
ing it as a mere name. All propositions,
he says, which predicate mere existence
"are more or less abbreviated or elliptical :
•when fully expressed they fall under either
co-existence or succession. When we say
there exists a conspiracy for *a particular
purpose, we mean that at the present time
a body of men have formed themselves
into a society for a particular object ; which
is a complex affirmation, resolvable into
propositions of co-existence and succession
(as causation). The assertion that the dodo
does not exist, points to the fact that this
animal, once known in a certain place, has
disappeared or become extinct ; is no longer
associated with the locality : all which
m;iy be better stated without the use of
the verb ' exist.' There is a debated ques-
tion— Does an ether exist ? but the con-
crete form would be this — ' Are heat and
light and other radiant influences propa-
gated by an ethereal medium diffused in
space ? ' which is a proposition of causation.
In like manner the question of the Exis-
tence of a Deity cannot be discussed in
that form. It is properly a question as to
the First Cause of the Universe, and as to

the explanations which will follow in
the Third Book, must be considered
provisionally as a distinct and peculiar
kind of assertion.

§ 6. To these four kinds of matter-
of-fact or assertion must be added

the continued exertion of that Cause in
providential superintendence " (i. 407).

Mr. Bain thinks it ' ' fictitious and un-
meaning language " to carry up the classi-
fication of Nature to one surnmum genus,
Being, or that which Exists ; since nothing
can be perceived or apprehended but by
way of contrast with something else, (of
which important truth, under the name of
Law of Relativity, he has been in our time
the pKincipal expounder and champion,)
and we have no other class to oppose to
Being, or fact to contrast with Existence.

I accept fully Mr. Bain's Law of Rela-
tivity, but I do not understand by it that
to enable us to apprehend or be conscious
of any fact, it is necessary that we should
contrast it with some other ixjsitive fact.
The antithesis necessary to consciousness
need not, I conceive, be an antithesis be-
tween two positives ; it may be between
one positive and its negative. Hobbes
was undoubtedly right when he said that
a single sensation indefinitely prolonged
would cease to be felt at all; but simple
mtermission, without other change, would
restore it to consciousness. In order to be
conscious of heat, it is not necessary that
we should pass to it from cold ; it suffices
that we should pass to it from a state of no
sensation, or from a sensation of some
other kind. The relative opposite of Being,
considered as a surnmum genus, is Non-
entity, or Nothing ; and we have, now and
then, occasion to consider and discuss
things merely in contrast with Non-entity.

I grant that the decision of questions of
Existence usually if not always depends
on a previous question of either Causation
or Co-existence. But Existence is never-
theless a different thing from Causation or
Co-existence, and can be predicated apart
from them. The meaning of the abstract
name Existence, and the connotation ot
the concrete name Being, consist, like the
meaning of all other names, in sensations
or states of consciousness : their peculiarity
is that to exist, is to excite, or be capable
of exciting, any sensations or states of con-
sciousness : no matter what, but it is in-
dispensable that there should be some. It
was from overlooking thi.s that Hegel, find-
ing that Being is an abstraction reached by
thinking away all particular attributes, ar
rived at the self -contradictory proposition
on which he founded all his philosophy,
that Being is the same as nothing. It is
really the name of Something, taken in the
most comprehensive sense of the word.

66

NAMES AND PROPOSITIONS.

a fifth, Resemblance. This was a
species of attribute which we found
it impossible to analyse ; for which
no fundamentum, distinct from the
objects themselves, could be assigned.
Besides propositions which assert a
sequence or co-existence between two
phenomena, there are therefore also
propositions which assert resemblance
between them ; as, This colour is like
that colour ; — The heat of to-day is
equal to the heat of yesterday. It is
true that such an assertion might
with some plausibility be brought
within the description of an affirma-
tion of sequence, by considering it as
an assertion that the simultaneous
contemplation of the two colours is
followed by a specific feeling termed
the feeling of resemblance. But there
would be nothing gained by encum-
bering ourselves, especially in this
place, with a generalisation which
may be looked upon as strained.
Logic does not undertake to analyse
mental facts into their ultimate ele-
ments. Resemblance between two
phenomena is more intelligible in
itself than any explanation could
make it, and under any classification
must remain specifically distinct from
the ordinary cases of sequence and
co-existence.

It is sometimes said, that all pro-
positions whatever, of which the pre-
dicate is a general name, do, in point
of fact, affirm or deny resemblance.
All sTich propositions affirm that a
thing belongs to a class ; but things
being classed together according to
their resemblance, everything is of
course classed with the things which
it is supposed to resemble most ; and
thence, it may be said, when we affirm
that Gold is a metal, or that Socrates
is a man, the affirmation intended is,
that gold resembles other metals, and
Socrates other men, more nearly than
they resemble the objects contained
in any other of the classes co-ordinate
with these.

There is some slight degree of
foundation for this remark, but no
more than a slight degree. The

arrangement of things into classes,
such as the class metal, or the class
mun, is grounded indeed on a resem-
blance among the things which are
placed in the same class, but not on a
mere general resemblance : the resem-
blance it is grounded on consists in
the possession by all those things of
certain common peculiarities ; and
those peculiarities it is which the
terms connote, and which the propo-
sitions consequently assert ; not the
resemblance. For though when I
say. Gold is a metal, I say by impli-
cation that if there be any other
metals it must resemble them, yet if
there were no other metals I might
still assert the proposition with the
same meaning as at present, namely,
that gold has the various properties
iii\plied in the word metal ; just as it
might be said. Christians are men,
even if there were no men who were
not Christians. Propositions, there-
fore, in which objects are referred to
a class, because they possess the
attributes constituting the class, are
so far from asserting nothing but
resemblance, that they do not, pro-
perly speaking, assert resemblance
atalL

But we remarked some time ago
(and the reasons of the remark will be
more fully entered into in a subse-
quent Book*) that there is some-
times a convenience in extending the
boundaries of a class so as to include
things which possess in a very inferior
degree, if in any, some of the char-
a<;teristic properties of the class, —
provided they resemble that class
more than any other, insomuch that
the general propositions which are
true of the class will be nearer to
being true of those things than any
other equally general propositions.
For instance, there are substances
called metals which have very few of
the properties by which metals are
commonly recognised ; and almost
every great family of plants or ani-
mals has a few anomalous genera or

* Book iv. cb. Tii.

. IMPORT OF PROPOSITIONS.

67

gpecies on its borders, which are
admitted into it by a sort of courtesy,
and concerning which it has been
matter of discussion to what family
they properly belonged. Now when
the class-name is predicated of any
object of this description, we do, by
so predicating it, affirm resemblance
and nothing more. And in order to
be scrupulously correct, it ought to be
said, that in every case in which we
predicate a general name, we aflBrm,
not absolutely that the object possesses
the properties designated by the
name, but that it either possesses
those properties, or, if it does not, at
any rate resembles the things which
do so, more than it resembles any
other things. In most cases, however,
it is unnecessary to suppose any such
alternative, the latter of the two
grounds being very seldom that on
which the assertion is made : and
when it is, there is generally some
slight difference in the form of the
expression, as, This species (or genus)
is considered, or may be ranked, as
belonging to such and such a family :
we should hardly say positively that
it does belong to it, unless it possessed
unequivocally the properties of which
the class-name is scientifically signi-
ficant.

There is still another exceptional
case, in which, though the predicate
is the name of a class, yet in predicat-
ing it we affirm nothing but resem-
blance, the class being founded not
on resemblance in any given parti-
cular, but on general unanalysable
resemblance. The classes in ques-
tion are those into which our simple
sensations, or rather simple feelings,
are divided. Sensations of white, for
instance, are classed together, not
because we can take them to pieces,
and say they are alike in this, and not
alike in that, but because we feel
them to be alike altogether, though
in different degrees. When, there-
fore, I say. The colour I saw yesterday
was a white colour, or, The sensation
I feel is one of tightness, in both
cases the attribute I afGj^ of the

colour or of the other sensation is
mere resemblance — simple likeness to
sensations which I have had before,
and which have had those names
bestowed upon them. The names
of feelings, like other concrete general
names, are connotative ; but they
connote a mere resemblance. When
predicated of any individual feeling,
the information they convey is that
of its likeness to the other feelings
which we have been accustomed to
call by the same name. Thus much
may suffice in illustration of the kind
of propositions in which the matter-
of-fact asserted (or denied) is simple
Resemblance,

Existence, Co-existence, Sequence,
Causation, Resemblance : one or
other of these is asserted (or denied)
in every proposition which is not
merely verbal. This fivefold division
is an exhaustive classification of
matters-of-fact ; of all things that
can be believed or tendered for be-
lief ; of all questions that can be pro-
pounded, and all answers that can be
returned to them.

Professor Bain* distinguishes two
kinds of Propositions of Co-existence.
" In the one kind, account is taken
of Place ; they may be described as
propositions of Order in Place." In
the other kind, the co-existence which
is predicated is termed by Mr. Bain
Coinherence of Attributes. "This
is a distinct variety of Propositions of
Co-existence. Instead of an arrange-
ment in place with numerical inter-
vals, we have the concurrence of two
or more attributes or powers in the
same part or locality. A mass of
gold contains, in every atom, the con-
curring attributes that mark the
substance — weight, hardness, colour,
lustre, incorrosibility, &c. An animal,
besides having parts situated in place,
has coinhering functions in the same
parts, exerted by the very same
masses and molecules of its substance.
. . . . The Mind, which affords no
Propositions of Order in Place, hag

* logic, 1. 103-X05.

68

NAMES AND PROPOSITIONS.

coinhering functions. We aflSrni
mind to contain Feeling, Will, and
Thought, not in local separation, but
in commingling exercise. The concur-
ring properties of minerals, of plants,
and of the bodily and the mental
structure of animals, are united in
affirmations of coinherence. "

The distinction is real and impor-
tant. But, as has been seen, an
Attribute, when it is anything but a
simple unanalysable Resemblance be-
tween the subject and some other
things, consists in causing impres-
sions of some sort on consciousness.
Consequently, the coinherence of two
attributes is but the co-existence of
the two states of consciousness im-
plied in their meaning : with the
difference, however, that this co-exis-
tence is sometimes potential only,
the attribute being considered as in
existence though the fact on which
it is grounded may not be actually,
but only potentially present. Snow,
for instance, is, with great conveni-
ence, said to be white even in a state
of total darkness, because, though we
are not now conscious of the colour,
we shall be conscious of it as soon as
morning breaks. Coinherence of at-
tributes is therefore still a case, though
a complex one, of co-existence of states
of consciousness : a totally different
thing, however, from Order in Place.
Being a part of simultaneity, it be-
longs not to Place but to Time.

We may, therefore, (and we shall
sometimes find it a convenience,) in-
stead of Co-existence and Sequence,
say, for greater particularity, Order
in Place and Order in Time : Order
in Place being a specific mode of co-
existence, not necessary to be more
particularly analysed here ; while the
mere fact of co-existence, whether be-
tween actual sensations, or between
the potentialities of causing them,
known by the name of attributes, may
be classed, together with Sequence,
under the head of Order in Time.

§ 7. In the foregoing inquiry into
^e import of Propositions, we have

thought it necessary to analyse
directly those alone, in which the
terms of the proposition (or the pre-
dicate at least) are concrete terms.
But, in doing so, we have indirectly
analysed those in which the terms are
abstract. The distinction between an
abstract term and its corresponding
concrete, does not turn upon any dif-
ference in what they are appointed to
signify ; for the real signification of a
concrete general name is, as we have
so often said, its connotation ; and
what the concrete term connotes forms
the entire meaning of the abstract
name. Since there is nothing in the
import of an abstract name which is
not in the import of the correspond-
ing concrete, it is natural to suppose
that neither can there be anything in
the import of a proposition of which
the terms are abstract, but what there
is in some proposition which can b«
framed of concrete terms.

And this presumption a closer exa-
mination will confirm. An abstract
name is the name of an attribute, or
combination of attributes. The cor-
responding concrete is a name given
to things, because of, and in order to
express, their possessing that attribute,
or that combination of attributes.
When, therefore, we predicate of any-
thing a concrete name, the attribute
is what we in reality predicate of it.
But it has now been shown that in all
propositions of which the predicate
is a concrete name, what is really
predicated is one of five things :
Existence, Co-existence, Causation,
Sequence, or Resemblance. An at-
tribute, therefore, is necessarily either
an existence, a co-existence, a causa-
tion, a sequence, or a resemblance.
When a proposition consists of a sub-
ject and predicate which are abstract
terms, it consists of terms which must
necessarily signify one or other of these
things. When we predicate of any-
thing an abstract name, we affirm of the
thing that it is one or other of these five
things ; that it is a case of Existence,
or of Co-existence, or of Causation,
or of Sequence, or of Resenablj^nce,

IMPORT OF PROPOSITIONS.

69

It is impossible to imagine any pro-
position expressed in abstract terms,
which cannot be transformed into a
precisely equivalent proposition in
which the terms are concrete ; namely,
either the concrete names which con-
note the attributes themselves, or the
names of the fundamenta of those
attributes ; the facts or phenomena on
which they are grounded. To illus-
trate the latter case, let us take this
proposition, of which the subject only
is an abstract name, '* Thoughtlessness
is dangerous." Thoughtlessness is
an attribute, grounded on the facts
which we call thoughtless actions ; and
the proposition is equivalent to this,
Thoughtless actions are dangerous.
In the next example the predicate as
well as the subject are abstract names:
" Whiteness is a colour ; " or " The
colour of snow is a whiteness." These
attributes being grounded on sensa-
tions, the equivalent propositions in
the concrete would be. The sensation
of white is one of the sensations called
those of colour, — The sensation of
sight, caused by looking at snow, is
one of the sensations called sensations
of white. In these propositions, as
we have before seen, the matter-of-
fact asserted is a Resemblance. In
the following examples, the concrete
terms are those which directly corre-
spond to the abstract names ; connot-
ing the attribute which these denote.
" Prudence is a virtue : " this may
be rendered, '* All prudent persons,
in so far as prudent, are virtuous : "
" Courage is deserving of honour,"
thus, " All courageous persons are
deserving of honour in so far as they
are courageous : " which is equivalent
to this — " All courageous persons de-
serve an addition to the honour, or a
diminution of the disgrace, which
would attach to them on other
grounds."

In order to throw still further light
upon the import of propositions of
which the terms are abstract, we will
subject one of the examples given
above to a minuter analysis. The
proposition we shall select is the fol-

lowing : — " Prudence is a virtue."
Let us substitute for the word virtue
an equivalent but more definite ex-
pression, such as "a mental quality
beneficial to society," or " a mental
quality pleasing to God, "or whatever
else we adopt as the definition of
virtue. What the proposition asserts
is a sequence, accompanied with causa-
tion : namely, that benefit to society,
or that the approval of God, is conse-
quent on, and caused by, prudence.
Here is a sequence ; but between
what ? We understand the conse-
quent of the sequence, but we have
yet to analyse the antecedent. Pru-
dence is an attribute ; and, in con-
nection with it, two things besides it-
self are to be considered ; prudent
persons, who are the subjects of the
attribute, and prudential conduct,
which ma}' be called the foundation
of it. Now is either of these the
antecedent ? and, first, is it meant
that the approval of God, or benefit
to society, is attendant upon all pru-
dent persons ? No, except in so far
as they are prudent ; for prudent per-
sons who are scoundrels can seldom
on the whole be beneficial to society,
nor can they be acceptable to a good
being. Is it upon prudential conduct,
then, that divine approbation and
benefit to mankind are supposed to
be invariably consequent ? Neither is
this the assertion meant, when it is
said that prudence is a virtue ; except
with the same reservation as before,
and for the same reason, namely, that
prudential conduct, although in so far
as it is beneficial to society, may yet,
by reason of some other of its quali-
ties, be productive of an injury out-
weighing the benefit, and deserve a
displeasure exceeding the approbation
which would be due to the prudence.
Neither the substance, therefore, (viz,
the person,) nor the phenomenon, (the
conduct,) is an antecedent on which
the other term of the sequence is
universally consequent. But the pro-
position, " Prudence is a virtue," is
an universal proposition. What is
it, then, upon which the proposition

70

NAMES AND PROPOSITIONS.

affirms the effects in question to be
universally consequent ? Upon that
in the person, and in the conduct,
which causes them to be called pru-
dent, and which is equally in them
when the action, though prudent, is
wicked ; namely, a correct foresight
of consequences, a just estimation of
their importance to the object in view,
and repression of any unreflecting
impulse at variance with the deliber-
ate purpose. These, which are states
of the person's mind, are the real
antecedent in the sequence, the real
cause in the causation, asserted by
the proposition. But these are also
the real ground, or foundation, of the
attribute Prudence ; since wherever
these states of mind exist we may
predicate prudence, even before we
know whether any conduct has fol-
lowed. And in this manner every
assertion respecting an attribute may
be transformed into an assertion
exactly equivalent respecting the fact
or plienomenon which is the ground
of the attribute. And no case can be
assigned, where that which is predi-
cated of the fact or phenomenon does
not belong to one or other of the five
species formerly enumerated : it is
either simple Existence, or it is some
Sequence, Co-existence, Causation, or
Resemblance.

And as these five are the only things
which can be affirmed, so are they the
only things which can be denied. " No
horses are web-footed," denies that
the attributes of a horse ever co-exist
with web-feet. It is scarcely neces-
sary to apply the same analysis to
particular affirmations and negations.
" Some birds are web-footed," affirms
that, with the attributes connoted by
bird, the phenomenon web-feet is
sometimes co-existent : " Some birds
are not web- footed," asserts that there
are other instances in which this co-
existence does not have place. Any
further explanation of a thing which,
if the previous exposition has been
assented to, is so obvious, may here
be spared.

CHAPTER Vt

OF PROPOSITIONS MERELY VERBAL.

§ I. As a preparation for the in-
quiry which is the proper object of
Logic, namely, in what manner pro-
positions are to be proved, we have
found it necessary to inquire what
they contain which requires, or is
susceptible of, proof ; or (which is the
same thing) what they assert. In the
course of this preliminary investiga-
tion into the import of Propositions,
we examined the opinion of the Con-
ceptualists, that a proposition is the
expression of a relation between two
ideas ; and the doctrine of the extreme
Nominalists, that it is the expression
of an agreement or disagreement be-
tween the meanings of two names.
We decided that, as general theories,
both of these are erroneous ; and that,
though propositions may be made
both respecting names and respecting
ideas, neither the one nor the other
are the subject-matter of Propositions
considered generally. We then exa-
mined the different kinds of Propo-
sitions, and found that, with the
exception of those which are merely
verbal, they assert five different kinds
of matters of fact, namely. Existence,
Order in Place, Order in Time, Causa-
tion, and Resemblance ; that in every
proposition one of these five is either
affirmed, or denied, of some fact or
phenomenon, or of some object the un-
known source of a fact or phenomenon.

In distinguishing, however, the dif-
ferent kinds of matters of fact asserted
in propositions, we reserved one class
of propositions, which do not relate to
any matter of fact, in the proper sense
of the term, at all, but to the mean-
ing of names. Since names and their
signification are entirely arbitrary,
such propositions are not, strictly
speaking, susceptible of truth or
falsity, but only of conformity or
disconformity to usage or convention ;
and all the proof they are capable
of, is proof of usage ; proof that
the words have been employed by
others in the acceptation in which the

VERBAL AND REAL PROPOSITIONS.

71

speaker or writer desires to use them.
These propositions occupy, however, a
conspicuous place in philosophy ; and
their nature and characteristics are
of as much importance in logic, as
those of any of the other classes of
propositions previously adverted to.

If all propositions respecting the
signification of words were as simple
and unimportant as those which
served us for examples when examin-
ing Hobbes' theory of predication,
viz. those of which the subject and
predicate are proper names, and which
assert only that those names have,
or that they have not, been conven-
tionally assigned to the same indivi-
dual, there would be little to attract
to such propositions the attention of
philosophers. But the class of merely
verbal propositions embraces not only
much more than these, but much
more than any propositions which at
first sight present themselves as ver-
bal ; comprehending a kind of asser-
tions which have been regarded not
only as relating to things, but as hav-
ing actually a more intimate relation
with them than any other propositions
whatever. The student in philosophy
will perceive that I allude to the dis-
tinction on which so much stress was
laid by the schoolmen, and which
has been retained either under the
same or under other names by most
metaphysicians to the present day,
viz. between what were called essen-
tial, and what were called accidental,
propositions, and between essential
and accidental properties or attri-
butes.

§ 2. Almost all metaphysicians prior
to Locke, as well as many since his
time, have made a great mystery of
Essential Predication, and of predi-
cates which are said to be of the
essence of the subject. The essence of
a thing, they said, was that without
which the thing could neither be,
nor be conceived to be. Thus, ration-
ality was of the essence of man, be-
cause without rationality man could
not be conceived to exist. The dif-

ferent attributes which made up the
essence of the thing were called its
essential properties ; and a proposi-
tion in which any of these were pre-
dicated of it was called an Essential
Proposition, and was considered to go
deeper into the nature of the thing,
and to convey more important infor-
mation respecting it than any other
proposition could do. All properties,
not of the essence of the thing, were
called its accidents ; were supposed
to have nothing at all, or nothing
comparatively, to do with its inmost
nature ; and the propositions in which
any of these were predicated of it
were called Accidental Propositions.
A connection may be traced between
this distinction, which originated
with the schoolmen, and the well-
known dogmas of substantia secundce
or general substances, and substantial
forms, doctrines which under varieties
of language pervaded alike the Aris-
totelian and the Platonic schools, and
of which more of the spirit has come
down to modem times than might be
conjectured from the disuse of the
phraseology. The false views of the
nature of classification and general-
isation which prevailed among the
schoolmen, and of which these dog-
mas were the technical expression,
afford the only explanation which can
be given of their having misunder-
stood the real nature of those Essences
which held so conspicuous a place in
their philosophy. They said, truly,
that man cannot be conceived with-
out rationality. But though man
cannot, a being may be conceived
exactly like a man in all points except
that one quality, and those others
which are the conditions or conse-
quences of it. All therefore which is
really true in the assertion that man
cannot be conceived without ration-
ality, is only that if he had not ration-
ality, he would not be reputed a man.
There is no impossibility in conceiv-
ing the thivg, nor, for aught we know,
in its existing : the impossibility is
in the conventions of language, which
will not allow the thing, even if it

72

NAMES AND PROPOSITIONS.

exist, to be called by the name which
is reserved for rational beings. Ra-
tionality, in short, is involved in the
meaning of the word man : is one of
the attributes connoted by the name.
The essence of man, simply means
the whole of the attributes connoted
\)y the word ; and any one of those
attributes taken singly is an essential
property of man.

But these reflections, so easy to us,
would have been difficult to persons
who thought, as most of the later
Aristotelians did, that objects were
made what they were called, that
gold (for instance) was made gold, not
by the possession of certain properties
to which mankind have chosen to
attach that name, but by participa-
tion in the nature of a certain general
substance, called gold in general,
which substance, together with all
the properties that belonged to it,
inhered in every individual piece of
gold.* As they did not consider
these universal substances to be at-
tached to all general names, but only
to some, they thought that an object
borrowed only a part of its properties
from an iiniversal substance, and that
the rest belonged to it individually :
the former they called its essence,
and the latter its accidents. The
scholastic doctrine of essences long
survived the theory on which it rested,
that of the existence of real entities
corresponding to general terms ; and
it was reserved for Locke at the end of
the seventeenth century, to convince
philosophers that the supposed essences
of classes were merely the significa-
tion of their names ; nor, among the
signal services which his writings ren-
dered to philosophy, was there one
more needful or more valuable.

* The doctrines which prevented the
realmeaiiiiigof Essences from being under-
stood, had not assumed so settled a shape
in the time of Aristotle and his immediate
followers, as was afterwards given to them
by the Realists of the Middle Ages. Aris-
totle himself (in his Treatise on the Cate-
gories) expressly denies that the Sevrepai
ova-ML, or substantice secundce, inhere in
a subject. They are only, he Bays, predi-
cated of it.

Now, as the most familiar of the
general names by which an object is
designated usually connotes not one
only, but several attributes of the ob-
ject, each of which attributes sepa-
rately forms also the bond of union of
some class, and the meaning of some
general name ; we may predicate of a
name which connotes a variety of at-
tributes, another name which connotes
only one of these attributes, or some
smaller number of them than all. In
such cases, the universal affirmative
proposition will be true ; since what-
ever possesses the whole of any set of
attributes, must possess any part of
that same set. A proposition of this
sort, however, conveys no information
to any one who previously understood
the whole meaning of the terms. The
propositions. Every man is a corporeal
being. Every man is a living creature,
Every man is rational, convey no
knowledge to any one who was already
aware of the entire meaning of the
word man, for the meaning of the word
includes all this : and that every man
has the attributes connoted by all these
predicates, is already asserted when he
is called a man. Now, of this nature
are all the propositions which have
been called essential. They are, in
fact, identical propositions.

It is true that a proposition which
predicates any attribute, even though
it be one implied in the name, is in
most cases understood to involve a
tacit assertion that there exists a thing
corresponding to the name, and pos-
sessing the attributes connoted by it ;
and this implied assertion may convey
information, even to those who under-
stood the meaning of the name. Bub
all information of this sort, conveyed
by all the essential propositions of
which man can be made the subject,
is included in the assertion, Men exist.
And this assumption of real existence
is, after all, the result of an imperfec-
tion of language. It arises from the
ambiguity of the copula, which, in
addition to its proper office of a mark
to show that an assertion is made, is
also, as formerly remarked, a concrete

VERBAL AND REAL PROPOSITIONS.

73

word connoting existence. The actual
existence of the subject of the propo-
sition is therefore only apparently, not
really, implied in the predication, if
an essential one : we may say, A ghost
is a disembodied spirit, without believ-
ing in ghosts. But an accidental, or
non-essential affirmation, does imply
the real existence of the subject, be-
cause in the case of a non-existent
subject there is nothing for the pro-
position to assert. Such a proposition
as. The ghost of a murdered person
haunts the couch of the murderer,
can only have a meaning if understood
as implying a belief in ghosts ; for
since the signification of the word
ghost implies nothing of the kind, the
speaker either means nothing, or means
to assert a thing which he wishes to
be believed to have really taken place.
It will be hereafter seen that when
any important consequences seem to
follow, as in mathematics, from an
essential proposition, or, in other
words, from a proposition involved in
the meaning of a name, what they
really flow from is the tacit assump-
tion of the real existence of the object
so named. Apart from this assump-
tion of real existence, the class of pro-
positions in which the predicate is of
the essence of the subject (that is, in
which the predicate connotes the
w^hole or part of what the subject con-
notes, but nothing besides) answer no
purpose but that of unfolding the whole
or some part of the meaning of the
name to those who did not previously
know it. Accordingly, the most use-
ful, and in strictness the only useful
kind of essential propositions, are
Definitions : which, to be complete,
should unfold the whole of what is
involved in the meaning of the word
defined ; that is, (when it is a con-
notative word,) the whole of what it
connotes. In defining a name, how-
ever, it is not usual to specify its
entire connotation, but so much only
as is sufficient to mark out the objects
usually denoted by it from all other
known objects. And sometimes a
merely accidental property, not in-

volved in the meaning of the name,
answers this purpose equally well.
The various kinds of definition which
these distinctions give rise to, and the
puiposes to which they are respec-
tively subservient, will be minutely
considered in the proper place.

§ 3. According to the above view
of essential propositions, no proposi-
tion can be reckoned such which re-
lates to an individual by name, that
is, in which the subject is a proper
name. Individuals have no essences.
When the schoolmen talked of the
essence of an individual, they did not
mean the properties implied in its
name, for the names of individuals
imply no properties. They regarded
as of the essence of an individual
whatever was of the essence of the
species in which they were accustomed
to place that individual ; i.e. of the
class to which it was most familiarly
referred, and to which, therefore, they
conceived that it by nature belonged.
Th\is, because the proposition Man is
a rational being, was an essential pro-
position, they affirmed the same thing
of the proposition, Julius Caesar is a
rational being. This followed very
naturally if genera and species were
to be considered as entities, distinct
from, but inha'ing in, the individuals
composing them. If man was a sub-
stance inhering in each individual
man, the essence of man (whatever
that might mean) was naturally sup-
posed to accompany it ; to inhere in
John Thompson, and to form the
common essence of Thompson and
Julius Caesar. It might then be fairly
said, that rationality, being of the
essence of Man, was of the essence
also of Thompson. But if Man alto-
gether be only the individual men
and a name bestowed upon them in
consequence of certain common pro-
perties, what becomes of John Thomp-
son's essence ?

A fundamental error is seldom ex-
pelled from philosophy by a single
victory. It retreats slowly, defends
every inch of ground, and often, after

74

NAMES AND PROPOSITIONS.

it has been driven from the open
country, retains a footing in some
remote fastness. The essences of in-
dividuals were an unmeaning figment
arising from a misapprehension of the
essences of glasses ; yet even Locke,
when he extirpated the parent error,
could not shake himself free from that
which was its fruit. He distinguished
two sorts of essences. Real and No-
minal. His nominal essences were
the essences of classes, explained
nearly as we have now explained
them. Nor is anything wanting to
render the third book of Locke's Essay
a nearly unexceptionable treatise on
the connotation of names, except to
free its language from the assumption
of what are called Abstract Ideas,
which unfortunately is involved in the
phraseology, though not necessarily
connected with the thoughts contained
in that immortal Third Book.* But
besides nominal essences, he admitted
real essences, or essences of individual
objects, which he supposed to be the
causes of the sensible properties of
those objects. We know not (said he)
what these are ; and this acknowledg-
ment rendered the fiction compara-
tively innocuous ; but if we did, we
could, from them alone, demonstrate
the sensible properties of the object,
as the properties of the triangle are
demonstrated from the definition of
the triangle. I shall have occasion
to revert to this theory in treating of
Demonstration, and of the conditions
under which one property of a thing

* The always acute and often profound
author of An Outline of Sematologi/ t Mr. B.
H. Smart) justly says, "Locke will be
much more intelligible, if, in the majority
of places, we substitute 'the knowledge of
for wiiat he calls ' tlie Idea of" (p. lo).
Among the many criticisms on Locke's use
of the word Idea, this is the one which, as
it appears to me, most nearly hits the
mark; and I quote it for the additional
reason that it precisely expresses the p'int
of difference respecting the import of Pro-

Eositions, between my view and what I
ave spoken of as tlie Conceptualist view
of them. Where a Conceptualist says that
a name or a proposition expresses our idea
of a thing, I should generally say (instead
of our Idea) our Knowledge, or Belief, con-
cerning the thing itself.

admits of being demonstrated from
another property. It is enough here to
remark that, according to this defini-
tion, the real essence of an object has, in
the progress of physics, come to be con-
ceived as nearly equivalent, in the case
of bodies, to their corpuscular struc-
ture : what it is now supposed to mean
in the case of any other entities, I
would not take upon myself to define.

§ 4. An essential proposition, then,
is one which is purely verbal ; which
asserts of a thing under a particular
name only what is asserted of it in
tlie fact of calling it by that name ;
and which therefore either gives no
information, or gives it respecting the
name, not the thing. Non-essential,
or accidental propositions, on the con-
trary, may be called Real Propositions,
in opposition to Verbal. They predi-
cate of a thing some fact not involved
in the signification of the name by
which the proposition speaks of it ;
some attribute not connoted by that
name. Such are all propositions
concerning things individually desig-
nated, and all general or particular
propositions in which the predicate
connotes any attribute not connoted
by the subject. All these, if tnie, add
to our knowledge : they convey infor-
mation, not already involved in the
names employed. When I am told
that all, or even that some objects,
which have certain qualities, or which
stand in certain relations, have also
certain other qualities, or stand in
certain other relations, I learn from
this proposition a new fact ; a fact
not included in my knowledge of the
meaning of the words, nor even of the
existence of Things answering to the
signification of those words. It is
this class of propositions only which
are in themselves instructive, or from
which any instructive propositions can
be inferred.*

* This distinction corresponds to that
which is drawn by Kant and other meta-
physicians between what they term analy-
tic and synthetic judgments ; the former
being those which can be evolved from tlie
meaning of the terms used.

VERBAL AND REAL PROPOSITIONS.

75

k

Nothing has probably contributed
more to the opinion so long prevalent
of the futility of the school logic,
than the circumstance that almost all
the examples used in the common
school-books to illustrate the doctrine
of predication and that of the syllo-
gism consist of essential propositions.
They were usually taken either from
the branches or from the main trunk
of the Predicamental Tree, which in-
cluded nothing but what was of the
essence of the species : Omne corpus est
substantia, Omne animal est corpus,
Omnis homo est corpus, Omnis homo
est animal, Omnis homo est rationalis,
and so forth. It is far from wonder-
ful that the syllogistic art should
have been thought to be of no use
in assisting correct reasoning, when
almost the only propositions which,
in the hands of its professed teachers,
it was employed to prove, were such-
as every one assented to without
proof the moment he comprehended
the meaning of the words ; and stood
exactly on a level, in point of evi-
dence, with the premises from which
they were drawn. I have, therefore,
throughout this work, avoided the
employment of essential propositions
as examples, except where the nature
of the principle to be illustrated speci-
fically required them.

§ 5. With respect to propositions
which do convey information — which
assert something of a Thing, under a
name that does not abeady presuppose
what is about to be asserted ; there
are two different aspects in which
these, or rather such of them as are
general propositions, may be con-
sidered : we may either look at them
as portions of speculative truth, or
as memoranda for practical use. Ac-
cording as we consider propositions
in one or the other of these lights,
their import may be conveniently ex-
pressed in one or in the other of two
formulas.

According to the formula which
we have hitherto employed, and which
is best adapted to express the import

of the proposition as a portion of our
theoretical knowledge, All men are
mortal, means that the attributes of
man are always accompanied by the
attribute mortality : No men are gods,
means that the attributes of man are
never accompanied by the attributes,
or at least never by all the attributes,
signified by the word god. But when
the proposition is considered as a
memorandum for practical use, we
shall find a different mode of express-
ing the same meaning better adapted
to indicate the office which the pro-
position performs.; The practical use
of a proposition is, to apprise or re-
mind us what we have to expect in
any individual case which comes with-
in the assertion contained in the pro-
position. In reference to this purpose,
the proposition. All men are mortal,
means that the attributes of man are
evidence of, are a mark of, mortality ;
an indication by which the presence
of that attribute is made manifest.
No men are gods, means that the
attributes of man are a mark or evi-
dence that some or all of the attri-
butes understood to belong to a god
are not there ; that where the former
are, we need not expect to find the
latter.

These two forms of expression are
at bottom equivalent ; but the one
points the attention more directly to
what a proposition means, the latter
to the manner in which it is to be used.

Now it is to be observed that Rea-
soning (the subject to which we are
next to proceed) is a process into which
propositions enter not as ultimate re-
sults, but as means to the establish-
ment of other propositions. We may
expect, therefore, that the mode of ex-
hibiting the import of a general pro-
position which shows it in its applica-
tion to practical use, will best express
the function which propositions per-
form in Reasoning. And accordingly,
in the theory of Reasoning, the mode
of viewing the subject which con-
siders a Proposition as asserting that
one fact or phenomenon is a mark
or evidence of another fact or pheno-

76

NAMES AND PROPOSITIONS.

menon, will be found almost indis-
pensable. For the purposes of that
Theory, the best mode of defining the
import of a proposition is not the mode
which shows most clearly what it is in
itself, but that which most distinctly
suggests the manner in which it may
be made available for advancing from
it to other propositions.

CHAPTER VII.

OP THE NATURE OF CLASSIFICATION,
AND THE FIVE PKEDICABLES.

§ I. In examining into the nature
of general propositions, we have ad-
verted much less than is usual with
logicians to the ideas of a Class and
Classification ; ideas which, since the
Realist doctrine of General Substances
went out of vogue, have formed the
basis of almost every attempt at a
philosophical theory of general terms
and general propositions. We have
considered general names as having
a meaning, quite independently of
their being the names of classes.
That circumstance is in truth acci-
dental, it being wholly immaterial to
the signification of the name whether
there are many objects, or only one,
to which it happens to be applicable,
or whether there be any at all. God
is as much a general term to the
Christian or Jew as to the Polytheist ;
and dragon, hippogriff, chimera, mer-
maid, ghost, are as much so as if real
objects existed, corresponding to those
names. Every name the signification
of which is constituted by attributes,
is potentially a name of an indefinite
number of objects ; but it needs not
be actually the name of any ; and if
of any, it may be the name of only
one. As soon as we employ a name
to connote attributes, the things, be
they more or fewer, which happen to
possess those attributes, are consti-
tuted ipso facto a class. But in pre-
dicating the name we predicate only
the attributes ; and the fact of belong-
ing to a class does not, in many cases,
come into view at all.

Although, however,Predicat!on does
not presuppose Classification, and
though the theory of Names and of
Propositions is not cleared up, but
only encumbered, by intruding the
idea of classification into it, there is
nevertheless aclose connection between
Classification and the employment of
General Names. By every general
name which we introduce, we create
a class, if there be any things, real or
imaginary, to compose it ; that is, any
Things corresponding to the significa-
tion of the name. Classes, therefore,
mostly owe their existence to general
language. But general language, also,
though that is not the most common
case, sometimes owes its existence to
classes. A general, which is as much
as to say a significant, name, is indeed
mostly introduced because we have a
signification to express by it ; because
we need a word by means of which
to predicate the attributes which it
connotes. But it is also true that a
name is sometimes introduced because
we have found it convenient to create
a class ; because we have thought it
useful for the regulation of our mental
operations, that a certain group of
objects should be thought of together.
A naturalist, for purposes connected
with his particular science, sees reason
to distribute the animal or vegetable
creation into certain groups rather
than into any others, and he requires
a name to bind, as it were, each of his
groups together. It must not how-
ever be supposed that such names,
when introduced, differ in any respect
as to their mode of signification from
other connotative names. The classes
which they denote are, as much as any
other classes, constituted by certain
common attributes, and their names
are significant of those attributes, and
of nothing else. The names of Cuvier's
classes and orders, Plantigrades, Digiti-
grades, &c., are as much the expres-
sion of attributes as if those names had
preceded, instead of grown out of, his
classification of animals. The only
peculiarity of the case is, that the con-
venience of classification was here the

CLASSIFICATION AND THE PREDICABLE&

11

primary motive for introducing the
names ; while in other cases the name
is introduced as a means of predica-
tion, and the formation of a class de-
noted by it is only an. indirect con-
eequence.

The principles which ought to regu-
late Classification as a logical process
subservient to the investigation of
truth, cannot be discussed to any
purpose until a much later stage of
our inquiry. But of Classification,
as resulting from, and implied in,
the fact of employing general lan-
guage, we cannot forbear to treat
here, without leaving the theory of
general names, and of their employ-
ment in predication, mutilated and
formless.

§ 2. This portion of the theory of
general language is the subject of
what is termed the doctrine of the
Predi cables ; a set of distinctions
handed down from Aristotle, and his
follower Porphyry, many of which
have taken a firm root in scientific,
and some of them even in popular,
phraseology. The predicables are a
fivefold division of General Names,
not grounded as usual on a difference
in their meaning, that is, in the
attribute which they connote, but on
a difference in the kind of class which
they denote. We may predicate of
a thing five different varieties of
class- name : —

A genui of the thing (-yeVof).
(elSos).

A species
A differentia
A proprium
An accidens

(Si.a<f>opa).
(<n;M/3e/3i)K6s).

It is to be remarked of these dis-
tinctions, that they express, not what
the predicate is in its own meaning,
but what relation it bears to the sub-
ject of which it happens on the par-
ticular occasion to be predicated.
There are not some names which are
exclusively genera, and others which
are exclusively species, or differentiae ;
but the same name is referred to one
or another predicable, according to
^be subject of which it is predicated

on the particular occasion. Animal,
for instance, is a genus with respect to
man or John ; a species with respect
to Substance or Being. Rectangular
is one of the Differentiae of a geo-
metrical square ; it is merely one of
the Accidentia of the table at which
I am writing. The words genus,
species, &c., are therefore relative
terms ; they are names applied to
certain predicates, to express the re-
lation between them and some given
subject : a relation grounded, as we
shall see, not on what the predicate
connotes, but on the class which it
denotes, and on the place which, in
some given classification, that class
occupies relatively to the particular
subject.

§ 3. Of these five names, two.
Genus and Species, are not only used
by naturalists in a technical accepta-
tion not precisely agreeing with their
philosophical meaning, but have also
acquired a popular acceptation, much
more general than either. In this
popular sense any two classes, one of
which includes the whole of the other
and more, may be called a Genus and
a Species. Such, for instance, are
Animal and Man ; Man and Mathe-
matician. Animal is a Genus ; Man
and Brute are its two species ; or we
may divide it into a greater number
of species, as man, horse, dog, &c.
Biped, or two-footed animal, may also
be considered a genus, of which man
and bird are two species. Taste is
a genus, of which sweet taste, sour
taste, salt taste, &c. are species.
Virtue is a genus ; justice, prudence,
courage, fortitude, generosity, &c.,
are its species.

The same class which is a genus
with reference to the sub-classes or
species included in it, may be itself a
species with reference to a more com-
prehensive, or, as it is often called, a
superior genus. Man is a species with
reference to animal, but a genus with
reference to the species Mathema-
tician. Animal is a genus, divided
into two species, man and brute;

78

NAMES AND PROPOSITIONS.

but animal is also a species, which,
with another species, vegetable, makes
up the genus, organised being.
Biped is a genus, with reference to
man and bird, but a species with re-
spect to the superior genus, animal.
Taste is a genus divided into species,
but also a species of the genus sensa-
tion. Virtue, a genus with refer-
ence to justice, temperance, &c,, is
one of the species of the genus,
mental quality.

In this popular sense the words
Genus and Species have passed into
common discourse. And it should be
observed that in ordinary parlance,
not the name of the class, but the
class itself, is said to be the genus or
species ; not, of course, the class in
the sense of each individual of the
class, but the individuals collectively,
considered as an aggregate whole ;
the name by which the class is desig-
nated being then called not the genus
or species, but the generic or specific
name. And this is an admissible
form of expression ; nor is it of any
importance which of the two modes
of speaking we adopt, provided the
rest of our language is consistent with
it ; but, if we call the class itself the
genus, we must not talk of predicat-
ing the genus. We predicate of man
the name mortal ; and by predicat-
ing the name, we may be said, in an
intelligible sense, to predicate what
the name expresses, the attHbute
mortality ; but in no allowable sense
of the word predication do we pre-
dicate of man the class mortal. We
predicate of him the fact of belong-
ing to the class.

By the Aristotelian logicians, the
terms genus and species were used
in a more restricted sense. They did
not admit every class which could be
divided into other classes to be a
genus, or every class which could be
included in a larger class to be a
species. Animal was by them con-
sidered a genus ; man and brute co-
ordinate species under that genus :
biped, however, would not have been
»4initted to be a genus with reference

to man, but a proprium or accidens
only. It was requisite, according to
their theory, that genus and species
should be of the essence of the subject.
Animal was of the essence of man ;
biped was not. And in every classi-
fication they considered some one
class as the lowest or injima species,
Man, for instance, was a lowest
species. Any further divisions into
which the class might be capable of
being broken down, as man into white,
black, and red man, or into priest and
layman, they did not admit to be
species.

It has been seen, however, in the
preceding chapter, that the distinc-
tion between the essence of a class,
and the attributes or properties which
are not of its essence — a distinction
which has given occasion to so much
abstruse speculation, and to which so
mysterious a character was formerly,
and by many writers is still, attached,
— amounts to nothing more than the
difference between those attributes of
the class which are, and those which
are not, involved in the signification
of the class-name. As applied to
individuals, the word Essence, we
found, has no meaning, except in con-
nection with the exploded tenets of the
Realists ; and what the schoolmen
chose to call the essence of an indivi-
dual, was simply the essence of the
class to which that individual was
most familiarly referred.

Is there no difference, then, save
this merely verbal one, between the
classes which the schoolmen admitted
to be genera or species, and those to
which they refused the title ? Is it
an error to regard some of the dif-
ferences which exist among objects
as differences in kind {genere or spe-
cie), and others only as differences in
the accidents ? Were the schoolmen
right or wrong in giving to some of
the classes into which things may be
divided the name of kinds, and con-
sidering others as secondary divisions,
grounded on differences of a compara-
tively superficial nature ? Examina-
tion will show that the Aristotelians

CLASSIFICATION AND THE PREDICABLES.

79

did mean something by this distinc-
tion, and something important ; but
which, being but indistinctly con-
ceived, was inadequately expressed
by the phraseology of essences, and
the various other modes of speech to
which they had recourse.

§ 4. It is a fundamental principle
in logic, that the power of framing
classes is unlimited, as long as there
is any (even the smallest) difference
to found a distinction upon. Take
any attribute whatever, and if some
things have it, and others have not,
we may ground on the attribute a
division of all things into two classes ;
and we actually do so the moment
we create a name which connotes the
attribute. The number of possible
classes, therefore, is boundless ; and
there are as many actual classes (either
of real or of imaginary things) as there
are general names, positive and nega-
tive together.

But if we contemplate any one of
the classes so formed, such as the class
animal or plant, or the class sulphur
or phosphorus, or the class white or
red, and consider in what particulars
the individuals included in the class
differ from those which do not come
within it, we find a very remarkable
diversity in this respect between some
classes and others. There are some
classes, the things contained in which
differ from other things only in certain
particulars which may be numbered,
while others differ in more than can
be numbered, more even than we need
ever expect to know. Some classes
have little or nothing in common to
characterise them by, except precisely
what is connoted by the name : white
things, for example, are not distin-
guished by any common properties
except whiteness ; or if they are, it is
only by such as are in some way de-
pendent on, or connected with, white-
ness. But a hundred generations
have not exhausted the common pro-
perties of animals or of plants, of
sulphur or of phosphorus ; nor do
we suppose them to be exhaustible, j

but proceed to new observations and
experiments, in the full confidence of
discovering new properties which
were by no means implied in those we
previously knew. While, if any one
were to propose for investigation the
common properties of all things which
are of the same colour, the same
shape, or the same specific gravity,
the absurdity would be palpable.
We have no ground to believe that
any such common properties exist,
except such as may be shown to be
involved in the supposition itself, or
to be derivable from it by some law
of causation. It appears, therefore,
that the properties, on which we
ground our classes, sometimes exhaust
all that the class has in common, or
contain it all by some mode of impli-
cation ; but in other instances we
make a selection of a few properties
from among not only a greater num-
ber, but a number inexhaustible by
us, and to which, as we know no
bounds, they may, so far as we are
concerned, be regarded as infinite.

There is no impropriety in saying
that, of these two classifications, the
one answers to a much more radical
distinction in the things themselves
than the other does. And if any one
even chooses to say that the one classi-
fication is made by nature, the other
by us for our convenience, he will be
right ; provided he means no more
than this : Where a certain apparent
difference between things (though per-
haps in itself of little moment) answers
to we know not what number of other
differences, pervading not only their
known properties, but properties yet
undiscovered, it is not optional but
imperative to recognise this difference
as the foundation of a specific dis-
tinction ; while, on the contrary, dif-
ferences that are merely finite and
determinate, like those designated by
the words white, black, or red, may
be disregarded if the purpose for
which the classification is made does
not require attention to those par-
ticular properties. The differences,
however, are made by nature, in both

So

NAMES AND PROPOSITIONS.

capses ; while the recognition of those
differences as grounds of classification
and of naming, is, equally in both
cases, the act of man : only in the
one case, the ends of language and of
classification would be subverted if no
notice were taken of the difference,
while in the other case, the necessity
of taking notice of it depends on the
importance or unimportance of the
particular qualities in which the dif-
ference happens to consist.

Now, these classes, distinguished
by unknown multitudes of properties,
and not solely by a few determinate
ones — which are parted off from one
another by an unfathomable chasm,
instead of a mere ordinary ditch with
a visible bottom — are the only classes
which, by the Aristotelian logicians,
were considered as genera or species.
Differences which extended only to a
certain property or properties, and
there terminated, they considered as
differences only in the accidents of
things ; but where any class differed
from other things by an infinite series
of differences, known and unknown,
they considered the distinction as of
one kind, and spoke of it as being an
essential difference, which is also one
of the current meanings of that vague
expression at the present day.

Conceiving the schoolmen to have
been justified in drawing a broad line
of separation between these two kinds
of classes and of class-distinctions, I
shall not only retain the division it-
self, but continue to express it in their
language. According to that lan-
guage, the proximate (or lowest) Kind
to which any individual is referrible,
is called its species. Conformably to
this, Isaac Newton would be said to
be of the species man. There are
indeed numerous sub-classes included
in the class man, to which Newton
also belongs ; for example, Christian,
and Englishman, and Mathematician.
But these, though distinct classes, are
not, in our sense of the term, distinct
Kinds of men. A Christian, for ex-
ample, differs from other human
beings ; but he differs only in the

attribute which the word expresses,
namely, belief in Christianity, and
whatever else that implies, either as
involved in the fact itself, or con-
nected with it through some law of
cause and effect. We should never
think of inquiring what properties,
unconnected with Christianity, either
as cause or effect, are common to all
Christians and peculiar to them ;
while in regard to all Men, physiolo-
gists are perpetually carrjdng on such
an inquiry ; nor is the answer ever
likely to be completed. Man, there-
fore, we may call a species ; Christian,
or Mathematician, we cannot.

Note here, that it is by no means
intended to imply that there may not
be different Kinds, or logical species,
of man. The various races and tem-
peraments, the two sexes, and even
the various ages, may be differences
of kind, within our meaning of the
term. I do not say that they are so.
For in the progress of physiology it
may almost be said to be made out,
that the differences which really exist
between different races, sexes, &c.,
follow as consequences, under laws of
nature, from a small number of pri-
mary differences which can be pre-
cisely determined, and which, as the
phrase is, account for all the rest. If
this be so, these are not distinctions
in kind ; no more than Christian, Jew,
Mussulman, and Pagan, a difference
which also carries many consequences
along with it. And in this way classes
are often mistaken for real Kinds,
which are afterwards proved not to
be so. But if it turned out that the
differences were not capable of being
thus accounted for, then Caucasian,
Mongolian, Negro, &c., would be
really different Kinds of human be-
ings, and entitled to be ranked as
species by the logician, though not
by the naturalist. For (as already
noticed) the word species is used in a
different signification in logic and in
natural history. By the naturalist,
organised beings are not usually said
to be of different species, if it is sup-
posed that they have descended from

CLASSIFICATION AND THE PREDICABLES.

gl

the same stock. That, however, is a
sense artificially given to the word,
for the technical purposes of a parti-
cular science. To the logician, if a
negro and a white man differ in the
same manner (however less in degree)
as a horse and a camel do, that is, if
their differences are inexhaustible,
and not referrible to any common
cause, they are different species,
whether tihey are descended from
common ancestors or not. But if
their differences can all be traced to
climate and habits, or to some one or
a few special differences in structure,
they are not, in the logician's view,
specifically distinct.

When the infima species, or proxi-
mate Kind, to which an individual
belongs, has been ascertained, the
properties common to that Kind in-
clude necessarily the whole of the
common properties of every other real
Kind to which the individual can be
referrible. Let the individual, for
example, be Socrates, and the proxi-
mate Kind, man. Animal, or living
creature, is also a real Kind, and in-
cludes Socrates ; but, since it likewise
includes man, or, in other words, since
all men are animals, the properties
common to animals form a portion of
the conmion properties of the sub-
class, man. And if there be any class
which includes Socrates without in-
cluding man, that class is not a real
Kind. Let the class, for example, be
flat -nosed ; that being a class which
includes Socrates, without including
all men. To determine whether it is
a real Kind, we must ask ourselves
this question : Have all flat-nosed
animals, in addition to whatever is
implied in their flat noses, any com-
mon properties, other than those
which are common to all animals
whatever ? If they had ; if a flat nose
were a mark or index to an indefinite
number of other peculiaritie?, not
deducible from the former by an as-
certainable law, then out of the class
man we might cut another class, flat-
nosed man, which, according to our
definition, would be a Kind. But if ,

we could do this, man would not be,
as it was assumed to be, the proxi-
mate Kind. Therefore, the properties
of the proximate Kind do comprehend
those (whether known or unknown) of
all other Kinds to which the indivi-
dual belongs ; which was the point
we undertook to prove. And hence,
every other Kind which is predicable
of the individual, will be to the proxi-
mate Kind in the relation of a genus,
according to even the popular accepta-
tion of the terms genus and species ;
that is, it will be a larger class, in-
cluding it and more.

We are now able to fix the logical
meaning of these terms. Every class
which is a real Kind, that is, which
is distinguished from all other classes
by an indeterminate multitude of
properties not derivable from one an-
other, is either a genus or a species.
A Kind which is not divisible into
other Kinds cannot be a genus, be-
cause it has no species under it ; but
it is itself a species, both with refer-
ence to the individuals below and to
the genera above (Species Priedica-
bilis and Species Subjicibilis). But
every Kind which admits of division
into real Kinds (as animal into mam-
mal, bird, fish, &c., or bird into
various species of birds) is a genus to
all below it, a species to all genera in
which it is itself included. And here
we may close this part of the discus-
sion, and pass to the three remaining
predicables, Difierentia, Propriunu
and Accidens.

§ 5. To begin with Differentia.
This word is correlative with the
words genus and species, and, as all
admit, it signifies the attribute which
distinguishes a given species from
every other species of the same genus.
This is so far clear : but we may still
ask, which of the distinguishing attri-
butes it signifies. For we have seen
that every Kind (and a species must
be a Kind) is distinguished from other
Kinds, not by any one attribute, but
by an indefinite number. Man, for
instance, is a species of the genus

82

NAMES AND PROPOSITIONS.

animal : Rational (or rationality, for
it is of no consequence here whether
we us« the concrete or the abstract
form) is generally assigned by logi-
cians as the Differentia ; and doubt-
less this attribute serves the purpose
of distinction : but it has also been
remarked of man, that he is a c(M)king
animal : the only animal that dresses
its food. This, therefore is another
of the attributes by which the spe-
cies man is distinguished from other
species of the same genus : would
this attribute serve equally well for
a differentia? The Aristotelians say
No; having laid it down that the
differentia must, like the genus and
species, be of the essence of the sub-
ject.

And here we lose even that vestige
of a meaning grounded in the nature
of the things themselves, which may
be supposed to be attached to the
word essence when it is said that
genus and species must be of the
essence of the thing. There can be
no doubt that when the schoolmen
talked of the essences of things as
opposed to their accidents, they had
confusedly in view the distinction
between differences of kind, and the
differences which are not of kind ;
they meant to intimate that genera
and species must be Kinds. Their
notion of the essence of a thing was a
vague notion of a something which
makes it what it is, i.e. which makes
it the Kind of thing that it is — which
causes it to have all that variety of
properties which distinguish its Kind.
But when the matter came to be
looked at more closely, nobody could
discover what caused the thing to
have all those properties, nor even
that there was anything which caused
it to have them. Logicians, however,
not liking to admit this, and being
unable to detect what made the thing
to be what it was, satisfied themselves
with what made it to be what it was
called. Of the innumerable properties
known and unknown that are com-
mon to the class man, a portion only,
Mud of course a very small portion,

are connoted by its name ; these few,
however, will naturally have been
thus distinguished from the rest either
for their greater obviousness, or for
greater supposed importance. These
properties, then, which were connoted
by the name, logicians seized upon,
and called them the essence of the
species ; and not stopping there, they
affirmed them, in the case of the
injima species, to be the essence of
the individual too ; for it was their
maxim, that the species contained the
" whole essence " of the thing. Meta-
physics, that fertile field of delusion
propagated by language, does not
afford a more signal instance of such
delusion. On this account it was that
rationality, being connoted by the
name man, was allowed to be a dif-
ferentia of the class ; but the peculi-
arity of cooking their food, not being
connoted, was relegated to the class
of accidental properties.

The distinction, therefore, between
Differentia, Pioprium, and Accidens,
is not grounded in the nature of things,
but in the connotation of names ; and
we must .seek it there if we wish to
find what it is.

From the fact that the genus in-
eludes the species, in other words, de-
notes more than the species, or is pre-
dicable of a greater number of indi-
viduals, it follows that the species
must connote more than the genus.
It must connote all the attributes
which the genus connotes, or there
would be nothing to prevent it from
denoting individuals not included in
the genus. And it must connote
something besides, otherwise it would
include the whole genus. Animal de-
notes all the individuals denoted by
man, and many more. Man, there-
fore, must connote all that animal
connotes, otherwise there might be
men who are not animals ; and it
must connote something more than
animal connotes, otherwise all animals
would be men. This surplus of con-
notation— this which the species con-
notes over and above the connotation of
thegenus — is the Differentia, or specific

CLASSIFICATION AND THE PREDICABLES.

83

differenc3 ; or, to state the same pro-
position in other words, the Differentia
is that which must be added to the
connotation of the genus, to complete
the connotation of the species.

The word man, for instance, exclu-
sively of what it connotes in connnon
with animal, also connotes rationality,
and at least some approximation to
that external form which we all know,
but which, as we have no name for it
considered in itself, we are content to
call the human. The Differentia, or
specific difference, therefore, of man,
as referred to the genus animal, is
that outward form and the possession
of reason. The Aristotelians said, the
possession of reason, without the out-
ward form. But if they adhered to
this, they would have been obliged to
call the Houyhnhnms men. The
question never arose, and they were
never called upon to decide how such
a case would have affected their notion
of essentiality. However this may be,
they were satisfied with taking such
a portion of the differentia as sufficed
to distinguish the species from all
other existing things, though by so
doing they might not exhaust the
connotation of the name.

§ 6. And here, to prevent the no-
tion of differentia from being restric-
ted within too narrow limits, it is
necessary to remark, that a species,
even as referred to the same genus,
will not alwa)^ have the same dif-
ferentia, but a different one, accord-
ing to the principle and purpose which
preside over the particular classifica-
tion. For example, a naturalist sur-
veys the various kinds of animals, and
looks out for the classification of them
most in accordance with the order in
which, for zoological purposes, he con-
siders it desirable that we should
think of them. With this view he
finds it advisable that one of his funda-
mental divisions should be into warm-
blooded and cold-blooded animals ; or
into animals which breathe with lungs
and those which breathe with gills ;
or into carnivorous and frugivorous or

graminivorous ; or into those which
walk on the flat part and those which
walk on the extremity of the foot, a
distinction on which two of Cuvier's
families are founded. In doing this,
the naturalist creates as many new
classes ; which are by no means those
to which the individual animal is fa-
miliarly and sixmtaneously referred;
nor should we ever think of assigning
to them so prominent a position in
our arrangement of the animal king-
dom, unless for a preconceived pur-
pose of scientific convenience. And
to the liberty of doing this there is
no limit. In the examples we have
given, most of the classes are real
Kinds, since each of the peculiarities
is an index to a multitude of properties
belonging to the class which it charac-
terises : but even if the case were
otherwise — if the other properties of
those classes could all be derived, by
any process known to us, from the
one peculiarity on which the class is
founded — even then, if these deriva-
tive properties were of primary im-
portance for the purposes of the na-
turalist, he would be warranted in
founding his primary divisions on
them.

If, however, practical convenience
is a sufficient warrant for making the
main demarcations in our arrange-
ment of objects run in lines not coin-
ciding with any distinction of Kind,
and so creating genera and species in
the popular sense which are not genera
or species in the rigorous sense at all ;
d foi'tiori must we be warranted,
when our genera and species are real
genera and species, in marking the
distinction between them by those of
their properties which considerations
of practical convenience most strongly
recommend. If we cut a species out
of a given genus — the species man,
for instance, out of the genus animal
— with an intention on our part that
the peculiarity by which we are to
be guided in the application of the
name man should be rationality, then
rationality is the differentia of the
species man. Suppose, however, that,

NAMES AND PROPOSITIONS.

being naturalists, we, for the purposes
of our particular study, cut out of the
genus animal the same species man,
but with an intention that the dis-
tinction between man and all other
species of animal should be, not
rationality, but the possession of "four
incisors in each jaw, tusks solitary.
and erect posture." It is evident that
the word man, when used by us as
naturalists, no longer connotes ration-
ality, but connotes the three other
properties specified ; for that which
we have expressly in view when we
impose a name, assuredly forms part
of the meaning of that name. We
may, therefore, lay it down as a maxim,
that wherever there is a Genus, and
a Species marked out from that genus
by an assignable differentia, the name
of the species must be connotative,
and must connote the differentia ;
but the connotation may be special —
not involved in the signification of the
term as ordinarily used, but given to
it when employed as a term of art or
science. The word Man in common
use connotes rationality and a certain
form, but does not connote the num-
ber or character of the teeth ; in the
Linnsean system it connotes the num-
ber of incisor and canine teeth, but
does not connote rationality nor any
particular form. The word man has,
therefore, two different meanings ;
though not commonly considered as
ambiguous, because it happens in both
cases to denote the same individual
objects. But a case is conceivable in
which the ambiguity would become
evident : we have only to imagine
that some new kind of animal were
discovered, having Linnseus s three
characteristics of humanity, but not
rational, or not of the human form.
In ordinary parlance, these animals
would not be called men ; but in
natural history they must still be
called so by those, if any there should
be, who adhere to the Linnaean clas-
sification ; and the queKstion would
arise, whether the word should con-
tinue to be used in two senses, or the
classification be given up, and the

technical sense of the term be aban*
doned along with it.

Words not otherwise connotative
may, in the mode just adverted to,
acquire a special or technical conno-
tation. Thus the word whiteness, as
we have so often remarked, connotes
nothing ; it merely denotes the attri-
bute corresponding to a certain sen-
sation : but if we are making a clas-
sification of colours, and desire to
justify, or even merely to point out,
the particular place assigned to white-
ness in our arrangement, we may
define it " the colon:.- produced by the
mixture of all the simple rays ; '* and
this fact, though by no means implied
in the meaning of the word whiteness
as ordinarily used, but only known
by subsequent scientific investigation,
is part of its meaning in the particular
essay or treatise, and becomes thi
differentia of the species.*

The differentia, therefore, of a
species may be defined to be, that
part of the connotation of the specific
name, whether ordinary or special and
technical, which distinguishes the
species in question from all other
species of the genus to which on the
particular occasion we are referring it.

§ 7. Having disposed of Genus,
Species, and Differentia, we shall not
find much difficulty in attaining a
clear conception of the distinction
between the other two predicables, as
well as between them and the first
three.

In the Aristotelian phraseology.
Genus and Differentia are of the
essence of the subject ; by which, as
we have seen, is really meant that the
properties signified by the genus and
those signified by the differentia, form
part of the connotation of the name
denoting the species. Proprium and

* If we allow a differentia to what is nut
really a species. For the distinction of
Kinds, in the sense explained by us, not
being in any way applicable to ai tributes,
it ot course follows that alt hough attributes
may be put into classes, those clashes can
be admitted to be genera or species only
by courtesy

CLASSIFICATION AND THE PREDICABLES.

85

Accidens, on the other hand, form
no part of the essence, but are predi-
cated of the species only accidentally.
Both are Accidents, in the wider
sense in which the accidents of a
thing are opposed to its essence ;
though in the doctrine of the Pre-
dicables, Accidens is used for one sort
of accident only, Proprium being
another sort. Proprium, continue the
schoolmen, is predicated accidentaUy
indeed, but necessarily ; or, as they
further explain it, signifies an attribute
which is not indeed part of the essence,
but which flows from, or is a con-
sequence of, the essence, and is,
therefore, inseparably attached to the
species ; e.g. the various properties of
a triangle, which, though no part of
its definition, must necessarily be pos-
sessed by whatever comes under that
definition. Accidens, on the contrary,
has no connection whatever with the
essence, but may come and go, and the
species still remain what it was before.
If a species could exist without its
Propria, it must be capable of existing
without that on which its Propria are
necessarily consequent, and therefore
without its essence, without that which
constitutes it a species. But an Acci-
dens, whether separable or inseparable
from the species in actual experience,
may be supposed separated, without
the necessity of supposing any other
alteration ; or at least, without sup-
posing any of the essential proper-
ties of the species to be altered, since
with them an Accidens has no connec-
tion.

A Proprium, therefore, of the species,
may be defined, any attribute which
belongs to all the individuals included
in the species, and which, though not
connoted by the specific name, (either
ordinarily if the classification we are
considering be for ordinary purposes,
or specially if it be for a special pur-
pose, ) yet follows from some attribute
which the name either ordinarily or
specially connotes.

One attribute may follow from an-
other in two ways ; and there are con-
sequently two kinds of Proprium. It

may follow as a conclusion follows pre-
mises, or it may follow as an effect
follows a cause. Thus, the attribute
of having the opposite sides equal,
which is not one of those connoted
by the word Parallelogram, neverthe-
less follows from those connoted by it,
namely, from having the opposite sides
straight lines and parallel, and the
number of sides four. The attribute,
therefore, of having the opposite sides
equal, is a Proprium of the class par-
allelogram ; and a Proprium of the
first kind, which follows from the con-
noted attributes by way of demonstra-
tion. The attribute of being capable
of understanding language is a Pro-
prium of the species man, since, with-
out being connoted by the word, it
follows from an attribute which the
word does connote, viz. from the attri-
bute of rationality. But this is a
Proprium of the second kind, which
follows by way of causation. How it
is that one property of a thing follows,
or can be inferred, from another ;
under what conditions this is possi-
ble, and what is the exact meaning of
the phrase ; are among the questions
which will occupy us in the two suc-
ceeding Books. At present it needs
only be said, that whether a Proprium
follows by demonstration or by causa-
tion, it follows necessarily ; that is to
say, its not following would be incon-
sistent with some law which we re-
gard as a part of the constitution either
of our thinking faculty or of the uni-

§ 8. Under the remaining predic-
able, Accidens, are included all attri-
butes of a thing which are neither in-
volved in the signification of the name,
(whether ordinarily or as a term of
art,) nor have, so far as we know, any
necessary connection with attributes
which are so involved. They are
commonly divided into Separable and
Inseparable Accidents. Inseparable
accidents are those which — although
we know of no connection between
them and the attributes constitutive of
the species, and although, therefore,

86

NAMES AND PROPOSITIONSL

80 far as we are aware, they might
be ah ent vA-ithout making the name
inapplicable and the species a differ-
ent species— are yet never in fact
known to be absent. A concise mode
of expressing the same meaning is,
that inseparable accidents are pro-
perties which are universal to the
species, but not necessary to it. Thus,
blackness is an attribute of a crow,
and, as far wa know, an imiversal one.
B\it if we were to discover a race of
white birds, in other respects resem-
bling crows, we should not say, These
are not crows ; we should say, These
are white crows. Crow, therefore,
does not connote blackness ; nor, from
any of the attributes which it does
connote, whether as a word in popu-
lar use or as a term of art, could
blackness be inferred. Not only, there-
fore, can we conceive a white crow,
but we know of no reason why such
an animal should not exist. Since,
however, none but black crows are
known to exist, blackness, in the pre-
sent state of our knowledge, ranks as
an accident, but an inseparable acci-
dent, of the species crow.

Separable Accidents are those which
are found, in point of fact, to be some-
times absent from the species ; which
are not only not necessary, but not
even universal. They are such as do
not belong to every individual of the
species, but only to some individuals ;
or if to all, not at all times. Thus
the colour of an European is one of
the separable accidents of the species
man, because it is not an attribute of
all human creatures. Being bom, is
also (speaking in the logical sense) a
separable accident of the species man,
because, though an attribute of all
human beings, it is so only at one
particular time. A fortiori those attri-
butes which are not constant even in
the same individual, as, to be in one
or in another place, to be hot or cold,
sitting or walking, must be ranked as
separable accidents.

CHAPTER Vin.

OF DEFINITION.

§ I . One necessary part of the theory
of Names and of Propositions remains
! to be treated of in this place : the the-
I ory of Definitions. As being the most
I important of the class of propositions
which we have characterised as purely
! verbal, they have already received
some notice in the chapter preceding
the last. But their fuller treatment
was at that time postponed, because
definition is so closely connected with
classification, that, until the nature of
the latter process is in some measure
understood, the former cannot be dis-
cussed to much purpose.

The simplest and most correct
notion of a Definition is, a proposi-
tion declaratory of the meaning of a
word ; namely, either the meaning
which it bears in common acceptation,
or that which the speaker or writer,
for the particular purposes of his dis-
course, intends to annex to it.

The definition of a word being the
proposition which enunciates its mean-
ing, words which have no meaning are
unsusceptible of definition. Proper
names, therefore, cannot be defined.
A proper name being a mere mark
put upon an individual, and of which
it is the characteristic property to
be destitute of meaning, its meaning
cannot of course be declared ; though
we may indicate by language, as we
might indicate still more conveniently
by pointing with the finger, upon
what individual that particular mark
has been, or is intended to be. put.
It is no definition of "John Thom-
son " to say he is " the son of General
Thomson ;" for the name John Thom-
son does not express this. Neither
is it any definition of "John Thom-
son " to say he is " the man now
crossing the .street." These proposi-
tions may serve to make known who
is the part cular man to whom the
name belongs, but that may be done
still more unambiguously by pointing
to him, which, however, has not been

DEFINITIOK.

8?

esteemed one of the modes of defini-
tion.

In the case of connotative names,
the meaning, as has been so often ob-
Berved, is the connotation ; and the
definition of a connotative name is
the proposition which declares its con-
notation. This might be done either
directly or indirectly. The direct
mode would be by a proposition in
this form: "Man" (or whatsoever
the word may be) " is a name connot-
ing such and such attributes," or "is
a name which, when predicated of
anything, signifies the possession of
such and such attributes by that
thing." Or thus : Man is everything
which possesses such and such attri-
butes ; Man is everything which pos-
sesses corporeity, organisation, life,
rationality, and certain peculiarities
of external form.

This form of definition is the most
precise and least equivocal of any ;
but it is not brief enough, and is be-
sides too technical for common dis-
course. The more usual mode ot de-
claring the connotation of a name is
to predicate of it another name or
names of known signification, which
connote the same aggregation of attri-
butes. This may be done either by
predicating of the name intended to
be defined another connotative name
exactly synonymous, as, "Man is a
human being," which is not commonly
accounted a definition at all ; or by
predicating two or more connotative
names, which make up among them
the whole connotation of the name to
be defined. In thia last case, again,
we may either compose our definition
of as many connotative names as there
are attributes, each attribute being
connoted by one, as, Man is a corpo-
real, organised, animated, rational
being, shaped so and so ; or we may
employ names which connote several
of the attributes at once, as, Man is
a rational animal, shaped so and so.

The definition of a name, according
to this view of it, is the sum total of
all the essential propositions which can
be framed with that name for their

subject. All propositions the truth
of which is implied in the name, all
those which we are made aware of by
merely hearing the name, are included
in the definition, if complete, and may
be evolved from it without the aid of
any other premises ; whether the de-
finition expresses them in two or three
words, or in a larger number. It is,
therefore, not without reason that
Condillac and other writers have
affirmed a definition to be an analysis.
To resolve any complex wliole into
the elements of which it is com-
! pounded, is the meaning of analysis ;
i and this we do when we replace one
I word which connotes a set of attri-
butes collectively, by two or more
which connote the same attributes
singly or in smaller groups.

§ 2. From this, however, the ques-
tion naturally arises, in what mannci
are we to define a name which coa-
notes only a single attribute : for iQ-
stance, "'white," which connotes no-
thing but whiteness ; " rational,"
which connotes nothing but the pos-
session of reason. It might seem that
the meaning of such names could only
be declared in two ways ; by a synony-
mous term, if any such can be found ;
or in the direct way already alluded
to : " White is a name connoting the
attribute whiteness." Let us see,
however, whether the analysis of the
meaning of the name, that is, the
breaking down of that meaning into
several parts, admits of being carried
farther. Without at present deciding
this queition as to the word white, it
is obvious that in the case of rational
some further explanation may be
given of its meaning than is contained
in the proposition, " Rational is that
which possesses the attribute of
reason ; " since the attribute reason
itself admits of being defined. And
here we must turn our attention to
the definitions of attributes, or rather
of the names of attributes, that is, of
abstract names.

In regard to such names of attri-
butes as are connotative, and exprees

S8

NAMES AND PROPOSITIONS.

attributes of those attributes, there is
no diJBBculty : like other eonnotative
names, they are defined by declaring
their connotation. Thus the word
(ault may be defined, " a quality pro-
ductive of evil or inconvenience."
Sometimes, again, the attribute to be
defined is not one attribute, but an
union of several : we have only, there-
fore, to put together the names of all
the attributes taken separately, and
we obtain the definition of the name
which belongs to them all taken to-
gether ; a definition which will cor-
respond exactly to that of the corre-
sponding concrete name. For, as we
define a concrete name by enumerat-
ing the attributes which it connotes,
and as the attributes connoted by a
concrete name form the entire signi-
fication of the corresponding abstract
name, the same enumeration will
serve for the definition of both. Thus,
if the definition of a human being be
this, " a being, corporeal, animated,
rational, shaped so and so," the defini-
tion of humanity will be corporeity
and animal life, combined with ration-
ality, and with such and such a shape.
When, on the other hand, the ab-
stract name does not express a com-
plication of attributes, but a single
attribute, we must remember that
every attribute is grounded on some
fact or phenomenon, from which, and
which alone, it derives its meaning.
To that fact or phenomenon, called in
a former chapter the foundation of
the attribute, we must, therefore,
have recourse for its definition. Now,
the foundation of the attribute may
be a phenomenon of any degree of
complexity consisting of many dif-
ferent parts, either co-existent or in
succession. To obtain a definition of
the attribute, we must analyse the
phenomenon into these parts. Elo-
quence, for example, is the name of
one attribute only ; but this attribute
is grounded on external effects of a
complicated nature, flowing from acts
of the person to whom we ascribe the
attribute ; and by resolving this pheno-
menon of causation into its two parts,

the cause and the effect, we obtain Sk
definition of eloquence, viz. the power
of influencing the feelings by speech
or writing.

A name, therefore, whether concrete
or abstract, admits of definition, pro-
vided we are able to analyse, that is,
to distinguish into parts, the attribute
or set of attributes which constitute
the meaning both of the concrete
name and of the corresponding ab-
stract : if a set of attributes, by enu-
merating them ; if a single attribute,
by dissecting the fact or phenomenon
(whether of perception or of internal
consciousness) which is the foundation
of the attribute. But, farther, even
when the fact is one of our simple
feelings or states of consciousness, and
therefore unsusceptible of analysis,
the names both of the object and of
the attribute still admit of definition :
or rather, would do so if all our simple
feelings had names. Whiteness may
be defined, the property or power of
exciting the sensation of white. A
white object may be defined, an
object which excites the sensation of
white. The only names which are
unsusceptible of definition, because
their meaning is unsusceptible of
analysis, are the names of the simple
feelings themselves. These are in
the same condition as proper names.
They are not indeed, like proper
names, unmeaning ; for the words
sensation of white signify, that the
sensation which I so denominate
resembles other sensations which I
remember to have had before, and to
have called by that name. But as
we have no words by which to recall
those former sensations, except the
very word which we seek to define, or
some other which, being exactly syno-
nymous with it, requires definition as
much, words cannot unfold the signi-
fication of this class of names ; and we
are obliged to make a direct appeal
to the personal experience of the
individual whom we address.

§ 3. Having stated what seems to
be the true idea of a Definition, I

DEFINITION.

89

proceed to examine some opinions of
philosophers, and some popular con-
ceptions on the subject, which conflict
more or less with that idea.

The only adequate definition of a
name is, as already remarked, one
which declares the facts, and the
whole of the facts, which the name
involves in its signification. But with
most persons the object of a definition
does not embrace so much ; they look
for nothing more, in a definition, than
a guide to the correct use of the term
— a protection against applying it in
a manner inconsistent with custom
and convention. Anjrthing, there-
fore, is to them a sufficient definition
of a term which will serve as a cor-
rect index to what the term denotes ;
though not embracing the whole, and
sometimes, perhaps, not even any
part, of what it connotes. This gives
rise to two sorts of imperfect or un-
scientific definition ; Essential but in-
complete Definitions, and Accidental
Definitions, or Descriptions. In the
former, a connotative name is defined
by a part only of its connotation ; in
the latter, by something which forms
no part of the connotation at all.

An example of the first kind of
imperfect definitions is the following :
— Man is a rational animal. It is
impossible to consider this as a com-
plete definition of the word Man,
since (as before remarked) if we ad-
hered to it we should be obliged to
call the Houyhnhnms men ; but as
there happen to be no Houyhnhnms,
this imperfect definition is sufficient
to mark out and distinguish from all
other things the objects at present
denoted by " man ; " all the beings
actually known to exist of whom the
name is predicable. Tliough the word
is defined by some only among the
attributes which it connotes, not by
all, it happens that all known objects
which possess the enumerated attri-
butes possess also those which are
omitted ; so that the field of predica-
tion which the word covers, and the
employment of it which is conform-
able to usage, are as well indicated

by the inadequate definition as by an
adequate one. Such definitions, how-
ever, are always liable to be over-
thrown by the discovery of new
objects in nature.

Definitions of this kind are what
logicians have had in view when
they laid down the rule that the
definition of a species should be per
genus et differentiam. Differentia be-
ing seldom taken to mean the whole
of the peculiarities constitutive of
the species, but some one of those
peculiarities only, a complete defini-
tion would be per genus et diffh'entias,
rather than differentiam. It would
include, with the name of the superior
genus, not merely some attribute
which distinguishes the species in-
tended to be defined from all other
species of the same genus, but aU the
attributes implied in the name of the
species, which the name of the supe-
rior genus has not already implied.
The. assertion, however, that a defini-
tion must of necessity consist of a
genus and differentiae, is not tenable.
It was early remarked by logicians,
that the summum genus in any classi-
fication, having no genus superior to
itself, could not be defined in this
manner. Yet we have seen that all
names, except those of our elementary
feelings, are susceptible of definition
in the strictest sense ; by setting forth
in words the constituent parts of the
fact or phenomenon, of which the
connotation of every word is ulti-
mately composed.

§ 4. Although the first kind of
imperfect definition, (which defines a
connotative term by a part only of
what it connotes, but a part sufficient
to mark out correctly the boundaries
of its denotation,) has been considered
by the ancients, and by logicians in
general, as a complete definition, it
has always been deemed necessary
that the attributes employed should
really form part of the connotation ;
for the rule was that the definition
must be drawn from the essence of
the class ; and this would not have

NAMES AND PROPOSITIONS.

been the case if it had been in any
degree made up of attributes not con-
noted by the name. The second kind
of imperfect definition, therefore, in
which the name of a class is defined
by any of its accidents, —that is, by
attributes which are not included in
its connotation,— has been rejected
from the rank of genuine Definition
by all logicians, and has been termed
Description.

This kind of imperfect definition,
however, takes its rise from the same
cause as the other, namely, the willing-
ness to accept as a definition anything
which, whether it expounds the mean-
ing of the name or not, enables us to
discriminate the things denoted by
the name from all other things, and
consequently to employ the term in
predication without deviating from
established usage. This purpose is
duly answered by stating any (no
matter what) of the attributes which
are common to the whole of the class,
and peculiar to it ; or any combina-
tion of attributes which happens to
be peculiar to it, though separately
each of those attributes may be com-
mon to it with some other things. It
is only necessary that the definition
(or description) thus formed should
be convertible with the name which it
professes to define ; that is, should be
exactly co-extensive with it, being
predicable of everything of which it
is predicable, and of nothing of which
it is not predicable ; though the attri-
butes specified may have no connec-
tion with those which mankind had
in view when they formed or recog-
nised the class, and gave it a name.
The following are correct definitions
of Man, according to this test : Man
is a mammiferous animal, having (by
nature) two hands (for the human
species answers to this description,
and no other animal does) : Man is
an animal who cooks his food : Man
is a featherless biped.

What would otherwise be a mere
description may be raised to the rank
of a real definition by the peculiar
purpose which the speaker or writer

has in view. As was seen in the
preceding chapter, it may, for the
ends of a particular art or science, or
for the more convenient statement of
an author's particular doctrines, be
advisable to give to some general
name, without altering its denotation,
a special connotation, different from
its ordinary one. When this is done,
a definition of the name by means of
the attributes which make up the
special connotation, though in general
a mere accidental definition or de-
scription, becomes on the particular
occasion and for the particular pur-
pose a complete and genuine defini-
tion. This actually occurs with re-
spect to one of the preceding examples,
"Man is a mammiferous animal
having two hands," which is the
scientific definition of man, considered
as one of the species in Cuvier's dis-
tribution of the animal kingdom.

In cases of this sort, though the
definition is stUl a declaration of the
meaning which in the particular in-
stance the name is appointed to con-
vey, it cannot be said that to state
the meaning of the word is the pur-
pose of the definition. The purpose
is not to expound a name, but a
classification. The special meaning
which Cuvier assigned to the word
Man, (quite foreign to its ordinary
meaning, though involving no change
in the denotation of the word,) was
incidental to a plan of arranging
animals into classes on a certain
principle, that is, according to a cer-
tain set of distinctions. And since
the definition of Man according to
the ordinary connotation of the word,
though it would have answered every
other purpose of a definition, would
not have pointed out the place which
the species ought to occupy in that
particular classification, he gave the
word a special connotation, that he
might be able to define it by the kind of
attributes on which, for reasons of scien-
tific convenience, he had resolved to
found his division of animated nature.

Scientific definitions, whether they
are definitions of scientific terms, or

DEFINITION.

91

of common terms used in a scientific
sense, are almost always of the kind
last spoken of : their main purpose is
to serve as the landmarks of scientific
classification. And since the classi-
fications in any science are continually
modified as scientific knowledge ad-
vances, the definitions in the sciences
are also constantly varying. A strik-
ing instance is afforded by the words
Acid and Alkali, especially the former.
As experimental discovery advanced,
the substances classed with acids have
been constantly multiplying, and by
a natural consequence the attributes
connoted by the word have receded
and become fewer. At first it con-
noted the attributes of combining
with an alkali to form a neutral sub-
stance (called a salt) ; being com-
pounded of a base and oxygen ;
causticity to the taste and touch ;
fluidity, &c. The true analysis of
muriatic acid into chlorine and
hydrogen caused the second property,
composition from a base and oxygen,
to be excluded from the connotation.
The same discovery fixed the atten-
tion of chemists upon hydrogen as
an important element in acids ; and
more recent discoveries having led to
the recognition of its presence in
sulphuric, nitric, and many other acids,
where its existence was not previously
suspected, there is now a tendency to
include the presence of this element
in the connotation of the word. But
carbonic acid, silica, sulphurous acid,
have no hydrogen in their composi-
tion ; that property cannot therefore
be connoted by the term, unless those
substances are no longer to be con-
sidered acids. Causticity and fluidity
have long since been excluded from
the characteristics of the class by
the inclusion of silica and many other
substances in it ; and the formation
of neutral bodies by combination with
alkalis, together with such electro-
chemical peculiarities as this is sup-
posed to imply, are now the only
differenticB which form the fixed con-
notation of the word Acid, as a term
of chemical science.

What is true of the definition of
any term of science is of course true
of the definition of a science itself ;
and accordingly, (as observed in the
Introductory Chapter of this work,)
the definition of a science must neces-
sarily be progressive and provisional
Any extension of knowledge or altera-
tion in the current opinions respecting
the subject-matter may lead to a
change more or less extensive in the
particulars included in the science ;
and its composition being thus altered,
it may Easily happen that a different
set of characteristics will be found
better adapted as differentiae for de-
fining its name.

In the same manner in which a
special or technical definition has for
its object to expound the artificial
classification out of which it grows ;
the Aristotelian logicians seem to
have imagined that it was also the
business of ordinary definition to ex-
pound the ordinary, and what they
deemed the natur^, classification of
things, namely, the division of them
into Kinds ; and to show the place
which each Kind occupies, as superior,
collateral, or subordinate, among other
Kinds. This notion would account
for the rule that all definition must
necessarily be per genus et differ en-
tiam, and would also explain why a
single differentia was deemed suflfi-
cient. But to expound, or express in
words, a distinction of Kind has
already been shewn to be an impossi-
bility : the very meaning of a Kind
is, that the properties which distin-
guish it do not grow out of one
another, and cannot therefore be set
forth in words, even by implication,
otherwise than by enumerating them
all : and all are not known, nor are
ever likely to be so. It is idle, there-
fore, to look to this as one of the
purposes of a definition : while, if it
be only required that the definition of
a Kind should indicate what kinds
include it or are included by it, any
definitions which expound the conno-
tation of the names will do this : for
the name of each class must neces-

92

NAMES AND PROPOSITIONS.

sarily connote enough of its properties
to fix the boundaries of the class. If
the definition, therefore, be a full
statement of the connotation, it is all
that a definition can be required to
be.*

§ 5. Of the two incomplete and
popular modes of definition, and in
what they differ from the complete
or philosophical mode, enough has
now been said. We shall next exa-
mine an ancient doctrine, once gene-
rally prevalent, and still by no means
exploded, which I regard as the
source of a great part of the obscurity
hanging over some of the most impor-
tant processes of the understanding

* Professor Bain, in his Logic, takes a
peculiar view of Definition. He holds (i.
71) with the present work, that "the de-
finition in its full import is the sum of all
the properties connoted by the name ; it
sxhausis the meaning of a word." But he
regards the meaning of a general name as
including, not indeed all the common pro-
perties of the class named, but all of tliem
that are ultimate properties not resolvable
into one another. " The enumeration of
tiie attributes of oxygen, of gold, of man,
should be an enumeration of the final, (so
far as can be made out,) the underivable,

{)owers or functions of each," and nothing
ess than this is a complete Definition (i.
75). An independent property, not deriv-
able from other properties, even if previ-
ously unknown, yet as soon as discovered
becomes, according to him, part of the
meaning of the term, and should be in-
cluded in the definition. " When we are
told that diamond, which we know to be
a transparent, glittering, hard, and high-
priced hubstance, is composed of carbon,
and is combustible, we must put these
additional properties on the same level as
the rest ; to us they are henceforth con-
noted by the name " (i. 73). Consequently
the propositions that diamond is composed
of carbon, and that it is combustible, are
regarded by Mr. Bain as merely verbal
propositions. He cai-ries this doctrine so
far as to say that unless mortality can be
shown to be a consequence of the ultimate
laws of animal organisation, mortality is
connoted by man, and " Man is mortal "
is a merely verbal proposition. And one
of the peculiarities (I think a disadvan-
tageous pi culiarity)of his able and valuable
treatise, is the large number of proposi-
tions requiring proof, and learnt by ex-
perience, which, in conformity with this
doctrine, he considers as not real, taut ver-
bal, propositions.

in the pursuit of truth. According
to this, the definitions of which we
have now treated are only one of two
sorts into which definitions may be
divided, viz. definitions of names, and
definitions of things. The former are
intended to explain the meaning of a
term ; the latter, the nature of a
thing ; the last being incomparably
the most important.

This opinion was held by the an-
cient philosophers, and by their fol-
lowers, with the exception of the
Nominalists ; but as the spirit of
modern metaphysics, until a recent
period, has been on the whole a No-
minalist spirit, the notion of defini-
tions of things has been to a certain
extent in abeyance, still continuing,
however, to breed confusion in logic,

The objection I have to this language is
that it confounds, or at least confuses, a
much more important distinction 'hanthat
which it draws. The only reason for divid-
ing Propositions into real and verbal, is in
order to discriminate propositions which
convey information about facts from those
which do not. A proposition which afiBrms
that an object has a given attribute, wliile
designating the object by a name which
already signifies the attribute, adds no
information to that which was already
possessed by all wiio understood the name.
But when this is said, it is implied that by
the signification of a name is meant the
signification attached to it in the common
usage of life. I cannot think we ought to
say that the meaning of a word includes
matters of fact which are unknown to
every pers^on who uses the word unless he
has learnt them by special study of a par-
ticular department of Nature; or that
because a few persons are aware of these
matters of fact, the affirmation of them is
a proposition conveying no information,
I hold that (special scientific conno; arion
apart) a name means, or connotes, only
the properties whicli it is a mark of in the
general mind ; and that in the case of any
additional properties, however uniformly
found to accompany these, it remains pos-
sible that a thing which did not possess
the properties might still be thought en-
titled to the name. Ruminant, accurding
to Mr. Bain's use of language, cot motes
cloven-hoofed, since tiie two properties are
always found tog^^ther, and no connection
has ever been discovered between them :
but ruminant does not mean cloven-hoofed ;
and were an animal to be discovered which
chews the cud, but has its feet undivided,
I venture to say that it would still be called
ruminant.

DEFINITION.

93

by its consequences indeed rather
than by itself. Yet the doctrine in
its own proper form now and then
breaks out, and has appeared (among
other places) where it was scarcely
to be expected, in a justly admired
work, Archbishop Whately's Loijic*
In a review of that work published
by me in the Westminster Review for
January 1 828, and containing some
opinions which I no longer entertain,
I find the following observations on
the question now before us ; observa-
tions with which my present view of
that question is still sufficiently in
accordance : —

* In the fuller discussion wliich Arch-
bisliop Whately has given to this subject
in his later editions, he almost ceases to
regard the definitions of names and those
of hings as, in any important sense, dis-
tinct. He seems (9th ei. p. 145) to limit
the no*^ion of a Real Definition to one which
" explains anything more of the nature of
tiie thing rhiin '^ implied in the name;"
(including under the word "implied," not
only what the name connotes, but every-
thing which can be deduced by reasoning
from the attributes connoted). Even this,
as he adds, is usually called, not a Defini-
tion, but a Description ; and (as it seems
to me) rightly so called. A Description, I
conceive, can only be ranked among De-
finitions when taken (as in the case of the
zoological definition of man) to fulfil the
true ofl&ce of a Definition, by declaring the
connotation given to a word in some special
use, as a term of science or art : which
special connotation of course would not l>e
expressed by the proper definition of the
word in its ordinary employment.

Mr. De Morgan, exactly reversing the
doctrine of Archljishop Whately, under-
stands by a Real Definition one which
contains less^ than the Nominal Definition,
provided only that what it contains i.s suf-
ficient for distinction, " By real definition
I mean such an explanation of the word,
be it the whole of the meaning or only part,
as will be sufficient to sepai-ate the things
contained under that word from all others.
Thus the following, I believe, is a complete
definition of an elephant : An animal which
naturally drinks by drawing the water into
its nose, and then spurting it into its
mouth." — Formal Logic, p. 36. Mr. De
Morgan's general proposition and his ex-
ample are at variance ; for the peculiar
mode of drinking of the elephant certainly
forms no part of the meaning of the word
elephant. It could not be said, because a
person happened to be ignorant of this
property, that he did not know what an
elephant means.

" The distinction between nominal
and real definitions, between defini-
tions of words and what are called
definitions of things, though conform-
able to the ideas of most of the Aris-
totelian logicians, cannot, as it appears
to us, be maintained. We apprehend
that no definition is ever intended to
' explain and unfold the nature of a
thing.' It is some confirmation of
our opinion that none of those writers
who have thought that there were
definitions of things have ever suc-
ceeded in discovering any criterion
by which the definition of a thing can
be distinguished from any other pro-
position relating to the thing. The
definition, they say, unfolds the nature
of the thing : but no definition can
unfold its whole nature ; and every
proposition in which any quality what-
ever is predicated of the thing un-
folds some part of its nature. The
true state of the case we take to be
this. All definitions are of names,
and of names only ; but, in some
definitions, it is clearly apparent that
nothing is intended except to explain
the meaning of the word, while in
others, besides explaining the meaning
of the word, it is intended to be im-
plied that there exists a thing corre-
sponding to the word. Whether this
be or be not implied in any given
case cannot be collected from the
mere form of the expression. *A
centaur is an animal with the upper
parts of a man and the lower parts of
a horse, ' and ' A triangle is a rectili-
neal figure with three sides,' are, in
form, expressions precisely similar ;
although in the former it is not im-
plied that any thing, conformable to
the term, really exists, while in the
latter it is ; as may be seen by sub-
stituting, in both definitions, the word
means for is. In the first expression,
*A centaur means an animal,' &c.,
the sense would remain unchanged :
in the second, 'A triangle means,'
&c., the meaning would be altered,
since it would be obviously impossible
to deduce any of the truths of geome-
try from a proposition expressive only

94

NAMES AND PROPOSITIONS.

of the manner in which we intend to
employ a particular sign.

" There are, therefore, expressions,
commonly passing for definitions,
which include in themselves more
than the mere explanation of the
meaning of a term. But it is not
correct to call an expression of this
sort a peculiar kind of detiiiition. Its
difference from the other kind con-
sists in this, that it is not a definition,
but a definition and something more.
The definition above given of a
triangle, obviously comprises not one,
but two propositions, perfectly distin-
guishable. The one is, 'There may
exist a figure, bounded by three
straight lines ; ' the other, ' And this
figure may be termed a triangle.'
The former of these propositions is
not a definition at all : the latter is a
mere nominal definition, or explana-
tion of the use and application of a
term. The first is susceptible of truth
or falsehood, and may therefore be
made the foundation of a train of
reasoning. The latter can neither be
true nor false ; the only character it
is susceptible of is that of conformity
or disconf ormity to the ordinary usage
of language."

There is a real distinction, then,
between definitions of names, and
what are erroneously called definitions
of things ; but it is. that the latter,
along with the meaning of a name,
covertly asserts a matter of fact. This
covert assertion is not a definition,
but a postulate. The definition is
a mere identical proposition, which
gives information only about the use
of language, and from which no con-
clusions affecting matters of fact can
possibly be drawn. The accompany-
ing postulate, on the other hand,
affirms a fact which may lead to con-
sequences of every degree of impor-
tance. It affirms the actual or possible
existence of Things possessing the
combination of attributes set forth in
the definition ; and this, if true, may
be foundation sufficient on which to
build a whole fabric of scientific
truth.

We have already made, and shall
often have to repeat, the remark,
that the philosophers who overthrew
Realism by no means got rid of the
consequences of Realism, but retained
long afterwards, in their own philo-
sophy, numerous propositions which
could only have a rational meaning
as part of a Realistic system. It had
been handed down from Aristotle,
and probably from earlier times, as
an obvious truth, that the science of
Geometry is deduced from definitions.
This, so long as a definition was con-
sidered to be a proposition " unfolding
the nature of the thing," did well
enough. But Hobbes followed, and
rejected utterly the notion that a de-
finition declares the nature of the
thing, or does anything but state the
meaning of a name ; yet he continued
to affirm as broadly as any of his pre-
decessors that the a.pxo-i< principia,
or original premises of mathematics,
and even of all science, are defini-
tions; producing the singular para-
dox, that systems of scientific truth,
nay, all truths whatever at which
we arrive by reasoning, are deduced
from the arbitrary conventions of
mankind concerning the signification
of words.

To save the credit of the doctrine
that definitions are the premises of
scientific knowledge, the proviso is
sometimes added, that they are so only
under a certain condition, namely,
that they be framed conformably to
the phenomena of natixre ; that is,
that they ascribe such meanings to
terms as shall suit objects actually
existing. But this is only an instance
of the attempt so often made, to
escape from the necessity of abandon-
ing old language after the ideas which
it expresses have been exchanged for
contrary ones. From the meaning of
a name (we are told) it is possible to
infer physical facts, provided the name
has corresponding to it an existing
thing. But if this proviso be neces-
sary, from which of the two is the
inference really drawn ? From the
existence of a thing having the pro-

DEFINITION.

95

p«rtie8, or from the existence of a
name meaning them ?

Take, for instance, any of the de-
finitions laid down as premises in
Euclid's Ekm»iits ; the definition,
let us say, of a circle. This, being
analysed, consists of two propositions ;
the one an assumption w.th respect to
a matter of fact, the other a genuine
definition. " A figure may exist, hav-
ing all the points in the line which
bounds it equally distant from a single
point within it : " " Any figure pos-
sessing this property is called a circle."
Let us look at one of the demonstra-
tions which are said to depend on this
definition, and observe to which of
the two propositions contained in it
the demonstration really appeals.
"About the centre A, describe the
circle B C D." Here is an assumption
that a figure, such aa the definition
expresses, may be described ; which
is no other than the postulate, or
covert assumption, involved in the so-
called definition. But whether that
figure be called a circle or not is quite
immaterial The purpose would be
as well answered in all respects except
brevity were we to say, ''Through
the point B, draw a line returning in-
to itself, of which every point shall be
at an equal distance from the point
A. " By this the definition of a circle
would be got rid of, and rendered
needless ; but not the postulate im-
plied in it ; without that the demon-
stration could not stand. The circle
being now described, let us proceed to
the consequence. '* Since B C D is a
circle, the radius B A is equal to the
radius C A." B A is equal to C A, not
because B C 1) is a circle, but because
B C D is a figure with the radii equal.
Our warrant for assuming that such a
figure about the centre A, with the
radius B A, may be made to exist, is
the postulate. Whether the admissi-
bility of these postulates rests on
intuition, or on proof, may be a matter
of dispute ; but in either case they
are the premises on which the theo-
rems depend ; and while these are
retained it would make no difference

in the certainty of geometrical truths,
though every definition in Euclid,
and every technical term therein
defin-'d, were laid aside.

It is, perhaps, superfluous to dwell
at so much length on what is so nearly
self-evident ; but when a distinction,
obvious as it may appear, has been
confounded, and by powerful intel-
lects, it is better to say too much
than too little for the purpose of ren-
dering such mistakes impossible in
future. I will, therefore, detain the
reader while I point out one of the
absurd consequences flowing from the
supposition that definitions, as such,
are the premises in any of our reason-
ings, except Huch as relate to words only.
If this opposition were true, we might
argue correctly from true premises,
and arrive at a false conclusion. We
should only have to assume as a pre-
mise the definition of a nonentity ; or
rather of a name which has no entity
corre8p<;nding to it. Let this, for
instance, be our definition :

A dragon is a serpent breathing
flame.

This proposition, considered only
as a definition, is indisputably correct.
A dragon i» a serpent breathing
flame : the word means that. The
tacit assumption, indeed, (if there
were any such understood assertion,)
of the existence of an object with
properties corresponding to the defi-
nition, would, in the present instance,
be false. Out of this definition we
may carve the premises of the follow-
ing syllogism :

A dragon is a thing which breathes
flame :

A dragon is a serpent :
From which the conclusion is,

Therefore some serpent or serpents
breathe flame : —
an unexceptional syllogism in the first
mode of the third figure, in which
both premises are true and yet the
conclusion false ; which every logician
knows to be an absurdity. The con-
clusion being false and the syllogism
correct, the premises cannot be true.
But the premises, considered as parts

96

NAMES AND PROPOSITIONS.

of a definition, are true. Therefore,
the premises considered as parts of a
definition cannot be the real ones.
The real premises must be —

A dragon is a really existing thing
which breathes flame :

A dragon is a really existing
serpent :
which implied premises being false,
the falsity of the conclusion presents
no absurdity.

If we would determine what con-
clusion follows from the same osten-
sible premises when the tacit assump-
tion of real existence is left out, let
us, according to the recommendation
in a previous page, substitute means
for is. We then have —

Dragon is a word meaning a thing
whicli breathes flame :

Dragon is a word meaning a
serpent :
From which the conclusion is,

Some word or icords which mean
a serpent, also mean a thing
which breathes flame :
where the conclusion (as well as the
premises) is true, and is the only kind
of conclusion which can ever follow
from a definition, namely, a proposi-
tion relating to the meaning of
words.

There is still another shape into
which we may transform this syl-
logism. We may suppose the middle
term to be the designation neither of
a thing nor of a name, but of an idea.
We then have —

The idea of a dragon is an idea of
a thing which breathes flame :

The idea of a dragon is an idea of
a serpent :

Therefore, there is an idea of a
serpent, which is an idea of a thing
breathing flame.

Here the conclusion is true, and
also the premises ; but the premises
are not definitions. They are pro-
positions affirming that an idea exist-
ing in the mind includes certain ideal
elements. The truth of the conclu-
sion follows from the existence of the
psychological phenomenon called the
idea of a dragon ; and therefore still

from the tacit assumption of a matter
of fact.*

When, as in this last syllogism, the
conclusion is a proposition respecting
an idea, the assumption on which it
depends may be merely that of the
existence of an idea. But when the
conclusion is a proposition concerning
a Thing, the postulate involved in the
definition which stands as the appar-
ent premise is the existence of a thing
conformable to the definition, and not
merely of an idea conformable to it.
This assumption of real existence we
always convey the impression that we
intend to make when we profess to

* In the only attempt which, so far as I
know, has been made to refute the preced-
ing argumentation, it is maintained that
in the first form of tlie syllogism,

A dragon is a thing which breathes
flame,

A dragon is a serpent,

Therefore some serpent or serpecta
breathe flame,
" there is just as much truth in the con-
clusion as there is in the premises, or,
rather no more in the latter than in the
former. If the general name serpent in-
cludes both real and imaginary serpents,
there is no falsity in the conclusion ; if
not, there is falsity in the minor premise."

Let us, then, try to set out the syllogism
on the hypothesis that the name serpent
includes imaginary serpents. We shall
find that it is now necessary to alter the
predicates : for it cann< )t be asserted that
an imaginary creature breathes flame ; in
predicating of it such a fact, we assert by
the most positive implication that it is
real and not imaginary. I'he conclusion
must run thus, "Some serpent or serpents
either do or are imagined to breathe flame."
And to prove this conclusion by the in-
stance of dragons, the premises must be,
A dragon is imagined as breattiing flame.
A dragon is a (real or imaginary) serpent :
from whicli it undoubtedly follows, that
there are serpents which are imagined to
breathe flame; but the major premise is
not a definition, nor part of a definition;
which is all that I am concerned to prove.

Let us now examine the other assertion
— that if the word serpent stands for none
but real serpents, the minor premise (a
dragon is a serpent) is false. This is exactly
what I have myself said of the premise,
considered as a stat rnent of fact : but it
is not false as part of the definition of a
dragon ; and since the premises, or one of
them, must be false, (the coiiclu.sion b-'ing
so,) the real premise cannot be the defini-
tion, which is true, but the statement of
fact which is false.

DEFINITION.

97

define any name which is already
known to be a name of really existing
objects. On this account it is, that
the assumption was not necessarily
implied in the definition of a dragon,
while there was no doubt of its being
included in the definition of a circle.

§ 6. One of the circumstances which
have contributed to keep up the notion
that demonstrative truths follow from
definitions rather than from the postu-
lates implied in those definitions, is, that
the postulates, even in those sciences
which are considered to surpass all
others in demonstrative certainty, are
not always exactly true. It is not
true that a circle exists, or can be
described, which has all its radii
exactly equal. Such accuracy is ideal
only ; it is not found in nature, still
less can it be realised by art. People
had a difficulty, therefore, in con-
ceiving that the most certain of all
conclusions could rest on premises
which, instead of being certainly true,
are certainly not true to the full ex-
tent asserted. This apparent paradox
will be examined when we come to
treat of Demonstration ; where we
shall be able to show that as much of
the postulate is true, as is required to
support as much as is true of the con-
clusion. Philosophers, however, to
whom this view had not occurred, or
whom it did not satisfy, have thought
it indispensable that there should be
found in definitions something more
certain, or at least more accurately
true, than the implied postulate of
the real existence of a corresponding
object. And this something they
flattered themselves they had found,
when they laid it down that a defini-
tion is a statement and analysis not
of the mere meaning of a word, nor
yet of the nature of a thing, but of
an idea. Thus, the proposition, "A
circle is a plane figure bounded by a
line all the points of which are at an
equal distance from a given point
within it," was considered by them,
not as an assertion that any real
circle has that property, (which would

not be exactly true,) but that we
conceive a circle as having it ; that
our abstract idea of a circle is an
idea of a figure with its radii exactly
equal.

Conformably to this it is said, that
the subject-matter of mathematics,
and of every other demonstrative
science, is not things as they really
exist, but abstractions of the mind.
A geometrical line is a line without
breadth ; but no such line exists in
nature ; it is a notion merely suggested
to the mind by its experience of nature.
The definition (it is said) is a defini-
tion of this mental line, not of any
actual line : and it is only of the
mental line, not of any line existing
in nature, that the theorems of geo-
metry are accurately true.

Allowing this doctrine respecting
the nature of demonstrative truth to
be correct (which, in a subsequent
place, I shall endeavour to prove that
it is not,) even on that supposition,
the conclusions which seem to follow
from a definition do not follow from
the definition as such, but from an
implied postulate. Even if it be true
that there is no object in nature
answering to the definition of a line,
and that the geometrical properties
of lines are not true of any lines in
nature, but only of the idea of a line ;
the definition, at all events, postulates
the real existence of such an idea : it
assumes that the mind can frame, or
rather has framed, the notion of length
without breadth, and without any
other sensible property whatever. To
me, indeed, it appears that the mind
cannot form any such notion ; it can-
not conceive length without breadth ;
it can only, in contemplating objects,
attend to their length, exclusively of
their other sensible qualities, and so
determine what properties may be
predicated of them in virtue of their
length alone. If this be true, the
postulate involved in the geometrical
definition of a line is the real exist-
ence, not of length without breadth,
but merely of length, that is, of long
objects. This is quite enough to

oS

NAMES AND PKOJi'OSlTIONS.

support all the truths of geometry,
?ince every property of a geometrical
line is really a property of all physical
objects in so far as possessing length.
But even what I hold to be the false
doctrine on the subject, leaves the
conclusion that our reasonings are
grounded on the matters of fact postu-
lated in definitions, and not on the de-
finitions themselves, entirely unaffect-
ed ; and accordingly this conclusion is
one which I have in common with Dr.
Whewell, in his Philosophy of the In-
ductive Sciences : though, on the nature
of demonstrative truth, Dr. Whewell's
opinions are greatly at variance with
mine. And here, as in many other
instances, I gladly acknowledge that
his writings are eminently serviceable
in clearing from confusion the initial
steps in the analysis of the mental
processes, even where his views re-
specting the ultimate analysis are such
as (though with unfeigned respect) I
cannot but regard as fundamentally
erroneous.

§ 7. Although, according to the
opinion here presented, Definitions
are properly of names only, and not
of things, it does not follow from this
that definitions are arbitrary. How
to define a name, may not only be an
inquiry of considerable difficulty and
intricacy, but may involve considera-
tions going deep into the nature of
the things which are denoted by the
name. Such, for instance, are the
inquiries which form the subjects of
the most important of Plato's Dia-
logues ; as, " What is rhetoric ? " the
topic of the Gorgias, or "What is
justice ? " that of the Republic. Such,
also, is the question scornfully asked
by Pilate, « What is truth ? " and the
fundamental question with speculative
moralists in all ages, "What is vir-
tue ? "

It would be a mistake to represent
these difficult and noble inquiries as
having nothing in view beyond ascer-
taining the conventional meaning of
a name. They are inquiries not so
mifch to determine what is, as what

should be, the meaning of a name ;
which, like other practical questions
of terminology, requires for its solu-
tion that we should enter, and some-
times enter very deeply, into the pro-
perties not merely of names but of
the things named.

Although the meaning of every
concrete general name resides in the
attributes which it connotes, the ob-
jects were named before the attri-
butes ; as appears from the fact that
in all languages, abstract names are
mostly compounds or other deriva-
tives of the concrete names which
correspond to them. Connotative
names, therefore, were, after proper
names, the first which were used :
and in the simpler cases, no doubt, a
distinct connotation was present to
the minds of those who first used the
name, and was distinctly intended by
them to be conveyed by it. The
first person who used the word white,
as applied to snow or to any other
object, knew, no doubt, very well what
quality he intended to predicate, and
had a perfectly distinct conception in
his mind of the attribute signified by
the name.

But where the resemblances and
differences on which our classifications
are founded are not of this palpable
and easily determinable kind ; especi-
ally where they consist not in any
one quality but in a number of
qualities, the effects of which, being
blended together, are not very easily
discriminated, and referred each to
its true source ; it often happens that
names are applied to nameable objects,
with no distinct connotation present
to the minds of those who apply them.
They are only influenced by a general
resemblance between the new object
and all or some of the old familiar
objects which they have been accus-
tomed to call by that name. This,
as we have seen, is the law which
even the mind of the philosopher must
follow, in giving names to the simple
elementary feelings of our nature;
but, where the things to be named
are complex wholes, a philosopher is

DEFINITION.

99

not content with noticing a general
resemblance ; he examines what the
resemblance consists in : and he only
gives the same name to things which
resemble one another in the same
definite particulars. The philosopher,
therefore, habitually employs his gen-
eral names with a definite connotation.
But language was not made, and can
only in some small degree be mended,
by philosophers. In the minds of
the real arbiters of language, general
names, especially where the classes
they denote cannot be brought before
the tribunal of the outward senses to
be identified and discriminated, con-
note little more than a vague gross
resemblance to the things which they
were earliest, or have been most,
accustomed to call by those names.
When, for instance, ordinary persons
predicate the words just or unjust of
any action, noble or mean of any senti-
ment, expression, or demeanour, sUites-
man or charlatan of any personage
figuring in politics, do they mean to
affirm of those various subjects any
determinate attributes, of whatever
kind ? No : they merely recognise,
as they think, some likeness, more or
less vague and loose, between these
and some other things which they
have been accustomed to denominate
or to hear denominated by those
appellations.

Language, as Sir James Mackin-
tosh used to say of governments, " is
not made, but grows." A name is
not imposed at once and by previous
purpose upon a class of objects, but is
first applied to one thing, and then
extended by a series of transitions to
another and another. By this process
(as has been remarked by several
writers, and illustrated with great
force and clearness by Dugald Ste-
wart in his Philosophical Essays) a
name not unfrequently passes by suc-
cessive links of resemblance from one
object to another, until it becomes
applied to things having nothing in
common with the first things to which
the name was given ; which, how-
ever, do not, for that reason, drop the

name ; so that it at last denotes a
confused huddle of objects, having
nothing whatever in common ; and
connotes nothing, not even a vague
and general resemblance. When a
name has fallen into this state, in
which by predicating it of any object
we assert literally nothing about the
object, it has become unfit for the
purposes either of thought or of the
communication of thought; and can
only be made serviceable by stripping
it of some part of its multifarious
denotation, and confining it to objects
possessed of some attributes in com-
mon, which it may be made to con-
note. Such are the inconveniences of
a language which " is not made, but
grows." Like the governments which
are in a similar case, it may be com-
pared to a road which is not made,
but has made itself : it requires con-
tinual mending in order to be passable.
From this it isalready evident why
the question respecting the definition
of an abstract name is often one of so
much difficulty. The question. What
is justice ? is, in other words. What
is the attribute which mankind mean
to predicate when they call an action
just ? To which the first answer is,
that having come to no precise agree-
ment on the point, they do not mean
to predicate distinctly any attribute
at all. Nevertheless, all believe that
there is some common attribute be-
longing to all the actions which they
are in the habit of calling just. The
question then must be, whether there
is any such common attribute ? and,
in the first place, whether mankind
agree sufficiently with one another as
to the particular actions which they
do or do not call just, to render the
inquiiy, what quality those actions
have in common, a possible one : if so,
whether the actions really have any
quality in common ; and if they have,
what it is. Of these three, the first
alone is an inquiry into usage and
convention ; the other two are in-
quiries into matters of fact. And if
the second question (whether the
actions form a class at all) has been

100

NAMES AND PROPOSITIONS.

answered negatively, there remains a
fourth, often more arduous than all the
rest, namely, how best to form a class
artificially, which the name may de-
note.

And here it is fitting to remark,
that the study of the spontaneous
growth of languages is of the utmost
importance to those who would logi-
cally remodel them. The classifica-
tions rudely made by established lan-
guage, when retouched, as they almost
all require to be, by the hands of the
logician, are often in themselves excel-
lently suited to his purposes. As
compared with the classifications of a
philosopher, they are like the custo-
mary law of a country, which has
grown up as it were spontaneously,
compared with laws methodised and
digested into a code : the former are
a far less perfect instrument than the
latter ; but being the result of a long,
though unscientific, course of experi-
ence, they contain a mass of materials
which may be made very usefully
available in the formation of the
systematic body of written law. In
like manner, the established grouping
of objects under a common name, even
when founded only on a gross and
general resemblance, is evidence, in
the first place, that the resemblance
is obvious, and therefore considerable ;
and, in the next place, that it is a
resemblance which has struck great
numbers of persons during a series of
years and ages. Even when a name,
by successive extensions, has come to
be applied to things among which
there does not exist this gross resem-
blance common to them all, still at
every step in its progress we shall
find such a resemblance. And these
transitions of the meaning of words
are often an index to real connections
between the things denoted by them,
which might otherwise escape the
notice of thinkers ; of those at least
who, from using a different language,
or from any difference in their habitual
associations, have fixed their attention
in preference on some other aspect of
the things. The history of philosophy

abounds in examples of such over-
sights, committed for want of perceiv-
ing the hidden link that connected to-
gether the seemingly disparate mean-
ings of some ambiguous word.*

Whenever the inquiry into the
definition of the name of any real
object consists of anything else than
a mere comparison of authorities, we
tacitly assume that a meaning must
be found for the name, compatible
with its continuing to denote, if pos-
sible all, but at any rate the greater
or the more important part, of the
things of which it is commonly pre-
dicated. The inquiry, therefore, into
the definition, is an inquiry into the
resemblances and differences among
those things : whether there be any
resemblance running through them
all ; if not, through what portion of
them such a general resemblance can
be traced : and finally, what are the
common attributes, the possession of
which gives to them all, or to that
portion of them, the character of re-
semblance which has led to their
being classed together. Wh^n these
common attributes have been ascer-
tained and specified, the name which
belongs in common to the resembling
objects acquires a distinct instead of
a vague connotation ; and by possess-

* " Few people " (I have said in another
place) "have reflected how great a know-
ledge of Things is required to enable a man
to aflSmi that any given argument turns
wholly upon words. There is, perhaps,
not one of the leading terms of philosophy
which is not used in almost innumerable
shades of meaning, to express ideas more
or less widely different from one another.
Between two of ttiese ideas a sagacious and
penetrating mind will discern, as it were
intuitively, an unobvious link of connec-
tion, upon which, though perhaps unable
to give a logical account of it, he will found
a perfectly valid argument, which his
critic, not having so keen an insight into
the Things, will mistake for a fallacy turn-
ing on the double meaning of a term. And
the greater the genius of him who thus
safely L aps over the chasm, the greater
will probably be the crowing and vainglory
of the mere logician, who, hobbling after
him, evinces his own superior wisdom by
pausing on its brink, and giving up as
desperate his proper business of bridging
it over. "

DEFINITION.

lOI

ing this distinct connotation, becomes
susceptible of definition. !

In giving a distinct connotation to
the general name, the philosopher will
endeavour to fix upon such attributes
as, while they are common to all the
things usually denoted by the name,
are also of greatest importance in
themselves ; either directly, or from
the number, the conspicuousness, or
the interesting character, of the con-
sequences to which they lead. He
will select, as far as possible, such
differentice as lead to the greatest
number of interesting propria. For
these, rather than the more obscure
and recondite qualities on which they
often depend, give that general char-
acter and aspect to a set of objects
which determine the groups into

which they naturally fall. But to
penetrate to the more hidden agree-
ment on which these obvious and
superficial agreements depend, is often
one of the most difficult of scientific
problems. As it is among the most
difficult, so it seldom fails to be
among the most important. And since
upon the result of this inquiry re-
specting the causes of the properties
of a class of things, there incidentally
depends the question what shall be
the meaning of a word, some of the
most profound and most valuable in-
vestigations which philosophy pre-
sents to us have been introduced by,
and have offered themselves under
the guise of, inquiries into the defini-
tion of a name.

BOOK 11.

OF EEASONING.

Ai(apia/jUvo}v 5c ro&rcjif Xiyuyfiep iiSri, Sid. rivwv, Kal irore, Kal ttws ylverai
Tras av\\oyL<TfJL6i' Darepov 5^ Xckt^ov irepl d7ro5et|ewj. UpSrepov ycip irepl
ffvWoyiiTfxov \€KT(iov, fj irepl dirodei^eus, 5ta t6 KadoXov /xdWou elval rdi'
crvWoytafidv. 'H fih ydp d7r65et|ts, avWoyuTfjids tis' 6 (TvWoyi(TiJL6s Si ov
Tof, dir656i^ts. Abist. Analyt. Prior. 1. i. cap. 4.

CHAPTER I.

OF INFERENCE, OR REASONING IN
GENERAL.

§1. In the preceding Book we have
been occupied not with the nature of
Proof, but with the nature of Asser-
tion : the import conveyed by a Pro-
position, whether that Proposition be
true or false ; not the means by which
to discriminate true from false Pro-
positions. The proper subject, how-
ever, of Logic is Proof. Before we
could understand what Proof is, it
was necessary to understand what
that is to which proof is applicable ;
what that is which can be a subject
of belief or disbelief, of affirmation or
denial : what, in short, the different
kinds of Propositions assert.

This preliminary inquiry we have
prosecuted to a definite result. Asser-
tion, in the first place, relates either
to the meaning of words, or to some
property of the things which words
signify. Assertions respecting the
meaning of words, among which de-

I finitions are the roost important, hold
I a place, and an indispensable one, in
' philosophy ; but as the meaning of
words is essentially arbitrary, this
class of assertions are not susceptible
of truth or falsity, nor therefore of
proof or disproof. Assertions respect-
ing Things, or what may be called
Real Propositions, in contradistinction
to verbal ones, are of various sorts.
We have analysed the import of each
sort, and have ascertained the nature
of the things they relate to, and the
nature of what they severally assert
respecting those • things. We found
that whatever be the form of the pro-
position, and whatever its nominal
subject or predicate, the real subject
of every proposition is some one or
more facts or phenomena of conscious-
ness, or some one or more of the
hidden causes or powers to which we
ascribe those facts ; and that what is
predicated or asserted, either in the
affirmative or negative, of those
phenomena or those powers, is always
either Existence, Order in Place,

104

REASONING.

Order in Time, Causation, or Resem-
blance. This, then, is the theory of
the Import of Propositions, reduced
to its ultimate elements : but there is
another and a less abstruse expression
for it, which, though stopping short
in an earlier stage of the analysis, is
sufficiently scientific for many of the
purposes for which such a general
expression is required. This expres-
sion recognises the commonly received
distinction between Subject and Attri-
bute, and gives the following as the
analysis of the meaning of proposi-
tions : — Every Proposition asserts, that
some given subject does or does not
possess some attribute ; or that some
attribute is or is not (either in all or
in some portion of the subjects in
which it is met with) conjoined with
some other attribute.

We shall now for the present take
our leave of this portion of our inquiry,
and proceed to the peculiar problem
of the Science of Logic, namely, how
the assertions, of which we have
analysed the import, are proved or
disproved ; such of them, at least, as,
not being amenable to direct con-
sciousness or intuition, are appropriate
subjects of proof.

We say of a fact or statement that it
is proved when we believe its truth by
reason of some other fact or statement
from which it is said to follow. Most
of the propositions, whether affirma-
tive or negative, universal, particular,
or singular, which we believe, are not
believed on their own evidence, but
on the ground of something previously
assented to, from which they are said
to be inferred. To infer a proposition
from a previous proposition or pro-
positions ; to give credence to it, or
claim credence for it, as a conclusion
from something else, is to reason, m
the most extensive sense of the term.
There is a narrower sense, in which
the name reasoning is confined to the
form of inference which is termed
ratiocination, and of which the syl-
logism is the general type. The
reasons for not conforming to this
restricted use of the term were stated

in an earlier stage of our inquiry, and
additional motives will be suggested
by the considerations on which we are
now about to enter.

§ 2. In proceeding to take into con-
sideration the cases in which infer-
ences can legitimately be drawn, we
shall first mention some cases in
which the inference is apparent, not
real ; and which require notice chiefly
that they may not be confounded with
cases of inference properly so called.
This occurs when the proposition
ostensibly inferred from another ap-
pears on analysis to be merely a re-
petition of the same, or part of the
same, assertion which was contained
in the first. All the cases mentioned
in books of Logic as examples of
sequipollency or equivalence of pro-
positions are of this nature. Thus,
if we were to argue. No man is incap-
able of reason, for every man is
rational ; or. All men are mortal, for
no man is exempt from death ; it
would be plain that we were not
proving the proposition, but only ap-
pealing to another mode of wording
it, which may or may not be more
readily comprehensible by the hearer,
or better adapted to suggest the real
proof, but which contains in itself no
shadow of proof.

Another case is where, from an
universal proposition, we affect to
infer another which differs from it
only in being particular : as All A is
B, therefore Some A is B : No A is
B, therefore Some A is not B. This,
too, is not to conclude one proposition
from another, but to repeat a second
time something which had been as-
serted at first ; with the difference,
that we do not here repeat the whole
of the previous assertion, but only an
indefinite part of it.

A third case is where the ante-
cedent having affirmed a predicate of
a given subject, the consequent affirms
of the same subject something already
connoted by the former predicate : as,
Socrates is a man, therefore Socrates
is a living creature ; where all that is

INFERENCE IN GENERAL.

105

connoted by living creature was aflBrm-
ed of Socrates when he was asserted
to be a man. If the propositions are
negative, we must invert their order,
thus : Socrates is not a living creature,
therefore he is not a man ; for if we
deny the less, the greater, which in-
cludes it, is already denied by impli-
cation. These, therefore, are not
really cases of inference ; and yet the
trivial examples by which, in manuals
of Logic, the rules of the Syllogism are
illustrated, are often of this ill-chosen
kind ; formal demonstrations of con-
clusions to which whoever understands
the terms used in the statement of the
data, has already, and consciously,
assented.*

The most complex case of this sort
of apparent inference is what is called
the Conversion of Propositions, which
consists in turning the predicate into
a subject, and the subject into a pre-
dicate, and framing out of the same
terms thus reversed another proposi-
tion, which must be true if the former
is true. Thus, from the particular
affirmative proposition. Some A is B,
we may infer that Some B is A. From
the universal negative. No A is B, we
may conclude that No B is A. From
the universal affirmative proposition,
All A is B, it cannot be inferred that,
All B is A ; though all water is liquid,
it is not implied that all liquid is
water ; but it is implied that some
liquid is so ; and hence the proposition,
All A is B, is legitimately convertible
into Some B is A. This process,
which converts an universal proposi-
tion into a particular, is termed con-
version per accidens. From the pro-
position, Some A is not B, we cannot
even infer that some B is not A ;
though some men are not Englishmen,
it does not follow that some English-
men are not men. The only mode

* The diiferent cases of ^quipollency,
or " Equivalent Prepositional Forms," are
set forth with some fulness in Professor
Bain's Logic. One of the commonest of
these changes of expression, that from
aflSrming a proposition to denying its nega-
tive, or vice vend, Mr. Bain designates,
very happily, by the name Obversion.

usually recognised of converting a
particular negative proposition, is in
the form. Some A is not B, therefore,
something which is not B is A ; and
this is termed conversion by contra-
position. In this case, however, the
predicate and subject are not merely
reversed, but one of them is changed.
Instead of [A] and [B], the terms of
the new proposition are [a thing which
is not BJ, and [A]. The original pro-
position, Some A is not B, is first
changed into a proposition aequipollent
with it. Some A is " a thing which is
not B ; " and the proposition, being
now no longer a particular negative,
but a particular affirmative, admits of
conversion in the first mode, or, as it
is called, simple conversion.*

In all these cases there is not really
any inference ; there is in the conclu-
sion no new truth, nothing but what
was already asserted in the premises,
and obvious to whoever apprehends
them. The fact asserted in the con-
clusion is either the very same fact, or
part of the fact, asserted in the original
proposition. This follows from our
previous analysis of the Import of
Propositions. "When we say, for ex-
ample, that some lawful sovereigns are
tyrants, what is the meaning of the
assertion ? That the attributes con-
noted by the term " lawful sovereign,"
and the attributes connoted by the
term "tyrant," sometimes coexist in
the same individual. Now this is also
precisely what we mean when we say
that some tyrants are lawful sove-
reigns ; which, therefore, is not a second
proposition inferred from the first, any
more than the English translation of
Euclid's elements is a collection of
theorems different from, and conse-
quences of, those contained in the
Greek original. Again, if we assert
that no great general is a rash man,
we mean that the attributes connoted
by " great general," and those connoted

* As Sir William Hamilton has pointed
out, " Some A is not B" may also be con-
verted in the following form : " No B is
tome A." Some men are not negroes ;
therefore. No negroes are tome men (e.g.
Europeans).

io6

EEASONING.

by " rash," never coexist in the same
subject ; which is also the exact mean-
ing which would be expressed by saying,
that no rash man is a great general.
When we say that all quadrupeds are
warm-blooded, we assert, not only that
the attributes connoted by "quad-
ruped " and those connoted by " warm-
blooded " sometimes coexist, but that
the former never exist without the
latter : now the proposition. Some
warm-blooded creatures are quadru-
peds, expresses the first half of this
meaning, dropping the latter half ;
andthereforehas been alreadyaflBrmed
in the antecedent proposition, All
quadrupeds are warm-blooded. But
that aU warm-blooded creatures are
quadrupeds, or, in other words, that
the attributes connoted by "warm-
blooded " never exist without those
connoted by "quadruped," has not
been asserted, and cannot be inferred.
In order to reassert, in an inverted
form, the whole of what was affirmed
in the proposition. All quadrupeds are
warm-blooded, we must convert it by
contraposition, thus. Nothing which
is not warm-blooded is a quadruped.
This proposition, and the one from
which it is derived, are exactly equi-
valent, and either of them may be
substituted for the other ; for, to say
that when the attributes of a quad-
ruped are present, those of a warm-
blooded creature are present, is to say
that when the latter are absent the
former are absent.

In a manual for young students, it
would be proper to dwell at greater
length on the conversion and aequi-
poUency of propositions. For though
that cannot be called reasoning or
inference which is a mere reassertion
in different words of what had been

asserted before, there is no more im-
portant intellectual habit, nor any the
cultivation of which falls more strictly
within the province of the art of logic,
than that of discerning rapidly and
surely the identity of an assertion
when disguised under diversity of
language. That im portant chapter in
logical treatises which relates to the
Opposition of Propositions, and the
excellent technical language which
logic provides for distinguishing the
different kinds or modes of opposition,
are of use chiefly for this purpose.
Such considerations as these, that con-
trary propositions may both be false,
but cannot both be true ; that sub-
contrary propositions may both be
true, but cannot both be false ; that
of two contradictory propositions one
must be true and the other false ; that
of two subaltemate propositions the
truth of the universal proves the truth
of the particular, and the falsity of the
particular proves the falsity of the
universal, but not vice versd ; * are apt
to appear, at first sight, very technical
and mysterious, but when explained,
seem almost too obvious to require so
formal a statement, since the same
amount of explanation which is neces-
sary to makethe principles intelligible,
would enable the truths which they
convey to be apprehended in any par-
ticular case which can occur. In this
respect, however, these axioms of logic
are on a level with those of mathe-
matics. That things which are equal
to the same thing are equal to one
another, is as obvious in any particular
case as it is in the general statement ;
and if no such general maxim had ever
been laid down, the demonstrations
in Euclid would never have halted for
any difficulty in stepping across the

lom:iSnotB}-^--*rarie8.
simeiSnotB}--tradictories.

also contradictories.

„„, No AisB
^^°- Some A is not B

Borne A is B

J- respectively subaltemate.

INFERENCE IN GENERAL.

107

gap which this axiom at present serves
to bridge over. Yet no one has ever
censured writers on geometry for
placing a list of these elementary
generalisations at the head of their
treatises, as a first exercise to the
learner of the faculty which will be
required in him at every step, that of
apprehending a general truth. And
the student of logic, in the discussion
even of such truths as we have cited
above, acquires habits of circumspect
interpretation of words, and of exactly
measuring the length and breadth of
his assertions, which are among the
most indispensable conditions of ariy
considerable mental attainment, and
which it is one of the primary objects
of logical discipline to cultivate.

§ 3. Having noticed, in order to ex-
clude from the province of Reasoning
or Inference properly so called, the
cases in which the progression from
one truth to another is only apparent,
the logical consequent being a mere
repetition of the logical antecedent ;
we now pass to those which are cases
of inference in the proper acceptation
of the term, those in which we set out
from known truths, to arrive at others
really distinct from them.

Reasoning, in the extended sense in
which I use the term, and in which it
is synonymous with Inference, is popu-
larly said to be of two kinds : reason-
ing from particulars to generals, and
reasoning from generals to particulars ;
the former being called Induction, the
latter Ratiocination or Syllogism. It
will presently be shown that there is
a third species of reasoning, which falls
underneitherof these descriptions, and
which, nevertheless, is not only valid,
butis thefoundation of both theothers.

It is necessary to observe, that the
expressions, reasoning from particulars
to generals, and reasoning from gene-
rals to particulars, are recommended
by brevity rather than by precision,
and do not adequately mark, without
the aid of a commentary, the distinc-
tion between Induction (in the sense
now adverted to) and Ratiocination.

The meaning intended by these ex-
pressions is, that Induction is inferring
a proposition from propositions less
general than itself, and Ratiocination
is inferring a proposition from proposi-
tions eqvxdly or m,ore general. When,
from the observation of a number of
individual instances, we ascend to a
general proposition, or when, by com-
bining a number of general proposi-
tions, we conclude from them another
proposition still more general, the pro-
cess, which is substantially the same
in both instances, is called Induction.
When from a general proposition, not
alone (for from a single proposition
nothing can be concluded which is not
involved in the terms), but by combin-
ing it with other propositions, we infer
a proposition of the same degree of
generality with itself, or a less general
proposition, or a proposition merely
individual, the process is Ratiocina-
tion. Wlien, in short, the conclusion
is more general than the largest of the
premises, the argument is commonly
called Induction ; when less general,
or equally general, it is Ratiocination.

As all experience begins with indi-
vidual cases, and proceeds from them
to generals, it might seem most con-
formable to the natural order of thought
that Induction should be treated of
before we touch upon Ratiocination.
It will, however, be advantageous, in
a science which aims at tracing our
acquired knowledge to its sources,
that the inquirer should commence
with the latter rather than with the
earlier stages of the process of con-
structing our knowledge ; and should
tracederivative truths backward to the
truths from which they are deduced,
and on which they depend for their
evidence, before attempting to point
out the original spring from which both
ultimately take their rise. The ad-
vantages of this order of proceeding
in the present instance will manifest
themselves as we advance, in a man-
ner superseding the necessity of any
further justification or explanation.

Of Induction, therefore, we shall
say no more at present, than that it

io8

REASONING.

at least is, without doubt, a process
of real inference. The conclusion in
an induction embraces more than is
contained in the premises. The prin-
ciple or law collected from particular
instances, the general proposition in
which we embody the result of our
experience, covers a much larger ex-
tent of ground than the individual
experiments which form its basis, A
principle ascertained by experience is
more than a mere summing up of
what has been specifically observed
in the individual cases which have
been examined ; it is a generalisation
grounded on those cases, and expres-
sive of our belief that what we there
found true is true in an indefinite
number of cases which we have not
examined, and are never likely to
examine. The nature and grounds
of this inference, and the conditions
necessary to make it legitimate, will
be the subject of discussion in the
Third Book : but that such inference
really takes place is not susceptible of
question. In every induction we pro-
ceed from truths which we knew to
truths which we did not know ; from
facts certified by observation to facts
which we have not observed, and even
to facts not capable of being now ob-
served ; future facts, for example ;
but which we do not hesitate to be-
lieve on the sole evidence of the in-
duction itself.

Induction, then, is a real process of
Reasoning or Inference. Whether,
and in what sense, as much can be
said of the Syllogism, remains to be
determined by the examination into
which we are about to enter.

CHAPTER II.

OP EATIOCINATION, OR SYLLOGISM.

§ I. The analysis of the Syllogism
has been so accurately and fully per-
formed in the common manuals of
Logic, that in the present work, which
is not designed as a manual, it is
sufficient to recapitulate, memories

causd, the leading results of that
analysis, as a foundation for the re-
marks to be afterwards made on the
functions of the Syllogism, and the
place which it holds in science.

To a legitimate syllogism it is
essential that there should be three,
and no more than three, propositions,
namely, the conclusion, or proposition
to be proved, and two other proposi-
tions which together prove it, and
which are called the premises. It is
essential that there should be three,
and no more than three, terms,
namely, the subject and predicate of
the conclusion, and another called the
middle term, which must be found in
both premises, since it is by means of
it that the other two terms are to be
connected together. The predicate of
the conclusion is called the major
term of the syllogism ; the subject of
the conclusion is called the minor
term. As there can be but three
terms, the major and minor terms
must each be found in one, and only
one of the premises, together with
the middle term which is in them
both. The premise which contains the
middle term and the m a jor term is called
the major premise ; that which con-
tains the middle term and the minor
term is called the minor premise.

Syllogisms are divided by some
logicians into three figures, by others
into four, according to the position of
the middle term, which may either be
the subject in both premises, the pre-
dicate in both, or the subject in one
and the predicate in the other. The
most common case is that in which
the middle term is the subject of the
major premise and the predicate of
the minor. This is reckoned as the
first figure. When the middle term
is the predicate in both premises, the
syllogism belongs to the second figure ;
when it is the subject in both, to the
third. In the fourth figure the mid-
dle term is the subject of the minor
premise and the predicate of the
major. Those writers who reckon no
more than three figures include this
case in the first.

RATIOCINATION, OR SYLLOGISM.

109

Each figure is divided into moods,
according to what are called the
quantity and qualiti/ of the proposi-
tions, that is, according as they are
universal or particular, affirmative or
negati ve. The following are examples

of all the legitimate moods, that is
all those in which the conclusion cor-
rectly follows from the premises. A
is the minor term, C the major, B the
middle term.

First Figure.
All B is C No B is C All B is 0

All A is B All A is B Some A is B
therefore therefore therefore

All A is 0 No A is C Some A is C

Second Figure.
No C is B All C is B No C is B
All A is B No A is B Some A is B
therefore therefore therefore

No A is C No A is C Some A is not C

No B is C

Some A is B

therefore
Some A is not C

AUG is B
Some A is not B

therefore
Some A is not C

Third Figure.

AUBisC NoBisC Some B is C All B is C Some Bis not C No B is C

All Bis A All Bis A All B is A Some B is A All B is A Some B is A

therefore therefore therefore therefore therefore therefore

Some A is C Some A is not C Some A is C Some A is C Some A is not C Some A is not C

Fourth Figure.

AH C is B All C is B Some C is B No C is B No C is B

All B is A No B is A All B is A All B is A Some B is A
therefore therefore therefore therefore therefore

Some A is C Some A is not C Some A is C Some A ia not C Some A is not C

In these exemplars, or blank forms
for making syllogisms, no place is
assigned to singular propositions ; not,
of course, because such propositions
are not used in ratiocination, but be-
cause, their predicate being affirmed
or denied of the whole of the subject,
they are ranked, for the purposes of
the syllogism, with universal proposi-
tions. Thus, these two syllogisms —

All men are mortal, All men are mortal,

All kings are men, Socrates is a man,

therefore therefore

All kings are mortal, Socrates is mortal,

are arguments precisely similar, and
are both ranked in the first mood of
the first figure.*

* Professor Bain denies the claim of
Singular Propositions to be classed, for the
purposes of ratiocination, with Universal ;
thnugh they come within the designation
which he himself proposes as an equivalent
for Universal, that of Total. He would
even, to use his own expression, banish
them entirely from the syllogism. He
takes as an example,

The reasons why syllogisms in any
of the above forms are legitimate, that
is, why, if the premises are true, the
conclusion must inevitably be so, and
why this is not the case in any other
possible mood, (that is, in any other
combination of universal and parti-
cular, affirmative and negative pro-
positions, ) any person taking interest
in these inquiries may be presumed to
have either learned from the common
school-books of the syllogistic logic, or
to be capable of discovering for him-
self. The reader may, however, be
referred for every needful explanation
to Archbishop Whately's Elements of
Logic, where he will find stated with

Socrates is wise,
Socrates is poor, therefore
Some poor men are wise,
or more properly, (as he observes.) "one
poor man is wise." "Now, if wise, poor,
and a man, are attributes belonging to 1 he
meaning of the word Socrates, there is
then no march of rea.«oning at all. We
have given in Soqrates, inter alia,, the facta

no

REASONING.

philosophical precision, and explained
with remarkable perspicuity, the whole
of the common doctrine of the syllo-
gism.

All valid ratiocination, all reason-
ing by which, from general proposi-
tions previously admitted, other pro-
positions equally or less general are
inferred, may be exhibited in some
of the above forms. The whole of
Eticlid, for example, might be thrown
without difficulty into a series of syl-
logisms, regular in mood and figure.

Though a syllogism framed accord-
ing to any of these formulae is a valid
argument, all correct ratiocination
admits of being stated in syllogisms

wise, poor, and a man, and we merely re-
peat the concurrence which is selected
from the whole aggregate of properties
making up the whole, Socrates. The case
is one under the head * Greater and Less
Connotation' in Equivalent Propositional
Forms, or Immediate Inference.

" But the example in this form does not
do j ustice to 1 1 1 e syllogism of singulars. We
must suppose both propositions to be real,
the predicates being in no way involved m
the subject. Thus

Socrates was the master of Plato,

Socrates fought at Delium,

The master of Plato fought at Delium.

" It may fairly be doubted whetlier the
transitions, in this instance, are anything
more than equivalent forms. For the pro-
position ' Socrates was the master of Plato
and fought at Delium,' compounded out of
the two premises, is obviously nothing
more than a grammatical abbieviation.
No one can say that there is here any
change of meaning, or anything beyond a
verbal modification of the original form.
Tne next step is, 'The master of Plato
fouglit at Delium,' which is the previous
statement cut down by the omission of
Socrates. It contents itself with reproduc-
ing a part of the meaning, or saying less
than had been previously said. The full
equivalent of the affirmation is, 'The master
of Plato fought at Delium, Jind the master
of Plato was Socrates : ' ttie new form omits
til e last piece of information, and gives only
the first. Now, we never consider that we
have made a real inference, a step in
advance, when we repeat less than we are
entitled to Sfiy, or drop from a complex
statement some portion not desiied at the
moment. Such an operation keeps strictly
within the domain of equivalence, or Im-
mediut'^ Inference. In no way therefote,
can a syllogism with two singular premises
bs viewed as a genuine tyliogistic or de-
ductive inference" (Logic, i. 159).

The first argument, aa will hav«> been

of the first figure alone. The rules
for throwing an argument in any of
the other figures into the first figure
are called rules for the reduction of
syllogisms. It is done by the conver-
sion of one or other, or both, of the
premises. Thus an argument in the
first mood of the second figure, as —

No C is B

All A is B

therefore

No A is 0,
may be reduced as follows. The pro-
position, No C is B, being an universal
negative, admits of simple conversion,
and may be changed into No B is C,
which, as we showed, is the very same

seen, rests upon the supposition that the
name Socrates has a meaning ; that man,
wise, and poor, are parts of this meaning ;
and that by predicating them of Socrates
we convey no information ; a view of the
sitrnification of names which, for reasons
already given,* I cannot admit, and which,
as applied to the class of names which
Socrates belongs to, is at war with Mr.
Bain's own definition of a Proper Name
(i. 148), "a single meaningless mark or
designation appropriuted to the tldng."
Such names, Mr. Bain proceeded to say,
do not necessarily indicate even human
beings: much less tlien does the name
Socrates include tlie meaning of wise or
poor. Otherwise it would follow that if
Socrates had grown rich, or had lost his
mental faculties by illness, he would no
longer have been called Socrates.

The second part of Mr Bain's argument,
in which he contends that even when the
premises convey real information, the con-
clusion is merely the premises with a part
left out, is applicable, if at all, as much to
universal propositions as to singular. In
every syllogism the conclusion contains
less than is asserted in the two premises
taken together. Suppose the syllogism
to be

All bees are intelligent,
All bees are insects, therefore
Some insects are intelligent :
one might use the same liberty taken by
Mr. Bain, of joining together the two pre-
mises a.s if they were one—" All bees are
insects and intelligent" — and might say
that in omitting the middle term bees we
make no real inference, but merely repro-
duce part of what iiad been previously
said. Mr. Bain's is really an objection to
the syllogism itself, or at all events to the
third figure : it has no special applicability
to singular propositions.

• Note to 5 4 of the chapter on Definition,
tupra, p. 92,

RATIOCINATION, OR SYLLOGISM.

Ill

assertion in other words — the same
fact differently expressed. Thistrans-
formation having been effected, the
argument assumes the following
form ; —

No B is C

All A is B

therefore

No A is C,

which is a good syllogism in the
second mood of the first figure. Again,
an argument in the first mood of the
third figxire must resemble the follow-
ing :—

All B is C

All B is A

therefore

Some A is C,

where the minor premise, All B is A,
conformably to what was laid down
in the last chapter respecting universal
affirmatives, does not admit of simple
conversion, but may be converted per
accidens, thus, Some A is B ; which,
though it does not express the whole
of what is asserted in the proposition
All B is A, expresses, as was formerly
shown, part of it, and must therefore
be true if the whole is true. We have
then, as the result of the reduction,
the following syllogism in the third
mood of the first figure : —

All B is C
Some A is B,
from which it obviously follows that
Some A is C.

In the same manner, or in a manner
on which after these examples it is
not necessary to enlarge, every mood
of the second, third, and fourth figures
may be reduced to some one of the
four moods of the first In other
words, every conclusion which can be
proved in any of the last three figures,
may be proved in the first figure from
the same premises, with a slight altera-
tion in the mere manner of expressing
them. Every valid ratiocination,
therefore, may be stated in the first
figure, that is, in one of the following
fonoa:

Every B is C

All A ). ^

Some A i ^ ^'

therefor©

All A ) . ^
IS C.

isB.

No B is C

AHA

Some A

therefore
No A is
Some A is not

C.

Some A

Or if more significant 83ntnbols are
preferred : —

To prove an affirmative, the argu-
ment must admit of being stated in
this form :

All animals are mortal ;
All men )

Some men > are animals ;
Socrates )

therefore
All men )
Some men > are mortal.
Socrates )

To prove a negative, the argument
must be capable of being expressed
in this form : —

No one who is capable of self-control

is necessarily vicious ;
All negroes ) , , . ,.

Some negroes i *''® ^^P*^^« «f ««1^-
Mr. A's negro S control;

therefore
No negroes are )

Some negroes are not ( necessarily
Mr. A's negro is not ) ^'^'®"^-

Though all ratiocination admits of
being thrown into one or the other of
these forms, and sometimes gains con-
siderably by the transformation, both
in clearness and in the obviousness of
its consequence : there are, no doubt,
cases in which the argument falls
more naturally into one of the other
three figures, and in which its con-
clusiveness is more apparent at the
first glance in those figures, than when
reduced to the first. Thus, if the
proposition were that pagans may be
virtuous, and the evidence to prove
it were the example of Aristides ; a
syllogism in the third figure,

Aristides was virtuous,
Aristides was a pagan,

therefore
Some pagan w«^s virtuous,

112

BEASONING.

would be a more natural mode of
stating the argument, and would carry
conviction more instantly home, than
the same ratiocination strained into
the first figure, thus—

Aristides was virtuous,
Some pagan was Aristides,

therefore
Some pagan was virtuous.
A German philosopher, Lambert,
whose Neues Organon (published in
the year 1764) contains among other
things one of the most elaborate and
complete expositions which had ever
been made of the syllogistic doctrine,
has expressly examined what sort of
arguments fall most naturally and
suitably into each of the four figures ;
and his investigation is characterised
by great ingenuity and clearness of
thought.* The argument, however,
is one and the same, in whichever
figure it is expressed ; since, as we
have already seen, the premises of a
syllogism in the second, third, or fourth
figure, and those of the syllogism in
the first figure to which it may be re-
duced, are the same premises in every-
thing except language, or, at least, as
much of them as contributes to the
proof of the conclusion is the same.
We are therefore at liberty, in confor-
mity with the general opinion of logi-
cians, to consider the two elementary
forms of the first figure as the universal
types of all correct ratiocination ; the
one, when the conclusion to be proved

* His conclusions are, " The first figure
is suited to the discovery or proof of the
properties of the thing ; the second to the
discovery or proof of the distinctions be-
tween things ; the third to the discovery
or proof of instances and exceptions ; the
fourth to the discovery, or exclusion, of
the different species of a genus." The re-
ference of syllogismsin the last three figures
to the dictum de omni et nullo is, in Lam-
bert's opinion, strained and unnatural : to
each of the three belongs, according to
him, a separate axiom, co-ordinate and of
equal authority with that dictum, and to
which he gives the names of dictum de
diverso for the second figure, dictum de
exemplo for the third and dictut^ de reci-
proco for the fourth. See part i. or Dianoio-
logie, chap. iv. § 229 et seq. Mr. Bailey,
(Theory of Reasoning, 2d ed. pp. 70-74)
takes a similar view of the subject.

is affirmative, the other, when it is
negative ; even though certain argu-
ments may have a tendency to clothe
themselves in the form of the second,
third, and fourth figures ; which, how-
ever, cannot possibly happen with the
only class of arguments which are of
first-rate scientific importance, those
in which the conclusion is an universal
affirmative, such conclusions being
susceptible of proof in the first figure
alone.*

* Since this chapter was written, two
treatises have appeared (or rather a treatise
and a fragment of a treatise) which aim
at a further improvement in the theory of
the forms of ratiocination : Mr. De Mor-
gan's " Formal Logic ; or, the Calculus of
Inference, Necessary and Probable ; " and
the "New Analytic of Logical Forms,"
attached as an Appendix to Sir William
Hamilton's Discussions on Philonophy, and
at greater length, to his posthumous Lec-
tures on Logic.

In Mr. De Morgan's volume— abounding,
in its more popular parts, with valuable
observations felicitously expressed — the
principal feature of originality is an at-
tempt to bring within strict technical
rules the cases in which a conclusion can
be drawn froiw premises of a form usually
classed as particular. Mr. De Morgan ob-
serves, very justly, that from the premises
Most 13s are Cs, most Bs are As, it may be
concluded with certainty that some As are
Cs, since two portions of the class B, each
of them comprising more than half, must
necessarily in part consist of the same in-
dividuals. Following out this line of
thought, it is equally evident that if we
knew exactly what proportion the " most "
in each of the premises bear to the entire
class B, we could increase in a corresponding
degree the definiteness of the conclusion.
Thus if 60 per cent, of B are included in C,
and 70 per cent, in A , 30 per cent, at least
must be common to both ; in other words,
the number of As which are Cs, and of Cs
which are As, must beat least equal to 30
per cent, of the class B. Proceeding on
this conception of " numerically definite
propositions," and extending it to such
forms as these : — "45 Xs (or more) are each
of them one of 70 Ys," or •' 45 Xs (or more)
are no one of them to be found among 70
Ys," and examining what inferences admit
of being: drawn from the various combina-
tions which may be made of premises of
this desci-iption, Mr. De Morgan establishes
universal formulae for such inferences ;
creating for that purpose not only a new
technical language, but a formidable array
of symbols analogous to those of algebra.

Since it is undeniable that inferences,
in tb© cases examined by Mr. De Morgan,

RATIOCINATION, OR SYLLOGISM.

"3

§ 2. On examining, then, these two
general formulae, we find that in both
of them, one premise, the major, is an
universal proposition ; and according
as this is affirmative or negative, the
conclusion is so too. All ratiocina-

can legitimately be drawn, and that the or-
dinary theory takes no account of them,
I will not say that it was not worth while
to >-how in detail how these also could be
reduced to forinulae as rigorous as those of
Aristotle. What Mr De Morgan has done
was worth doing once (perhaps more than
once, as a school exercise) ; but I question
if its results are worth studying and mas-
tering for any practical purpose. The prac-
tical use of technical forms of reasoning is
to bar out fallacies ; but the lallacie 5 which
require: to be guarded against in ratiocina-
tion properly so called, arise from the in-
cautious use of the common forms of lan-
guage ; and the logician must track the
fiUlacy into thar. territory, instead of wait-
ing for it on a territory of his own. While
he remains among propositions which have
acquired the numerical {)recision of the
Calculus of Probabilities, the enemy is left
in possession of tue only ground on which
he can be formidable. And since the pro-
positions (short of universal) on which a
thinker lias to depend, either for purposes
of speculation or of practice, do not, except
in a few peculiar cases, admit of any nume-
rical j)recision, common reasoning cannot
be translated into Mr. De Morgan's forms,
which therefore Ciinnot serve any purpose
as a test of it.

Sir William Hamilton's theory of the
" quantification of the predicate " may be
described as follows :—

"Logically" (I quote his words) "we
ought to take into account the quantity,
always vmderstood in thought, but usually,
for manifest reasons, elided in its expres-
sion, not only of the subject, but also of
the predicate of a judgment." All A is B,
is equivalent to all A is some B. No A is
B, to No A is any B. Some A is B, is tanta-
mount to Some A is some B. Some A is
not B, to Some A is not any B. As in these
forms of assertion the predicate is exactly
co-extensive with the subject, they all ad-
mit of simple conversion ; and by this we
obtain two additional forms— Some B is all
A and no B is some A. We may also make
the assertion All A is all B, which will be
true if the classes A and B are exactly co-
extensive. The last three forms, though
conveying real asst rtions, have no place in
the ordinary classification of Propositions.
All propositions, then, being supposed to
be translated into this language, and writ-
ten each in that one of the preceding forms
which answers to its signification, there
emerges a new set of syllogistic rules, mate-
rially different from the common ones. A
general view of tbp uointa of difference

tion, therefore, starts from a general
proposition, principle, or assumption :
a proposition in which a predicate is
affirmed or denied of an entire class ;
that is, in which some attribute, or
the negation of some attribute, is

may be given in the words of Sir W.
Hamilton {Discussions, ad ed. p. 651) : —

"The revocation of tiie two terms of a
Proposition to their true relation ; a pro-
position being always an equation of its
subject and its predicate.

"The consequent reduction of the Con-
version of Prop sitions from three species
to one — that of Simple Conversion.

"The reduction of all the General Laws of
Categorical Syllogisms to a single Canon.

"The evolution from that one canon of
all the Species and varieties of Syllogisms.

" The abrogation of all the Special Laws
of Syllogism.

"A demonstration of the exclusive pos-
sibility of Three Syllogistic Figures ; and
(on new grounds) the scientific and final
abolition of the Fourth.

"A manifestation tiiat Figure is an un-
essential variation in syllogistic form ; and
the consequent absurdity of Reducing the
syllogisms of the other figures to tlie first.

"An enouncement of one Organic Prin-
ciple for each Figure.

" A determination of the true number of
the Legitimate Moods ; with

" Their amplification in number (thirty-
six);

" Their numerical equality under all the
figures ; and

"Their relative equivalence, or virtual
identity, tiiroughoiit every schematic dif-
ference.

"That, in the second and third figures,
the extremes holdint? both the same rela-
tion to the middle term, there is not, as in
the first, an opposition and subordination
between a term major and a term minor,
mutually containing and contained, in the
counter wholes of Extension and Compre-
hension.

"Consequently, in the second and third
figures, there is no determinate major and
minor premise, and there are two indiffe-
rent conclusions ; whereas in the first the
premises are determinate, and there is a
single proximate conclusion."

This doctrine, like tiiatof Mr. De Morgan
previously noticed, is a real addition to the
syllogistic theory ; and has moreover this
advantage over Mr. De Morgan's " numeri-
cally definite syllogism," that the forms it
supplies are really available as a test of the
correctne.ss of ratiocination ; since proposi-
tions in the common form may always have
their predicates quantified, and so be made
amenable to Sir W. Hamilton's rules. Con-
sidered however as a contribution to the
Science of Logic, that is, to the analysis of
the mental processes concerned in reason-
B

"4

REASONING.

asserted of an indefinite number of
objects distinguished by a common
characteristic, and designated in con-
sequence by a common name.

The other premise is always afiBrma-
tive, and asserts that something ( which
may be either an individual, a class,
or part of a class) belongs to, or is
included in, the class respecting which
something was aflfirmed or denied in
the major premise. It follows that
the attribute affirmed or denied of
the entire class may (if that affirma-
tion or denial was correct) be affirmed
or denied of the object or objects
alleged to be included in the class :
and this is precisely the assertion
made in the conclusion.

Whether or not the foregoing is an
adequate account of the constituent
parts of the syllogism will be presently
considered ; but as far as it goes it is
a true account. It has accordingly
been generalised, and erected into a
logical maxim, on which all ratiocina-
tion is said to be founded, insomuch
that to reason and to apply the maxim
are supposed to be one and the same
thing. The maxim is, That whatever
can be affirmed (or denied) of a class,
may be affirmed (or denied) of every-
thing included in the class. This
axiom, supposed to be the basis of
the syllogistic theory, is termed
by logicians ths dictum de omni et
nullo.

This maxim, however, when con-
sidered as a principle of reasoning,
appears suited to a system of meta-
physics once indeed generally received,
but which for the last two centuries

ing, the new doctrine appears to me, I
confess, not merely superfluous but erron-
eous ; since tiie form in which it clothes
propositions does not, like the ordiuary
form, express wliat is in tiie mind of the
speaker when he enunciates the proposi-
tion. I cannot think Sir William Hamilton
right in maintaining that the quantity of
the predicate is "always understood in
tliovigiit." It is implied, but is not present
to the mind of the person who asserts the
prop sition. The quantification of the pre-
dicate, instead of being a mans of bring-
ing out more clearly the meaning of tlie
proposition, actually leads the mind out
iA th« proposition tnto another order of

has been considered as finally aban-
doned, though there have not been
wanting in our own day attempts at
its revival. So long as what ar«
termed Universals were regarded as
a peculiar kind of substances, having
an objective existence distinct from
the individual objects classed under
them, the dictum de omni conveyed
an important meaning, because it ex-
pressed the intercommunity of nature,
which it was necessary on that theory
that we should suppose to exist be-
tween those general substances and
the particular substances which were
subordinated to them. That every-
thing predicable of the universal was
predicable of the various individuals
contained under it, was then no
identical proposition, but a statement
of what was conceived as a funda-
mental law of the universe. The
assertion that the entire nature and
properties of the substantia secunda
formed part of the nature and pro-
perties of each of the individual sub-
stances called by the same name —
that the properties of Man, for
example, were properties of all men —
was a proposition of real significance
when man did not mean all men, but
something inherent in men, and vastly
superior to them in dignity. Now,
however, when it is kno^vn that a
class, an universal, a genus or species,
is not an entity per se, but neither
more nor less than the individual sub-
stances themselves which are placed
in the class, and that there is nothing
real in the matter except those objects,
a common name given to them, and

ideas. For when we say, All men are mor-
tal, we simply mean to affirm the attribute
mortality of all men ; without thinking at
all of the clasx mortal in the concrete, or
troubling ourselves about whether it con-
tains any other beings or not It is only
for some artificial purpose that we overlook
at the proposition in the aspect in which
the predicate also is thought of as a class-
name, either including the suV)ject only,
or the subject and something moie. (See
above, p. 60.)

For a fuller discussion of this subject,
see the twenty-second chapter of a work
already referred to, ' ' An Examination of
Sir William Hamilton's Philosophy."

RATIOCINATION. OR SYLLOGISM.

"5

common attributes indicated by the
name ; what, I should be glad to know,
do we learn by being told, that what-
ever can be affirmed of a class may
be affirmed of every object contained
in the class ? The class is nothing
but the objects contained in it : and
the dictum de omni merely amounts
to the identical proposition, that
whatever is true of certain objects is
true of each of those objects. If all
ratiocination were no more than the
application of this maxim to particular
cases, the syllogism would indeed be,
what it has so often been declared to
be, solemn trifling. The dictum de
omni is on a par with another truth,
which in its time was also reckoned
of great importance, "Whatever is,
is." To give any real meaning to the
dictum de omni, we must consider it
not as an axiom, but as a definiticm ;
we must look upon it as intended to
explain, in a circuitous and para-
phrastic manner, the meaning of the
word class.

An error which seemed finally re-
futed and dislodged from thought,
often needs only put on a new suit of
phrases, to be welcomed back to its
old quarters, and allowed to repose
unquestioned for another cycle of ages.
Modern philosophers have not been
sparing in their contempt for the
scholastic dogma that genera and
species are a peculiar kind of sub-
stances, which general substances
being the only permanent things,
while the individual substances com-
prehended under them are in a per-
petual flux, knowledge, which neces-
sarily imports stability, can only have
relation to those general substances or
universals, and not to the facts or
particulars included under them.
Yet, though nominally rejected, this
very doctrine, whether disguised under
the Abstract Ideas of Locke, whose
speculations, however, it has less
vitiated than those of perhaps any
other writer who has been infected
with it,) under the ultra-nominalism
of Hobbes and Condillac, or the onto-
logy of the later German schools, has

never ceased to poison philosophy.
Once accustomed to consider scientific
investigation as essentially consisting
in the study of universals. men did
not drop this habit of thought when
they ceased to regard universals as
possessing an independent existence :
and even those who went the length
of considering them as mere names,
could not free themselves from the
notion that the investigation of truth
consisted entirely or partly in some
kind of conjuration or juggle with
those names. When a philosopher
adopted fully the Nominalist view of
the signification of general language,
retaining along with it the dictum de
omni as the foundation of all reason-
ing, two such premises fairl}- put to-
gether were likely, if he was a consis-
tent thinker, to land him in rather
startling conclusions. Accordingly it
has been seriously held, by writers
of deserved celebrity, that the process
of arriving at new truths by reasoning
consists in the mere substitution of
one set of arbitrary signs for another ;
a doctrine which they suppose to de-
rive irresistible confirmation from the
example of algebra. Jf there were
any process in sorcery or necromancy
more preternatural than this, I should
be much surprised. The culminating
point of this philosophy is the noted
aphorism of Condillac, that a science
is nothing, or scarcely anything, but
une langue bienfaite; in other words
that the one sufficient rule for dis-
covering the nature and properties of
objects is to name them properly : as
if the reverse were not the truth, that
it is impossible to name them properly
except in propo; tion as we are already
acquainted with their nature and pro-
perties. Can it be necessary to say,
that none, not even the most trivial
knowledge with respect to Things,
ever was or could be originally got at
by any conceivable manipulation of
mere names, as such ; and that what
can be learned from names, is only
what somebody who used the names
knew before ? Philo>ophical analysis
confirms the indication of common

1x6

EEASONING.

sense, that the function of names is |
but that of enabling us to remember
and communicate our thoughts. That
they also strengthen, even to an incal-
culable extent, the power of thought
itself, is most true : but they do this
by no intrinsic and peculiar virtue ;
they do it by the power inherent in
an artificial memory, an instrument
of which few have adequately con-
sidered the immense potency. As an
artificial memory, language truly is,
what it has so often been called, an
instrument of thought ; but it is one
thing to be the instrument, and
another to be the exclusive subject
upon which the instrument is exercised.
We think, indeed, to a considerable
extent by means of names, but what we
think of are the things called by those
names ; and there cannot be a greater
error than to imagine that thought
can be carried on with nothing in our
mind but names, or that we can make
the names think for us.

§ 3. Those who considered the dic-
tum de omni as the foundation of the
syllogism, looked upon arguments in a
manner corresponding to the errone-
ous view which Hobbes took of pro-
positions. Because there are some
propositions which are merely verbal,
Hobbes, in order apparently that his
definition might be rigorously uni-
versal, defined a proposition as if no
propositions declared anything except
the meaning of words. If Hobbes
was right ; if no further account than
this could be given of the import of
propositions, no theory could be given
but the commonly received one of the
combination of propositions in a syl-
logism. If the minor premise asserted
nothing more than that something
belongs to a class, and if the major
premise asserted nothing of that class
except that it is included in another
class, the conclusion would only be
that what was included in the lower
class is included in the higher, and
the result, therefore, nothing except
that the classification is consistent
with itself. But we have seen that

it is no sufficient account of the mean-
ing of a proposition to say that it
refers something to, or excludes some-
thing from, a class. Every proposition
which conveys real information asserts
a matter of fact, dependent on the laws
of nature, and not on classification.
It asserts that a given object does or
does not possess a given attribute ;
or it asserts that two attributes, or
sets of attributes, do or do not (con-
stantly or occasionally) co-exist. Since
such is the purport of all propositions
which convey any real knowledge, and
since ratiocination is a mode of acquir-
ing real knowledge, any theory of ratio-
cination which does not recognise this
import of propositions, cannot, we may
be sure, be the true one.

Applying this view of propositions
to the two wemises of a syllogism,
we obtain th^^ollowing results. The
major premiseTwhich, as already re-
marked, is always universal, asserts
that all things which have a certain
attribute (or attributes) have or have
not along with it a certain other
attribute (or attributes). The minor
premise asserts that the thing or set
of things which are the subject of
that premise have the first-mentioned
attribute ; and the conclusion is, that
they have (or that they have not)
the second. Thus in our former
example,

All men are mortal,

Socrates is a man,
therefore

Socrates is mortal,
the subject and predicate of the major
premise are connotative terms, denot-
ing objects and connoting attributes.
The assertion in the major premise is,
that along with one of the two sets of
attributes, we always find the other ;
that the attributes connoted by "man "
never exist unless conjoined with the
attribute called mortality. The asser-
tion in the minor premise is that the
individual named Socrates possesses
the former attributes ; and it is con-
cluded that he possesses also the
attribute mortality. Or if both the
premises are general propositions, as —

RATIOCINATION, OR SYLLOGISM.

117

All men are mortal,
All kings are men,

therefore
All kings are mortal,
the minor premise asserts that the
attributes denoted by kingship only
exist in conjunction with those signi-
fied by the word " man." The major
asserts as before, that the last-men-
tioned attributes are never found
without the attribute of mortality.
The conclusion is, that wherever the
attributes of kingship are found, that
of mortality is found also.

If the major premise were negative,
as. No men are omnipotent, it would
assert, not that the attributes con-
noted by " man " never exist without,
but that they never exist with, those
connoted by "omnipotent : " from
which, together with the minor pre-
mise, it is concluded that the same
incompatibility exists between the
attribute omnipotence and those con-
stituting a king. In a similar man-
ner we might analyse any other ex-
ample of the syllogism.

If we generalise this process, and
look out for the principle or law in-
volved in every such inference, and
presupposed in every syllogism, the
propositions of which are anything
more than merely verbal ; we find,
not the unmeaning dictum de omni et
nidlo, but a fundamental principle, or
rather two principles, strikingly re-
sembling the axioms of mathematics.
The first, which is the principle of
affirmative syllogism, is, that things
which co-exist with the same thing,
co-exist with one another : or (still
more precisely) a thing which co-
exists with another thing, which other
co-exists with a third thing, also co-
exists with that third thing. The
second is the principle of negative
syllogisms, and is to this effect : that
a thing which co-exists with another
thing, with which other a third thing
does not co-exist, is not co-existent
with that third thing. These axioms
manifestly relate to facts, and not
to conventions ; and one or other of
them is the ground of the legitimacy

of every argument in which facts and
not conventions are the matter treated
of.*

§ 4. It remains to translate this
exposition of the syllogism from the

* Mr. Herbert Spencer (Principles of Psy-
chology, pp. 125-7) though his tlieory of the
s> llogism coincides with all that i> essen-
tial of mine, thinks it a logical fallacy to
present the two axioms in the text as the
regulating principles of syllogism. He
charges me with falling into the error,
pointed oiit by Archbishop Whately and
myself, of confounding exact likeness with
literal identity; and maintains tliat we
ought not to say that Socrates possesses
the savie attributes which are connoted by
the word Man, but only that he possesses
attributes exactly like them : according to
which phraseology, Socrates and the attri-
bute mortality are not two things co-exist-
ing with the same thing, as the axiom
asserts, but two things co-existing with
two different things.

The question between Mr. Spencer and
me is merely one ot language ; for neither
of U8(if I understand Mr. Spencer's opinions
rightly) believes an attrihuie to be a real
thing, possessed of objective existence ; we
believe it to be a particular mode of nam-
ing our sensations, or our expectations of
sensation, when looked at in their relation
to an external object which excites them.
The question raised by Mr. Spencer does
not, therefore, concern the properties of
any really existing thing, but the compara-
tive appropriateness, for philosophical pur-
poses, of two different njodes of using a
name. Considered in this point of view,
the phraseology I have employed, which is
that commonly used by philosophers, seems
to me to be the best. Mr. Spencer is of
opinion that because Socrates and Alcibi-
ades are not the same man, the attribute
which constitutes them men should not be
called the same attribute ; that because the
humanity of one man and that of another
express themselves to our senses not by
the same individual sensations, but by sen-
sations exactly alike, humanity ought to
be regarded as a different attribute in every
different man. But on this showing, the
humanity even of any one man should be
considered as different attributes now and
half-an-hour hence ; for the sensations by
whicii it will then manifest it-elf to my
organs will not be a continuation of my
present sensations but a repetition of them ;
fresh sensations, not identical with, but
only exactly like the present. If every
gt-neral conception, instead ot being "the
One in the Many," were considered to be
as many different conceptions as there are
things to which it is applicable, there
would be no such tiling as general lan-
guage. A name would have no general

ii8

REASONING.

one into the other of the two lan-
guages in which we formerly re-
marked * that all propositions, and of
course therefore all combinations of
propositions, might be expressed. We
observed that a proposition might be
considered in two different lights ;

meaning if man connoted one thing when
predicated of John, and another though
closely resembling thing wnen predicated
of William. Accordingly a recent pamphlet
asserts the impossibility of general know-
ledge on this precise ground

The meaning of any general name is some
outward or inward phenomenon, consist-
ing, in the last resort, of feelings ; and
these feelings, if their continuity is for an
instant broken, are no longer the same
feelings, in the sense of individual identity
What, then, is the common something
which gives a meaning to the general
name ? Mr. Spencer can only say. it is the
similarity of the feelings : and I rejom,
the attribute is precisely that similarity.
The names of attributes are in their idti-
mate analysis names for the resemblances
of our sensations (or other feelings). Every
general name, whether abstractor concrete,
denotes or connotes one or more of those
resemblances. It will not. probably, be
denied, that if a hundred -ensations are un-
distinguishably alike, their resemblance
ought to be spoken of as one resemblance,
and not a hundred resemblances which
merely resemble one another. The tlnnga
compared are many, but the something
common to all of them must be conceived
as one, just as the name is conceived a8
one, though coiresponding to numerically
different sensations ot sound each time it
is pronounced. The general term man
does not connote the sensations derived
once fron^ one man, wnich, once gone, can
no more occur again than the same flash
of ligiirning. It counotes tlie general type
of the sensations derived from all men,
and I he power (always thought of as one)
of producing sensations of that type. And
the axiom mitjht be tiius worded : Two
types of sensation, each of which co-exists
with a third type, co-exist with another ;
or, Two poicers, each of wnich co-exists with
a third power, co-exist with one another.

Mr. Spencer has misunderstood me in
another particular. He supposes that the
co-existence spoken of in the axiom, of two
things wirh the same third tiling, means
Bimultaneousness in time. 'I'he co-exis-
tence me int is that of being jointly attri-
butes of the same subject. The attribute
of beins: born without teeth, and the attri-
bute of having thirty-two teeth in mature
age, are in tiiis sense co-existent, both being
attributes of man, though ex vi termini
never of the same man at the same time.

* Supra, p. 75. .

as a portion of our knowledge of
nature, or as a memorandum for our
guidance. Under the former, or
speculative aspect, an affirmative
general proposition is an i<ssertion of
a speculative truth, viz. that whatever
has a certain attribute has a certain
other attribute. Under the other
aspect, it is to be regarded not as a
part of our knowledge, but as an aid
for our practical exigencies, by en-
abling us, when we see or learn that
an object possesses one of the two
attributes, to infer that it possesses
the other ; thus employing the first
attribute as a mark or evidence of the
second. Thus regarded, every s^'llo-
gism comes within the following gen-
eral formula : —

Attribute A is a mark of attribute B,
The given object has the mark A,

therefore
The given object has the attribute B.
Referred to this type, the argu-
ments which we have lately cited as
specimens of the syllogism will ex-
press themselves in the following
manner : —
The attributes of man are a mark of

the attribute mortality,
Socrates has the attributes of man,

therefore
Socrates has the attribute mortality.

And again,
The attributes of man are a mark of

the attribute mortality.
The attributes of a king are a mark of
the attributes of man,
therefore
The attributes of a king are a mark of
the attribute mortality.
And, lastly.
The attributes of man are a mark of
the absence of the attribute omni-
potence.
The attributes of a king are a mark of
the attributes of man,
therefore
The attributes of a king are a mark
of the absence of the attribute
signified by the word omnipotent
(or, are evidence of the absence of
that attribute).
To correspond with this alteration

I^tTNCnONS AND VALtTE OF THE SYLLOGISM. ii^

in the form of the syllogisms, the
axioms on which the syllogistic process
is founded must undergo a correspond-
ing transformation. In this altered
phraseology, both these axioms may
be brought under one general expres-
sion, namely, that whatever has any
mark, has that which it is a mark of.
Or, when the minor premise as well as
the major is universal, we may state
it thus : Whatever is a mark of any
mark, is a mark of that which this
last is a mark of. To trace the
identity of these axioms with those
previously laid down may be left to
the intelligent reader. We shall find,
as we proceed, the great convenience
of the phraseology into which we have
last thrown them, and which is better
adapted than any I am ac(|uainted
with to express with precision and
force what is aimed at, and actually
accomplished, in every case of the
ascertainment of a truth by ratiocina-
tion.*

♦Professor Bikin (Logic, i. 157) considers
the axiom (or rather axioms) here proposed
as a sub>titure for the dictum de omni to
possess certain advaiitages, but to be " un-
■workable as a basis of tiie sylloijisin. The
fatal defect consists in this, that it is ill-
adapted to brinu' out the difference between
total and partial coincidence of terms, the
observation of which is tlie essential pre-
caution in 63'llogisiiig correctly. If all the
termo wero co-extensive, the axiom would
flow on admirably; A carries B. all Band
none but B ; T. carries C in the Fame man-
ner; at once A carries C^ without limitation
or reserve. But in point of fact, we know
that while A carries B, otuer things carry
B also ; whence a process of limitation I's
required, in transfeiring A lO C through B.
A (in common with other things) carries
B ; B (in common witli other thinjifs) carries
C; whence A(in common with other things)
carries C. Tlie axiom provides no means
of making this limitation ; if we were to
fo low A lierally, we should be led to sup-
pose A and (J co-extensive : for such is the
only obvious meaning of ' the attribute A
coincides with the attribute C"

It is certainly possible th;it a careless
learner here and there may suppose that if
A c-.rries B, it follows that B carries A.
But if anyone isso incautious as to commit
this mistake, the very earliest lesson in the
logic of infer nee, tlie Conversion of Pro-
positions, will coiTectit. The first of the
two formsin which I have stated the axiom
is in some de^jree open to Mr. Bain's criti-

CHAPTER IIL

OF THE FUNCTIONS AND LOGICAL
VALUE OF THE SYLLOGISM.

§ I. We have shown what is the
real nature of the truths with which
the Syllogism is conversant, in contra-
distinction to the more superficial
manner in which their import is con-

cism : when B is said to co-exist with A,
(it must be by h lapsus calami that Mr.
Bain uses the word coincide,) it is possible,
in tlie absence of warning, to suppose the
meaning to bo that tiie two things are only
found totrei her. But tins misinterpretation
is excluded by the other, orpiactcal, form
of the maxim ; Nota notce est nota rei
ipxius. No one would be in any danger of
inferring that because a is a mark or 6, 6
can never exist without a; that because
being in a confirmed consumption is a mark
of being about to die, 1,0 one ciieswho is
not in a consumption ; that because being
coal is a mark of having come out of the
earth, nothing can come out of the earth
except coal. Ordinary knowledge of Eng-
lish seems a sufficient p otection against
these mistakes, since inspeaking of a mark
of anything we are never understood as
implying reciprocity.

A more fundamental objection isptated
j by Mr. Bain in a subsequent passage (p.
j 158). "The axiom does not accommodate
j itself to the tvpeof Deductive Reasoning as
! contrasted with Induction — the application ^
' of a general principle to a special case.
Anything that fads to make prouiinent
this circumstance is not adapted as a
foundation for the syllogism. " But though
it may be proper to limit tlie term Deduc-
tion to the application of a general prin-
ciple to a special case, it has never been
held that Ratiocination or Svllogism is
subject to the same limitation ; and tlie
adoption of it would excludea^^r atamouut
of valid and conclusive syllogistic reason-
ing. Moreover, if the dictum deomni makes
prominent the fact of tlie application of a
general principle to a particular case, the
axiom I propose makes prominenttiie con-
dition which alone makes that apphcaiiou
a real inference.

I conclude, therefore, that both forms
have their value, and their place in Logic.
The dictum de omni should be retained as
the fundamental axiom of the logic of mere
consistency, often ca led Formal Logic ; nor
have I ever quarrelled with the use of it in
that character, nor proposed to banish it
from treatises on Formal Losric. But tti«
other is the proper axiom for the logic of
the pursuit of truth by w;ty of Deduction ;
and the recoL'nition of it can alone show
how It is possib e that deductive reasoniuc
can be a road to truth.

t20

HEASONlNa.

ceived in the common theory ; and
what are the fundamental axioms on
which its probative force or conclusive-
ness depends. We have now to in-
quire whether the syllogistic process,
that of reasoning from generals to
particulars, is, or is not, a process of
inference ; a process from the known
to the unknown : a means of coming
to a knowledge of something which
we did not know before.

Logicians have been remarkably
unanimous in their mode of answering
this question. It is universally allow-
ed that a syllogism is vicious if there
be anything more in the conclusion
than was assumed in the premises.
But this is, in fact, to say that nothing
ever was, orcanbe, proved by syllogism
which was not known, or assumed to
be known, before. Is ratiocination,
then, not a process of inference ? And
is the syllogism, to which the word
reasoning has so often been represent-
ed to be exclusively appropriate, not
really entitled to be called reasoning
at all ? This seems an inevitable con-
sequence of the doctrine, admitted by
all writers on the subject, that a syl-
logism can prove no more than is
involved in the premises. Yet the
acknowledgment so explicitly made,
has not prevented one set of writers
from continuing to represent the syl-
logism as the correct analysis of what
the mind actually performs in discover-
ing and proving the larger half of the
truths, whether of science or of daily
life, which we believe ; while those
who have avoided this inconsistency,
and followed out the general theorem
respecting the logical value of the syl-
logism to its legitimate corollary, have
been led to impute uselessness and
frivolity to the syllogistic theory itself,
on the ground of the petitio principii
which they allege to be inherent in
every syllogism. As I believe both
these opinions to be fundamentally
erroneous, I must request the atten-
tion of the reader to certain considera-
tions, without which any just appre-
ciation of the true character of the
syllogism, and the functions it per-

forms in philosophy, appears to me
impossible ; but which seem to have
been either overlooked, or insuffi-
ciently adverted to, both by the de-
fenders of the syllogistic theory and
by its assailants.

§ 2. It must be granted that m
every syllogism, considered as an
argument to prove the conclusion,
there is a petitio principii. When we
say,

All men are mortal,

Socrates is a man,
therefore

Socrates is mortal ;
it is unanswerably urged by the adver-
saries of the syllogistic theory, that
the proposition, Socrates is mortal,
is presupposed in the more general
assumption. All men are mortal : that
we cannot be assured of the mortality
of all men, unless we are already cer-
tain of the mortality of every indi-
vidual man : that if it be still doubt-
ful whether Socrates, or any other
individual we choose to name, be
mortal or not, the same degree of
uncertainty must hang over the asser-
tion, All men are mortal : that the
general principle, instead of being
given as evidence of the particular
case cannot itself be taken for true
without exception, until every shadow
of doubt which could affect any case
comprised with it, is dispelled by evid-
ence aliunde ; and then what remains
for the syllogism to prove ? That, in
short, no reasoning from generals to
particulars can, as such, prove any-
thing, since from a general principle
we cannot infer any particulars, but
those which the principle itself assumes
as known.

This doctrine appears to me irre-
fragable ; and if logicians, though
unable to dispute it, have usually
exhibited a strong disposition to ex-
plain it away, this was not because
they could discover any flaw in the
argument itself, but because the con-
trary opinion seemed to rest on argu-
ments equally indisputable. In the
syllogism last referred to, for example,

FUNCTIONS AND VALtTE OF THE SYLLOGISM, 121

or in any of those which we previously
constructed, is it not evident that the
conclusion may, to the person to whom
the syllogism is presented, be actually
and bond fide a new truth ? Is it not
matter of daily experience that truths
previously unthought of, facts which
have not been, and cannot be, directly
observed, are arrived at by way of
general reasoning ? We believe that
the Duke of Wellington is mortal.
We do not know this by direct observa-
tion, so long as he is not yet dead.
If we were asked how, this being the
case, we know the Duke to be mortal,
we should probably answer, Because
all men are so. Here, therefore, we
arrive at the knowledge of a truth not
(as yet) susceptible of observation, by
a reasoning which admits of being
exhibited in the following syllogism: —
All men are mortal,

The Duke of Wellington is a man,
therefore

The Duke of Wellington is mortal.
And since a large portion of our
knowledge is thus acquired, logicians j
have persisted in representing the
syllogism as a process of inference or
proof, though none of them has cleared
up the difficulty which arises from the
inconsistency between that assertion
and the principle that if there be
anything in the conclusion which was
not already asserted in the premises,
the argument is vicious. For it is
impossible to attach any serious scien-
tific value to such a mere salvo as the
distinction drawn between being in-
volved hy implication in the premises,
and being directly asserted in them.
When Archbishop Whately says* that
the object of reasoning is " merely to
expand and unfold the assertions
wrapt up, as it were, and implied in
those with which we set out, and to
bring a person to perceive and acknow-
ledge the full force of that which he
has admitted." he does not, I think,
meet the real difficulty requiring to
be explained, namely, how it happens
that a science, like geometry, can be

* Logic, p. 239 (gth ed.)

all " wrapt up " in a few definitions
and axioms. Nor does this defence
of the syllogism differ much from
what its assailants urge against it as
an accusation, when they charge it
with being of no use except to those
who seek to press the consequences of
an admission into which a person has
been entrapped without having con-
sidered and understood its full force.
When you admitted the major pre-
mise, you asserted the conclusion ;
but, says Archbit>hop Whately, you
asserted it by implication merely :
this, however, can here only mean
that you asserted it unconsciously ;
that you did not know you were
asserting it ; but, if so, the difficulty
revives in this shape — Ought you not
to have known ? Were you warranted
in asserting the general proposition
without having satisfied yourself of
the truth of everything which it fairly
includes ? And if not, is not the
syllogistic art primd facie what its
assailants affirm it to be, a contrivance
for catching you in a trap, and hold-
ing you fast in it ? *

§ 3. From this difficulty there ap-
pears to be but one issue. The pro-
position that the Duke of Wellington
is mortal, is evidently an inference ;

* It is hardly necessary to say, that I
am not contending for any such absurdity
as that we actually " ought to iiave known "
and considered the case of every individual
man, past, present, and future, before
affirming that all men are mortal : although
this interpretation has been, strangely
enough, put upon the preceding obsei-va-
tions. There is no difference between me
and Archbisliop Whately, or any other
defender of the syllogism, on the practical
part of the matter ; I am only pointing out
an inconsistency in the logical theory of
it, as conceived by almost all writers. I
do not say that a person who affirmed,
before the Duke of Wellington was born,
that all men are mortal, kneie that the
Duke of Wellington was moi-tal ; but I do
say that he asserted it : and I ask for an
explanation of the apparent logical fallacy
of adducing in proof of the Duke of Wel-
lington's mortality a general statement
which presupposes it. Finding no suf-
ficient resolution of this difficulty in any
of the writers on Logic, I have attempted
to supply one.

td2

feJEASONlNa.

it is got at as a conclusion from some-
thing else ; but do we, in reality, con-
clude it from the proposition, All men
are mortal ? I answer, No.

The error committed is, T conceive,
that of overlooking the distinction
between two parts of the process of
philosophising, the inferring part, and
the registering part, and ascribing to
the latter the functions of the former.
The mistake is that of referring a
person to his own notes for the origin
of his knowledge. If a person is asked
a question, and is at the moment un-
able to answer it, he may refresh his
memory by turning to a memorandum
which he carries about with him. But
if he were asked, how the fact came
to his knowledge, he would scarcely
answer, because it was set down in his
notebook : unless the book was writ-
ten, like the Koran, with a quill from
the wing of the angel Gabriel.

Assuming that the proposition, The
Duke of Wellington is mortal, is im-
mediately an inference from the pro-
position. All men are mortal ; whence
do we derive our knowledge of that
general truth ? Of course from obser-
vation. Now, all which man can ob-
serve are individual cases. From
these all general truths must be drawn,
and into these they may be again
resolved ; for a general truth is but
an aggregate of particular truths ; a
comprehensive expression, by which
an indefinite number of individual
facts are affirmed or denied at once.
But a general proposition is not merely
a compendious form for recording and
preserving in the memory a number
of particular facts, all of which have
been observed. Generalisation is not
a process of mere naming, it is also a
process of inference. From instances
which we have observed, we feel war-
ranted in concluding, that what we
found true in those instances, holds
in all similar ones, past, present, and
future, however numerous they may
be. We then, by that valuable con-
trivance of language which enables
us to speak of many as if they were
one, record all that we have observed,

together with all that we infer from
our observations, in one concise ex-
pression ; and have thus only one
proposition, instead of an endless
number, to remember or to communi-
cate. The results of many observa-
tions and inferences, and instructions
for making innumerable inferences in
unforeseen cases, are compressed into
one short sentence.

When, therefore, we conclude from
the death of John and Thomas, and
every other person we ever heard of
in whose case the experiment had
been fairly tried, that the Duke of
Wellington is mortal like the rest,
we may, indeed, pass through the
generalisation. All men are mortal, as
an intermediate stage ; but it is not
in the latter half of the process, the
descent from all men to the Duke of
Wellington, that the inference re-
sides. The inference is finished when
we have asserted that all men are
mortal. What remains to be per-
formed afterwards is merely decipher-
ing our own notes.

Archbishop Whately has contended
that syllogising, or reasoning from
generals to particulars, is not, agree-
ably to the vulgar idea, a peculiar
mode of reasoning, but the philo-
sophical analysis of the mode in which
all men reason, and must do so if they
reason at all. With the deference
due to so high an authority, I cannot
help thinking that the vulgar notion
is, in this case, the more correct. If,
from our experience of John, Thomas,
&c., who once were living, but are
now dead, we are entitled to conclude
that all human beings are mortal, we
might surely without any logical in-
consequence have concluded at once
from those instances that the Duke
of Wellington is mortal. The mor-
tality of John, Thomas, and others
is, after all, the whole evidence we
have for the mortality of the Duke of
Wellington. Not one iota is added
to the proof by interpolating a gen-
eral proposition. Since the indivi-
dual cases are all the evidence we
! can possess, evidence which no logical

FtJNCTIONS AKD VALtJE OF THE SYLLOGISM.

123

form into which we choose to throw
it can make greater than it is : and
since that evidence is either sufficient
in itself, or, if insufficient for the one
purpose, cannot be sufiicient for the
other ; I am unable to see why we
should be forbidden to take the short-
est cut from these sufficient premises
to the conclusion, and constrained to
travel the " high priori road," by the
arbitrary fiat of logicians. I cannot
perceive why it should be impossible
to journey from one place to another
unless we " march up a hill, and then
march down again." It may be the
safest road, and there may be a rest-
ing-place at the top of the hill,
affording a commanding view of the
surrounding country ; but for the
mere purpose of arriving at our
journey's end, our taking that road is
perfectly optional ; it is a question of
time, trouble, and danger.

Not only may we reas«m from par-
ticulars to particulars without passing
through generals, but we perpetually
do so reason. All our earliest infer-
ences are of this nature. From the
first dawn of intelligence we draw in-
ferences, but years elapse before we
learn the use of general language.
The child who, having burnt his
fingers, avoids to thrust them again
into the fire, has reasoned or inferred,
though he has never thought of the
general maxim. Fire burns. He
knows from memory that he has been
burnt, and on this evidence believes,
when he sees a candle, that if he puts
his finger into the flame of it, he will
be burnt again. He believes this in
every case which happens to arise ;
but without looking, in each instance,
beyond the present case. He is not
generalising ; he is inferring a par-
ticular from particulars. In the same
way, also, brutes reason. There is
no ground for attributing to any of
the lower animals the use of signs of
such a nature as to render general
propositions possible. But those ani-
mals profit by experience, and avoid
what they have found to cause them
pain, in the same manner, though not

always with the same skill, as a human
creature. Not only the burnt child,
but the burnt dog, dreads the fire.

I believe that, in point of fact, when
drawing inferences from our personal
experience, and not from maxims
handed down to us by books or tra-
dition, we much oftener conclude from
particulars to particulars directly,
than through the intermediate agency
of any general proposition. We are
constantly reasoning from ourselves
to other people, or from one person to
another, without giving ourselves the
trouble to erect our observations into
general maxims of human or external
nature. "When we conclude that some
person will, on some given occasion,
feel or act so and so, we sometimes
judge from an enlarged consideration
of the manner in which human beings
in general, or persons of some particu-
lar character, are accustomed to feel
and act ; but much oftener from
merely recollecting the feelings and
conduct of the same person in some
previous instance, or from considering
how we should feel or act ourselves.
It is not only the village matron, whQ
when called to a consultation upon
the case of a neighbour's child, pro-
nounces on the evil and its remedy
simply on the recollection and autho-
rity of what she accounts the similar
case of her Lucy. We all, where we
have no definite maxims to steer by,
guide ourselves in the same way ; and
if we have an extensive experience,
and retain its impressions strongly,
we may acquire in this manner a very
considerable power of accurate judg-
ment, which we may be utterly incap-
able of justifying or of communicating
to others. Among the higher order
of practical intellects there have been
many of whom it was remarked how
admirably they suited their means to
their ends, without being able to give
any sufficient reasons for what they
did ; and applied, or seemed to apply,
recondite principles which they were
wholly unable to state. This is a
natural consequence of having a mind
stored with appropriate particulars,

124

REASONING.

and having been long accustomed to
reason at once from these to fresh
particulars, without practising the
habit of stating to oneself or to others
the corresponding general propositions.
An old warrior, on a rapid glance at
the outlines of the ground, is able at
once to give the necessary orders for
a skilful arrangement of his troops ;
though if he has received little theo-
retical instruction, and has seldom
been called upon to answer to other
people for his conduct, he may never
have had in his mind a single general
theorem respecting the relation be-
tween ground and array. But his
experience of encampments, in cir-
cumstances more or less similar, has
left a number of vivid, unexpressed,
ungeneralised analogies in his mind,
the most appropriate of which, in-
stantly suggesting itself, determines
him to a judicious arrangement.

The skill of an uneducated person
in the use of weapons or of tools is
of a precisely similar nature. The
savage who executes unerringly the
exact throw which brings down his
game, or his enemy, in the manner
most suited to his purpose, under the
operation of all the conditions neces-
sarily involved, the weight and form
of the weapon, the direction and dis-
tance of the object, the action of the
wind, &c., owes this power to a long
series of previous experiments, the
results of which he certainly never
framed into any verbal theorems or
rules. The same thing may generally
be said of any other extraordinary
manual dexterity. Not long ago a
Scotch manufacturer procured from
England, at a high rate of wages, a
working dyer, famous for producing
very fine colours, with the view of
teaching to his other workmen the
same skill. The workman came ; but
his mode of proportioning the ingredi-
ents, in which lay the secret of the
effects he produced, was by taking
them up in handfuls, while the com-
mon method was to weigh them. The
manufacturer sought to make him
turn his handling system into an equi-

valent weighing system, that the
general principle of his peculiar mode
of proceeding might be ascertained.
This, however, the man found himself
quite unable to do, and therefore could
impart his skill to nobody. He had,
from the individual cases of his own
experience, established a connection
in his mind between fine effects of
colour, and tactual perceptions in
handling his dyeing materials ; and
from these perceptions he could, in
any particular case, infer the means
to be employed, and the effects which
would be produced, but could not put
others in possession of the grounds on
which he proceeded, from having
never generalised them in his own
mind, or expressed them in language.
Almost every one knows Lord
Mansfield's advice to a man of practi-
cal good sense, who, being appointed
governor of a colony, had to preside
in its court of justice, without pre-
vious judicial practice or legal educa-
tion. The advice was to give his
decision boldly, for it would probably
be right ; but never to venture on
assigning reasons, for they would
almost infallibly be wrong. In cases
like this, which are of no uncommon
occurrence, it would be absurd to
suppose that the bad reason was the
source of the good decision. Lord
Mansfield knew that if any reason
were assigned it would be necessarily
an afterthought, the judge being in
fact guided by impressions from past
experience, without the circuitous pro-
cess of framing general principles
from them, and that if he attempted
to frame any such he would assuredly
fail. Lord Mansfield, however, would
not have doubted that a man of equal
experience who had also a mind stored
with general propositions derived by
legitimate induction from that experi-
ence, would have been greatly prefer-
able as a judge to one, however saga-
cious, who could not be trusted with
the explanation and justification of
his own judgments. The cases of
men of talent performing wonderful
things they know not how, are ex-

FUNCTIONS AND VALUE OF THE SYLLOGISM. 125

amples of the rudest and most spon-
taneous form of the operations of
superior minds. It is a defect in
them, and often a source of errors,
not to have generalised as they went
on ; but generalisation, though a help,
the most important indeed of all helps,
is not an essential.

Even the scientifically instructed,
who possess, in the form of general
propositions, a systematic record of
the results of the experience of man-
kind, need not always revert to those
general propositions in order to apply
that experience to a new case. It is
justly remarked by Dugald Stewart,
that though the reasonings in mathe-
matics depend entirely on the axioms,
it is by no means necessary to our
seeing the conclu.siveness of the proof
that the axioms should be expressly
adverted to. When it is inferred that
A B is equal to C D because each of
them is equal to E F, the most un-
cultivated understanding, as soon as
the propositions were understood,
would assent to the inference, without
having ever heard of the general truth
that " things which are equal to the
same thing are equal to one another."
This remark of Stewart, consistently
followed out, goes to the root, as I
conceive, of the philosophy of ratio-
cination ; and it is to be regretted
that he himself stopt short at a much
more limited application of it. He
saw that the general propositions on
which a reasoning is said to depend
may, in certain cases, be altogether
omitted, without impairing its pro-
bative force. But he imagined this
to be a peculiarity belonging to
axioms ; and argued from it, that
axioms are not the foundations or
first principles of geometry from
which all the other truths of the
science are synthetically deduced, (as
the laws of motion and of the com-
position of forces in dynamics, the
equal mobility of fluids in hydro-
statics, the laws of reflection and
refraction in optics, are the first
principles of those sciences,) but are
merely necessary assumptions, self-

evident indeed, and the denial of
which would annihilate all demon-
stration, but from which, as premises,
nothing can be demonstrated. In the
present, as in many other instances,
this thoughtful and elegant writer has
perceived an important truth, but
only by halves. Finding, in the case
of geometrical axioms, that general
names have not any talismanic virtue
for conjuring new truths out of the
well where they lie hid, and not seeing
that this is equally true in every other
case of generalisation, he contended
that axioms are in their nature barren
of consequences, and that the really
fruitful truths, the real first principles
of geometry, are the definitions ; that
the definition, for example, of the circle
is to the properties of the circle what
the laws of equilibrium and of the
pressure of the atmosphere are to the
rise of the mercury in the Torricellian
tube. Yet all that he had asserted
respecting the function to which the
axioms are confined in the demon-
strations of geometry holds equally
true of the definitions. Every demon-
stration in Euclid might be carried on
without them. This is apparent from
the ordinary process of proving a pro-
position of geometry by means of a
diagram. What assumption, in fact,
do we set out from to demonstrate by
a diagram any of the pi'operties of the
circle? Not that in all circles the
radii are equal, but only that they are
so in the circle ABC. As our warrant
for assuming this, we appeal, it is true,
to the definition of a circle in general ;
but it is only necessary that the
assumption be granted in the case of
the particular circle supposed. From
this, which is not a general but a
singular proposition, combined with
other propositions of a similar kind,
some of which when generalised are
called definitions, and others axioms,
we prove that a certain conclusion is
true, not of all circles, but of the
particular circle ABC ; or at least
would be so, if the facts precisely
accorded with our assumptions. The
enunciation, as it is called, that is, the

126

REASONING.

general theorem which stands at the
head of the demonstration, is not the
proposition actually demonstrated.
One instance only is demonstrated :
but the process by which this is done
is a process which, when we consider
its nature, we perceive might be
exactly copied in an indefinite number
of other instances ; in every instance
which conforms to certain conditions.
The contrivance of general language
furnishing us with terms which con-
note these conditions, we are able to
assert this indefinite multitude of
truths in a single expression, and this
expression is the general theorem.
By dropping the use of diagrams, and
substituting, in the demonstrations,
general phrases for the letters of the
alphabet, we might prove the general
theorem directly, that is, we might
demonstrate all the cases at once ;
and to do this we must, of course,
employ as our premises the axioms
and definitions in their general form.
But this oidy means, that if we can
prove an individual conclusion by
assuming an individual fact, then in
whatever case we are warranted in
making an exactly similar assumption,
we may draw an exactly similar con-
clusion. The definition is a sort of
notice to ourselves and others what
assumptions we think ourselves en-
titled to make. And so in all cases,
the general propositions, whether
called definitions, axioms, or laws of
nature, which we lay down at the
beginning of our reasonings, are
merely abridged statements, in a
kind of shorthand, of the particular
facts, which, as occasion arises, we
either think we may pnxjeed on as
proved, or intend to assume. In any
one demonstration it is enough if we
assume for a particular case, suitably
selected, what by the statement of the
definition or principle we announce
that we intend to assume in all cases
which may arise. The definition of
the circle, therefore, is to one of
Euclid's demonstrations exactly what,
according to Stewart, the axioms are ;
that is, the demonstration does not

depend on it, but yet if we deny it
the demonstration fails. The proof
does not rest on the general assump-
tion, but on a similar assumption con-
fined to the particular case : that case,
however, being chosen as a specimen
or paradigm of the whole class of cases
included in the theorem, there can be
nogroundformaking the assumption in
that case which does not exist in every
other ; and to deny the assumption
as a general truth is to deny the right
of making it in the particular instance.
There are, undoubtedly, the most
ample reasons for stating both the
principles and the theorems in their
general form, and these will be ex-
plained presently, so far as explana-
tion is requisite. But, that unprac-
tised learners, even in making use of
one theorem to demonstrate another,
reason rather from particular to parti-
cular than from the general proposi-
tion, is manifest from the difficulty
they find in applying a theorem to a
case in which the configuration of the
diagram is extremely unlike that of
the diagram by which the original
theorem was demonstrated. A diflB-
culty which, except in cases of unusual
mental power, long practice can alone
remove, and removeschiefly byrender-
ing us familiar with all the configura-
tions consistent with the general con-
ditions of the theorem.

§ 4. From the considerations now
adduced the following conclusions
seem to be established. All inference
is from particulars to particulars :
General propositions are merely re-
gistersof such inferences already made,
and short formulae for making more :
The major premise of a syllogism, con-
sequently, is a formula of this descrip-
tion ; and the conclusion is not an
inference drawn /?-om the formula, but
an inference drawn according to the
formula ; the real logical antecedent
or premise being the particular facts
from which thegeneral proposition was
collected by induction. Those facts,
: and the individual instances which
I supplied them, may have been for-

FUNCTIONS AND VALUE OF THE SYLLOGISM. 127

gotten ; but a record remains, not
indeed descriptive of the f;icts them-
■elves, but showing how those cases
may be distinguished, respecting
which, the facts, when known, were
considered to warrant a given infer-
ence. According to the indications
of this record we draw our conclusion ;
which is, to all intents and purposes,
a conclusion from the forgotten facts.
For this it is essential that we should
read the record correctly ; and the
rules of the syllogism are a set of pre-
cautions to ensure our doing so.

This view of the functions of the
syllogism is confirmed by the con-
sideration of precisely those cases which
might be expected to be least favour-
able to it, namely, those in which
ratiocination is independent of any
previous induction. We have already
observed that the syllogism, in the
ordinary course of our reasoning, is
only the latter half of the process of
travelling from premises to a conclu-
sion. There are, however, some pecu-
liar cases in which it is the whole
process. Particulars alone are cap-
able of being subjected to observation ;
and all knowledge which is derived
from observation begins, therefore,
of necessity, in particulars ; but our
knowledge may, in cases of certain
descriptions, be conceived as coming
to us from other sources than observa-
tion. It may present itself as coming
from testimony, which, on the occa-
sion and for the purpose in hand, is
accepted as of an authoritative char-
acter : and the information thus
communicated may be conceived to
comprise not only particular facts but
general propositions, as when a
scientific doctrine is accepted without
examination on the authority of
writers, or a theological doctrine on
that of Scripture. Or the generalisa-
tion may not be, in the ordinary sense,
an assertion at all, but a command ; a
law, not in the philosophical, but in
the moral and political sense of the
term : an expression of the desire of a
superior, that we, or any number of
otb«r personB, ehail conform our con-

duct to certain general instructions.
So far as this asserts a fact, namely, a
volition of the legislator, that fact is
ail individual fact, and the proposition,
therefore, is not a general proposition.
But the description therein contained
of the conduct which it is the will of
the legislator that his subject should
observe, is general. The proposition
asserts, not that all men are anything,
but that all men shall do sometliing.

In both these cases the generalities
are the original data, and the parti-
culars are elicited from them by a
process which correctly resolves itself
into a series of syllogisms. The real
nature, however, of the supposed de-
ductive process is evident enough.
The only point to be determined is,
whether the authority which declared
the general proposition intended to
include this case in it ; and whether
the legislator intended his command
to apply to the present case among
others or not ? This is ascertained by
examining whether the case possesses
the marks by which, as those autho-
rities have signified, the cases which
they meant to certify or to influence
may be known. The object of the in-
quiry is to make out the witness's or
the legislator's intention, through the
indication given by their words. This
is a question, as the Germans express
it, of hermeneutics. The operation is
not a process of inference, but a process
of interpretation.

In this last phrase we have obtained
an expression which appears to me to
characterise, moreaptly than any other,
the functions of the syllogism in all
cases. When the premises are given
by authority, the function of Reason-
ing is to ascertain the testimony of a
witness, or the will of a legislator, by
interpreting the signs in which the
one has intimated his assertion and
the other his command. In like man-
ner, when the premises are derived
from observation, the function of
Reasoning is to ascertain what we
(or our predecessors) formerly thoujrht
might be inferred from the observed
facte, and to do this by interpreting

128

REASONING.

a memorandum of ours, or of theirs.
The memorandum reminds us, that
from evidence, more or less carefully
weighed, it formerly appeared that a
certain attribute might be inferred
wherever we perceive a certain mark.
The proposition, All men are mortal,
for instance, shows that we have had
experience from which we thought it
followed that the attributes connoted
by the term " man " are a mark of mor-
tality. But when we conclude that
the Duke of Wellington is mortal, we
do not infer this from the memoran-
dum, but from the former experience.
All that we infer from the memor-
andum is our own previous belief (or
that of those who transmitted to us the
proposition) concerning the inferences
which that former experience would
warrant.

This view of the nature of the
syllogism renders consistent and in-
telligible what otherwise remains ob-
scure and confused in the theory of
Archbishop Whately and other en-
lightened defenders of the syllogistic
doctrine respecting the limits to which
its functions are confined. They affirm
in as explicit terms as can be used,
that the sole office of general reason-
ing is to prevent inconsistency in our
opinions ; to prevent us from assent-
ing to anything, the truth of which
would contradict something to which
we had previously on good grounds
given our assent. And they tell us,
that the sole ground which a syllogism
affords for assenting to the conclusion,
is that the supposition of its being
false, combined with the supposition
that the premises are true, would lead
to a contradiction in terms. Now
this would be but a lame account of
the real grounds which we have for
believing the facts which we learn
from reasoning, in contradistinction
to observation. The true reason why
we believe that the Duke of Welling-
ton will die, is that his fathers, and
our fathers, and all other persons who
were cotemporary with them, have
died. Those facts are the real pre-
mises of the reasoning. But we are

not led to infer the conclusion from
those premises, by the necessity of
avoiding any verbal inconsistency.
There is no contradiction in supposing
that all those persons have died, and
that the Duke of Wellington may,
notwithstanding, live for ever. But
there would be a contradiction if we
first, on the ground of those same
premises, made a general assertion
including and covering the case of the
Duke of Wellington, and then refused
to stand to it in the individual case.
There is an inconsistency to be avoided
between the memorandum we make
of the inferences which may be justly
drawn in future cases, and the infer-
ences we actually draw in those cases
when they arise. With this view we
interpret our own formula, precisely
as a judge interprets a law ; in order
that we may avoid drawing any in-
ferences not conformable to our for-
mer intention, as a judge avoids giving
any decision not conformable to the
legislator's intention. The rules for
this interpretation are the rules of the
syllogism : and its sole purpose is to
maintain consistency between the con-
clusions we draw in every particular
case, and the previous general direc-
tions for drawing them ; whether
those general directions were framed
by ourselves as the result of induc-
tion, or were received by us from an
authority competent to give them.

§ 5. In the above observations it
has, I think, been shown, that, though
there is always a process of reasoning
or inference where a syllogism is used,
the syllogism is not a correct analysis
of that process of reasoning or infer-
ence ; which is, on the contrary (when
not a mere inference from testimony)
an inference from particulars to par-
ticulars, authorised by a previous in-
ference from particulars to generals,
and substantially the same with it ;
of the nature, therefore, of Induction.
But while these conclusions appear to
me undeniable, I must yet enter a
protest, as strong as that of Arch-
bishop Whately himself, against the

FUNCTIONS AND VALUE OF THE SYLLOGISM.

129

doctrine that the syllogistic art is use-
less for the purposes of reasoning.
The reasoning lies in the act of gene-
ralisation, not in interpreting the
record of that act ; but the syllogis-
tic form is an indispensable collateral
security for the correctness of the
generalisation itself.

It has already been seen, that if we
have a collection of particulars suflB-
cient for grounding an induction, we
need not frame a general proposition ;
we may reason at once from those
particulars to other particulars. But
it is to be remarked withal, that
whenever, from a set of particular
cases, we can legitimately draw any
inference, we may legitimately make
our inference a general one. If, from
observation and experiment, we can
conclude to one new case, so may we
to an indefinite number. If that
which has held true in our past experi-
ence will therefore hold in time to
come, it will not hold merely in some
individual case, but in all cases of
some given description. Every induc-
tion, therefore, which suffices to prove
one fact, proves an indefinite multi-
tude of facts : the experience which
justifies a single prediction must be
such as will suffice to bear out a
general theorem. This theorem it is
extremely important to ascertain and
declare in its broadest form of gene-
rality, and thus to place before our
minds, in its full extent, the whole of
what our evidence must prove if it
proves anything.

This throwing of the whole body of
possible inferences from a given set of
particulars into one general expression
operates as a security for their being
just inferences, in more ways than
one. First, the general principle pre-
sents a larger object to the imagina-
tion than any of the singular proposi-
tions which it contains. A process of
thought which leads to a compnehen-
sive generality is felt as of greater
importance than one which terminates
in an insulated fact ; and the mind
is, even unconsciously, led to bestow
greater attention upon the process, and

to weigh more carefully the sufficiency
of the experience appealed to for
supporting the inference grounded
upon it. There is another, and a more
important, advantage. In reasoning
from a course of individual observa-
tions to some new and unobserved
case, which we are but imperfectly
acquainted with, (or we should not be
inquiring into it,) and in which, since
we are inquiring into it, we probably
feel a peculiar interest, there is very
little to prevent us from giving way
to negligence, or to any bias which
may afifect our wishes or our imagina-
tion, and, under that influence, accept-
ing insufficient evidence as sufficient.
But if, instead of concluding straight
to the particular case, we place before
ourselves an entire class of facts — the
whole contents of a general proposi-
tion, every tittle of which is legiti-
mately inferrible from our premises, if
that one particular conclusion is so ;
there is then a considerable likelihood
that if the premises are insufficient,
and the general inference, therefore,
groundless, it will comprise within it
some fact or facts the reverse of which
we already know to be true ; and we
shall thus discover the error in our
generalisation by a reductio ad im-
possibile.

Thus if, during the reign of Mar-
cus Aurelius, a subject of the Roman
Empire, under the bias naturally given
to the imagination and expectations
by the lives and characters of the
Antonines, had been disposed to ex-
pect that Commodus would be a just
ruler ; supposing him to stop there, he
might only have been undeceived by
sad experience. But if he reflected
that this expectation could not be
justifiable unless from the same
evidence he was warranted in con-
cluding some general proposition, as,
for instance, that all Roman emperors
are just rulers ; he would immediately
have thought of Nero, Domitian, and
other instances, which, showing the
falsity of the general conclusion, and
therefore the insufficiency of the pre-
mises, would have warned him that

J

I30

REASONING.

those premises could not prove in
the instance of Commodus, what they
were inadequate to prove in any col-
lection of casts in which his was
included.

The advantage, in judging whether
any controverted inference is legiti-
mate, of referring to a parallel case,
is universally acknowledged. But by
ascending to the general proposition,
we bring under our view not one
parallel case only, but all possible
parallel cases at once ; all cases to
which the same set of evidentiary
considerations are applicable.

When, therefore, we argue from a
number of known cases to another
case supposed to be analogous, it is
always possible, and generally advan-
tageous, to divert our argument into
the circuitous channel of an induction
from those known cases to a general
proposition, and a subsequent appli-
cation of that general proposition to
the unknown case. This second part
of the operation, which, as before ob-
Ferved, is essentially a process of in-
terpretation, will be resolvable into a
syllogism or a series of syllogisms, the
majors of which will be general pro-
positions embracing whole classes of
cases ; every one of which propositions
must be true in all its extent, if the
argument is maintainable. If, there-
fore, any fact fairly coming within
the range of one of these general pro-
positions, and consequently asserted
by it, is known or suspected to be
other than the proposition asserts it
to be, this mode of stating the argu-
ment causes us to know or to suspect
that the original observations, which
are the real grounds of our conclusion,
are not sufficient to support it. And
in proportion to the greater chance of
our detecting the inconclusiveness of
our evidence, will be the increased
reliance we are entitled to place in
it if no such evidence of defect shall
appear.

The value, therefore, of the syllo-
gistic form, and of the rules for using
it correctly, does not consist in their
being th« form and the rules accord-

ing to which our reasonings are neces-
sarily, or even usually made ; but in
their furnishing us with a mode in
which those reasonings may always
be represented, and which is admir-
ably calculated, if they are incon-
clusive, to bring their inconclusiveness
to light An induction from parti-
culars to generals, followed by a syl-
logistic process from those generals
to other particulars, is a form in which
we may always state our reasonings
if we please. It is not a form in which
we miist reason, but it is a form in
which we may reason, and into which
it is indispensable to throw our reason-
ing when there is any doubt of its
validity : though when the case is
familiar and little complicated, and
there is no suspicion of error, we may,
and do, reason at once from the known
particular cases to unknown ones.*

These are the uses of syllogism, as
a mode of verifying any given argu-
ment. Its ulterior uses, as respects
the general course of our intellectual
operations, hardly require illustration,
being in fact the acknowledged uses
of general language. They amount
substantially to this, that the induc-
tions may be made once for all : a
single careful interrogation of experi-
ence may suffice, and the result may
be registered in the form of a general
proposition, which is committed to
memory or to writing, and from which
afterwards we have only to syllogise.
The particulars of our experiments
may then be dismissed from the
memory, in which it would be impos-

* The language of ratiocination would, I
think, be brought into closer agreement
with the real nature of the pi ocess if the
general propositions employed m reason-
ing, instead of being in the form All men
are mortal, or Every man is mortal, were
expressed in the form Any man is mortal.
This mode of expression, exhibiting as the
type of all reasoning from expeiience, "The
men A, B, G, (fcc. , are so and so, therefore
any man is so and so," would much better
manifest the true idea — that inductive
reasoning is always, at bottom, inference
from particulars to j)articiilar8, and that
the wliole function ox general proiwgltions
in reasoning is to vouch for th« legitimacy
of such inference*.

FUNCTIONS AND VALUE OF THE SYLLOGISM.

Oi

sible to retain so great a multitude of
details ; while the knowledge which
those details afforded for future use,
and which would otherwise be lost
as soon as the observations were for-
gotten, or as their record became too
bulky for reference, is retained in a
commodious and immediately avail-
able shape by means of general lan-
guage.

Against this advantage is to be set
the countervailing inconvenience, that
inferences originally made on insuffi-
cient evidence become consecrated,
and, as it were, hardened into general
maxims ; and the mind cleaves to
them from habit after it has outgrown
any liability to be misled by similar
fallacious appearances if they were
now for the first time presented ; but
having forgotten the particulars, it
does not think of revising its own
former decision. An inevitable draw-
back, which, however considerable in
itself, forms evidently but a small set-
off against the immense benefits of
general language.

The use of the syllogism is in truth
no other than the use of general pro-
positions in reasoning. We can
reason without them ; in simple and
obvious cases we habitually do so ;
minds of great sagacity can do it in
cases not simple and obvious, provided
their experience supplies them with in-
stances essentially similar to every j
combination of circumstances likely to i
arise. But other minds, and the same
minds where they have not the same
pre-eminent advantages of personal
experience, are quite helpless without
the aid of general propositions, where- j
ever the case presents the smallest :
complication ; and if we made no
general propositions, few persons
would get much beyond those simple
inferences which are drawn by the
more intelligent of the brutes. Though
not necessary to reasoning, general pro-
positions are necessary to any consi-
derable progress in reasoning. It is,
therefore, natural and indispensable
to separate the process of investigation
ioto two parts ; fmd obtain general j

formulae for determining what infer-
ences may be drawn, before the occa-
sion arises for drawing the inferences.
The work of drawing them is then that
of applying the formulae ; and the rules
of syllogism are a system of securities
for the correctness of the application.

§ 6. To complete the series of con-
siderations connected with the philo-
sophical character of the syllogism,
it is requisite to consider, since the
syllogism is not the universal type of
the reasoning process, what is the real
type. This resolves itself into the
question, what is the nature of the
minor premise, and in what manner it
contributes to establishthe conclusion :
for as to the major, we now fully under-
stand, that the place which it nomi-
nally occupies in our reasonings, pro-
perly belongs to the individual facts
or observations of which it expresses
the general result ; the major itself
being no real part of the argument,
but an intermediate halting-place for
the mind, interposed by an artifice of
language between the real premises
and the conclusion, by way of a secu-
rity, which it is in a most material
degree, for the correctness of the pro-
cess. The minor, however, being an
indispensable part of the syllogistic
expression of an argument, without
doubt either is, or corresponds to, an
equally indispensable part of the argu-
ment itself, and we have only to in-
quire what part.

It is perhaps worth while to notice
here a speculation of a philosopher to
whom mental science is much indebted,
but who, though a very penetrating,
was a very hasty thinker, and whose
want of due circumspection rendered
him fully as remarkable for what he
did not see, as for what he saw. I
allude to Dr. Thomas Brown, whose
theory of ratiocination is peculiar.
He saw the peti'io prinripii which is
inherent in every syllogism, if we con-
sider the majorto be itself the evidence
by which the conclusion is proved, in-
stead of being, what in fact it is,
an assertion of the existence of evi«

132

REASONING.

dence sufficient to prove any conclusion
of a given description. Seeing this,
Dr. Brown not only failed to see the
immense advantage, in point of secu-
rity for correctness, which is gained
by interposing this step between the
real evidence and the conclusion, but
he thought it incumbent on him to
strike out the major altogether from
the reasoning process, without substi-
tuting anything else, and maintained
that our reasonings consist only of the
minor premise and the conclusion,
Socrates is a man, therefore Socrates
is mortal : thus actually suppressing,
as an unnecessary step in the argu-
ment, the appeal to former experience.
The absurdity of this was disguised
from him by the opinion he adopted,
that reasoning is merely analysing
our own general notions or abstract
ideas ; and that the proposition, Soc-
rates is mortal, is evolved from the
proposition, Socrates is a man, simply
by recognising the notion of mortality
as already contained in the notion we
form of a man.

After the explanations so fully en-
tered into on the subject of proposi-
tions, much further discussion cannot
be necessary to make the radical error
of this view of ratiocination apparent.
If the word man connoted mortality ;
if the meaning of " mortal " were in-
volved in the meaning of "man," we
might, undoubtedly, evolve the con-
clusion from the minor alone, because
the minor would have already asserted
it. Hut if, as is in fact the case, the
word man does not connote mortality,
how does it appear that in the mind
of every person who admits Socrates
to be a man, the idea of man must
include the idea of mortality? Dr.
Brown could not help seeing this
difficulty, and, in order to avoid it,
was led, contrary to his intention, to
re-establish, under another name, that
step in the argument which corre-
sponds to the major, by affirming the
necessity of previously perceiving the
relation between the idea of man and
the idea of mortal. If the reasoner
))^ not previously perceived this rela-

tion, he will not, says Dr. Brown, in-
fer, because Socrates is a man, that
Socrates is mortal. But even this
admission, though amounting to a
surrender of the doctrine that an
argument consists of the minor and
the conclusion alone, will not save the
remainder of Dr. Brown's theory.
The failure of assent to the argument
does not take place merely because
the reasoner, for want of due analysis,
does not perceive that his idea of man
includes the idea of mortality ; it
takes place, much more commonly
because in his mind that relation be-
tween the two ideas has never existed.
And in truth it never does exist, ex-
cept as the result of experience. Con-
senting, for the sake of the argument,
to discuss the question on a supposi-
tion of which we have recognised the
radical incorrectness, namely, that
the meaning of a proposition relates
to the ideas of the things spoken of,
and not to the things themselves ; I
must yet observe, that the idea of
man, as an universal idea, the com-
mon property of all rational creatures,
cannot involve anything but what is
strictly implied in the name. If any
one includes in his own private idea
of man, as no doubt is always the
case, some other attributes, such, for
instance, as mortality, he does so only
as the consequence of experience, after
having satisfied himself that all men
possess that attribute : so that what-
ever the idea contains, in any person's
mind, beyond what is included in
the conventional signification of the
word, has been added to it as the
result of assent to a proposition ; while
Dr. Brown's theory requires us to sup-
pose, on the contrary, that assent to
the proposition is produced by evolv-
ing, through an analjrtic process, this
very element out of the idea. This
theory, therefore, may be considered
as sufficiently refuted ; and the minor
premise must be regarded as totally
insufficient to prove the conclusion,
except with the assistance of the
major, or of that which the major re-
presents, namely, the various singular

FUNCTIONS AND VALUE OF THE SYLLOGISM.

133

propositions expressive of the series of
observations of which the generalisa-
tion called the major premise is the
result.

In the argument, then, which proves
that Socrates is mortal, one indispen-
sable part of the premises will be as
follows : " My father, and my father's
father. A, B, C, and an indefinite num-
ber of other persons, were mortal : "
which is only an expression in diffe-
rent words of the observed fact that
they have died. This is the major
premise divested of the petitio prin-
cipii, and cut down to as much as is
really known by direct evidence.

In order to connect this proposition
with the conclusion Socrates is mortal,
the additional link necessary is such
a proposition as the following : " So-
crates resembles my father, and my
father's father, and the other indi-
viduals specified." This proposition
we assert when we say that Socrates
is a man. By saying so we likewise
assert in what respect he resembles
them, namely, in the attributes con-
noted by the word man. And we
conclude that he further resembles
them in the attribute mortality.

§ 7. We have thus obtained what
we were seeking, an universal type of
the reasoning process. We find it re-
solvable in all cases into the following
elements : Certain individuals have a
given attribute ; an individual or in-
dividuals resemble the former in cer-
tain other attributes ; therefore they
resemble them also in the given attri-
bute. This type of ratiocination does
not claim, like the syllogism, to be
conclusive from the mere form of the
expression ; nor can it possibly be so.
That one proposition does or does not
assert the very fact which was already
asserted in another, may appear from
the form of the expression, that is,
from a comparison of the language ;
but when the two propositions assert
facts which are bond fide different,
whether the one fact proves the other
or not can never appear from the lan-
guage, but must depend on other con-

siderations. Whether, from the attri-
butes in which Socrates resembles
those men who have heretofore died,
it is allowable to infer that he re-
sembles them also in being mortal, is
a question of Induction ; and is to be
decided by the principles or canons
which we shall hereafter recognise as
tests of the correct performance of
that great mental operation.

Meanwhile, however, it is certain,
as before remarked, that if this infer-
ence can be drawn as to Socrates, it
can be drawn as to all others who
resemble the observed individuals in
the same attributes in which he re-
sembles them ; that is (to express the
thing concisely) of all mankind. If,
therefore, the argument be admissible
in the case of Socrates, we are at
liberty, once for all, to treat the pos-
session of the attributes of man as a
mark, or satisfactory evidence, of the
attribute of mortality. This we do
by laying down the universal proposi-
tion. All men are mortal, and inter-
preting this, as occasion arises, in its
application to Socrates and others.
By this means we establish a very
convenient division of the entire
logical operation into two steps ; first,
that of ascertaining what attributes
are marks of mortality ; and, secondly,
whether any given individuals possess
those marks. And it will generally
be advisable, in our speculations on
the reasoning process, to consider this
double operation as in fact taking
place, and all reasoning as carried on
in the form into which it must neces-
sarily be thrown to enable us to apply
to it any test of its correct perform-
ance.

Although, therefore, all processes
of thought in which the ultimate pre-
mises are particulars, whether we con-
clude from particulars to a general
formula, or from particulars to other
particulars according to that formula,
are equally Induction ; we shall yet,
conformably to usage, consider the
name Induction as more peculiarly
belonging to the process of establish-
ing the general proposition, and the

J34

REASONING.

remaining operation, which is sub-
stantially that of interpreting the
general proposition, we shall call by
its usual name, Deduction. And we
shall consider every process by which
anything is inferred i"especting an
unobserved case as consisting of an
Induction followed by a Deduction ;
because, although the process needs
not necessarily be carried on in this
form, it is always susceptible of the
form, and must be thrown into it
when assurance of scientific accuracy
is needed and desired.

§8. The theory of the syllogism
laid down in the preceding pages has
obtained, among other important ad-
hesions, three of peculiar value ; those
of Sir John Herschel, * Dr. Whewell,t
and Mr. Bailey ; X Sir John Herschel
considering the doctrine, though not
strictly "a discovery," having been
anticipated by Berkeley, § to be "one
of the greatest steps which have yet
been made in the philosophy of Logic."
" When we consider " (to quote the
further words of the same authority)
" the inveteracy of the habits and pre-
judices which iib has cast to the winds,"
there is no cause for misgiving in the
fact that other thinkers, no less en-
titled to consideration, have formed
a very different estimate of it. Their
principal objection cannot be better
or more succinctly stated than by
borrowing a sentence from Archbishop
Whately. || " In every case where an

* Review of Quetelet on Probabilities,
Esmya, p. 367.

t Philosophy/ of Discovery, p. 289.

J Theory of Reasoning, ch. iv., to which I
may refer for an able statement and en-
forcement of the ^rounds of the doctrine.

§ On a recent careful reperusal of Ber-
keley's whole works, I have been unable
to find this doctrine in them. Sir John
H' rschel probably meant that it is implied
iTi Berkeliy's argument against abstract
idea-^. But I cmnot find that Berkeley
saw the implication, or had e^er asked
himself what bearing his argument had on
the theory of the syllocrism. Still less can
I admit that the doctrine is (hs has been
aflBrmed by one of my ablest and most
candid critics) "among the standing marks
of whnt is called the empirical pliilo80i)hy."

I Logic, book iv. ch. 1. sect. i.

inference is drawn from Induction,
(unless that name is to be given to a
mere random guess without any
grounds at all,) we must form a judg-
ment that the instance or instances
adduced are sufficient to authorise the
conclusion ; that it is allowable to take
these instances as a sample warrant-
ing an inference respecting the whole
class ; " and the expression of this
judgment in words (it has been said
by several of my critics) w the major
premise.

I quite admit that the major is an
affirmation of the sufficiency of the
evidence on which the conclusion rests.
That it is so is the very essence of
my own theory. And whoever admits
that the major premise is only this,
adopts the theory in its essentials.

But I cannot concede that this
recognition of the sufficiency of the
evidence — that is, of the correctness
of the induction — is a part of the
induction itself ; unless we ought to
say that it is a part of everything we
do, to satisfy ourselves that it has
been done rightly. We conclude from
known instances to unknown by the
impulse of the generalising propensity;
and (until after a considerable amount
of practice and mental discipline) the
question of the sufficiency of the evi-
dence is only raised by a retrospective
act, turning back upon our own foot-
steps, and examining whether we were
warranted in doing what we have
provisionally done. To speak of this
reflex operation as part of the original
one, requiring to be expressed in words
in order that the verbal formula may
correctly represent the psychological
process, appears to me false psycho-
logy.* We review our syllogistic as
well as our in,ductive processes, and
recognise that they have been cor-
rectly performed ; but logicians do
not add a third premise to the syllo-
gism, to express this act of recogni-
tion. A careful copyist verifies his
transcript by collating it with the

♦ See the Important chapter on Belief,
in Professor Bain's great treatise, The Smo-
tiom and the Will, pp. 58i-584'

FUNCTIONS AND VALUE OF THE SYLLOGISM. 135

original ; and if no error appears, he
recognises that the transcript has
been correctly made. But we do not
call the examination of the copy a
part of the act of copying.

The conclusion in an induction is
inferred from the evidence itself, and
not from a recognition of the suffi-
ciency of the evidence : as I infer that
my friend is walking towards me be-
cause I see him, and not because I
recognise that my eyes are open, and
that eyesight is a means of knowledge.
In all operations which require care,
it is good to assure ourselves that the
process has been performed accurately;
but the testing of the process is not
the process itself; and, besides, may
have been omitted altogether, and yet
the process be correct. It is pre-
cisely because that operation is omitted
in ordinary unscientific reasoning,
that there is anything gained in cer-
tainty by throwing reasoning into the
syllogistic form. To make sure, as
far as possible, that it shall not be
omitted, we make the testing opera-
tion a part of the reasoning process
itself. We insist that the inference
from particulars to particulars shall
pass through a general proposition.
But this is a security for good reason-
ing, not a condition of all reasoning ;
and in some cases not even a security.
Our most familar inferences are all
made before we learn the use of
general propositions : and a person of
untutored sagacity will skilfully apply
his acquired experience to adjacent
cases, though he would bungle griev-
ously in fixing the limits of the appro-
priate general theorem. But though
he may conclude rightly, he never,
properly speaking, knows whether he
has done so or not ; he has not tested
his reasoning. Now, this is precisely
what forms of reasoning do for us.
We do not need them to enable us
to reason, but to enable us to know
whether we reason correctly.

In still further answer to the ob-
jection, it may be added that— even
when the test has been applied, and
the suflficiency of the evidence recog-

nised, if it is suflicient to support the
general proposition, it is sufl&cient
also to support an inference from par-
ticulars to particulars without passing
through the general propositions. The
inquirer who has logically satisfied
himself that the conditions of legiti-
mate induction were realised in the
cases A, B, C, would be as much
justified in concluding directly to the
Duke of Wellington as in concluding
to all men. The general conclusion
is never legitimate, unless the particu-
lar one would be so too ; and in no sense
intelligible to me can the particular
conclusion be said to be drawn from
the general one. Whenever there is
ground for drawing any conclusion at
all from particular instances, there is
ground for a general conclusion ; but
that this general conclusion should
be actually drawn, however useful,
cannot be an indispensable condition
of the validity of the inference in the
particular case. A man gives away
sixpence by the same power by which
he disposes of his whole fortune ; but
it is not necessary to the legality
ot the smaller act that he should
make a formal assertion of his right
to the greater one.

Some additional remarks, in reply
to minor objections, are appended.*

* A writer in the " British Qaarterly
Review " (August, 1846), in a review of tliis
treatise, endeavours to show that tlier* is
no petitio principii in the syllogi-m, by
denying that the proposition, All men are
mortal, asserts or sissumes that Socrates is
mortal. Insupport of tliis denial, Reargues
that we may, and in fact do, admit the
general proposition tliatall men are mortal,
without having particularly examined the
case of Socrates, and even without know-
ing whether the individual so named is a
man or something else. But tliis of course
was never denied. That we can and do
draw conclusions concerning cases speci-
fically unknown to us is the datum from
which all who discuss this subject must
set out. The question is, in what terms
the evidence or ground on which we draw
these conclusions may best be designated
— whether it is most correct to say, that
the unknown case is proved by known
Crises, or that it i.s proved by a general pro-
position including both sets of cases, tlie
unknown and the known? I contend for
the former mode of expression. I hold it

156

REASONING.

§ 9. The preceding considerations
enable us to understand the true
nature of what is termed, by recent
writers, Formal Logic, and the rela-
tion between it and Logic in the
widest sense. Logic, as I conceive

an abuse of language to say, that the proof
that Socrates is mortal is that all men are
mortal. Turn it in what way we will, this
seems to me to be asserting that a thing is
the proof of itself. Whoever pronounces
the words, All men are mortal, has affirmed
that Socrates is mortal, though he may
never have heard of Socrates; for since
Socrates, whether known to be so or not,
really is a man, he is included in the words,
All men, and in every assertion of which
they are the subject. If the reviewer does
not see that there is a difficulty here, I can
only advise him to reconsider the subject
until he does : after which he will be a
better judge of the success or failure of an
attempt to remove the difficulty. That be
had reflected very little on the point when
he wrote his remarks is shown by his over-
sight respecting the dictum de omni et nuUo.
He acknowledges that this maxim as com-
monly expressed, "Whatever is true of a
class is true of everything included in the
class," is a mere identical proposition, since
the class is nothing but the things included
in it. But he thinks this defect would
be cured by wording the maxim thus, —
" Whatever is true of a class is true of
everything which can be shown to be a
membei- of the class : " as if a thing could
'* be shown " to be a member of the class
without being one. If a class means the
sum of all the things included in the class,
the things which can " be shown " to be
included in it are part of the sum, and the
dictum is as much an identical proposition
with respect to them as to the rest. One
would almost imagine that in the reviewer's
opinion things are not members of a class
until they are called up publicly to take
their place in it— that so long, in fact, as
Socrates is not known to be a man he is not
a man, and any assertion which can be
made concerning men does not at all re-
gard him, nor is affected as to its truth or
falsity by anything in which he is con-
cerned.

The difference between the reviewer's
theory and mine may be thus stated. Both
admit that when we say, All men are
mortal, we make an assertion reaching
beyond the sphere of our knowledge of
individual cases ; and that when a new
individual, Socrates, is brought within the
field of our knowledge by means of the
minor premise, we learn that we have
already made an assertion respecting Soc-
rates without knowing it : our own gene-
ral formula being, to that extent, for the
first time interpreted to us. But according
to the reviewer's theory, the smaller asser-

it, is the entire theory of the ascer-
tainment of reasoned or inferred truth.
Formal Logic, therefore, which Sir
William Hamilton from his own point
of view, and Archbishop Whately
from his, have represented as the

j tion is proved by the larger : while I con-
tend that both assertions are proved to-
] gether by the same evidence, namely, the
j grounds of experience on which the gene-
I ral assertion was made, and by which it
I must be justified.

I Tiie reviewer says, that if the major pre-
I mise included the concluson, "we should
be able to affirm the conclusion without the
intervention of the minor premise ; but
every one sees that that is impossible."
A similar argument is urged by Mr. De
Morg&n (For 7nal Logic, -p. 259): "The whole
objection tacitly assumes the superfluity
of the minor; that is, tacitly assumes we
know Socrates* to be a man as soon as
we know him to be Socrates." The objec-
tion would be well grounded if the asser-
tion that the major premise includes the
conclusion, meant that it individually
specifies all it includes. As, however, the
only indication it gives is a description by
marks, we have still to compare any new
individual with the marks; and to show
that this comparison has been made is the
office of the minor. But since, by suppo-
sition, the new individual has the marks,
whether we have ascertained him to have
them or not ; if we have affirmed the major
premise, we have asserted him to be mortal.
Now my position is that this assertion can-
not be a necessary part of the argument.
It cannot be a necessary condition of
reasoning that we should begin by making
an assertion whicli is afterwards to be em-
ployed in proving a part of itself. I can
conceive only one way out of this difficulty,
viz. that what really forms the proof is the
other part of the assertion ; the portion of
it, the truth of which has been ascertained
previously ; and that the unproved part is
bound up in one foimula with the proved
part in mere anticipation, and as a memo-
randum of the nature of the conclusions
which we are prepared to prove.

With respect to the minor premise in
its formal shape, the minor as it stands in
the syllogism, predicating of Socrates a
definite class name, I readily admit that it
is no more a necessary part of reasoning
than the major. When there is a major,
doing its work by means of a class name,
minors are needed to interpret it : but
reasoning can be carried on without either
the one or the other. They are not the
conditions of reasoning, but a precaution

* Mr. De Morgan says "Plato," but to
prevent confusion I have kept to my own
exemplum.

TRAINS OF REASONING.

137

whole of Logic properly so called, is
really a very subordinate part of it,
not being directly concerned with the
process of Reasoning or Inference in
the sense in which that process is a
part of the Investigation of Truth.
What, then, is I ormal Logic ? The
name seems to be properly applied to
all that portion of doctrine which re-
lates to the equivalence of different
modes of expression ; the rules for
determining when assertions in a
given form imply or suppose the truth
or falsity of other assertions. This
includes the theory of the Import of
Propositions, and of their Conversion,
iEquipollence, and Opposition : of
those falsely called Inductions (to be
hereafter spoken of *), in which the
apparent generalisation is a mere
abridged statement of cases known
individually ; and finally, of the syl-
logism : while the theory of Naming,
and of (what is inseparably connected

against erroneous reasoning. The only
minor premise necessary to reasoning in
the example under consideration is, Soc-
i-ates is like A, B, C, and the other indi-
viduals who are known to have died. And
this is the only universal type of that step
in the reasoning process which is repre-
sented by the minor. Experience, how-
ever, of the uncertainty of this loose mode
of inference teaches the exi)ediency of de-
termining beforehand wliat kind of likeness
to the cases observed is necessary to bring
an unobserved case within the same predi-
cate ; and the answer to this question is
the major. The minor then identifies the
precise kind of likeness possessed by Soc-
rates, as being the kind required by the
formula. Thus the syllogistic mrijor and
the syllogi.stic minor start into existence
together, and are called forth by the same
exigency. When we conclude from per-
sonal experience without referring to any
record— to any general theorems, either
written, or traditional, or mentally regis-
tered by ourselves as conclusions of our
own drawing — we do not use, in our
thoughts, either a major or a minor, such
as the syllogism puts into words. When,
however, we revise this rough inference
from particulars to particulars, and substi-
tute a careful one, the revision consists in
selectiner two syllogistic premises. But
this neither alters nor adds to the evidence
we had before ; it only puts us in a better
position for judging whether our inference
from particulars to particulars ia well
grounded.
* Infra, book iii. ch. ii.

with it) Definition, though belonging
still more to the other and larger kind
of logic than to this, is a necessary
preliminary to this. The end aimed
at by Formal Logic, and attained by
the observance of its precepts, is not
truth, but consistency. It has been
seen that this is the only direct pur-
pose of the rules of the syllogism ;
the intention and effect of which is
simply to keep our inferences or con-
clusions in complete consistency with
our general formulae or directions for
drawing them. The Logic of Con-
sistency is a necessary auxiliary to
the Logic of Truth, not only because
what is inconsistent with itself or with
other truths cannot be true, but also
because truth can only be successfully
pursued by drawing inferences from
experience, which, if warrantable at
all, admit of being generalised, and,
to test their warrantableness, require
to be exhibited in a generalised form ;
after which the correctness of their
application to particular cases is a
question which specially concerns the
Logic of Consistency. This Logic,
not requiring any preliminary know-
ledge of the processes or conclusions
of the various sciences, may be studied
with benefit in a much earlier stage
of education than the Logic of Truth :
and the practice which has empirically
obtained of teaching it apart, through
elementary treatises which do not
attempt to include anything else,
though the reasons assigned for the
practice are in general very far from
philosophical, admits of philosophical
justification.

CHAPTER IV.

OF TRAINS OP REASONING AND
DEDUCTIVE SCIENCES.

§ I. In our analysis of the syl-
logism, it appeared that the minor
premise always affirms a resemblance
between a new case and some cases
previously known ; while the major
premise asserts something which,

tss

REASONING.

having been found true of those
known cases, we consider ourselves
warranted in holding true of any
other case resembling the former in
certain given particulars.

If all ratiocinations resembled, as
to the minor premise, the examples
which were exclusively employed in
the preceding chapter ; if the resem-
blance, which that premise asserts,
were obvious to the senses, as in the
proposition " Socrates is a man," or
were at once ascertainable by direct
observation ; there would be no neces-
sity for trains of reasoning, and De-
ductive or Ratiocinative Sciences
would not exist. Trains of reasoning-
exist only for the sake of extending
an induction founded, as all induc-
tions must be, on observed cases, to
other cases in which we not only
cannot directly observe the fact which
is to be proved, but cannot directly
observe even the mark which is to
prove it.

§ 2. Suppose the syllogism to be.
All cows ruminate ; the animal which
is before me is a cow ; therefore it
i-uminates. The minor, if true at all,
is obviously so : the only premise
the establishment of which requires
any anterior process of inquiry is the
major ; and provided the induction
of which that premise is the expres-
sion was correctly performed, the con-
clusion respecting the animal now
present will be instantly drawn ;
because, as soon as she is compared
with the formula, she will be identi-
fied as being included in it. But
suppose the syllogism to be the fol-
lowing : — All arsenic is poisonous,
the substance which is before me is
arsenic, therefore it is poisonous.
The truth of the minor may not here
be obvious at first sight ; it may not
be intuitively evident, but may itself
be known only by inference. It may
be theconclusion of another argument,
which, thrown into the syllogistic
form, would stand thus : — Whatever
when lighted prcxiuces a dark spot on
a piece of white porcelain held in the

flame, which spot is soluble in hypo-
chloride of calcium, is arsenic ; the
substance before me conforms to this
condition ; therefore it is arsenic
To establish, therefore, the ultimate
conclusion, The substance before me
is poisonous, requires a process which,
in order to be syllogistically expressed,
stands in need of two syllogisms ; and
we have a Train of Reasoning.

When, however, we thus add syl-
logism to syllogism, we are really
adding induction to induction. Two
separate inductions must have taken
place to render this chain of inference
possible ; inductions founded, pro-
bably, on different sets of individual
instances, but which converge in their
results, so that the instance which is
the subject of inquiry comes within
the range of them both. The record
of these inductions is contained in the
majors of the two syllogisms. First,
we, or others for us, have examined
various objects which yielded under
the given circumstances a dark spot
with the given property, and found
that they possessed the properties
connoted by the word arsenic ; they
were metallic, volatile, their vapour
had a smell of garlic, and so forth.
Next, we, or others for us, have exa-
mined various specimens which pos-
sessed this metallic and volatile cha-
racter, whose vapour had this smell,
&c., and have invariably found that
they were poisonous. The first obser-
vation we judge that we may extend
to all substances whatever which yield
that particular kind of dark spot ;
the second, to all metallic and vola-
tile substances resembling those we
examined ; and consequently, not to
those only which are seen to be such,
but to those which are concluded to
be such by the prior induction. The
substance before us is only seen to
come within one of these inductions ;
but by means of this one it is brought
within the other. We are still, as
before, concluding from particulars
to particulars ; but we are now con-
cluding from particulars observed, to
other particulars which are not, as in

TRAINS OF REASONING.

139

the simple case, seen to resemble them
in material points, but inferred to do
so, because resembling them in some-
thing else, which we have been led
by quite a different set of instances to
consider as a mark of the former re-
semblance.

This first example of a train of
reasoning is still extremely simple,
the series consisting of only two syl-
logisms. The following is somewhat
more complicated : — No government,
which earnestly seeks the good of its
subjects is likely to be overthrown ;
some particular government earnestly
seeks the good of its subjects, there-
fore it is not likely to be overthrown.
The major premise in this argument
we shall suppose not to be derived
from considerations a priori, but to
be a generalisation from history,
which, whether correct or erroneous,
must have been founded on observa-
tion of governments concerning whose
desire of the good of their subjects
there was no doubt. It has been
found, or thought to be found, that
these were not easily overthrown, and
it has been deemed that those in-
stances warranted au extension of the
same predicate to any and every
government which resembles them in
the attribute of desiring earnestly the
good of its subjects. But does the
government in question thus resemble
them ? This may be debated pro and
con by many arguments, and must, in
any case, be proved by another induc-
tion ; for we cannot directly observe
the sentiments and desires of the per-
sons who carry on the government.
To prove the minor, therefore, we
require an argument in this form :
Every government which acts in a
certain manner desires the good of
its subjects : the supposed govern-
ment acts in that particular manner,
therefore it desires the good of its
subjects. But is it true that the
government acts in the manner sup-
posed ? This minor also may require
proof ; still another induction, as
thus : — What is asserted by intelli-
gent and disinterested witnesses may

be believed to be true ; that the go-
vernment acts in this manner is as-
serted by such witnesses, therefore it
may be believed to be true. The argu-
ment hence consists of three steps.
Having the evidence of our senses
that the case of the government under
consideration resembles a number of
former cases, in the circumstance of
having something asserted respecting
it by intelligent and disinterested wit-
nesses, we infer, first, that, as in those
former instances, so in this instance,
the assertion is true. Secondly, what
was asserted of the government being
that it acts in a particular manner,
and other governments or persons
having been observed to act in the
same manner, the government in ques-
tion is brought into known resem-
blance with those other governments
or persons ; and since they were
known to desire the good of the people,
it is thereupon, by a second induction,
inferred that the particular govern-
ment spoken of desires the good of
the people. This brings that govern-
ment into known resemblance with
the other governments which were
thought likely to escape revolution,
and thence, by a third induction, it is
concluded that this particular govern-
ment is also likely to escape. This
is still reasoning from particulars to
particulars, but we now reason to the
new instance from three distinct sets
of former instances : to one only of
those sets of instances do we directly
perceive the new one to be similar ;
but from that similarity we induc-
tively infer that it has the attribute
by which it is assimilated to the next
set, and brought within the corre-
sponding induction ; after which by
a repetition of the same operation we
infer it to be similar to the third set,
and hence a third induction conducts
us to the ultimate conclusion.

§ 3. Notwithstanding the superior
complication of these examples, com-
pared with those by which in the pre-
ceding chapter we illustrated the
general theory of reasoning, every

140

REASONING.

doctrine which we then laid down
holds equally true in these more in-
tricate cases. The successive general
propositions are not steps in the
reasoning, are not intermediate links
in the chain of inference between the
particulars observed and those to
which we apply the observation. If
we had sufficiently capacious memo-
ries, and a sufficient power of main-
taining order among a huge mass of
details, the reasoning could go on with-
out any general propositions ; they are
mere formulae for inferring particulars
from particulars. The principle of
general reasoning is (as before ex-
plained), that if, from observation of
certain known particulars, what was
seen to be true of them can be inferred
to be true of any others, it may be
inferred of all others which are of a
certain description. And in order
that we may never fail to draw this
conclusion in a new case when it can
be drawn correctly, and may avoid
drawing it when it cannot, we deter-
mine once for all what are the dis-
tinguishing marks by which such
cases may be recognised. The sub-
sequent process is merely that of
identifying an object, and ascertain-
ing it to have those marks ; whether
we identify it by the very marks
themselves, or by others which we
have ascertained (through another and
a similar process) to be marks of those
marks. The real inference is always
from particulars to particulars, from
the observed instances to an unob-
served one ; but in drawing this in-
ference, we conform to a formula
which we have adopted for our guid-
ance in such operations, and which is
a record of the criteria by which we
thought we had ascertained that we
might distinguish when the inference
could, and when it could not, be drawn.
The real premises are the individual
observations, even though they may
have been forgotten, or, being the
observations of others and not of our-
selves, may, to us, never have been
known : but we have before us proof
that we or others once thought them

sufficient for an induction, and we
have marks to show whether any new
case is one of those to which, if then
known, the induction would have been
deemed to extend. These marks we
either recognise at once, or by the aid
of other marks, which by another pre-
vious induction we collected to be
marks of the first. Even these marks
of marks may only be recognised
through a third set of marks ; and
we may have a train of reasoning, of
any length, to bring a new case with-
in the scope of an induction grounded
on particulars its similarity to which
is only ascertained in this indirect
manner.

Thus, in the preceding example, the
ultimate inductive inference was, that
a certain government was not likely
to be overthown ; this inference was
drawn according to a formula in which
desire of the public good was set down
as a mark of not being likely to be
overthrown ; a mark of this mark
was acting in a particular manner ;
and a mark of acting in that manner
was being asserted to do so by intelli-
gent and disinterested witnesses : this
mark the government under discus-
sion was recognised by the senses as
possessing. Hence that government
fell within the last induction, and by
it was brought within all the others.
The perceived resemblance of the
case to one set of observed particular
cases brought it into known resem-
blance with another set, and that with
a third.

In the more complex branches of
knowledge, the deductions seldom
consist, as in the examples hitherto
exhibited, of a single chain, a a mark
of b, b of c, c of d, therefore a a mark
of d. They consist (to carry on the
same metaphor) of several chains
united at the extremitv, as thus : a a
mark of d. ft of e, c of f, d ef of n,
therefore a b c a mark of n. Suppose,
for example, the following combina-
tion of circumstances : i st, rays of
light impinging on a reflecting sur-
face ; 2nd, that surface parabolic ;
3rd, those rays parallel to each other

TRAINS OF REASONING.

141

and to the axis of the surface. It is
to be proved that the concourse of
these three circumstances is a mark
that the reflected rays will pass
through the focus of the parabolic
surface. Now, each of the three cir-
cumstances is singly a mark of somek-
thing material to the case. Rays of
light impinging on a reflecting sur-
face are a mark that those rays will
be reflected at an angle equal to the
angle of incidence. The parabolic
fonn of the surface is a mark that,
from any point of it a line drawn to
the focus and a line parallel to the
axis will make equal angles with the
surface. And finally, the parallelism
of the rays to the axis is a mark that
their angle of incidence coincides with
one of these equal angles. The three
marks taken together are therefore a
mark of all these three things united.
But the three united are evidently a
mark that the angle of reflection must
coincide with the other of the two
equal angles, that formed by a line
drawn to the focus ; and this again,
by the fundamental axiom concerning
straight lines, is a mark that the re-
flected rays pass through the focus.
Most chains of physical deduction are
of this more complicated type ; and
even in mathematics such are abun-
dant, as in all propositions where the
hypothesis includes numerous condi-
tions : " If a, circle be taken, and if
Avithin that circle a point be taken,
not the centre, and if straight lines be
drawn from that point to the circum-
ference, then,' &c.

§ 4. The considerations now stated
remove a serious difficulty from the
view we have taken of reasoning,
which view might otherwise have
seemed not easily reconcilable with
the fact that there are Deductive or
Ratiocinative Sciences. It might seem
to follow, if all reasoning be induction,
that the difficulties of philosophical
investigation must lie in the induc-
tions exclusi.vely, and that when these
were easy, and susceptible of no doubt
or hesitation, there could be no science,

or, at least, no difficulties in science.
The existence, for example, of an ex-
tensive Science of Mathematics, re-
quiring the highest scientific genius
in those who contributed to its crea-
tion, and calling for a most continued
and vigorous exertion of intellect in
order to appropriate it when created,
may seem hard to be accounted for on
the foregoing theory. But the con-
siderations more recently adduced re-
move the mystery, by showing that
even when the inductions themselves
are obvious, there may be much diffi-
culty in finding whether the particular
case which is the subject of inquiry
comes within them ; and ample room
for scientific ingenuity in so combin-
ing various inductions, as, by means
of one within which the case evidently
falls, to bring it within others in which
it cannot be directly seen to be in-
cluded.

When the more obvious of the in-
ductions which can be made in any
science from direct observations have
been made, and general formulas have
been framed, determining the limits
within which these inductions are ap-
plicable ; as often as a new case can
be at once seen to come within one of
the formulas, the induction is applied
to the new case, and the business is
ended. But new cases are continually
arising, which do not obviously come
within any formula whereby the ques-
tion we want solved in respect of them
could be answered. Let us take an
instance from geometry : and as it is
taken only for illustration, let the
reader concede to us for the present,
what we shall endeavour to prove in
the next chapter, that the first prin-
ciples of geometry are results of in-
duction. Our example shall be the
fifth proposition of the first book of
Euclid. The inquiry is, Are the
angles at the base of an isosceles tri-
angle equal or unequal? The first
thing to be considered is, what in-
ductions we have, from which we can
infer equality or inequality. For in-
ferring equality we have the following
formulae : — Things which being ap-

142

REASONING.

plipd to each other coincide are equals.
Things which are equal to the same
thing are equals. A whole and the
sum of its parts are equals. The sums
of equal things are equals. The dif-
ferences of equal things are equals.
There are no other original formulae
to prove equality. For inferring in-
equality we have the following : — A
whole and its parts are unequals.
The sums of equal things and unequal
things are unequals. The differences
of equal things and unequal things
are unequals. In all, eight formulEe.
The angles at the base of an isosceles
triangle do not obviously come within
any of these. The formulae specify
certain marks of equality and of in-
equality, but the angles cannot be
perceived intuitively to have any of
those marks. On examination it ap-
pears that they have ; and we ulti-
mately succeed in bringing them
within the formula, " The differences
of equal things are equal." Whence
comes the difficulty of recognising
these angles as the differences of
equal things? Because each of them
is the difference not of one pair only,
but of innumerable pairs of angles ;
and out of these we had to imagine
and select two, which could either
be intuitively perceived to be equals,
or poasessed some of the marks of
equality set down in the various for-
mulae. By an exercise of ingenuity,
which, on the part of the first inven-
tor, deserves to be regarded as con-
siderable, two pairs of angles were
hit upon which united these requi-
sites. First, it could be perceived
intuitively that their differences were
the angles at the base ; and, secondly,
they possessed one of the marks of
equality, namely, coincidence when
applied to one another. This coin-
cidence, however, was not perceived
intuitively, but inferrediu coniormity
to another fi)rmula.

For greater clearness, I subjoin an
analysisof Lliedemonstratiou. Kuclid,
it will be remembered, demonstrates
his fitth proposition by means of the
fourth. This is uut aliowabU for U4

to do, because we are undertaking to
trace deductive truths not to prior
deductions, but to their original in-
ductive foundation. We must there-
fore use the premises of the fourth
proposition instead of its conclusion,
and prove the fifth directly from
first principles. To do so requires
six formulas. (We must begin, as in
Euclid, by prolonging the equal sides
AB, AC, to equal distances, and join-
ing the extremities BE, DC. )

First Formula. — The sums of equals
are equal.

AD and AE are sums of equals by
the supposition. Having that mark
of equality, they are concluded by
this formula to be equal.

Second Formula. — Equal straight
lines or angles, being applied to one
another, coincide.

AC, AB, are within this formula
by supposition ; AD, AE, have been
brought within it by the preceding
step. The angle at A considered as
an angle of the triangle ABE, and
the same angle considered as an angle
of the triangle ACD, are of course
within the formula. All these pairs
therefore possess the property which,
according to the second formula, is a
mark that when applied to one ano-
ther they will coincide. Conceive
them, then, applied to one another
by turning over the triangle ABE,
and laying it on the triangle ACD in
such a manner that AB of the one
shall lie upoQ AC qf the other. Then,

TRAINS OF REASONING.

143

by the equality of the angles, AE will
Ue on AD. But AB and AC, AE
and AD are equals ; therefore they
will coincide altogether, and of course
at their extremities, D, E, and B, C.

Third Fobmvla.— Straight lines, hav-
ing their extremities coincident, coin-
cide.

B E and CD have been brought
within this formula by the preceding
induction ; they will, therefore, coin-
cide.

Fourth Formula. — Angles, having
their sides coincident, coincide.
The third induction having shown
that BE and CD coincide, and the
second that AB, AC, coincide, the
angles ABE and ACD are thereby
brought within the fourth formula,
and accordingly coincide.

Fifth Formula. — Things which coin-
cide are equal.
The angles ABE and ACD are
brought within this formxila by the
induction immediately preceding.
This train of reasoning being also
applicable, mutatis mutandis, to the
angles EBC, DCB, these also are
brought within the fifth formula.
And, finally.

Sixth Formula. — The differences of
equals are equaL

The angle ABC being the differ-
ence of ABE, CBE, and the angle
ACB being the difference of ACD,
DCB ; which have been proved to be
equals ; ABC and ACB are brought
within the last formula by the whole
of the previous process.

The difficulty here encountered is
chiefly that of figuring to ourselves
the two angles at the base of the
triangle ABC as remainders made by
cutting one pair of angles out of an-
other, while each pair shall be corre-
sponding angles of triangles which
have two sides and the intervening
angle equal It is by this happy con-
trivance that so many different iqduc-

tions are brought to bear upon the
same particular case. And this not
being at all an obvious thought, it
may be seen from an example so near
the threshold of mathematics how
much scope there may well be for
scientific dexterity in the higher
branches of that and other sciences,
in order so to combine a few simple
inductions as to bring within each of
them innumerable cases which are not
obviously included in it ; and how
long, and numerous, and complicated
may be the processes for bringing the
inductions together, even when each
induction may itself be very easy and
simple. All the inductions involved
in all geometry are comprised in those
simple ones, the fornmlse of which are
the Axioms, and a few of the so-called
Definitions. The remainder of the
science is made up of the processes
employed forbringingunforeseen cases
within these inductions ; or (in syllogis-
tic language) for proving the minors
necessary to complete the syllogisms ;
the majors being the definitions and
axioms. In those definitions and
axioms are laid down the whole of
the marks, by an artful combination
of which it has been found possible
to discover and prove all that is
proved in geometry. The marks
being so few, and the inductions which
furnish them being so obvious and
familiar ; the connecting of several of
them together, which constitutes De-
ductions or Trains of Reasoning, forms
the whole difficulty of the science, and,
with a trifling exception, its whole
bulk ; and hence Geometry is a De-
ductive Science.

§ 5. It will be seen hereafter * that
there are weighty scientific reasons
for giving to every science as much of
the character of a Deductive Science
as possible ; for endeavouring to con-
struct the science from the fewest and
the simplest possible inductions, and
to make these, by any combinations
however complicated, suffice for prov-

* Infra, book lii. ch. iv. $ 3, and else-
where.

144

REASONING

ing even such truths, relating to com-
plex cases, as could be proved, if we
chose, by inductions from specific
experience. Every branch of natural
philosophy was originally experimen-
tal ; each generalisation rested on a
special induction, and was derived
from its own distinct set of observa-
tions and experiments. From being
sciences of pure experiment, as the
phrase is, or, to speak more correctly,
sciences in which the reasonings
mostly consist of no more than one
step, and are expressed by single
syllogisms, all these sciences have
become to some extent, and some of
them in nearly the whole of their
extent, sciences of pure reasoning ;
whereby multitudes of truths, already
known by induction from as many
different sets of experiments, have
come to be exhibited as deductions or
corollaries from inductive propositions
of a simpler and more universal char-
acter. Thus mechanics, hydrostatics,
optics, acoustics, thermology, have
successively been rendered mathe-
matical ; and astronomy was brought
by Newton within the laws of general
mechanics. Why it is that the sub-
stitution of this circuitous mode of
proceeding for a process apparently
much easier and more natural, is held,
and justly, to be the greatest triumph
of the investigation of nature, we are
not, in this stage of our inquiry, pre-
pared to examine. But it is neces-
sary to remark, that although, by
this progressive transformation, all
sciences tend to become more and
more Deductive, they are not, there-
fore, the less Inductive ; every step
in the Deduction is still an Induc-
tion. The opposition is not between
the terms Deductive and Inductive,
but between Deductive and Experi-
mental. A science is experimental,
in proportion as every new case, which
presents any peculiar features, stands
in need of a new set of observations
and experiments — a fresh induction.
It is deductive, in proportion as it
can draw conclusions, respecting cases
pf a new kind, by processes which

bring those cases under old induc-
tions ; by ascertaining that cases
which cannot be observed to have
the requisite marks, have, however,
marks of those marks.

We can now, therefore, perceive
what is the generic distinction be-
tween sciences which can be made
Deductive, and those which must as
yet remain Experimental. The dif-
ference consists in our having been
able, or not yet able, to discover
marks of marks. If by our various
inductions we have been able to pro-
ceed no farther than to such proposi-
tions as these, a a mark of b, or a
and b marks of one another, c a mark
of d, or c and d marks of one another,
without anything to connect a or 6
with c or d; we have a science of
detached and mutually independent
generalisations, such as these, that
acids redden vegetable blues, and that
alkalies colour them green ; from
neither of which propositions could
we, directly or indirectly, infer the
other ; and a science, so far as it is
composed of such propositions, ia
purely experimental. Chemistry, in
the present state of our knowledge,
has not yet thrown off this character.
There are other sciences, however, of
which the propositions are of this
kind : a a mark of b, b a. mark of c,
c ot d, d of e, &c. In these sciences,
we can mount the ladder from a to g
by a process of ratiocination ; we can
conclude that a is a mark of e, and
that every object which has the mark
a has the property e, although, per-
haps, we never were able to observe
a and e together, and although even
d, our only direct mark of e, may not
be perceptible in those objects, but
only inferrible. Or, varying the first
metaphor, we may be said to get from
a to e underground : the marks b, c,
d, which indicate the route, must all
be possessed somewhere by the objects
concerning which we are inquiring ;
but they are below the surface : a is
the only mark that is visible, and by
it we are able to trace in succession
all the rest.

TRAINS OF REASONING.

H5

§ 6. We can now understand how
an experimental may transform itself
into a deductive science by the mere
progress of experiment. In an ex-
perimental science, the inductions, as
we have said, lie detached, as a a
mark of 6, c a mark oi d, e a. mark of
/, and so on : now, a new set of in-
stances, and a consequent new induc-
tion, may at any time bridge over the
interval between two of these uncon-
nected arches ; b, for example, may
be ascertained to be a mark of c,
which enables us thenceforth to prove
deductively that a is a mark of c.
Or, as sometimes happens, some com-
prehensive induction may raise an
arch high in the air, which bridges
over hosts of them at once : b, d, f,
and all the rest, turning out to be
marks of some one thing, or of things
between which a connection has
already been traced. As when New-
ton discovered that the motions,
whether regular or apparently ano-
malous, of all the bodies of the solar
system (each of which motions had
been inferred by a separate logical
operation from separate marks) were
all marks of moving round a common
centre, with a centripetal force vary-
ing directly as the mass, and inversely
as the square of the distance from
that centre. This is the greatest
example which has yet occurred of
the transformation, at one stroke, of
a science which was still to a great
degree merely experimental, into a
deductive science.

Transformations of the same nature,
but on a smaller scale, continually
take place in the less advanced
branches of physical knowledge, with-
out enabling them to throw off the
character of experimental sciences.
Thus with regard to the two un-
connected propositions before cited,
namely, Acids redden vegetable blues,
Alkalies make them green ; it is re-
marked by Liebig, that all blue
colouring matters which are reddened
by acids (as well as, reciprocally, all
red colouring matters which are ren-
dered blue by alkalies) contain nitro-

gen : and it is quite possible that
this circumstance may one day furnish
a bond of connection between the two
propositions in question, by showing
that the antagonistic action of acids
and alkalies in producing or destroy-
ing the colour blue is the result of
some one, more general, law. Al-
though this connecting of detached
generalisations is so much gain, it
tends but little to give a deductive
character to any science as a whole ;
because the new courses of observa-
tion and experiment, which thus en-
able us to connect together a few
general truths, usually make known
to us a still greater number of uncon-
nected new ones. Hence chemistry,
though similar extensions and simpli-
fications of its generalisations are
continually taking place, is still in
the main an experimental science,
and is likely so to continue unless
some comprehensive induction should
be hereafter arrived at, which, like
Newton's, shall connect a vast num-
ber of the smaller known inductions
together, and change the whole
method of the science at once. Chem-
istry has already one great generalisa-
tion, which, though relating to one of
the subordinate aspects of chemical
phenomena, possesses within its limited
sphere this comprehensive character ;
the principle of Dalton, called the
atomic theory, or the doctrine of
chemical equivalents, which, by en-
abling us to a certain extent to fore-
see the proportions in which two
substances will combine, before the
experiment has been tried, constitutes
undoubtedly a source of new chemical
truths obtainable by deduction, as
well as a connecting principle for all
truths of the same description pre-
viously obtained by experiment

§ 7. The discoveries which change
the method of a science from experi-
mental to deductive mostly consist in
establishing, either by deduction or by
direct experiment, that the varieties
of a particular phenomenon uniformly
accompany the varieties of some other

146

REASONING.

phenomenon better known. Thus the
science of sound, which previously
stood in the lowest rank of merely
experimental science, became deduc-
tive when it was proved by experiment
that every variety of sound was con-
sequent on, and therefore a mark of,
a distinct and definable variety of
oscillatory motion among the particles
of the transmitting medium. When
this was ascertained it followed that
every relation of succession or co-ex-
istence which obtained between phe-
nomena of the more known class,
obtained also between the phenomena
which correspond to them in the
other class. Every sound, being a
mark of a particular oscillatory mo-
tion, became a mark of everything
which, by the laws of dynamics, was
known to be inferrible from that
motion ; and everything which by
those same laws was a mark of any
oscillatory motion among the particles
of an elastic medium became a mark
of the corresponding sound. And thus
many truths, not before suspected,
concerning sound become deducible
from the known laws of the propaga-
tion of motion through an elastic
medium ; while facts already empiri-
cally known respecting sound become
an indication of corresponding pro-
perties of vibrating bodies, previously
undiscovered.

But the grand agent for trans-
forming experimental into deductive
sciences is the science of number.
The properties of number, alone
among all known phenomena, are, in
the most rigorous sense, properties
of all things whatever. All things
are not coloured, or ponderable, or
even extended ; but all things are
numerable. And if we consider this
science in its whole extent, from
common arithmetic up to the calculus
of variations, the truths already ascer-
tained seem all but infinite, and
admit of indefinite extension.

These truths, though affirmable of
all things whatever, of course apply
to them only in respect of their
quantity. But if it comes to be dis-

covered that variations of quality in
any class of phenomena correspond
regularly to variations of quantity
either in those same or in some other
phenomena ; every formula of mathe-
matics applicable to quantities which
vary in that particular manner be-
comes a mark of a corresponding
general truth respecting the varia-
tions in quality which accompany
them ; and the science of quantity
being (as far as any science can be)
altogether deductive, the theory of
that particular kind of qualities be-
comes, to this extent, deductive like-
wise.

The most striking instance in point
which history affords (though not an
example of an experimental science
rendered deductive, but of an unparal-
leled extension given to the deductive
process in a science which was deduc-
tive already) is the revolution in
geometry which originated with Des-
cartes and was completed by Clair-
aut. These great mathematicians
pointed out the importance of the
fact, that to every variety of position
in points, direction in lines, or form
in curves or surfaces, (all of which
are Qualities,) there corresponds a
peculiar relation of quantity between
either two or three rectilineal co-ordi-
nates ; insomuch that if the law were
known according to which those co-
ordinates vary relatively to one an-
other, every other geometrical pro-
perty of the line or surface in ques-
tion, whether relating to quantity or
quality, would be capable of being
inferred. Hence it followed that
every geometrical question could be
solved, if the corresponding alge-
braical one could ; and geometry
received an accession (actual or poten-
tial) of new truths, corresponding to
every property of numbers which the
progress of the calculus had brought,
or might in future bring, to light. In
the same general manner, mechanics,
astronomy, and in a less degree every
branch of natural philosophy com-
monly so called, have been made
algebraical. The varieties of physi-

DEMONSTRATION AND NECESSARY TRUTHS.

147

cal phenomena with which those
sciences are conversant have been
found to answer to determinable
varieties in the quantity of some
circumstance or other ; or at least to
varieties of form or position for which
corresponding equations of quantity
had already been, or were susceptible
of being, discovered by geometers.

In these various transformations,
the propositions of the science of
number do but fulfil the function
proper to all propositions forming a
train of reasoning, viz. that of enabling
us to arrive in an indirect method, by
marks of marks, at such of the pro-
perties of objects as we cannot directly
ascertain (or not so conveniently) by
experiment. We travel from a given
visible or tangible fact through the
truths of numbers to the facts sought.
The given fact is a mark that a cer-
tain relation subsists between the
quantities of some of the elements
concerned ; while the fact sought pre-
supposes a certain relation between
the quantities of some other elements.
Now, if these last quantities are de-
pendent in some known manner upon
the former, or mce versd, we can
argue from the numerical relation
between the one set of quantities to
determine that which subsists between
the other set ; the theorems of the
calculus affording the intermediate
links. And thus one of the two
physical facts becomes a mark of the
other, by being a mark of a mark of
a mark of it.

CHAPTER V.

or DEMONSTRATION AND NECESSARY
TRUTHS.

§ I. If, as laid down in the two
preceding chapters, the foundation of
all sciences, even deductive or demon-
strative sciences, is Induction ; if every
step in the ratiocinations even of geo-
metry is an act of induction ; and if
a train of reasoning is but bringing
many inductions to b«ar upon the

same subject of inquiry, and drawing
a case within one induction by means
of another ; wherein lies the pecu-
liar certainty always ascribed to the
sciences which are entirely, or almost
entirely, deductive ? Why are they
called the Exact Sciences? Why
are mathematical certainty, and the
evidence of demonstration, common
phrases to express the very highest
degree of assurance attainable by
reason ? Why are mathematics by
almost all phi^-isophers, and (by some)
even those branches of natural philo-
sophy which, through the medium of
mathematics, have been converted in-
to deductive sciences, considered to be
independent of the evidence of experi-
ence and observation, and character-
ised as systems of Necessary Truth ?

The answer I conceive to be, that
this character of necessity ascribed
to the truths of mathematics, and even
(with some reservations to be hereafter
made) the peculiar certainty attributed
to them, IS an illusion ; in order to
sustain which, it is necessary to sup-
pose that those truths relate to, and
express the properties of purely ima-
ginary objects. It is acknowledged
that the conclusions of geometry are
deduced, partly at least, from the so-
called Definitions, and that those de-
finitions are assumed to be correct
representations, as far as they go, trf
the objects with which geometry is
conversant. Now we have pointed
out that, from a definition as such, no
proposition, unless it be one concern-
ing the meaning of a word, can ever
follow ; and that what apparently
follows from a definition, follows in
reality from an implied assumption
that there exists a real thing con-
formable thereto. This assumption
in the case of the definitions of geo-
metry, is not strictly true : there
exist no real things exactly conform-
able to the definitions. There exist
no points without magnitude ; no
lines without breadth, nor perfectly
straight ; no circles with all their
radii exactly equal, nor squares with
all their angles perfectly right. It

148

REASONING.

will perhaps be said that the assump-
tion does not extend to the actual,
but only to the possible existence of
such things. I answer that, accord-
ing to any test we have of possibility,
they are not even possible. Their
existence, so far as we can form any
judgment, would seem to be incon-
sistent with the physical constitution
of our planet at least, if not of the
universe. To get rid of this diflfi-
culty, and at the same time to save
the credit of the supposed system of
necessary truth, it is customary to say
that the points, lines, circles, and
squares which are the subject of geo-
metry, exist in our conceptions merely,
and are part of our minds ; which
minds, by working on their own
materials, construct an A priori
science, the evidence of which is
purely mental, and has nothing what-
ever to do with outward experience.
By howsoever high authorities this
doctrine may have been sanctioned, it
appears to me psychologically incor-
rect. The points, lines, circles, and
squares which any one has in his
mind, are (I apprehend) simply copies
of the points, lines, circles, and squares
which he has known in his experience.
Our idea of a point I apprehend to
be simply our idea of the minimum
visibUe, the smallest portion of sur-
face which we can see. A line as
defined by geometers is wholly incon-
ceivable. We can reason about a line
as if it had no breadth ; because we
have a power, which is the foundation
of all the control we can exercise over
the operations of our minds ; the
power, when a perception is present
to our senses or a conception to our
intellects, of attending to a part only
of that perception or conception, in-
stead of the whole. But we cannot
conceive a line without breadth ; we
can form no mental picture of such a
line ; all the lines which we have in
our minds are lines possessing breadth.
If any one doubts this, we may refer
him to his own experience. I much
question if any one who fancies that
Oe can conceive what is called a mathe-

matical line, thinks so from the evi<
dence of his consciousness : I suspect
it is rather because he supposes that
unless such a conception were possible,
mathematics could not exist as a
science : a supposition which there
will be no difficulty in showing to be
entirely groundless.

Since, then, neither in nature, nor
in the human mind, do there exist
any objects exactly corresponding to
the definitions of geometry, while yet
that science cannot be supposed to be
conversant about non-entities ; no-
thing remains but to consider geo-
metry as conversant with such lines,
angles, and figures as really exist ;
and the definitions, as they are called,
must be regarded as some of our first
and most obvious generalisations con-
cerning those natural objects. The
correctness of those generalisations,
as generalisations, is without a flaw :
the equality of all the radii of a circle
is true of all circles, so far as it ia
true of any one : but it is not exactly
true of any circle ; it is only nearly
true ; so nearly that no error of any
importance in practice will be incurred
by feigning it to be exactly true.
When we have occasion to extend
these inductions, or their consequences,
to cases in which the error would be
appreciable — to lines of perceptible
breadth or thickness, parallels which
deviate sensibly from equidistance,
and the like — we correct our conclu-
sions by combining with them a fresh
set of propositions relating to the
aberration ; just as we also take in
propositions relating to the physical
or chemical properties of the material,
if those properties happen to introduce
any modification into the result ;
which they easily may, even with re-
spect to figure and magnitude, as in
the case, for instance, of expansion
by heat. So long, however, as there
exists no practical necessity for at-
tending to any of the properties of
the object except its geometrical pro-
perties, or to any of the natural irre-
gularities in those, it is convenient to
neglect the consideration of the other

DEMONSTRATION AND NECESSARY TRUTHS.

149

properties and of the irregularities,
and to reason as if these did not
exist : accordingly, we formally an-
nounce in the definitions, that we in-
tend to proceed on this plan. But it
is an error to suppose, because we re-
solve to confine our attention to a
certain number of the properties of
an object, that we therefore conceive,
or have an idea of, the object denuded
of its other properties. We are think-
ing, all the time, of precisely such
objects as we have seen and touched,
and with all the properties which
naturally belong to them ; but, for
scientific convenience, we feign them
to be divested of all properties, except
those which are material to our pur-
pose, and in regard to which we de-
sign to consider them.

The peculiar accuracy, supposed to
be characteristic of the first principles
of geometry thus appears to be ficti-
tious. The assertions on which the
reasonings of the science are founded
do not, anymore than in other sciences,
exactly correspond with the fact, but
we suppose that they do so for the
sake of tracing the consequences
which follow from the supposition.
The opinion of Dugald Steward re-
specting the foundations of geometry,
is, I conceive, substantially correct ;
that it is built on hypotheses ; that
it owes to this alone the peculiar
certainty supposed to distinguish it ;
and that in any science whatever, by
reasoning from a set of hypotheses,
we may obtain a body of conclusions
as certain as those of geometry, that
is, as strictly in accordance with the
hypotheses, and as irresistibly com-
pelling assent, on condition that those
hypotheses are true.*

* It is justly remarked by Professor Bain
(Logic, ii. 134) that the word Hypothesis is
used here in a somewhat peculiar sense.
An hypothesis, in science, usually means
a supposition not proved to be true, btit
surmised to be so because if true it would
account for certain known fact.5 ; and the
final result of the speculation may be to
prove its truth. The hypotheses .sjjoken
of in the text are of a different character ;
they arc known not to be literally true,
while as much of them as is true is not

When, therefore, it is affirmed that
the conclusions of geometry are neces-
sary truths, the necessity consists in
reality only in this, that they correctly
follow from the suppositions from
which they are deduced. Those
suppositions are so far from being
necessary, that they are not even
true ; they purposely depart, more or
less widely, from the truth. The
only sense in which necessity can be
ascribed to the conclusions of any
scientific investigation, is that of
legitimately following from some as-
sumption, which, by the conditions
of the inquiry, is not to be questioned.
In this relation, of course, the deriva-
tive truths of every deductive science
must stand to the inductions, or as-
sumptions, on which the science is
founded, and which, whether true or
untrue, certain or doubtful in them-
selves, are always supposed certain
for the purposes of the particular
science. And therefore the conclu-
sions of all deductive sciences were
said by the ancients to be necessary
propositions. We have observed al-
ready that to be predicated necessarily
was characteristic of the predicable
Proprium, and that a proprium was
any property of a thing which could
be deduced from its essence, that is,
from the properties included in its
definition.

§ 2. The important doctrine of
Dugald Stewart, which I have en-
deavoured to enforce, has been con-
hypothetical, but certain. The two cases,
however, resemble in the circumstance
that in both we reason, not from a truth,
but from an assumption, and the truth
therefore of the conclu.sions is conditional,
not categorical. This suffices to justify, iu
point of logical propriety, Stewart's use of
the term. It is of course needful to bear
in mind that the hypothetical element in
the definitions of geometry is the assump-
tion tliat what is very nearly true is exactly
so. Thi.s unreal exactiivide might be called
a fiction, as properly as an hypothesis ; but
that appellation, still more tlmn the other,
would fail to point out the close relation
which exists between the fictitious point
or line and the points and lines of which
we have exjierience.

ISO

REASONING.

tested by Dr. Whewell, both in the
dissertation appended to his excellent
Mechanical Euclid, and in his elabo-
rate work on the Philosophy of the
Inductive Sciences; in which last he
also replies to an article in the Edin-
burgh Review, (ascribed to a writer
of great scientific eminence,) in which
Stewart's opinion was defended against
his former strictures. The supposed
refutation of Stewart consists in prov-
ing against him (as has also been done
in this work) that the premises of
geometry are not definitions, but
assumptions of the real existence of
things corresponding to those defini-
tions. This, however, is doing little
for Dr. Whewell's purpose ; for it is
these very assumptions which are
asserted to be hypotheses, and which
he, if he denies that geometry is
founded on hypotheses, must show to
be absolute truths. All he does,
however, is to observe, that they, at
any rate, are not arbitrary hypotheses;
that we should not be at liberty to
substitute other hypotheses for them;
that not only "a definition, to be
admissible, must necessarily refer to
and agree with some conception
which we can distinctly frame in our
thoughts," but that the straight lines,
for instance, which we define, must
be "those by which angles are con-
tained, those by which triangles are
bounded, those of which parallelism
may be predicated, and the like."*
And this is true : but this has never
been contradicted. Those who say
that the premises of geometry are
hypotheses, are not bound to main-
tain them to be hypotheses which
have no relation whatever to fact.
Since an hypothesis framed for the
purpose of scientific inquiry must
relate to something which has real
existence, (for there can be no science
respecting non -entities,) it follows
that any hypothesis we make respect-
ing an object, to facilitate our study
of it, must not involve anything which
is distinctly false, and repugnant to

* Mechanical Suclid, pp. 149 ei ttq.

its real nature : we must not ascribe
to the thing any property which it
has not ; our liberty extends only to
slightly exaggerating some of those
which it has, (by assuming it to be
completely what it really is very
nearly,) and suppressing others, under
the indispensable obligation of restor-
ing them whenever, and in as far as,
their presence or absence would make
any material difference in the truth
of our conclusions. Of this nature,
accordingly, are the first principles in-
volved in the definitions of geometry.
That the hypotheses should be of this
particular character is, however, no
further necessary, than inasmuch as
no others could enable us to deduce
conclusions which, with due correc-
tions, would be true of real objects :
and in fact, when our aim is only to
illustrate truths, and not to investi-
gate them, we are not under any
such restriction. We might suppose
an imaginary animal, and work out
by deduction, from the known laws
of physiology, its natural history ; or
an imaginary commonwealth, and
from the elements composing it
might argue what would be its fate.
And the conclusions which we might
thus draw from purely arbitrary
hypotheses might form a highly
useful intellectual exercise : but as
they could only teach us what would
be the properties of objects which do
not really exist, they would not con-
stitute any addition to our knowledge
of nature : while, on the contrary, if
the hypothesis merely divests a real
object of some portion of its properties,
without clothing it in false ones, the
conclusions will always express, under
known lia-bility to correction, actual
truth.

§ 3. But though Dr. Whewell has
not shaken Stewart's doctrine as to
the hypothetical character of that
portion of the first principle* of
geometry which are involved in the
so-called definitions, he has, I con-
ceive, greatly the advantage of Stewart
on another important point in the

DEMONSTRATION AND NECESSARY TRUTHS.

i5t

theory of geometrical reasoning ; the
necessity of admitting, among those
first principles, axioms as well as
definitions. Some of the axioms of
Euclid might, no doubt, be exhibited
in the form of definitions, or might
be deduced, by reasoning, from pro-
positions similar to what are so called.
Thus, if instead of the axiom, Mag-
nitudes which can be made to coin-
cide are equal, we introduce a defini-
tion, "Equal magnitudes are those
which may be so applied to one
another as to coincide ; " the three
axioms which follow (Magnitudes
Avhich are equal to the same are
equal to one another — If equals are
added to equals the sums are equal —
If equals are taken from equals the
remainders are equal) may be proved
by an imaginary superposition, re-
sembling that by which the fourth
proposition of the first book of Euclid
is demonstrated. But though these
and several others may be struck out
of the list of first principles, because,
though not requiring demonstration,
they are susceptible of it : there will
be found in the list of axioms two or
three fundamental truths not capable
of being demonstrated : among which
must be reckoned the proposition
that two straight lines cannot, enclose
a space, (or its equivalent, Straight
lines which coincide in two points
coincide altogether,) and some pro-
perty of parallel lines, other than
that which constitutes their defini-
tion ; one of the most suitable for
the purpose being that selected by
Professor Play fair : "Two straight
lines which intersect each other can-
not both of them be parallel to a
third straight line."*

The axioms, as well those which
are indemonstrable as those which

* We might, it is true, insert this pro-
perty into the definition of parallel lines,
framing the definition so as to require,
both that when produced indefinitely they
shall never meet, and also that any straight
line which intersects one of them shall, if
prolonged, meet the other. But by doing
this we by no means get rid of the as8umx>
tion ; we are still obliged to take for granted
the geometrical truth that all straight lines

admit of being demonstrated, differ
from that other class of fundamental
principles which are involved in the
definitions, in this, that they are true
without any mixture of hypothesis.
That things which are equal to the
same thing are equal to one another,
is as true of the lines and figures in
nature, as it would be of the imagi-
nary ones assumed in the definitions.
In this respect, however, mathematics
are only on a par with most other
sciences. In almost all sciences there
are some general propositions which
are exactly true, while the greater
part are only more or less distant
approximations to the truth. Thus
in mechanics, the first law of motion
(the continuance of a movement once
impressed, until stopped or slackened
by some resisting force) is true with-
out qualification or error. The rota-
tion of the earth in twenty- four hours,
of the same length as in our time, has
gone on since the first accurate ob-
servations, without the increase or
diminution of one second in all that
period. These are inductions which
require no fiction to make them be
received as accurately true : but along
with them there are others, as, for
instance, the propositions respecting
the figure of the earth, which are but
approximations to the truth ; and in
order to use them for the further
advancement of our knowledge, we
must feign that they are exactly true,
though they really want something
of being so.

§ 4. It remains to inquire, what is
the ground of our belief in axioms —
what is the evidence on which they
rest ? I answer, they are experi-
mental truths ; generalisations from
observation. The proposition, Two
in the same plane, which have the former
of these properties, have also the latter.
For if it were possible that they should not,
ts at is, if any straight lines in the same
plane, other than those which aie parallel
according to the definition, had the pro-
perty of never meeting although inde-
finitely produced, the demonstrations of
the subsequent portions of the theory of
parallels could not be maintained.

152

HIJASONING.

straight lines cannot enclose a space
— or, in other words, two straight
lines which have once met do not
meet again, but continue to diverge
— is an induction from the evidence
of our senses.

This opinion runs counter to a
scientific prejudice of long standing
and great strength, and there is pro-
bably no proposition enunciated in
this work for which a more unfavour-
able reception is to be expected. It
is, however, no new opinion ; and
even if it were so, would be entitled
to be judged, not by its novelty, but
by the strength of the arguments by
which it can be supported. I con-
sider it very fortunate that so emi-
nent a champion of the contrary
opinion as Dr. Whewell has found
occasion for a most elaborate treat-
ment of the whole theory of axioms,
in attempting to construct the philo-
sophy of the mathematical and physi-
cal sciences on the basis of the doc-
trine against which I now contend.
Whoever is anxious that a discussion
should go to the bottom of the subject
must rejoice to see the opposite side
of the question worthily represented.
If what is said by Dr. Whewell, in
support of an opinion which he has
made the foundation of a systematic
work, can be shown not to be con-
clusive, enough will have been done,
without going elsewhere in quest of
stronger arguments and a more power-
ful adversary.

It is not necessary to show that the
truths which we call axioms are
originally suggested by observation,
and that we should never have known
that two straight lines cannot enclose
a space if we had never seen a straight
line : thus much being admitted by
Dr. Whewell and by all, in recent
times, who have taken his view of the
subject. But they contend that it
is not experience which proves the
axiom ; but that its truth is per-
ceived d priori, by the constitution
of the mind itself, from the first
moment when the meaning of the
proposition is apprehended, and with-

out any necessity for verifpng it by
repeated trials, as is requisite in the
case of truths really ascertained by
observation.

They cannot, however, but allow
that the truth of the axiom, Two
straight lines cannot enclose a space,
even if evident independently of ex-
perience, is also evident from expe-
rience. Whether the axiom needs
confirmation or not, it receives con-
firmation in almost every instant of
our lives, since we cannot look at
any two straight lines which intersect
one another without seeing that from
that point they continue to diverge
more and more. Experimental proof
crowds in upon us in such endless
profusion, and without one instance
in which there can be even a suspicion
of an exception to the rule, that we
should soon have stronger ground for
believing the axiom, even as an ex-
perimental truth, than we have for
almost any of the general truths which
we confessedly learn from the evi-
dence of our senses. Independently
of d priori evidence we should cer-
tainly believe it with an intensity of
conviction far greater than we accord
to any ordinary physical truth : and
this too at a time of life much earlier
than that from which we date almost
any part of our acquired knowledge,
and much too early to admit of our
retaining any recollection of the his-
tory of our inteUectuaal operations at
that period. Where then is the neces-
sity for assuming that our recognition
of these truths has a different origin
from the rest of our knowledge, when
its existence is perfectly accounted
for by supposing its origin to be the
same? when the causes which pro-
duce belief in all other instances
exist in this instance, and in a degree
of strength as much superior to what
exists in other cases as the intensity
of the belief itself is superior? The
burden of proof lies on the advo-
cates of the contrary opinion : it is
for them to point out some fact in-
consistent with the supposition that
this part of our knowledge of nature

DEMONSTRATION AND NECESSARY TRUTHS.

153

18 derived from the same sources as
every other part. *

This, for instance, they would be
able to do, if they could prove chrono-
logically that we had the conviction
(at least practically) so early in infancy
as to be anterior to those impressions
on the senses, upon which, on the other
theory, the conviction is founded. This
however, cannot be proved : the point
being too far back to be within the
reach of memory, and too obscure for
external observation. The advocates
of the d priori theory are obliged to
have recourse to other arguments.
These are reducible to two, which I
shall endeavour to state as clearly and
as forcibly as possible.

§ 5. In the first place, it is said
that if our assent to the proposition
that two straight lines cannot enclose
a space, were derived from the senses,
we could only be convinced of its
truth by actual trial, that is, by see-
ing or feeling the straight lines;

* Some persons find themselves pre-
vented from believing that the axiom, Two
straight lines cannot enclose a space, could
ever become known to us through experi-
ence, by a diflSculty which may be stated
as follows. If the straight lines spoken of
are those contemplated in the definition —
lines absolutely without breadth and abso-
lutely straight ; — that such are incapable
of enclosing a space is not proved by ex-
perience, for lines such as these do not pre-
sent themselves in our experience. If, on
the other hand, the lines meant are such
straight lines as we do meet with in ex-
perience, lines straight enough for practical
purposes, but in reality slightly zig-zag,
and with some, however trifling, breadth ;
as applied to these lines the axiom is not
true, for two of them may, and sometimes
do, enclose a small portion of space. In
neither case, therefore, does experience
prove the axiom.

Those who employ this argument to
show that geometrical axioms cannot be
proved by induction, show themselves
unfamiliar with a common and perfectly
valid mode of inductive proof — proof by
approximation. Though experience fur-
nishes us with no lines so uuimpeachably
straight that two of them are incapable of
enclosing the smallest space, it presents
us with gradations of lines possessing less
and less either of breadth or of flexure, of
which series the straight line of the defini-
tion is the ideal limit. And observation

whereas in fact it is seen to be true
by merely thinking of them. That
a stone thrown into water goes to the
bottom, may be perceived by our
senses, but merely thinking of a stone
thrown into the water would never
have led us to that conclusion : not
so, however, with the axioms relating
to straight lines : if I could be made
to conceive what a straight line is,
without having seen one, I should at
once recognise that two such lines
cannot enclose a space. Intuition is
" imaginary looking ; " * but experi-
ence must be real looking : if we see a
property of straight lines to be true by
merely fancjnng ourselves to be look-
ing at them, the ground of our belief
cannot be the senses, or experience ;
it must be something mental.

To this argument it might be added
in the case of this particular axiom,
(for the assertion would not be true
of all axioms) that the evidence of
it from actual ocular inspection is not
only imnecessary but unattainable.
What says the axiom? That two
straight lines cannot enclose a space ;
that after having once intersected, if
they are prolonged to infinity they do
not meet, but continue to diverge from
one another. How can this, in any
single case, be proved by actual ob-
servation ? We may follow the lines
to any distance we please ; but we
cannot follow them to infinity : for
aught our senses can testify, they
may, immediately beyond the farthest
point to which we have traced them,
begin to approach, and at last meet.
Unless, therefore, we had some other

shows that just as much, and as nearly, as
the straight lines of experience approxi-
mate to having no breadth or flexure, so
much and so nearly does the space-enclos-
ing power of any two of them approach to
zero. The inference that if they had no
breadth or flexure at all, they would enclose
no space at all, is a correct inductive in-
ference from these facts, conformable to
one of the four Inductive Methods herein-
after characterised — the Method of Conco-
mitant Variations, of which the Mathe-
matical Doctrine of Limits presents the
extreme case.

* Whewell's History of Scientific Ideas, I.
140.

t54

REASONING.

proof of the impossibility than obser-
vation affords us, we should have no
ground for believing the axiom at
all.

To these arguments, which I trust
I cannot be accused of understating,
a satisfactory answer will, I conceive,
be found, if we advert to one of the
characteristic properties of geometri-
cal forms — their capacity of being
painted in the imagination with a dis-
tinctness equal to reality : in other
words, the exact resemblance of our
ideas of form to the sensations which
suggest them. This, in the first place,
enables us to make (at least with a
little practice) mental pictures of all
possible combinations of lines and
angles, which resemble the realities
quite as well as any which we could
make on paper ; and in the next place,
make those pictures just as fit sub-
jects of geometrical experimentation as
the realities themselves ; inasmuch as
pictures, if sufficiently accurate, ex-
hibit of course all the properties which
would be manifested by the realities
at one given instant, and on simple
inspection : and in geometry we are
concerned only with such properties,
and not with that which pictures
could not exhibit, the mutual action
of bodies one upon another. The
foundations of geometry would there-
fore be laid in direct experience, even
if the experiments (which in this case
consist merely in attentive contem-
plation) were practised solely upon
what we call our ideas, that is, upon
the diagrams in our minds, and not
upon outward objects. For in all
systems of experimentation we take
some objects to serve as representa-
tives of all which resemble them ; and
in the present case the conditions
which qualify a real object to be the
representative of its class are com-
pletely fulfilled by an object existing
only in our fancy. Without denying,
therefore, the possibility of satisfying
ourselves that two straight lines can-
not enclose a space, by merely think-
ing of straight lines without actually
looking at them ; I contend that we

do not believe this truth on the ground
of the imaginary intuition simply, but
because we know that the imaginary
lines exactly resemble real ones, and
that we may conclude from them to
real ones with quite as much certainty
as we could conclude from one real
line to another. The conclusion, there-
fore, is still an induction from obser-
vation. And we should not be autho-
rised to substitute observation of the
image in our mind for observation of
the reality if we had not learnt by long-
continued experience that the proper-
ties of the reality are faithfully repre-
sented in the image ; just as we should
be scientifically warranted in describ-
ing an animal which we have never
seen from a picture made of it with
a daguerreotype ; but not until we
had learnt by ample experience that
observation of such a picture is pre-
cisely equivalent to observation of the
original

These considerations also remove
the objection arising from the impos-
sibility of ocularly following the lines
in their prolongation to infinity. For
though, in order actually to see that
two given lines never meet, it would
be necessary to follow them to infinity;
yet without doing so we may know
that if they ever do meet, or if, after
diverging from one another, they be-
gin again to approach, this must take
place not at an infinite, but at a finite
distance. Supposing, therefore, such
to be the case, we can transport our-
selves thither in imagination, and
can frame a mental image of the ap-
pearance which one or both of the
lines must present at that point,
which we may rely on as being pre-
cisely similar to the reality. Now,
whether we fix our contemplation
upon this imaginary picture, or call
to mind the generalisations we have
had occasion to make from former
ocular observation, we learn by the
evidence of experience, that a line
which, after diverging from another
straight line, begins to approach to
it, produces the impression on our
which we describe by the ex-

DEMONSTRATION AND NECESSARY TRUTHS.

t55

pression, "a bent line," not by the
expression, " a straight line." *

The preceding argument, which is,
to my mind, unanswerable, merges,
however, in a still more comprehen-

• Dr. Whowell {Philosophy of Discovery,
p. 289) thinks it unreasonable to contend
that we know by experience that our idea
of a line exactly resembles a real line. "It
does not appear," he snys, *' how we can
compare our ideas with the realities, since
we know the realities only by our ideas."
We ki)Ow the realities by our sensations.
Dr. Whewell surely does not hold the "doc-
trine of perception by means of ideas,"
which Reid gave himself ao much trouble
to refute.

Jf Dr. Whewell doubts whether we com-
pare our ideas with the corresponding
^ellsations, and assume that they resemble,
let me ask on what evidence do we judge
that a portrait of a person not present is
like the original. Surely because it is like
our idea, or mental image of the person, and
because our idea is like the man liimself .

Dr. Whewell also says, that it does not
appear why this resemblance of ideas to
thu sensations of which they are copies,
should be spoken of as if it were a pecu-
liarity ot one class of Ideas, those of space.
My reply is, that I do not so speak of it.
The peculiarity I contend for is only one
of degree. All our ideas of sensation of
course resemble the corresponding sensa-
tion.s, but they do so with very different
d egrees of exactness a 1 ■ d of reliabili t y. No
one, I presume, can recall in imagination
H colour or an odour with the same dis-
tinctness and accuracy with which almost
every one can mentally reproduce an image
of a straight line or a triangle. To the ex-
tent, however, of their capabilities of ac-
curacy, our recollections of colouis or of
odours may serve as subjects of experi-
mentation, as well as those of lines and
spaces, and may yield conclusions which
will be true of their external prototypes.
A person in whom, either from natural
gift or from cultivation, the impressions
of colour were peculiarly vivid and distinct,
if asked which of two blue flowers was of
the darker tinge, though he might never
have compared the two, or even looked at
them together, might be able to give a
confident answer on the faith of his dis-
tinct recollection of tiie colours ; that is.
he miglit examine his mental pictures, and
find there a property of the outward ob-
jects. But in hardly any case except tiiat
of simple geometrical forms, could this be
done by mankind generally, with a degree
of assurance equal to that which is given
by a contemplation of tlie objects them-
selves. Persons differ most widely in the
precision of their recollection, even of
forms : one person, when he has looked
any one in the face for half a minute, can

sive one, which is stated most clearly
and conclusively by Professor Bain.
The psychological reason why axioms,
and indeed many prof)Ositions not
ordinarily classed as such, may be
learnt from the idea only, without
referring to the fact, is that in the
process of acquiring the idea we have
learnt the fact. The proposition is
assented to as soon as the terms are
understood, because in learning to
understand the terms we have ac-
quired the experience which proves
the proposition to be true. " We re-
quired," says Mr. Bain,* "concrete
experience in the first instance to at-
tain to the notion of whole and part ;
but the notion, once arrived at, implies
that the whole is greater. In fact,
we could not have the notion without
an experience tantamount to this con-
clusion When we have mas-
tered the notion of straightness, we
have also mastered that aspect of it
expressed by the affirmation that two
straight lines cannot enclose a space.
No intuitive or innate powers or per-
ceptions are needed in such cases.

We cannot have the full

meaning of Straightness, without go-
ing through a comparison of straight
objects among themselves and with
their opposites, bent or crooked ob-
jects. The result of this comparison
is, inter alia, that straightness in two
lines is seen to be incompatible with
enclosing a space ; the enclosure of
space involves crookedness in at least
one of the lines." And similarly in
the case of every first principle,+
•' the same knowledge that makes it

draw an accurate likeness of him from
memory ; another may have seen him every
day for six months, and hardly know
whether his nose is long or short. But
everybody has a perfectly distinct mental
image of a straight line, a circle, or a rec-
tangle. And every one concludes confi-
dently from the.se mental images to the
corresponding outward things. The truth
is, that we may, and continually do, study
nature in our recollections, when the ob-
jects themselves are absent ; and in the
case of geometrical forms we can perfectly,
but in most other cases only imperfectly,
trust our recollectiona.
* Logic, i. 222. f Ibid. 226.

156 REASONING.

understood, suffices to verify it." The
more this observation is considered
the more (I am convinced) it will be
felt to go to the very root of the con-
troversy.

§ 6. The first of the two arguments
in support of the theory that axioms
are d priori truths, having, I think,
been sufficiently answered, I proceed
to the second, which is usually the
most relied on. Axioms ( it is asserted)
are conceived by us not only as true,
but as universally and necessarily true.
Now, experience cannot possibly give
to any proposition this character. I
may have seen snow a hundred times,
and may have seen that it was white,
but this cannot give me entire assur-
ance even that all snow is white ; much
less that snow must be white. " How-
ever many instances we may have
observed of the truth of a proposition,
there is nothing to assure us that the
next case shall not be an exception
to the rule. If it be strictly true that
every ruminant animal yet known has
cloven hoofs, we still cannot be sure
that some creature will not hereafter
be discovered which has the first of
these attributes, without having the
other. . . . Experience must always
consist of a limited number of observa-
tions ; and, however numerous these
may be, they can show nothing with
regard to the infinite number of cases
in which the experiment has not been
made." Besides, Axioms are not only
universal, they are also necessary.
Now " experience cannot offer the
smallest ground for the necessity of a
proposition. She can observe and re-
cord what has happened ; but she can-
not find, in any case, or in any accu-
mulation of cases, any reason for what
must happen. She may see objects
side by side ; but she cannot see a
reason why they must ever be side by
side. She finds certain events to occur
in succession ; but the succession sup-
plies, in its occurrence, no reason for
its recurrence. She contemplates ex-
ternal objects ; but she cannot detect
any internal bond, which indissolubly

connects the future with the past, the
possible with the real. To learn a
proposition by experience, and to see
it to be necessarily true, are two alto-
gether dififerent processesof thought."*
And Pr. Whewell adds, " If any one
does not clearly comprehend this dis-
tinction of necessary and contingent
truths, he will not be able to go along
with us in our researches into the
foundations of human knowledge ; nor,
indeed, to pursue with success any
speculation on the subject." f

In the following passage we are told
what the distinction is, the non-recog-
nition of which incurs this denuncia-
tion. " Necessary truths are those in
which we not only learn that the pro-
position is true, but see that it must
be true ; in which the negation of the
truth is not only false, but impossible ;
in which we cannot, even by an effort
of imagination, or in a supposition,
conceive the reverse of that which is
asserted. That there are such truths
cannot be doubted. We may take,
for example, all relations of number.
Three and Two added together made
Five. We cannot conceive it to be
otherwise. We cannot, by any freak
of thought, imagine Three and Two
to make Seven." +

Although Dr. Whewell has natu-
rally and properly employed a variety
of phrases to bring his meaning more
forcibly home, he would, I presume,
allow that they are all equivalent ;
and that what he means by a necessary
truth, would be sufficiently defined, a
proposition the negation of which is
not only false but inconceivable. I
am unable to find in any of his expres-
sions, turn them what way you will,
a meaning beyond this, and I do not
believe he would contend that they
mean anything more.

This, therefore, is the principle
asserted : that propositions, the nega-
tion of which is inconceivable, or in
other words, which we cannot figure to
ourselves as being false, must rest on
evidence of a higher and more cogent

* History of Scientijie Ideas, i. 65-67.
t Ibid. 60. } Ibid. 58, 59.

DEMONSTRATION AND NECESSARY TRUTHS.

157

description than any which experience
can afford.

Now I cannot but wonder that so
much stress should be laid on the cir-
cumstance of inconcnivableness, when
there is such ample experience to show
that our capacity or incapacity of con-
ceiving a thing has very little to do
with the possibility of the thing in
itself, but is in truth very much an
affair of accident, and depends on the
past history and habits of our own
minds. There is no more generally ac-
knowledged fact in human nature than
the extreme difficulty at first felt in
conceiving anything as possible which
is in contradiction to long-established
and familiar experience, or even to
old familiar habits of thought. And
this difficulty is a necessary result
of the fundamental laws of the human
mind. When we have often seen and
thought of two things together, and
have never in any one instance either
seen or thought of them separately,
there is by the primary law of asso-
ciation an increasing difficulty, which
may in the end become insuperable,
of conceiving the two things apart.
This is most of all conspicuous in un-
educated persons, who are in general
utterly unable to separate any two
ideas which have once become firmly
associated in their minds ; and if
persons of cultivated intellect have
any advantage on the point, it is only
because, having seen and heard and
read more, and being more accustomed
to exercise their imagination, they
have experienced their sensations and
thoughts in more varied combinations,
and have been prevented from form-
ing many of these inseparable asso-
ciations. But this advantage has
necessarily its limits. The most
practised intellect is not exempt from
the universal laws of our conceptive
faculty. If daily habit presents to
any one for a long period two facts
in combination, and if he is not led
during that period either by accident
or by his voluntary mental operations
to think of them apart, he will pro-
bably in time become incapable of

doing so even by the strongest effort ;
and the supposition that the two
facts can be separated in nature will
at last present itself to his mind with
all the characters of an inconceivable
phenomenon.* There are remarkable
instances of this in the history of
science : instances in which the most
instructed men rejected as impossible,
because inconceivable, things which
their posterity, by earlier practice
and longer perseverance in the at-
tempt, found it quite easy to con-
ceive, and which everybody now
knows to be true. There was a time
when men of the most cultivated
intellects, and the most emancipated
from the dominion of early prejudice,
could not credit the existence of
antipodes ; were unable to conceive,
in opposition to old association, the
force of gravity acting upwards in-
stead of downwards. The Cartesians
long rejected the Newtonian doctrine
of the gravitation of all bodies to-
wards one another, on the faith of a
general proposition, the reverse of
which seemed to them to be incon-
ceivable— the proposition that a body
cannot act where it is not. All the
cumbrous machinery of imaginary
vortices, assumed without the smallest
particle of evidence, appeared to these
philosophers a more rational mode of
explaining the heavenly motions, than
one which involved what seemed to
them so great an absurdity.f And

* " If all mankind had spoken one lan-
guage, we cannot doubt that there would
have been a powerful, perhaps a universal,
school of philosophers, who would have
believed in the inherent connection be-
tween names and things, who would have
taken the sound man to be the mode of
agitating the air which is essentially com-
municative of the ideas of rea-on, cookery,
bipedality, <fec." — De Morgan, Formal Logic,
p. 246.

t It would be diflBcult to luime a man
more remarkable at once for the great-
ness and the wide range of his mentol ac-
complishments than Leibnitz. Yet this
eminent man gave as a reason for rejecting
Newton's scheme of the solar system, that
God could not make a body revolve round
a distant centre, unless either by some
impelling mechanism, or by miracle : —
"Tout oe qui n'eat pas explicable," says he

158

REASONING.

they no doubt found it as impossible
to conceive that a body should act
upon the earth from the distance of
the siin or moon, as we find it to con-
ceive an end to space or time, or two
straight lines enclosing a space.
Newton himself had not been able
to realise the conception, or we should
not have had his hypothesis of a
subtle ether, the occult cause of gra-
vitation ; and his writings prove, that
though he deemed the particular
nature of the intermediate agency a
matter of conjecture, the necessity of
some such agency appeared to him
indubitable.

If, then, it be so natural to the
human mind, even in a high state of
culture, to be incapable of conceiving,
and on that ground to believe impos-
sible, what is afterwards not only
found to be conceivable but proved to
be true ; what wonder if in cases
where the association is still older,
more confirmed, and more familiar,
and in which nothing ever occurs to
shake our conviction, or even suggest
to us any conception at variance with
the association, the acquired incapa-
city should continue, and be mistaken
for a natural incapacity ? It is true,
our experience of the varieties in
nature enables us, within certain
limits, to conceive other varieties
analogous to them. We can conceive
the sun or moon falling ; for though
we never saw them fall, nor ever
perhaps imagined them falling, we
have seen so many other things fall,
that we have innumerable familiar
analogies to assist the conception ;
which, after all, we should probably

in a letter to the Abb6 Conti, "par la nature
des creatures est miraculeui. II ne sufl&t
pas de dire : Dieu a fait une telle loi de
nature ; done la chose est uaturelle. II
faut que la loi soit executable par les na-
tures des creatures. Si Dieu donnait cette
loi. par exemple, k un coips libre, de
tourner k I'entour d'un certain centre, il
faudrait ou qu'il y joignlt d'autres corps qui
par leur impulsion i'obligeassent de renter
toujours dans son orbite circulaire, ou qu'il
mU un ange d ses trousses, ou evfin il faudrait
qu'il y concourUt extraordinairement ; car
naturellement il s'^cartera par latangente."
'^ Works of Leibnitz, ed. Dutens, iii. 446.

have some difficulty in framing, were
we not well accustomed to see the sun
and moon move, (or appear to move,)
so that we are only called upon to
conceive a slight change in the direc-
tion of motion, a circumstance familiar
to our experience. But when experi-
ence affords no model on which to
shape the new conception, how is it
possible for us to form it ? How, for
example, can we imagine an end to
space or time ? We never saw any
object without something beyond it,
nor experienced any feeling without
something following it. When, there-
fore, we attempt to conceive the last
point of space, we have the idea
irresistibly raised of other points be-
yond it. When we try to imagine
the last instant of time, we cannot
help conceiving another instant after
it. Nor is there any necessity to
assume, as is done by a modern
school of metaphysicians, a peculiar
fundamental law of the mind to
account for the feeling of infinity
inherent in our conceptions of space
and time ; that apparent infinity is
sufficiently accounted for by simpler
and universally acknowledged laws.

Now, in the case of a geometrical
axiom, such, for example, as that two
straight lines cannot enclose a space,
— a truth which is testified to us by
our very earliest impressions of the
external world, — how is it possible
(whether those external impressions
be or be not the ground of our belief)
that the reverse of the proposition
could be otherwise than inconceivable
to us ? What analogy have we, what
similar order of facts in any other
branch of our experience, to facilitate
to us the conception of two straight
lines enclosing a space ? Nor is even
this all. I have already called atten-
tion to the peculiar property of our
impressions of form, that the ide»,s or
mental images exactly resemble their
prototypes, and adequately represent
them for the purposes of scientific
observation. From this, and from the
intuitive character of the observation,
which in this case reduces itself to

DEMONSTRATION AND NECESSARY TRUTHS.

159

simple inspection, we cannot so much
as call up in our imagination two
straight lines, in order to attempt to
conceive them enclosing a space, with-
out by that very act repeating the
scientific experiment which establishes
the contrary. Will it really be con-
tended that the inconceivableness of
the thing, in such circumstances,
proves anything against the experi-
mental origin of the conviction ? Is
it not clear that in whichever mode
our belief in the proposition may have
originated, the impossibility of our
conceiving the negative of it must,
on either hypothesis, be the same?
As, then, Dr. Whewell exhorts those
who have any difficulty in recognising
the distinction held by him between
necessary and contingent truths to
study geometry, — a condition which
I can assure him I have conscien-
tiously fulfilled, — I, in return, with
equal confidence, exhort those who
agree with him, to study the general
laws of association ; being convinced
that nothing more is requisite than a
moderate familiarity with those laws
to dispel the illusion which ascribes
a peculiar necessity to our earliest
inductions from experience, and
measures the possibility of things in
themselves by the human capacity of
conceiving them.

I hope to be pardoned for adding,
that Dr. Whewell himself has both
confirmed by his testimony the effect
of habitual association in giving to an
experimental truth the appearance of
a necessary one, and afforded a striking
instance of that remarkable law in his
own person. In his Philosophy of the
Inductive Sciences he continually as-
serts, that propositions which not only
are not self-evident, but which we
know to have been discovered gradu
ally and by great efforts of genius and
patience, have, when once established,
appeared so self-evident that, but for
historical proof, it would have been
impossible to conceive that they had
not been recognised from the first
by all persons in a sound state of
their faculties, " We now despise

those who, in the Copemican contro-
versy, could not conceive the apparent
motion of the sun on the heliocentric
hypothesis ; or those who, in opposi-
tion to Galileo, thought that a uni-
form force might be that which
generated a velocity proportional to
the space ; or those who held there
was something absurd in Newton's
doctrine of the different refrangibility
of different coloured rays ; or those
who imagined that when elements
combine, their sensible qualities must
be manifest in the compound ; or
those who were reluctant to give up
the distinction of vegetables into
herbs, shrubs, and trees. We cannot
help thinking that men must have
been singularly dull of comprehension
to find a difficulty in admitting what
is to us so plain and simple. We
have a latent persuasion that we in
their place should have been wiser
and more clear - sighted ; that we
should have taken the right side, and
given our assent at once to the truth.
Yet in reality such a persuasion is a
mere delusion. The persons who, in
such instances as the above, were on
the losing side, were very far, in most
cases, from being persons more preju-
diced, or stupid, or narrow-minded,
than the greater part of mankind now
are ; and the cause for which they
fought was far from being a mani-
festly bad one, till it had been so
decided by the result of the war. . . ,
So complete has been the victory of
truth in most of these instances, that
at present we can hardly imagine the
struggle to have been necessary. The
very essence of these triumphs is, that
they lead us to regard the views we
reject as not only false but inconceiv-
able."*

This last proposition is precisely
what I contend for ; and I ask no
more, in order to overthrow the whole
theory of its author on the nature of
the evidence of axioms. For what
is that theory? That the truth of
axioms cannot have been learnt from

* Ifovum Organum Renovatum, pp. 32, 33.

l6o

REASONING.

experience, because their falsity is in-
conceivable. But Dr. WheweU him-
self says that we are continually led,
by the natural progress of thought,
to regard as inconceivable what our
forefathers not only conceived but
believed, nay even (he might have
added) were unable to conceive the
reverse of. He cannot intend to justify
this mode of thought : he cannot mean
to say that we can be right in re-
garding as inconceivable what others
have conceived, and as self-evident
what to others did not appear evident
at all. After so complete an admis-
sion that inconceivableness is an
accidental thing, not inherent in the
phenomenon itself, but dependent on
the mental history of the person who
tries to conceive it, how can he ever
call upon us to reject a proposition as
impossible on no other ground than
its inconceivableness? Yet he not
only does so, but has unintentionally
afforded some of the most remarkable
examples which can be cited of the very
illusion which he has himself so clearly
pointed out. I select as specimens his
remarks on the evidence of the three
laws of motion, and of the atomic
theory.

With respect to the laws of motion,
Dr. Whewell says : " No one can
doubt that, in historical fact, these
laws were collected from experience.
That such is the case is no matter of
conjecture. We know the time, the
persons, the circumstances, belonging
toeach step of each discovery."* After
this testimony, to adduce evidence of
the fact would be superfluous. And
not only were these laws by no means
intuitively evident, but some of them
were originally paradoxes. The first
law was especially so. That a body,
once in motion, would continue forever
to move in the same direction with un-
diminished velocity unless acted upon
by some new force, was a proposition
which mankind found for a long time
the greatest difficulty in crediting.
It stood opposed to apparent experi-

• Hiitoi-y of Scientific Ideas, i. 264.

ence of the most familiar kind, which
taught that it was the nature of mo-
tion to abate gradually, and at last
terminate of itself. Yet when once
the contrary doctrine was firmly es-
stablished, mathematicians, as Dr.
Whewell observes, speedily began to
believe that laws, thus contradictory
to first appearances, and which, even
after full proof had been obtained, it
had required generations to render
familiar to the minds of the scientific
world, were under a " demonstrable
necessity, compelling them to be such
as they are and no other ; " and he
himself, though not venturing "abso-
lutely to pronounce" that aU these
laws " can be rigorously traced to an
absolute necessity in the nature of
things,"* does actually so think of
the law just mentioned, of which he
says, "Though the discovery of the
first law of motion was made, histori-
cally speaking, by means of experi-
ment, we have now attained a point
of view in which we see that it might
have been certainly known to be true
independently of experience." f Can
there be a more striking exemplifica-
tion than is here afforded of the effect
of association which we have described ?
Philosophers, for generations, have the
most extraordinary difficulty in put-
ting certain ideas together ; they at
last succeed in doing so ; and after a
sufificient repetition of the process,
they first fancy a natural bond be-
tween the ideas, then experience a
growing difficulty, which at last, by
the continuation of the same progress,
becomes an impossibility, of severing
them from one another. If such be
the progress of an experimental con-
viction of which the date is of yester-
day, and which is in opposition to first
appearances, how must it fare with
those which are conformable to appear-
ances familiar from the first dawn of
intelligence, and of the conclusiveness
of which, from the earliest records of
human thought, no sceptic has sug-
gested even a momentary doubt ?

* Hist. Se. Id., i. 263. t Ibid. 240.

DEMONSTRATION AND NECESSARY TRUTHS.

i6i

The other instance which I shall
quote is a truly astonishing one, and
may be called the reductio ad absur-
dum of the theory of inconceivableness.
Speaking of the laws of chemical com-
position, Dr. Whewell says : * ** That
they could never have been clearly
understood, and therefore never firmly
established, without laborious and ex-
act experiments, is cei-tain ; but yet
we may venture to say, that being
once known, they possess an evidence
beyond that of mere experiment. For
how in fact can we conceive combina-
tions otherwise than as definite in kind
and quality ? If we were to suppose
each element ready to combine with
any other indifferently, and indiffer-
ently in any quantity, we should have
a world in which all would be con-
fusion and indefiniteness. There
would be no fixed kinds of bodies.
Salts, and stones, and ores would
approach to and graduate into each
other by insensible degrees. Instead
of this, we know that the world con-
sists of bodies distinguishable from
each other by definite differences, cap-
able of being classified and named,
and of having general propositions
asserted concerning them. And as
we cannot conceive a world in which
this shduld not be the case, it would
appear that we cannot conceive a
state of things in which the laws of
the combination of elements should
not be of that definite and measured
kind which we have above asserted."

That a philosopher of Dr. Whewell's
eminence should gravely assert that
we cannot conceive a world in which
the simple elements should combine
in other than definite proportions ;
that by dint of meditating on a
scientific truth, the original discoverer
of which was still living, he should
have rendered the association in his
own mind between the idea of com-
bination and that of constant propor-
tions so familiar and intimate as to
be unable to conceive the one fact
without the other, is so signal an

* History of Scientific Idea*, ii. 25, 26,

instance of the mental law for which
I am contending, that one word mor«
in illustration must be superfluous.

In the latest and most complete
elaboration of his metaphysical system,
(the Philosophy of Discovery, ) as well
as in the earlier discourse on the
Fundamental Antithesis of Philosophy,
reprinted as an appendix to that
work. Dr. Whewell, while very can-
didly admitting that his language was
open to misconception, disclaims hav-
ing intended to say that mankind in
general can now perceive the law of
definite proportions in chemical com-
bination to be a necessary truth. All
he meant was that philosophical
chemists in a future generation may
possibly see this. " Some truths may
be seen by intuition, but yet the
intuition of them may be a rare and
a difficult attainment."* And he
explains that the inconceivableness
which, according to his theory, is
the test of axioms, " depends entirely
upon the clearness of the ideas which
the axioms involve. So long as those
ideas are vague and indistinct, the
contrary of an axiom may be assented
to, though it cannot be distinctly con-
ceived. It may be assented to, not
because it is possible, but because we
do not see clearly what is possible.
To a person who is only beginning to
think geometrically, there may appear
nothing absurd in the assertion that
two straight lines may enclose a space.
And in the same manner, to a person
who is only beginning to think of
mechanical truths, it may not appear
to be absurd, that in mechanical pro-
cesses, Reaction should be greater or
less than Action ; and so, again, to
a person who has not thought steadily
about Substance, it may not appear
inconceivable, that by chemical opera-
tions, we should generate new matter,
or destroy matter which already
exists." t Necessary truths, there-
fore, are not those of which we can-
not conceive, but " those of which we
cannot distinctly conceive the con-

rhil. of J)itc,. p. 339.

t Ibid. p. 338.

1 62

REASONING.

trary." * So long as our ideas are
indistinct altogether, we do not know
what is or is not capable of being dis-
tinctly conceived ; but, by the ever-
increasing distinctness with which
acientific men apprehend the general
conceptions of science, they in time
come to perceive that there are cer-
tain laws of nature, which, though
historically and as a matter of fact
they were learnt from experience, we
cannot, now that we know them,
distinctly conceive to be other than
they are.

The account which I should give of
this progress of the scientific mind is
somewhat different. After a general
law of natiire has been ascertained,
men's minds do not at first acquire a
complete facility of familiarly repre-
senting to themselves the phenomena
of nature in the character which that
law assigns to them. The habit which
constitutes the scientific cast of mind,
that of conceiving facts of all descrip-
tions conformably to the laws which
regulate them— phenomena of all de-
scriptions according to the relations
which have been ascertained really to
exist between them ; this habit, in the
case of newly discovered relations,
comes only by degrees. So long as it
is not thoroughly formed, no necessary
character is ascribed to the new truth.
But in time the philosopher attains a
state of mind in which his mental
picture of nature spontaneously re-
presents to him all the phenomena
with which the new theory is con-
cerned, in the exact light in which
the theory regards them : all images
or conceptions derived from any other
theory, or from the confused view of
the facts which is anterior to any
theory, having entirely disappeared
from his mind. The mode of repre-
senting facts which results from the
theory has now become, to his facul-
ties, the only natural mode of con-
ceiving them. It is a known truth,
that a prolonged habit of arranging
phenomena in certain groups, and

* Phil, of Disc, p. 463.

explaining them by means of certain
principles, makes any other arrange-
ment or explanation of these facts be
felt as unnatural : and it may at last
become as difficult to him to represent
the facts to himself in any other mode,
as it often was, originally, to represent
them in that mode.

But, further, (if the theory is true,
as we are supposing it to be,) any other
mode in which he tries, or in which he
was formerly accustomed, to represent
the phenomena, will be seen by him to
be inconsistent with the facts that sug-
gested the new theory — facts which
now form a part of his mental picture
of natura And since a contradiction
is always inconceivable, his imagina-
tion rejects these false theories, and
declares itself incapable of conceiving
them. Their inconceivableness to him
does not, however, result from anything
in the theories themselves intrinsically
and d, priori repugnant to the human
faculties ; it results from the repug-
nance between them and a portion
of the facts, which facts as long as
he did not know, or did not dis-
tinctly realise in his mental repre-
sentations, the false theory did not
appear other than conceivable ; it be-
comes inconceivable merely from the
fact that contradictory elements can-
not be combined in the same concep-
tion. Although, then, his real reason
for rejecting theories at variance
with the true one is no other than
that they clash with his experience,
he easily falls into the belief that he
rejects them because they are incon-
ceivable, and that he adopts the true
theory because it is self-evident, and
does not need the evidence of experi-
ence at all.

This I take to be the real and suf-
ficient explanation of the paradoxical
truth, on which so much stress is laid
by Dr. Whewell, that a scientifically
cultivated mind is actually, in virtue
of that cultivation, unable to conceive
suppositions which a common man
conceives without the smallest diffi-
culty. For there is nothing incon-
ceivable in the suppositions them-

DEMONSTRATION AND l^ECESSARY TRUTHS.

163

selves ; the impossibility is in com-
bining them with facts inconsistent
with them, as part of the same mental
picture ; an obstacle of course only
felt by those who know the facts, and
are able to perceive the inconsistency.
As far as the suppositions themselves
are concerned, in the case of many of
Dr. Whewell's necessary truths the
negative of the axiom is, and probably
will be as long as the human race
lasts, as easily conceivable as the
affirmative. There is no axiom (for
example) to which Dr. Whewell as-
cribes a more thorough character of
necessity and self -evidence than that
of the indestructibility of matter.
That this is a true law of nature I
fully admit ; but I imagine there is
no human being to whom the opposite
supposition is inconceivable — who has
any difficulty in imagining a portion
of matter annihilated, inasmuch as
its apparent annihilation, in no respect
distinguishable from real by our un-
assisted senses, takes place every time
that water dries up, or fuel is con-
sumed. Again, the law that bodies
combine chemically in definite propor-
tions is undeniably true ; but few
besides Dr. Whewell have reached the

Eoint which he seems personally to
ave arrived at, (though he only dares
prophesy similar success to the multi-
tude after the lapse of generations,)
that of being unable to conceive a
world in which the elements are ready
to combine with one another " indif-
ferently in any quantity ; " nor is it
likely that we shall ever rise to this
sublime height of inability, so long as
all the mechanical mixtures in our
planet, whether solid, liquid, or aeri-
form, exhibit to our daily observation
the very phenomenon declared to be
inconceivable.

According to Dr. Whewell, these
and similar laws of nature cannot be
drawn from experience, inasmuch as
they are, on the contrary, assumed in
the interpretation of experience. Our
inability to "add to or diminish the
quantity of matter in the world," is
» truth which "neither i« nor can be

derived from experience : for the ex-
periments which we make to verify it
presuppose its truth. . . . When
men began to use the balance in
chemical analysis, they did not prove
by trial, but took for granted, as self-
evident, that the weight of the whole
must be found in the aggregate weight
of the elements."* True, it is as-
sumed ; but, I apprehend, no otherwise
than as all experimental inquiry as-
sumes provisionally some theory or
hypothesis, which is to be finally held
true or not, according as the experi-
ments decide. The hypothesis chosen
for this purpose will naturally be one
which groups together some consider-
able number of facts already known.
The proposition that the material of
the world, as estimated by weight, is
neither increased nor diminished by
any of the processes of nature or art,
had many appearances in its favour to
begin with. It expressed truly a great
number of familiar facts. There were
other facts which it had the appear-
ance of conflicting with, and which
made its truth, as an universal law
of nature, at first doubtful Because
it was doubtful, experiments were
devised to verify it. Men assumed
its truth hypothetically, and proceeded
to try whether, on more careful exa-
mination, the phenomena which ap-
parently pointed to a different con-
clusion would not be found to be
consistent with it. This turned out
to be the case ; and from that time
the doctrine took its place as an uni-
versal truth, but as one proved to be
such by experience. That the theory
itself preceded the proof of its truth
— that it had to be conceived before
it could be proved, and in order that
it might be proved — does not imply
that it was self-evident and did not
need proof. Otherwise all the true
theories in the sciences are necessary
and self-evident ; for no one knows
better than Dr. Whewell that they
all began by being assumed, for the
purpose of connecting them by deduc-

* J>Ml, ofJ)itc., pp. 472, 473.

164

REASONING.

tions with those facts of experience
on which, as evidence, they now con-
fessedly rest.*

CHAPTER VI.

THE SAME SUBJECT CONTINUED.

§ I. In the examination which
formed the subject of the last chapter

* The Quarterly Reviexo for June 1841
contained an article of great ability on Dr.
Whewell's two great ^rorks (since acknow-
ledged and reprinted in Sir John Herschel's
Essays) which maintains, on the subject
of axioms, the doctrine advanced in the
text, that they are generalisations from
experience, and supports that opinion by
a line of argument strikingly coinciding
with mine. When I state that the whole
of the present chapter (except the last four
pages, added in the fifth edition) was
written before I had seen the article, (rhe
greater part, indeed, before it was pub-
lished,) it is not my object to occupy the
readei's attention with a matter so unim-
portant as the degree of oiiginality which
may or may not belong to any portion of
my own speculations, but to obtain for an
opinion which is opposed to reigning doc-
trines the recommendation derived from
a striking concurrence of seiuiment be-
tween two inquirers entirely independent
of one another. I embrace the opportunity
of citing from a writer of the extensive
acquirements in physical and metaphysical
knowledge and the capacity of systematic
thought which the article evinces, passages
so remarkably in unison with my own
views as the following :—

"The truths of geometry are summed
up and embodied in its definitions and
axioms. . . . Let us turn to the axioms,
and what do we find ? A string of proposi-
tions concerning magnitude in the abstract,
which are equally true of space, time,
force, number, and every other magnitude
suscepiible of aggregation and subdivision.
Such propositions, where they are not
mere definitions, as some of them are, carry
their inductive origin on the face of their
enunciation. . . . Those which declare that
two straight lines cannot enclose a space,
and that two straight lines which cut one
another cannot both be parallel to a third,
are in reality the only ones which express
characteristic properties of space, and these
it will be worth while to consider more
nearly. Now the only clear notion we can
form of straightuess is uniformity of direc-
tion, for space in its ultimate analysis is
nothing but an assemblage of distances and
directions. And (not to dwell on the
notion of continued contemplation, i.e.,
wental experience, as included in the very

into the nature of the evidence of those
deductive sciences which are commonly
represented to be systems of necessary
truth, we have been led to the follow-
ing conclusions. The results of those
sciences are indeed necessary, in the
sense of necessarily following from
certain first principles, commonly
called axioms and definitions ; that
is, of being certainly true if those
axioms and definitions are so ; for

idea of uniformity : nor on that of transfer
of the contemplating being from point to
point, and of experience, during such
transfer, of the homogeneity of the mterval
passed over) we cannot even propose the
proposition in an intelligible form to any
one whose experience ever since he was
born has not assured him of the fact. The
unity of direction, or that we cannot march
from a given point by more tlian one path
direct to the same object, is matter of prac-
tical experience long before it can by pos-
sibility become matter of abstract thought.
We cannot attempt mentally to exemplify the
conditions of the assertion in an imaginary
case opposed to it, without violating our
habitual recollections of this experience, and
defacing our mental picture of space as
grounded on it. What but experience, we
may ask, can possibly assure us of tha
homogeneity of the parts of distance, time,
force, and measurable aggregates in gene-
ral, on which the truth of the other axioms
depends? As regards the latter axiom,
after what has been said it must be clear
that the very same course of remarks
equally applies to its case, and that its
truth is quite as much forced on the mind
as that of the former by daily and hourly
experience, . . . including always, be it
observed, in our notion of experience, that
which is gained by contemplation of the in-
ward picture which the mind forms to itself
in any proposed case, or which it arbitrarily
selects as an example — such picture, in virtue
of the extreme simplicity of these primary re-
lations, being called up by the imagination
with as much vividness and clearness as
could be done by any external impression,
which is the only meaning we can attach to
the word intuition, as applied to such rela-
tions."

And again, of the axioms of mechanics :
--"As we admit no such propositions,
other than as truths inductively collected
from observation, even in geometry itself,
it can hardly be expected that, in a science
of obviously contingent relations, we should
acquiesce in a contrary view. Let us take
one of ttiese axioms and examine its evi-
dence : for instance, that equal forces per-
pendictxlarly applied at the opposite ends
of equal arms of a straight lever will balance
each other. What but experience, we may
sisk, in the first place, can possibly inform

DEMONSTRATION AND NECESSARY TRUTHS.

i6s

the word necessity, even in this ac-
ceptation of it, means no more than
certainty. But their claim to the
character of necessity in any sense
beyond this, as implying an evidence

us that a force so applied will have any
tendency to turn the lever on its centre at
all ? or that force c;in be so transmitted
along a rigid line perpendicular to its di-
rection as to act elsewhere in space tlian
along its own line of action ? Surely this
is so far from being self-evident that it
has even a paradoxical appearance, which
is only to be removed by giving our lever
thickness, material composition, and mole-
cular powers. Again, we conclude that
the two forces, being equal and applied
under precisely similar circumstances,
must, if they exert any effort at all to turn
the lever, exert equal and opposite efforts :
but what d priori reasoning can possibly
assure us that they do act under precisely
similar circumstances ? that points which
differ in place are similarly circumstanced
as regards the exertion of force ? that uni-
versal space may not have relations to
universal force— or, at all events, that tiie
organisation of the material universe may
not be such as to place that portion of
space occupied by it in sue a relations to
the forces exerted in it, as may invalidate
the absolute similarity of circumstances
assumed? Or we may argue, what have
we to do with the notion of angular move-
ment in the lever at all ? The case is one of
rest, and of quiescent destruction of force
by force. Now how is this destruction
effected? Assuredly by the counter-pres-
sure which supports the fulcrum. But
would not this destruction equally arise,
and by the same amount of counteracting
force, if each force simply pressed its own
half of the lever aurainst the fulcrum ? And
what can assure us that it is not so, except
removal of one or other force, and conse-
quent tilting of the lever ? The other fun-
dament al axiom of statics, that the pres
sure on tiie point of support is the sum of
the weights, ... is merely a scientific
transformation and more refined mode of
stating a coarse and obvious result of uni-
versal experience, viz. that the weight of
a rigid body is the same, handle it or sus-
pend it in what position or by what point
we will, and that whatever sustains it
sustains its total weight. Assuredly, as
Mr. Wliewell justly romarks, ' No one pro-
bably ever made a trial for the purpose of
showing that the pressure on the support
is equal to the sum of the weights.' . . .
But it is precisely because in every action
of his life from earliest infancy he has been
continually making the trial, and seeing it
made by every other living being about
him, that he never dreams of staking its
result on one additional attempt made
With scientific accuracy. This would be

independent of and superior to obser-
vation and experience, must depend
on the previous establishment of such
a claim in favour of the definitions
and axioms themselves. With regard

as if a man should resolve to decide by
experiment whether liis eyes were usetul
for the purpose of seeintr by hermetically
sealing himself up for half an hour in a
metal case. "

On the "paradox of universal proposi-
tions obtained by experience," the same
writer says: "If there be necessary and
universal truths expressible in pro[)Osition8
of axiomatic simplicity and obviousness,
and having for their siibject-matter the
elements of all our experience and all our
knowledge, surely these are the truths
which, if experience suggests to us any
truths at all, it ought to suggest most
readily, clearly, and unceasingly. If it
were a truth, universal and necessary, that
a net is spread over the whole surface erf
every planetary globe, weshotdd not travel
far in our own without getting entangled
in its meshes, and making the necessity
of some means of extrication an axiom
of locomotion. . . . There is, therefore,
nothing paradoxical, but the reverse, in
our bemg led by observation to a recogni-
tion of such truths as general propositions,
co-extensive at least with all human ex-
perieiice. That they pervade all the objects
of experience must ensure their continual
suggestion by experience ; tliat they are
true, must ensure that consistency of sug-
gestion, that iteration of uncontradicted
assertion, which commandsimplicit assent,
and removes all occasion of exception ; that
they are simple, and admit of no misunder-
standing, must secure their admission by
every mind."

"A truth, necessary and universal, re-
lative to any object of our knowledge,
must verity itself in every instance where
til at object is before our contemplation,
and if at the same time it be simple and
intelligible, its verification must be ob-
vious. The sentiment of such a truth cannot,
therefore, but be present to our minds when-
ever that object is contemplated , and must
therefore make a part of the mental picture
or idea of that object which we may on any
occasion summon before our imagination.
. . . All propositions, therefore, become not
only untrue but inconceivable, if . . .
axioms be violated in their enunciation."

Another eminent mathematician had
previously sanctioned by his authority the
doctrine of the origin of geometrical axioms
in experience " Giometry is thus founded
likewise on observation ; but of a kind so
familiar and obvious that the pri-nary
notions which it furnishes might seem
intuitive."— 6'ir John Leslie, quoied by
Sir Wilham Hamilton, Discourses, die, p.
272.

t66

REASONlNa

to axioms, we found that, considered
as experimental truths, they rest on
superabundant and obviona evidence.
We inquired whether, since this is the
case, it be imperative to suppose any
other evidence of those ti-uths than
experimental evidence, any other ori-
gin for our belief of them than an
experimental origin. We decided
that the burden of proof lies with
those who maintain the affirmative,
and we examined, at considerable
length, such arguments as they have
produced. The examination having
led to the rejection of those argu-
ments, we have thought ourselves
warranted in concluding that axioms
are but a class, the most universal
class, of inductions from experience ;
the simplest and easiest cases of gene-
ralisation from the facts furnished to
us by our senses or by our internal
consciousness.

While the axioms of demonstrative
sciences thus appeared to be experi-
mental truths, the definitions, as
they are incorrectly called, in those
sciences, were found by us to be
generalisations from experience which
are not even, accurately speaking,
truths ; being propositions in which,
while we assert of some kind of ob-
ject some property or properties which
observation shows to belong to it, we
at the same time deny that it pos-
sesses any other properties, though in
truth other properties do in every
individual instance accompany, and
in almost all instances modify, the
property thus exclusively predicated.
The denial, therefore, is a mere fic-
tion or supposition, made for the
purpose of excluding the considera-
tion of those modifying circumstances,
when their influence is of too trifling
amount to be worth considering, or
adjourning it, when important, to a
more convenient moment.

From these considerations it would
appear that Deductive or Demonstra-
tive Sciences are all, without excep-
tion, Inductive Sciences ; that their
evidence is that of experience ; but
that they are also, in virtue of the

peculiar character of one indispensable
portion of the general formulae accord-
ing to which their inductions are made.
Hypothetical Sciences. Their conclu-
sions are only true on certain suppo-
sitions, which are, or ought to be,
approximations to the truth, but are
seldom, if ever, exactly true; and to this
h3rpothetical character is to be ascribed
the peculiar certainty which is sup-
posed to be inherent in demonstration.
What we have now asserted, how-
ever, cannot be received as universally
true of Deductive or Demonstrative
Sciences, until verified by being
applied to the most remarkable of all
those sciences, that of Numbers ; the
theory of the Calculus ; Arithmetic
and Algebra. It is harder to believe
of the doctrines of this science than of
any other, either that they are not
truths d priori, but experimental
truths, or that their peculiar certainty
is owing to their being not absolute,
but only conditional truths. This,
therefore, is a case which merits exa-
mination apart ; and the more so,
because on this subject we have a
double set of doctrines to contend
with ; that of the d priori philosophers
on one side ; and on the other, a theory
the most opposite to theirs, which was
at one time very generally received,
and is still far from being altogether
exploded among metaphysicians.

§ 2. This theory attempts to solve
the difficulty apparently inherent in
the case, by representing the proposi-
tions of the science of numbers as
merely verbal, and its processes as
simple transformations of language,
substitutions of one expression for
another. The proposition, Two and
one is equal to three, according to
these writers, is not a truth, is not
the assertion of a really existing fact,
but a definition of the word three ; a
statement that mankind have agreed
to use the name three as a sign exactly
equivalent to two and one ; to call by
the former name whatever is called
by the other more clumsy phrase.
According to this doctrine the longest

DEMONSTRATION AND NECESSARY TRUTHS.

;67

process in algebra is but a succession
of changes in terminology, by which
equivalent expressions are substituted
one for another ; a series of transla-
tions of the same fact, from one into
another language ; though how, after
such a series of translations, the fact
itself comes out changed, (as when we
demonstrate a new geometrical theo-
rem by algebra,) they have not ex-
plained ; and it is a difficulty which
is fatal to their theory.

It must be acknowledged that there
are peculiarities in the processes of
arithmetic and algebra which render
the theory in question very plausible,
and have not unnaturally made those
sciences the stronghold of Nominalism.
The doctrine that we can discover
facts, detect the hidden processes of
nature, by an artful manipulation of
language, is so contrary to common
sense, that a person must have made
some advances in philosophy to believe
it ; men fly to so paradoxical a belief
to avoid, as they think, some even
greater difl&culty, which the vulgar
do not see. What has led many to
believe that reasoning is a mere verbal
process is, that no other theory seemed
reconcilable with the nature of the
Science of Numbers. For we do not
carry any ideas along with us when
we use the symbols of arithmetic or of
algebra. In a geometrical demonstra-
tion we have a mental diagram, if not
one on paper ; AB, AC, are present to
our imagination as lines, intersecting
other lines, forming an angle with
one another, and the like ; but not so
a and b. These may represent lines
or any other magnitudes, but those
magnitudes are never thought of ;
nothing is realised in our imagination
but a and 6. The ideas which, on the
particular occasion, they happen to re-
present, are banished from the mind
during every intermediate part of the
process, between the beginning, when
the premises are translated from
things into signs, and the end, when
the conclusion is translated back from
signs into things. Nothing, then, being
in the reasoner's mind but the symbols,

what can seem more inadmissible than
to contend that the reasoning process
hastodowithanjrthingmore? Weseem
to have come to one of Bacon's Pre-
rogative Instances ; an experimentum
cruets on the nature of reasoning itself.
Nevertheless, it will appear on con-
sideration, that this apparently so de-
cisive instance is no instance at all ;
that there is in every step of an arith-
metical or algebraical calculation a
real induction, a real inference of facts
from facts ; and that what disguises
the induction is sifnply its compre-
hensive nature and the consequent
extreme generality of the language.
All numbers must be numbers of
something ; there are no such things
as numbers in the abstract. Ten must
mean ten bodies, or ten sounds, or ten
beatings of the pulse. But though
numbers must be numbers of some-
thing, they may be numbers of any-
thing. Propositions, therefore, con-
cerning numbers have the remarkable
peculiarity that they are propositions
concerning all things whatever ; all
objects, ail existences of every kind,
known to our experience. All things
possess quantity ; consist of parts
which can be numbered ; and in that
character possess all the properties
which are called properties of numbers.
That half of four is two, must be true
whatever the word four represents,
whether four hours, four miles, or four
pounds weight. We need only con-
ceive a thing divided into four equal
parts (and all things may be conceived
as so divided) to be able to predicate
of it every property of the number four,
that is, every arithmetical proposition
in which the number four stands on
one side of the equation. Algebra
extends the generalisation still farther:
every number represents that par-
ticular number of all things without
distinction, but every algebraical
s5mabol does more, it represents all
numbers without distinction. As soon
as we conceive a thing divided into
equal parts, without knowing into
what number of parts, we may call
it a or X, and apply to it, without

i68

REASONING.

danger of error, every algebraical for-
mula in the books. The proposition,
2 (a + b) = 2 a + 2 6, is a truth co-ex-
tensive with all nature. Since then
algebraical truths are true of all things
whatever, and not, like those of
geometry, true of lines only or of
angles only, it is no wonder that the
symbols should not excite in our
minds ideas of any things in particu-
lar. When we demonstrate the forty-
seventh proposition of Euclid, it is
not necessary that the words should
raise in us an image of all right-
angled triangles, but only of some
one right-angled triangle ; so in
algebra we need not, under the
symbol a, picture to ourselves all
things whatever, but only some one
thing ; why not, then, the letter
itself ? The mere written characters,
a, 6, X, y, z, serve as well for repre-
sentatives of Things in general, as
any more complex and apparently
more concrete conception. That we
are conscious of them, however, in
their character of things, and not of
mere signs, is evident from the fact
that our whole process of reasoning is
carried on by predicating of them the
properties of things. In resolving an
algebraic equation, by what rules do
we proceed? By applying at each
step to a, b, and x, the proposition
that equals added to equals make
equals ; that equals taken from equals
leave equals ; and other propositions
founded on these two. These are not
properties of language, or of signs as
such, but of magnitudes, which is as
much as to say, of all things. The
inferences, therefore, which are suc-
cessively drawn, are inferences con-
cerning things, not symbols ; though
as any Things whatever will serve the
turn, there is no necessity for keeping
the idea of the Thing at all distinct,
and consequently the process of
thought may, in this case, be allowed
without danger to do what all pro-
cesses of thought, when they have
been performed often, will do if per-
mitted, namely, to become entirely
mechanical. Hence the general lan-

guage of algebra comes to be used
familiarly without exciting ideas, as
all other general language is prone
to do from mere habit, though in no
other case than this can it be done
with complete safety. But when we
look back to see from whence the pro-
bative force of the process is derived,
we find that at every single step,
unless we suppose ourselves to be
thinking and talking of the things,
and not the mere symbols, the evi-
dence fails.

There is another circumstance,
which, still more than that which we
have now mentioned, gives plausibility
to the notion that the propositions of
arithmetic and algebra are merely
verbal. That is, that when considered
as propositions respecting Things, they
all have the appearance of beingidenti-
cal propositions. The assertion, Two
and one is equal to three, considered
as an assertion respecting objects, as
for instance " Two pebbles and one
pebble are equal to three pebbles,"
does not affirm equality between two
collections of pebbles, but absolute
identity. It affirms that if we put
one pebble to two pebbles, those very
pebbles are three. The objects, there-
fore, being the very same, and the
mere assertion that " objeqts are them-
selves " being insignificant, it seems
but natural to consider the proposition
Two and one is equal to three, as
asserting mere identity of signification
between the two names.

This, however, though it looks so
plausible, will not bear examination.
The expression " two pebbles and one
pebble," and the expression " three
pebbles," stand indeed for the same
aggregation of objects, but they by no
means stand for the same physical
fact. They are names of the same
objects, but of those objects in two
different states : though they c?enote
the same things, their coTinotation is
different. Three pebbles in two sepa-
rate parcels, and three pebbles in one
parcel, do not make the same impres-
sion on our senses ; and the assertion
that the very same pebbles may by

DEMONSTRATION AND NECESSARY TRUTHS.

169

an alteration of place and arrange-
ment be made to produce either the
one set of sensations or the other,
though a very familiar proposition, is
not an identical one. It is a truth
known to us by early and constant
experience — an inductive truth ; and
such truths are the foundation of the
science of Numbers. The fundamental
truths of that science all rest on the
evidence of sense ; they are proved
by showing to our eyes and our fingers
that any given number of objects,
ten balls, for example, may by separa-
tion and rearrangement exhibit to
our senses all the different sets of
numbers the sum of which is equal to
ten. All the improved methods of
teaching arithmetic to children pro-
ceed on a knowledge of this fact.
All who wish to carry the child's
mind along with them in learning
arithmetic ; all who wish to teach
numbers, and not mere ciphers — now
teach it through the evidence of the
fsenses, in the manner we have de-
scribed.

We may, if we please, call the pro-
position, "Three is two and one," a
definition of the number three, and
assert that arithmetic, as it has been
asserted that geometry, is a science
founded on definitions. But they are
definitions in the geometrical sense,
not the logical ; asserting not the
meaning of a term only, but along
with it an observed matter of fact.
The proposition, " A circle is a figure
bounded by a line which has all its
points equally distant from a point
within it," is called the definition of
a circle ; but the proposition from
which so many consequences follow,
and which is really a first principle
in geometry, is, that figures answering
to this description exist. And thus
we may call " Three is two and one "
a definition of three ; but the calcula-
tions which depend on that proposi-
tion do not follow from the definition
itself, but from an arithmetical theorem
presupposed in it, namely, that collec-
tions of objects exist, which while they
impress the senses thus, **^<', may be

separated into two parts, thus, ©o e.
This proposition being granted, we
term all such parcels Threes, after
which the enunciation of the above-
mentioned physical fact will serve
also for a definition of the word
Three.

The Science of Numbers is thus no
exception to the conclusion we previ-
ously arrived at, that the processes
even of deductive sciences are alto-
gether inductive, and that their first
principles are generalisations from ex-
perience. It remains to be examined
whether this science resembles geome-
try in the further circumstance that
some of its inductions are not exactly
true ; and that the peculiar certainty
ascribed to it, on account of which
its propositions are called necessary
truths, is fictitious and hypothetical,
being true in no other sense than that
those propositions legitimately follow
from the hypothesis of the truth of
premises which are avowedly mere
approximations to truth.

§ 3. The inductions of arithmetic
are of two sorts : first, those which
we have just expounded, such as One
and one are two. Two and one are
three, &c., which may be called the
definitions of the various numbers, in
the improper or geometrical sense of
the word Definition ; and secondly,
the two following axioms : The sums
of equals are equal, The differences
of equals are equal. These two are
sufficient ; for the corresponding pro-
positions respecting unequals may be
proved from these by a reductio ad
ahsurdum.

These axioms, and likewise the so-
called definitions, are, as has already
been said, results of induction ; true
of all objects whatever, and, as it may
seem, exactly true, without the hy-
pothetical assumption of unqualified
truth where an approximation to it is
all that exists. The conclusions, there-
fore, it will naturally be inferred, are
exactly true, and the science of
numbers is an exception to other
demonstrative sciences in this, that

t7o

REASONING.

the categorical certainty which is
predicable of its demonstrations is
independent of all hypothesis.

On more accurate investigation,
however, it will be found that, even
in this case, there is one hypothetical
element in the ratiocination. In all
propositions concerning numbers, a
condition is implied, without which
none of them would be true ; and
that condition is an assumption which
may be false. The condition is, that
1 = 1; that all the numbers are
numbers of the same or of equal
units. Let this be doubtful, and not
one of the propositions of arithmetic
will hold true. How can we know
that one pound and one pound make
two pounds, if one of the pounds may
be troy, and the other avoirdupois ?
They may not make two pounds of
either, or of any weight. How can
we know that a forty- horse power is
alwajrs equal to itself, unless we
assume that all horses are of equal
strength ? It is certain that i is
always equal in number to i ; and
where the mere number of objects,
or of the parts of an object, without
supposing them to be equivalent in
any other respect, is all that is
material, the conclusions of arith-
metic, so far as they go to that alone,
are true without mixture of hypo-
thesis. There are such cases in
statistics ; as, for instance, an inquiry
into the amount of the population of
any country. It is indifferent to that
inquiry whether they are grown people
or children, strong or weak, tall or
short ; the only thing we want to
ascertain is their number. But when-
ever, from equality or inequality of
number, equality or inequality in any
other respect is to be inferred, arith-
metic carried into such inquiries be-
comes as hypothetical a science as
geometry. All units must be assumed
to be equal in that other respect ; and
this is never accurately true, for one
actual pound weight is not exactly
equal to another, nor one measured
mile's length to another ; a nicer
balance, or more accurate measuring

instruments, would always detect some
difference.

What is commonly called mathe-
matical certainty, therefore, which
comprises the twofold conception of
unconditional truth and perfect accu-
racy, is not an attribute of all mathe-
matical truths, but of those only
which relate to pure Number, af
distinguished from Quantity in the
more enlarged sense ; and only so
long as we abstain from supposing
that the numbers are a precise index
to actual quantities. The certainty
usually ascribed to the conclusions
of geometry, and even to those of
mechanics, is nothing whatever but
certainty of inference. We can have
full assurance of particular results
under particular suppositions, but we
cannot have the same assurance that
these suppositions are accurately true,
nor that they include all the data
which may exercise an influence over
the result in any g\ven instance.

§ 4. It appears, therefore, that the
method of all Deductive Sciences
is hypothetical. They proceed by
tracing the consequences of certain
assumptions ; leaving for separate con-
sideration whether the assumptions
are true or not, and if not exactly true,
whether they are a sufficiently near
approximation to the truth. The
reason is obvious. Since it is only in
questions of pure number that the
assumptions are exactly true, and even
there, only so long as no conclusions
except purely immerical ones are to be
founded on them ; it must, in all other
cases of deductive investigation, form
a part of the inquiry to determine
how much the assumptions want of
being exactly true in the case in hand.
This is generally a matter of observa-
tion, to be repeated in every fresh case ;
or if it has to be settled by argument
instead of observation, may require in
every different case different evidence,
and present every degree of difficulty,
from the lowest to the highest. But
the other part of the process — namely,
to determine what else may be con-

1)EM0NSTRAT10N AND NECESSARY TRUTHS.

171

eluded if we find, and in proportion as
we find, the assumptions to be true —
may be performed once for all, and
the results held ready to be employed
as the occasions turn up for use. We
thus do all beforehand that can be so
done, and leave the least possible work
to be performed when cases arise and
press for a decision. This inquiry
into the inferences which can be drawn
from assumptions is what properly
constitutes Demonstrative Science.

It is of course quite as practicable
to arrive at new conclusions from facts
assumed, as from facts observed ;
from fictitious, as from real, induc-
tions. Deduction, as we have seen,
consists of a series of inferences in
this form — a is a mark of 6, 6 of c, c
of c?, therefore a is a mark of d, which
last may be a truth inaccessible to
direct observation. In like manner
it is allowable to say, suppose that a
were a mark of h, h of c, and c oi d, a
would be a mark of rf, which last
conclusion was not thought of by
those who laid down the premises.
A system of propositions as compli-
cated as geometry might be deduced
from assumptions which are false ; as
was done by Ptolemy, Descartes, and
others, in their attempts to explain
synthetically the phenomena of th'
solar system on the supposition that
the apparent motions of the heavenly
bodies were the real motions, or were
produced in some way more or less
different from the true one. Some-
times the same thing is knowingly
done for the purpose of showing the
falsity of the assumption ; which is
called a reductio ad absurdum. In
such cases the reasoning is as fol-
lows : a is a mark of 6, and 6 of c ;
now if c were also a mark of d, a
would be a mark of d ; but d is
known to be a mark of the absence of
a ; consequently a would be a mark
of its own absence, which is a contra-
diction ; therefore c is not a mark of d.

§ 5. It has even been held by some
writers that all ratiocination rests in
the last resort on a reductio ad ab-

surdum, since the way to enforce
assent to it, in case of obscurity, would
be to show that if the conclusion be
denied we must deny some one at
least of the premises, which, as they
are all supposed true, wotild be a con-
tradiction. And in accordance with
this, many have thought that the
peculiar nature of the evidence of
ratiocination consisted in the impos-
sibility of admitting the premises and
rejecting the conclusion without a
contradiction in terms. This theory,
however, is admissible as an explana-
tion of the grounds on which ratiocina-
tion itself rests. If any one denies
the conclusion notwithstanding his
admission of the premises, he is not
involved in any direct and express
contradiction until he is compelled to
deny some premise ; and he can only
be forced to do this by a reductio ad
absurdum, that is, by another ratioci-
nation : now, if he denies the validity
of the reasoning process itself, he can
no more be forced to assent to the
second syllogism than to the first. In
truth, therefore, no one is ever forced
to a contradiction in terms : he can
only be forced to a contradiction (or
rather an infringement) of the funda-
mentalmaximof ratiocination, namely,
that whatever has a mark, has what it
is a mark of ; or, (in the case of uni-
versal propositions,) that whatever is
a mark of anything, is a mark of what-
ever else that thing is a mark of.
For in the case of every correct argu-
ment, as soon as thrown into the
syllogistic form, it is evident without
the aid of any other syllogism, that he
who, admitting the premises, fails to
draw the conclusion, does not conform
to the above axiom.

We have now proceeded as far in
the theory of Deduction as we can
advance in the present stage of our
inquiry. Any further insight into the
subject requires that the foundation
shall have been laid of the philosophic
theory of Induction itself ; in which
theory that of Deduction, as a mode
of Induction, which we have now
shown it to be, will assume spontane-

t72

HEASONING.

ously the place which belongs to it,
and will receive its share of whatever
light may be thrown upon the great
intellectual operation of which it forms
80 important a part.

CHAPTER VIL

EXAMINATION OF SOME OPINIONS OP-
POSED TO THE PRECEDING DOC-
TRINES.

§ I. Polemical discussion is foreign
to the plan of this work. But an
opinion which stands in need of much
illustration can often receive it most
effectually, and least tediously, in the
form of a defence against objections.
And on subjects concerning which
speculative minds are still divided, a
writer does but half his duty by
stating his own doctrine, if he does not
also examine, and to the best of his
ability judge, those of other thinkers.

In the dissertation which Mr.
Herbert Spencer has prefixed to his,
in many respects, highly philosophical
treatise on the mind,* he criticises
some of the doctrines of the two pre-
ceding chapters, and propounds a
theory of his own on the subject of
first principles. Mr. Spencer agrees
with me in considering axioms to be
" simply our earliest inductions from
experience." But he differs from me
" widely as to the worth of the test of
inconceivableness." He thinks that
it is the ultimate test of all beliefs.
He arrives at this conclusion by two
steps. First, we never can have any
stronger ground for believing anything
than that the belief of it " invariably
exists." Whenever any fact or pro-
position is invariably believed — that
is, if I understand Mr. Spencer rightly,
believed by all persons, and by one-
self at all times— it is entitled to be
received as one of the primitive truths
or original premises of our knowledge.
Secondly, the criterion by which we
decide whether anything is invariably

* JPrineiplet of Psychology.

believed to be true is our inability to
conceive it as false. "The incon-
ceivability of its negation is the test
by which we ascertain whether a given
belief invariably exists or not."
" For our primary beliefs, the fact of
invariable existence, tested by an
abortive effort to cause their non-
existence, is the only reason assign-
able." He thinks this the sole ground
of our belief in our own sensations.
If I believe that I feel cold, I only
receive this as true because I cannot
conceive that I am not feeling cold.
" While the proposition remains true,
the negation of it remains inconceiv-
able." There are numerous other be-
liefs which Mr. Spencer considers to
rest on the same basis, being chiefly
those, or a part of those, which the
metaphysicians of the Reid and
Stewart school consider as truths of
immediate intuition. That there ex-
ists a material world ; that this is the
very world which we directly and im-
mediately perceive, and not merely the
hidden cause of our perceptions ; that
Space, Time, Force, Extension, Figure,
are not modes of our consciousness,
but objective realities ; are regarded
by Mr. Spencer as truths known by
the inconceivableness of their nega-
tives. We cannot, he says, by any
effort, conceive these objectsof thought
as mere states of our mind ; as not
having an existence external to us.
Their real existence is, therefore, as
certain as our sensations themselves.
The truths which are the subject of
direct knowledge, being, according to
this doctrine, known to be truths only
by the inconceivability of their nega-
tion, and the truths which are not
the object of direct knowledge, being
known as inferences from those which
are : and those inferences being be-
lieved to follow from the premises
only because we cannot conceive them
not to follow, inconceivability is thus
the ultimate ground of all assured
beliefs.

Thus far there is no very wide dif-
ference between Mr. Spencer's doc-
trine and the ordinary one of philo-

THEORIES CONCERNING AXIOMS.

173

sophers of the intuitive school, from
Descartes to Dr. Whewell ; but at
this point Mr. Spencer diverges from
them. For he does not, like them,
set up the test of inconceivability as
infallible. On the contrary, he holds
that it may be fallacious, not from
any fault in the test itself, but because
" men have mistaken for inconceivable
things some things which were not
inconceivable." And he himself, in
this very book, denies not a few pro-
positions usually regarded as among
the most marked examples of truths
whose negations are inconceivable.
But occasional failure, he says, is in-
cident to all tests. If such failure
vitiates "the test of inconceivable-
ness," it "must similarly vitiate all
tests whatever. We consider an in-
ference logically drawn from estab-
lished premises to be true. Yet in
millions of cases men have been wrong
in the inferences they have thought
thus drawn. Do we therefore argue
that it is absurd to consider an infer-
ence true on no other ground than
that it is logically drawn from estab-
lished premises ? No : we say that
though men may have taken for logi-
cal inferences inferences that were
not logical, there nevertheless are logi-
cal inferences, and that we are justi-
fied in assuming the truth of what
seem to us such, until better instructed.
Similarly, though men may have
thought some things inconceivable
which were not so, there may still be
inconceivable things ; and the inabil-
ity to conceive the negation of a thing
may still be our best warrant for be-
lieving it. . . . Though occasionally
it may prove an imperfect test, yet,
as our most certain beliefs are capable
of no better, to doubt any one belief
because we have no higher guarantee
for it is really to doubt all beliefs."
Mr. Spencer's doctrine, therefore, does
not erect the curable, but only the
incurable limitations of the human
concept! ve faculty into laws of the
outward universe.

I 2. The doctrine that "a belief

which is proved by the inconceivable-
ness of its negation to invariably
exist is true," Mr. Spencer enforces
by two arguments, one of which may
be distinguished as positive, and the
other as negative.

The positive argument is, that every
such belief represents the aggregate
of all past experience. " Conceding
the entire truth of " the " position,
that during any phase of human pro-
gress, the ability or inability to form
a specific conception wholly depends
on the experiences men have had ;
and that, by a widening of their ex-
periences, they may, by and by, be
enabled to conceive things before in-
conceivable to them, it may still be
argued that as, at any time, the best
warrant men can have for a belief is
the perfect agreement of all pre-exist-
ing experience in support of it, it
follows that, at any time, the incon-
ceivableness of its negation is the
deepest test any belief admits of. . . .
Objective facts are ever impressing
themselves upon us ; our experience
is a register of these objective facta ;
and the inconceivableness of a thing
implies that it is wholly at variance
with the register. Even were this
all, it is not clear how, if every truth
is primarily inductive, any better test
of truth could exist. But it must be
remembered that whilst many of these
facts impressing themselves upon us
are occasional, whilst others again
are very general, some are universal
and unchanging. These universal
and unchanging facts are, by the
hypothesis, certain to establish beliefs
of which the negations are incon-
ceivable ; whilst the others are not
certain to do this ; and if they do,
subsequent facts will reverse their
action. Hence if, after an immense
accumulation of experiences, there
remain beliefs of which the negations
are still inconceivable, most, if not all
of them, must correspond to universal
objective facts. If there be . . . cer-
tain absolute uniformities in nature ;
if these uniformities produce, as they
must, absolute uniformities in o\^r es-

174

REASONING.

perience ; and if . . . these absolute
uniformities in our experience disable
us from conceiving the negations of
them ; then answering to each ab-
solute uniformity in nature which we
can cognise, there must exist in us a
belief of which the negation is incon-
ceivable, and which is absolutely true.
In this wide range of cases subjective
inconceivableness must correspond to
objective impossibility. Tiirther ex-
perience will produce correspondence
where it may not yet exist ; and we
may expect the correspondence to be-
come ultimately complete. In nearly
all cases this test of inconceivableness
must be valid now " — (I wish I could
think we were so nearly arrived at
omniscience) — " and where it is not, it
still expresses the net result of our
experience up to the present time ;
which is the most that any test can
do."

To this I answer, first, that it is
by no means true that the inconceiv-
ability, by us, of the negative of a
proposition proves all, or even any,
•* pre-existing experience " to be in
favour of the affirmative. There may
have been no such pre-existing experi-
ences, but only a mistaken supposi-
tion of experience. How did the in-
conceivability of antipodes prove that
experience had given any testimony
against their possibility? How did
the incapacity men felt of conceiving
sunset otherwise than as a motion of
the sun, represent any " net result "
of experience in support of its being
the sun and not the earth that moves ?
It is not experience that is repre-
sented, it is only a superficial resem-
blance of experience. The only thing
proved with regard to real experience
is the negative fact that men have
not had it of the kind which would
have made the inconceivable proposi-
tion conceivable.

Next : Even if it were true that in-
conceivableness represents the net
result of all past experience, why should
we stop at the representative when we
can get at the thing represented ? If
our incapacity to conceive the negation

of a given supposition is proof of ita
truth, because proving that our ex-
perience has hitherto been uniform in
its favour, the real evidence for the
supposition is not the inconceivable-
ness, but the uniformity of experience.
Now this, which is the substantial
and only proof, is directly accessible.
We are not obliged to presume it from
an incidental consequence. If all past
experience is in favour of a belief, let
this be stated, and the belief openly
rested on that ground : after which
the question arises, what that fact
may be worth as evidence of its truth ?
For uniformity of experience is evi-
dence in very different degrees : in
some cases it is strong evidence, in
others weak, in others it scarcely
amounts to evidence at all. That all
metals sink in water, was an uniform
experience, from the origin of the
human race to the discovery of potas-
sium in the present century by Sir
Humphry Davy. That all swans are
white, was an uniform experience down
to the discovery of Australia. In the
few cases in which uniformity of ex-
perience does amount to the strongest
possible proof, as with such proposi-
tions as these, Two straight lines can-
not enclose a space, Every event has
a cause, it is not because their nega-
tions are inconceivable, which is not
always the fact, but because the ex-
perience, which has been thus uniform,
pervades all nature. It will be shown
in the following Book that none of
the conclusions either of induction or
of deduction can be considered certain,
except as far as their truth is shown
to be inseparably bound up with truths
of this class.

I maintain then, first, that unifor-
mity of past experience is very far
from being universally a criterion of
truth. But, secondly, inconceivable-
ness is still farther from being a test
even of that test. Uniformity of
contrary experience is only one of
many causes of inconceivability. Tra-
dition handed down from a period of
more limited knowledge is one of the
commonest, The mere familiarity of

THEORIES CONCERNING AXIOMS.

m

one mode of production of a pheno-
menon often suffices to make every
other mode appear inconceivable.
Whatever connects two ideas by a
strong association may, and conti-
nually does, render their separation
in thoiaght impossible ; as Mr. Spencer
in other parts of his speculations fre-
quently recognises. It was not for
want of experience that the Cartesians
were unable to conceive that one body
could produce motion in another with-
out contact. They had as much ex-
perience of other modes of producing
motion as they had of that mode.
The planets had revolved, and heavy
bodies had fallen, every hour of their
lives. But they fancied these pheno-
mena to be produced by a hidden
machinery which they did not see,
because without it they were unable
to conceive what they did see. The
inconcei vableness, insteadof represent-
ing their experience, dominated and
overrode their experience. Without
dwelling further on what I have
termed the positive argument of Mr, |
Spencer in support of his criterion of '
truth, I pass to his negative argument, j
on which he lays more stress.

§ 3. The negative argument is,
that, whether inconceivability be good
evidence or bad, no stronger evidence
is to be obtained. That what is in-
conceivable cannot be true is postu-
lated in every act of thought It is
the foundation of all our original
premises. Still more it is assumed in
all conclusions from those premisea
The invariability of belief, tested by
the inconceivableness of its negation,
"is our sole warrant for every de-
monstration. Logic is simply a sjrste-
matisation of the process by which we
indirectly obtain this warrant for
beliefs that do not directly possess it.
To gain the strongest conviction pos-
sible respecting any complex fact, we
either analytically descend from it by
successive steps, each of which we
unconsciously test by the inconceiv-
ableness of its negation, until we reach
lome axiom or truth which we have

similarly tested ; or we synthetically
ascend from such axiom or truth by
such steps. In either case we connect
some isolated belief with a belief
which invariably exists by a series of
intermediate beliefs which invariably
exist." The following passage sums
up the theory : *' When we perceive
that the negation of the belief is incon-
ceivable, we have all possible warrant
for asserting the invariability of its
existence ; and in asserting this, we
express alike our logical justification
of it, and the inexorable necessity we

are under of holding it We

have seen that this is the assumption
on which every conclusion whatever
xUtimately rests. We have no other
guarantee for the reality of conscious-
ness, of sensations, of personal exist-
ence ; we have no other guarantee for
any axiom ; we have no other guar-
antee for any step in a demonstration.
Hence, as being taken for granted in
every act of the understanding, it
must be regarded as the Universal
Postulate." But as this postulate
which we are under an "inexorable
j necessity " of holding true, is some-
[ times false ; as •* beliefs that once
I were shown by the inconceivableness
'■ of their negations to invariably exist
have since been found untrue," and
I as " beliefs that now possess this char-
{ acter may some day share the same
fate ; " the canon of belief laid down
by Mr. Spencer, is, that "the most
certain conclusion " is that ** which
involves the postulate the fewest
times." Reasoning, therefore, never
ought to prevail against one of the
immediate beliefs, (the belief inMatter,
in the outward reality of Extension,
Space, and the like,) because each of
these involves the postulate only once;
while an argument, besides involving
it in the premises, involves it again in
every step of the ratiocination, no one
of the successive acts of inference
being recognised as valid except
because we cannot conceive the con-
clusion not to follow from the pre-
mises.

It will be convenient to take the

1^6

REASONING.

last part of this argument first. In
every reasoning, according to Mr.
Spencer, the assumption of the postu-
late is renewed at every step. At
each inference we judge that the con-
clusion follows from the premises, our
sole warrant for that judgment being
that we cannot conceive it not to follow.
Consequently if the postulate is fal-
lible, the conclusions of reasoning are
more vitiated by that uncertainty
than direct intuitions ; and the dispro-
portion is greater, the more numerous
the steps of the argument.

To test this doctrine, let us first
suppose an argument consisting only
of a single step, which would be repre-
sented by one syllogism. This argu-
ment does rest on an assumption, and
we have seen in the preceding chapters
what the assumption is. It is, that
whatever has a mark, has what it is a
mark of. The evidence of this axiom
I shall not consider at present ; * let
us suppose it (with Mr. Spencer) to be
the inconceivableness of its reverse.

Let us now add a second step to the
argument: we require, what? Another
assumption ? No : the same assump-
tion a second time ; and so on to a
third and a fourth. I confess I do
not see how, on Mr. Spencer's own
principles, therepetition of the assump-
tion at all weakens the force of the
argument. If it were necessary the
second time to assume some other
axiom, the argument would no doubt
be weakened, since it would be neces-
sary to its validity that both axioms
should be true, and it might happen
that one was true and not the other :
making two chances of error instead
of one. But since it is the same
axiom, if it is true once it is true every
time ; and if the argument, being of
a hundred links, assumed the axiom a
hundred times, these hundred assump-
tions would make but one chance of
error among them all. It is satis-

* Mr. Spencer is mistaken in supposing
me to claim any peculiar " necessity " for
this axiom as compared with others. I
have corrected the expressions which led
him into that misapprehension of my

factory that we are not obliged to
suppose the deductions of pure mathe-
matics to be among the most uncertain
of argumentative processes, which on
Mr. Spencer's theory they could
hardly fail to be, since they are the
longest. But the number of steps in
an argument does not subtract from
its reliableness, if no new premises, of
an uncertain character, are taken up
by the way.*

* Mr. Spencer, in recently returning to
the subject, (Principles of Psychology, new
edition, ch. xiL, "The Test of Relative
Validity,") makes two answers to the pre-
ceding remarks. One is :

" Were an argument formed by repeating
the same proposition over and over again,
it would be true that any intrinsic falli-
bility of the postulate would not make the
conclusion more untrustworthy than tho
first step. But an argument consists of un-
like propositions. Now since Mr. Mill's
criticism on the Universal Postulate is that
in some cases, which he names, it has proved
to be an untrustworthy test, it follows
that in any argument consisting of hete-
rogeneous propositions, there is a risk, in-
creasing as the number of propositions
increases, that some one of them belongs
to this class of cases, and is wrongly
accepted because of the inconceivableness
of its negation."

No doubt : but this supposes new premise
to be taken in. The point we are discussing
is the fallibility not of the premises, but of
the reasoning, as distinguished from the
premises. Now the validity of the reason-
ing depends always upon the same axiom,
repeated (in thought) " over and over
again," viz. that whatever has a mark, has
what it is a mark of. Even, therefore, ou
the assumption that this axiom rests ulti-
mately on the Universal Postulate, and
that, the Postulate not being wholly trust-
worthy, the axiom may be one of the cases
of its failure ; all the risk there is of this
is incurred at the very first step of the
reasoning, and is not added to, however
long may be the series of subsequent steps.

I am here arguing, of course, from Mr.
Spencer's point of view. From my own
the case is still clearer ; for, in my view,
the truth that whatever has a mark has
what it is a mark of, is wholly trustworthy,
and derives none of its evidence from so
very untrustworthy a test as the inconceiv-
ability of the negative.

Mr. Spencer's second answer is valid up
to a certain point ; it is, that every pro-
longation of the process involves additional
chances of casual error, fiom carelessness
in the reasoning operation. This is an im-
portant consideration in the private specu-
lations of an individual reasouer ; and even
with respect to mankind at large, it must

THEORIES CONCERNING AXIOMS.

177

To speak next of the premises.
Our assurance of their truth, whether
they be generalities or individual
facts, is grounded, in Mr. Spencer's
opinion, on the inconceivableness of
their being false. It is necessary to
advert to a double meaning of the
word inconceivable, which Mr. Spen-
cer is aware of, and would sincerely
disclaim founding an argument upon,
but from which his case derives no
little advantage notwithstanding. By
inconceivableness is sometimes meant
inability to form or get rid of an idea ;
sometimes, inability to form or get rid
of a belief. The former meaning is
the most conformable to the analogy
of language ; for a conception always
means an idea, never a belief. The
wrong meaning of " inconceivable " is,
however, fully as frequent in philo-
sophical discussion as the right mean-
ing, and the intuitive school of meta-
physicians could not well do without
either. To illustrate the difference,
we will take two contrasted examples.
The early physical speculators con-
sidered antipodes incredible, because
inconceivable. But antipodes were
not inconceivable in the primitive
sense of the word. An idea of them
could be formed without difficulty :
they could be completely pictured to
the mental eye. What was difficult,
and as it then seemed impossible,
was to apprehend them as believable.
The idea could be put tc^ether of
men sticking on by their feet to the

be admitted that, though mere oversights
in the syllogistic process, like errors of
addition in an account, are special to the
individual, and seldom escape detection,
confusion of thought produced (for ex-
ample) by ambiguous terms has led whole
nations or ages to accept fallacious reason-
ing as valid. But this very fact points to
causes of error so much more dangerous
than the mere length of the process, as
quite to vitiate the doctrine that the "test
of the relative vaUdities of conflicting con-
clusions " is the number of times the funda-
mental postulate is involved. Ou the con-
trary, the subject on v^hich the trains of
reasoning are longest, and the assumption
therefore, oftenest repeated, are in general
those which are best fortified against the
really formidable causes of fallacy ; as in
the example already given of roathematica

under side of the earth ; but the
belief would follow that they must
fall off. Antipodes were not unima-
ginable, but they were unbelievable.

On the other hand, when I endea-
vour to conceive an end to extension,
the two ideas refuse to come together.
When I attempt to form a conception
of the last point of space, I cannot
help figuring to myself a vast space
beyond that last point. The com-
bination is, under the conditions of
our experience, unimaginable. This
double meaning of inconceivable it is
very important to bear in mind, for
the argument from inconceivableness
almost always turns on the alternate
substitution of each of those meanings
for the other.

In which of these two senses does
Mr. Spencer employ the term, when
he makes it a test of the truth of a
proposition that its negation is incon-
ceivable? Until Mr, Spencer ex-
pressly stated the contrary, I inferred
from the course of his argument that
he meant unbelievable. He has, how-
ever, in a paper published in the fifth
immber of the Fortnightly Review, dis-
claimed this meaning, and declared
that by an inconceivable proposition
he means now and always, "one of
which the terms cannot, by any effort,
be brought before consciousness in that
relation which the proposition asserts
between them — a proposition of which
the subject and predicate offer an in-
surmountable resistance to union in
thought." We now, therefore, know
positively that Mr. Spencer always
endeavours to use the word inconceiv-
able in this, its proper sense : but it
may yet be questioned whether his
endeavour is always successful ; whe-
ther the other, and popular use of the
word does not sometimes creep in
with its associations, and prevent him
from maintaining a clear separation
between the two. When, for example,
he says, that when I feel cold I can-
not conceive that I am not feeling
cold, this expression cannot be trans-
lated into " I cannot conceive myself
not feeling cold," for it is evident that

178

REASONING.

I can : the word conceive, therefore,
is here used to express the recognition
of a matter of fact — the perception of
truth or falsehood ; which I apprehend
to be exactly the meaning of an act of
belief, as distinguished from simple
conception. Again, Mr. Spencer calls
the attempt to conceive something
which IS inconceivable "an abortive
effort to cause the non-existence " not
of a conception or mental representa-
tion, but of a belief. There is need,
therefore, to revise a considerable part
of Mr. Spencer's language, if it is to
be kept always consistent with his
definition of inconceivability. But in
truth the point is of little importance,
since inconceivability, in Mr. Spencer's
theory, is only a test of truth, inasmuch
as it is a test of believability. The
inconceivableness of a supposition is
the extreme case of its unbelievability.
This is the very foundation of Mr.
Spencer's doctrine. The invariability
of the belief is with him the real
guarantee. The attempt to conceive
the negative is made in order to test
the inevitableness of the belief. It
should be called, an attempt to believe
the negative. When Mr. Spencer says
that while looking at the sun a man
cannot conceive that he is looking into
darkness, he should have said that a
man cannot believe that he is doing so.
For it is surely possible, in broad day-
light, to imagine oneself looking into
darkness.* As Mr. Spencer himself
says, speaking of the belief of our own
existence : " That he might not exist,
he can conceive well enough : but
that he does not exist, he finds it im-
possible to conceive," i.e., to believe.
So that the statement resolves itself
into this : That I exist and that I
have sensations, I believe, because I
cannot believe otherwise. And in

* Mr. Spencer makes a distinction be-
tween conceiving myself looking into dark-
ness, and conceiving that I am then and
there looking into darkness. To me it
seems that this change of the expression
to the form / am, just marks the transition
from conception to belief, and that the
phrase "to conceive that / am," or "that
anything is," is not consistent with using
th« word " concelvg " in its rigoroiis sense.

this case every one will admit that
the impossibility is real. Any one's
present sensations, or other states of
subjective consciousness, that one per-
son inevitably believes. They are
facts known per se : it is impossible
to ascend beyond them. Their nega-
tive is really unbelievable, and there-
fore there is never any question about
believing it. Mr. Spencer's theory is
not needed for these truths.

But according to Mr. Spencer there
are other beliefs, relating to other
things than our own subjective feel-
ings, for which we have the same
guarantee — which are in a similar
manner invariable and necessary.
With regard to these other beliefs,
they cannot be necessary, since they
do not always exist. There have been,
and are, many persons who do not be-
lieve the reality of an external world,
still less the reality of extension and
figure as the forms of that external
world ; who do not believe that space
and time have an existence indepen-
dent of the mind — nor any other of
Mr. Spencer's objective intuitions.
The negations of these alleged invari-
able beliefs are not unbelievable, for
they are believed. It may be main-
tained, without obvious error, that
we cannot imagine tangible objects as
mere states of our own and other
people's consciousness ; that the per-
ception of them irresistibly suggests
to us the idea of something external
to ourselves : and I am not in a con-
dition to say that this is not the fact
(though I do not think any one is en-
titled to affirm it of any person besides
himself). But many thinkers have
believed, whether they could conceive
it or not, that what we represent to
ourselves as material objects are mere
modifications of consciousness ; com-
plex feelings of touch and of muscu-
lar action. Mr. Spencer may think
the inference correct from the un-
imaginable to the unbelievable, be-
cause he holds that belief itself is but
the persistence of an idea, and that
what we can succeed in imagining we
cannot at the moment help apprehend-

THEORIES CONCERNING AXIOMS.

179

ing as believable. But of what con-
sequence is it what we apprehend at
the moment, if the moment is in con-
tradiction to the permanent state of
our mind? A person who has been
frightened when an infant by stories
of ghosts, though he disbelieves them
in after years, (and perhaps never be-
lieved them,) may be unable all his
life to be in a dark place, in circum-
stances stimulating to the imagination,
without mental discomposure. The
idea of ghosts, with all its attendant
terrors, is irresistibly called up in his
mind by the outward circumstances.
Mr. Spencer may say, that while he
is under the influence of this terror he
does not disbelieve in ghosts, but has
a temporary and uncontrollable belief
in them. Be it so ; but allowing it
to be so, which would it be truest to
say of this man on the whole — that
he believes in ghosts, or that he does
not believe in them ? Assuredly that
he does not believe in them. The
case is similar with those who dis-
believe a material world. Though
they cannot get rid of the idea ;
though while looking at a solid object
they cannot help having the concep-
tion, and therefore, according to Mr.
Spencers metaphysics, the momentary
belief, of its externality ; even at that
moment they would sincerely deny
holding that belief : and it would be
incorrect to call them other than dis-
believers of the doctrine. The belief,
therefore, is not invariable ; and the
test of inconceivableness fails in the
only cases to which there could ever
be any occasion to apply it.

That a thing may be perfectly be-
lievable, and yet may not have be-
come conceivable, and that we may
habitually believe one side of an alter-
native, and conceive only in the other,
is familiarly exemplified in the state
of mind of educated persons respect-
ing sunrise and sunset. All educated
persons either know by investigation,
or believe on the authority of science,
that it is the earth and not the sun
which moves : but there are probably
few who habitually conceive the pheno-

menon otherwise than as the ascent
or descent of the sun. Assuredly no
one can do so without a prolonged
trial ; and it is probably not easier
now than in the first generation after
Copernicus. Mr. Spencer does not
say, " In looking at sunrise it is im-
possible not to conceive that it is the
sun which moves, therefore this is
what everybody believes, and we have
all the evidence for it that we can
have for any truth." Yet this would
be an exact parallel to his doctrine
about the belief in matter.

The existence of matter, and other
Noumena, as distinguished from the
phenomenal world, remains a question
of argument, as it was before ; and
the very general, but neither necessary
nor universal, belief in them.s tands
as a psychological phenomenon to be
explained, either on the hypothesis
of its truth, or on some other. The
belief is not a conclusive proof of its
own truth, unless there are no such
things as idola tribds ; but being a
fact, it calls on antagonists to show,
from what except the real existence
of the thing believed, so general and
apparently spontaneous a belief can
have originated. And its opponents
have never hesitated to accept this
challenge.* The amount of their
success in meeting it will probably
determine the ultimate verdict of
philosophers on the question.

§ 4. In a revision, or rather recon-
struction of his "Principles of Psy-
chology," as one of the stages or plat-
forms in the imposing structure of his
System of Philosophy, Mr. Spencer
has resumed what he justly terms f
the '* amicable controversy that has
been long pending between us ; " ex-
pressing at the same time a regret,
which I cordially share, that "this
lengthened exposition of a single point
of difference, unaccompanied by an

* I have myself accepted the contest, and
fought it out on this battle-ground, in the
eleventh chapter of An Examination 0/ Sir
William Hamilton't Philosophy.

t Chap. xi.

l8o

REASONING.

exposition of the numerous points of
concurrence, unavoidably produces an
appearance of dissent very far greater
than that which exists." I l^lieve,
with Mr. Spencer, that the difference
between us, if measured by our con-
clusions, is "superficial rather than
substantial ; " and the value I attach
to so great an amount of agreement,
in the field of analytic psychology,
with a thinker of his force and depth,
is such as I can hardly overstate. But
I also agree with him that the differ-
ence which exists in our premises is
one of *' profound importance, philo-
sophically considered ; " and not to
be dismissed while any part of the
case of either of us has not been fully
examined and discussed.

In his present statement of the
Universal Postulate, Mr. Spencer has
exchanged his former expression,
" beliefs which invariably exist, " for
the following : " cognitions of which
the predicates invariably exist along
with their subjects." And he says
that "an abortive effort to conceive
the negation of a proposition, shows
that the cognition expressed is one of
which the predicate invariably exists
along with its subject ; and the dis-
covery that the predicate invariably
exists along with its subject is the
discovery that this cognition is one we
are compelled to accept." Both these
premises of Mr. Spencer's syllogism I
am able to assent to, but in different
senses of the middle term. If the
invariable existence of the predicate
along with its subject is to be under-
stood in the most obvious meaning,
as an existence in actual Nature, or in
other words, in our objective or sen-
sational experience, I of course admit
that this, once ascertained, compels us
to accept the proposition : but then I
do not admit that the failure of an
attempt to conceive the negative
proves the predicate to be always co-
existent with the subject in actual
Nature. If, on the other hand, (which
I believe to be Mr. Spencer's mean-
ing,) the invariable existence of the
predicate along with the subject is to

be understood only of our concept! ve
faculty, i.e. that the one is inseparable
from the other in our thoughts ; then,
indeed, the inability to separate the
two ideas proves their inseparable con-
junction, here and now in the mind
which has failed in the attempt ; but
this inseparability in thought does not
prove a corresponding inseparability
in fact, nor even in the thoughts of
other people, or of the same person in
a possible future.

" That some propositions have been
wrongly accepted as true, because
their negations were supposed incon-
ceivable when they were not," does
not, in Mr. Spencer's opinion, "dis-
prove the validity of the test ; " not
only because any test whatever "is
liable to yield untrue results, either
from incapacity or from carelessness
in those who use it," but because the
propositions in question " were com-
plex propositions, not to be established
by a test applicable to propositions no
further decomposable. " " A test legi-
timately applicable to a simple pro-
position the subject and predicate of
which are in direct relation, cannot
be legitimately applied to a complex
proposition, the subject and predicate
of which are indirectly related through
the many simple propositions implied."
" That things which are equal to the
same thing are equal to one another,
is a fact which can be known by direct
comparison of actual or ideal relations.
. . . . But that the square of the
hypothenuse of a right-angled triangle
equals the sum of the squares of the
other two sides, cannot be known
immediately by comparison of two
states of consciousness : here the
truth can be reached only mediately,
through a series of simple judgments
respecting the likenesses or unlike -
nesses of certain relations." More-
over, even when the proposition admits
of being tested by immediate con-
sciousness, people often neglect to do
it. A schoolboy, in adding up a
column of figures, will say " 35 and
9 are 46," though this is contrary to
the verdict which consciousness gives

THEORIES CONCERNING AXIOMS.

i8i

when 35 and 9 are really called up
before it ; but this is not done. And
not only schoolboys, but men and
thinkers, do not always "distinctly
translate into their equivalent states
of consciousness the words they use."
It is but just to give Mr. Spencer's
doctrine the benefit of the limitation
he claims, viz. that it is only applicable
to propositions which are assented to
on simple inspection, without any in-
tervening media of proof. But this
limitation does not exclude some of
the most marked instances of proposi-
tions now known to be false or ground-
less, but whose negative was once
found inconceivable : such as, that in
sunrise and sunset it is the sun which
moves ; that gravitation may exist
without an intervening medium ; and
even the case of antipotles. The dis-
tinction drawn by Mr Spencer is real ;
but, in the case of the propositions
classed by him as complex, conscious-
ness, until the media of proof are
supplied, gives no verdict at all : it
neither declares the equality of the
square of the hypothenuse with the
sum of the squares of the sides to be
inconceivable, nor their inequality to
be inconceivable. But in all the three
cases which I have just cited, the in-
conceivability seemsto be apprehended
directly ; no train of argument was
needed, as in the case of the square of
the hypothenuse, to obtain the verdict
of consciousness on the point. Neither
is any of the three a case like that of
the schoolboy's mistake, in which the
mind was never really brought into
contact with the proposition. They
are cases in which one of two opposite
predicates, mero adspectu,^ seemed to
be incompatible with the subject, and
the other, therefore, to be proved
always to exist with it.*

* In one of the three cases, Mr. Spencer,
to my no small surprise, thinks tnat the
belief of mankind " cannot be rightly said
to have undergone " the change I allege.
Mr. Spencer himself still thinks we are un-
able to conceive gravitation acting through
empty space. "If an astronomer vowed
that he could conceive gravitative force as
exercised through space absolutely void,

As now limited by Mr. Spencer,
the ultimate cognitions fit to be sub-
mitted to his test are only those of so
universal and elementary a character
as to be represented in the earliest
and most unvarying experience, or
apparent experience, of all mankind.
In such cases the inconceivability of
the negative, if real, is accounted for
by the experience : and why (I have
asked) should the truth be tested by
the inconceivability, when we can go
farther back for proof — namely, to
the experience itself? To this Mr.
Spencer answers, that the experiences
cannot be all recalled to mind, and if
recalled, would be of unmanageable
multitude. To test a proposition by
experience seems to him to mean that
" before accepting as certain the pro-
position that any rectilineal figure
must have as many angles as it ha8
sides," I have "to think of every
triangle, square, pentagon, hexagon,
&c., which I have ever seen, and to
verify the asserted relation in each
case." I can only say, with surprise,
that I do not understand this to be
the meaning of an appeal to experi-
ence. It is enough to know that one
has been seeing the fact all one's life,
and has never remarked any instance
to the contrary, and that other people,
with every opportunity of observation,

my private opinion would be that he mis.
took the nature of conception. Conception
implies representation. Here the elements
of the representation are the two bodies
and an agency by which either affects the
other. To conceive this agency is to re-
present it in some terms derived from our
experiences — that is, from our sensations.
As this agency gives us no sensai ions, we
are obliged (if we try to conceive it) to use
symbols idealised from our sensations —
imponderable units forming a medium."

If Mr. Spencer means that the action of
gravitation gives us no sensations, the
assertion is one than which I have not seen,
j in the writings of philosophers, many more
startling. What other sensation do wo
need than the sensation of one body moving
towards another? "The elements of the
representation" are not two bodies and
an " agency," but two bodies and an
effect, viz. the fact of their approaching
one another. If we are able to conceive a
vacuum, is there any difficulty in conceiv-
ing a body falling to the earth through itf

l82

REASONING.

unanimously declare the same thing.
It is true, even this experience may
be insufficient, and so it might be
even if I could recall to mind every
instance of it : but its insufficiency,
instead of being brought to light, is
disguised, if, instead of sifting the
experience itself, I appeal to a test
which bears no relation to the suffi-
ciency of the experience, but, at the
most, only to its familiarity. These
remarks do not lose their force even
if we believe, with Mr. Spencer, that
mental tendencies originally derived
from experience impress themselves
permanently on the cerebral structure
and are transmitted by inheritance,
BO that modes of thinking which are
acquired by the race become innate
and a priori in the individual, thus
representing, in Mr. Spencer's opinion,
the experience of his progenitors, in
addition to his own. All that would
follow from this is, that a conviction
might be really innate, i.e. prior to
individual experience, and yet not be
true, since the inherited tendency to
accept it may have been originally
the result of other causes than its
truth.

Mr. Spencer would have a much
stronger case if he could really show
that the evidence of Reasoning rests
on the Postulate, or, in other words,
that we believe that a conclusion
follows from premises only because
we cannot conceive it not to follow.
But this statement seems to me to be
of the same kind as one I have pre-
viously commented on, viz. that I
believe I see light, because I cannot,
while the sensation remains, conceive
that I am looking into darkness.
Both these statements seem to me
incompatible with the meaning (as
very rightly limited by Mr. Spencer)
of the verb to conceive. To say that
when I apprehend that A is B and
that B is C, I cannot conceive that A
is not C, is to my mind merely to say
that I am compelled to believe that A
is C. If to conceive be taken in its
proper meaning, viz. to form a mental
representation, I may be able to con-

ceive A as not being C After
assenting, with full understanding,
to the Copernican proof that it is the
earth and not the sun that moves, I
not only can conceive, or represent to
myself, sunset as a motion of the sun,
but almost every one finds this con-
ception of sunset easier to form than
that which they nevertheless know to
be the true one.

§ 5. Sir William Hamilton holds as
I do, that inconceivability is no crite-
rion of impossibility. "There is no
ground for inferring a certain fact to
be impossible, merely from our inabil-
ity toconceive its possibility." "Things
there are which may, nay must, be
true, of which the understanding is
wholly unable to construe to itself the
possibility." * Sir William Hamilton
is, however, a firm believer in the a
priori character of many axioms, and
of the sciences deduced from them ;
and is so far from considering those
axioms to rest on the evidence of ex-
perience, that he declares certain of
them to be true even of Noumena — of
the Unconditioned — of which it is one
of the principal aims of his philosophy
to prove that the nature of our facul-
ties debars us from having any know-
ledge. The axioms to which he attri-
butes this exceptional emancipation
from the limits which confine aU our
other possibilities of knowledge ; the
chinks through which, as he represents,
one ray of light finds its way to us
from behind the curtain which veils
from us the mysterious world of Things
in themselves, — are the two principles
which he terms, after the schoolmen,
the Principle of Contradiction and
the Principle of Excluded Middle:
the first, that two contradictory pro-
positions cannot both be true ; the
second, that they cannot both be false.
Armed with these logical weapons,
we may boldly face Things in them-
selves, and tender to them the double
alternative, sure that they must abso-
lutely elect one or the other side,

* Discussions, (be, 2d ed. p. 634.

THEORIES CONCERNING AXIOMS.

x83

though we may be for ever precluded
from discovering which. To take his
favourite example, we cannot conceive
the infinite divisibility of matter, and
we cannot conceive a minimum, or end
to divisibility : yet one or the other
must be true.

As I have hitherto said nothing of
the two axioms in question, those of
Contradiction andof Excluded Middle,
it is not unseasonable to consider them
here. The former asserts that an
affirmative proposition and the cor-
responding negative proposition can-
not both be true ; which has generally
been held to be intuitively evident.
Sir William Hamilton and the Ger-
mans consider it to be the statement
in words of a form or law of our
thinking faculty. Other philosophers,
not less deserving of consideration,
deem it to be an identical proposition,
an assertion involved in the meaning
of the terms ; a mode of defining
Negation, and the word Not.

I am able to go one step with these
last. An affirmative assertion and its
negative are not two independent
assertions, connected with each other
only as mutually incompatible. That
if the negative be true, the affirmative
must be false, really is a mere identi-
cal proposition ; for the negative pro-
position asserts nothing but the falsity
of the affirmative, and has no other
sense or meaning whatever. The
Principium Contradictionis should
therefore put off the ambitious phrase-
ology which gives it the air of a fun-
damental antithesis pervading nature,
and should be enunciated in the
simpler form, that the same proposi-
tion cannot at the same time be false
and true. But I can go no farther
with the Nominalists ; for I cannot
look upon this last as a merely verbal
proposition. I consider it to be, like
other axioms, one of our first and most
familiar generalisations from experi-
ence. The original foundation of it
I take to be, that Belief and Disbelief
are two different mental states, ex-
cluding one another. This we know
by the simplest observation of our own

minds. And if we carry our observa-
tion outwards, we also find that light
and darkness, sound and silence, mo-
tion and quiescence, equality and in-
equality, preceding and following, suc-
cession and simultaneousness, any
positive phenomenoi^ whatever and
its negative, are distinct phenomena,
pointedly contrasted, and the one
always absent where the other is pre-
sent. I consider the maxim in ques-
tion to be a generalisation from all
these facts.

In like manner as the Principle of
Contradiction (that one of two contra-
dictories must be false) means that an
assertion cannot be both true and false,
so the Principle of Excluded Middle,
or that one of two contradictories
must be true, means that an assertion
must be either true or false : either
the affirmative is true, or otherwise
the negative is true, which means that
the affirmative is false. I cannot help
thinking this principle a surprising
specimen of a so called necessity of
Thought, since it is not even true, un-
less with a large qualification. A pro-
position must be either true or false,
provided that the predicate be one
which can in any intelligible sense be
attributed to the subject (and as this
is always assumed to be the case in
treatises on logic, the axiom is always
laid down there as of absolute truth).
" Abracadabra is a second intention "
is neither true nor false. Between
the true and the false there is a third
possibility, the Unmeaning ; and this
alternative is fatal to Sir William
Hamilton's extension of the maxim
to Noumena. That Matter must
either have a minimum of divisibility
or be infinitely divisible, is more than
we can ever know. For in the first
place, Matter, in any other than the
phenomenal sense of the term, may
not exist ; and it will scarcely be said
that a non-entity must be either in-
finitely or finitely divisible. In the
second place, though matter, con-
sidered as the occult cause of oun
sensations, do really exist, yet what
we caU divisibility may be an attri-

t84

REASONING.

bute only of our sensations of sight
and touch, and not of their uncognis-
able cause. Divisibility may not be
predicable at all, in any intelligible
sense, of Things in Themselves, nor
therefore of Matter in itself ; and
the assumed necessity of being either
infinitely or finitely divisible may be
an inapplicable alternative. On this
question I am happy to have the full
concurrence of Mr. Herbert Spencer,
from whose paper in the Fortnightly
Review I extract the following pas-
sage. The germ of an idea identical
with that of Mr. Spencer may be
found in the present chapter, about
a page back, but in Mr. Spencer it
is not an undeveloped thought, but
a philosophical theory.

"When rememberingacertain thing
as in a certain place, the place and the
thing are mentally represented toge-
ther ; while to think of the non-exis-
tence of the thing in that place implies
a consciousness in which the place is
represented, but not the thing. Simi-
larly, if instead of thinking of an ob-
ject as colourless, we think of its
having colour, the change consists in
the addition to the concept of an
element that was before absent from
it — the object cannot be thought of
first as red and then as not red,
without one component of the thought

being totally expelled from the mind
by another. The law of the Excluded
Middle, then, is simply a generalisa-
tion of the universal experience that
some mental states are directly de-
structive of other states. It formu-
lates a certain absolutely constant
law, that the appearance of any posi-
tive mode of consciousness cannot
occur without excluding a correlative
negative mode ; and that the negative
mode cannot occur without excluding
the correlative positive mode, the an-
tithesis of positive and negative being,
indeed, merely an expression of this
experience. Hence it follows that if
consciousness is not in one of the two
modes it must be in the other." *

I must here close this supplementary
chapter, and with it the Second Book.
The Theory of Induction, in the most
comprehensive sense of the term, will
form the subject of the Third.

* Professor Bain {Logic, i. i6) identifies
the Principle of Contradiction with hia
Law of Relativity, viz. that "everything
that can be thought of, every affirmation
that can be made, has an opposite or
counter notion or aifirmation ; " a propo-
sition which is one of the general results
of the whole body of human experience.
For further considerations respecting the
axioms of Contradiction and Excluded
Middle, see the twenty-first chapter of
An Examination of Sir Williani Hamilton'$
Philosophy,

BOOK HI.

OF INDUCTION.

*• According to the doctrine now stated, the highest, or rather the only proper object
of physics, is to ascertain those established conjunctions of successive events, which
constitute the order of the universe ; to record the phenomena which it exhibits to our
observation or which it discloses to our experiments ; and to refer these phenomena to
their general laws. "— D. Stewart, EUnunts of the Philoio^y of the human Mind, vol. ii.
chap. iv. sect. i.

CHAPTER L

PKELIMINAKY OBSERVATIONS ON IN-
DUCTION IN GENERAL.

§ I. The portion of the present in-
quiry upon which we are now about
to enter may be considered as the
principal, both from its surpassing in
intricacy all the other branches, and
tecause it relates to a process which
has been shown in the preceding
Book to be that in which the inves-
tigation of nature essentially consists.
We have found that all Inference,
consequently all Proof, and all dis-
covery of truths not self-evident, con-
sists of inductions, and the interpre-
tation of inductions ; that all our
knowledge, not intuitive, comes to
us exclusively from that source. What
Induction is, therefore, and what con-
ditions render it legitimate, cannot
but be deemed the main question of
the science of logic — the question
which includes all othere. It is,
however, one which professed writers
on logic have almost entirely pa.ssed
ever. The generalities of the subject I

have not been altogether neglected by
metaphysicians ; but, for want of suf-
ficient acquaintance with the processes
by which science has actually suc-
ceeded in establishing general truths,
their analysis of the inductive opera-
tion, even when unexceptionable as
to correctness, has not been specific
enough to be made the foundation of
practical rules, which might be for in-
duction itself what the rules of the
syllogism are for the interpretation
of induction ; while those by whom
physical science has been carried to
its present state of improvement—
and who, to arrive at a complete
theory of the process, needed only to
generalise, and adapt to all varieties
of problems, the methods which they
themselves employed in their habitual
pursuits — never until very lately made
any serious attempt to philosophise on
the subject, nor regarded the mode in
which they arrived at their conclusions
as deserving of study, independently
of the conclusions themselves.

§ 2. For the purposes of the present

iS6

INDUCTION.

inquiry, Induction may be defined, the
operation of discovering and proving
general propositions. It is true that
(as already shown) the process of in-
directly ascertaining individual facts
is as truly inductive as that by which
we establish general truths. But it
is not a different kind of induction ;
it is a form of the very same process :
since, on the one hand, generals are
but collections of particulars, definite
in kind but indefinite in number ; and
on the other hand, whenever the evi-
dence which we derive from observa-
tion of known cases justifies us in
drawing an inference respecting even
one unknown case, we should on the
same evidence be justified in drawing
a similar inference with respect to a
whole class of cases. The inference
either does not hold at all, or it holds
in all cases of a certain description ;
in all cases which, in certain definable
respects, resemble those we have ob-
served.

If these remarks are just ; if the
principles and rules of inference are
the same whether we infer general
propositions or individual facts ; it
follows that a complete logic of the
sciences would be also a complete
logic of practical business and com-
mon life. Since there is no case of
legitimate inference from experience,
in which the conclusion may not
legitimately be a general proposition,
an analysis of the process by which
general truths are arrived at is vir-
tually an analysis of all induction
whatever. Whether we are inquir-
ing into a scientific principle or into
an individual fact, and whether we
proceed by experiment or by ratio-
cination, every step in the train of
inferences is essentially inductive,
and the legitimacy of the induction
depends in both cases on the same
conditions.

True it is that in the case of the
practical inquirer, who is endeavour-
ing to ascertain facts not for the pur-
poses of science but for those of busi-
ness, such, for instance, as the advocate
or the judge, the chief difficulty is one

in which the principles of induction
will afford him no assistance. It
lies not in making his inductions,
but in the selection of them ; in choos-
ing from among all general proposi-
tions ascertained to be trtie, those
which furnish marks by which he
may trace whether the given subject
possesses or not the predicate in
question. In arguing a doubtful
question of fact before a jury, the
general propositions or principles to
which the advocate appeals are mostly,
in themselves, sufficiently trite, and
assented to as soon as stated : his
skill lies in bringing his case under
those propositions or principles ; in
calling to mind such of the known or
received maxims of probability as ad-
mit of application to the case in hand,
and selecting from among them those
best adapted to his object. Success
is here dependent on natural or ac-
quired sagacity, aided by knowledge
of the particular subject and of sub-
jects allied with it. Invention, though
it can be cultivated, cannot be reduced
to rule ; there is no science which will
enable a man to bethink himself of
that which will suit his purpose.

But when he has thought of some-
thing, science can tell him whether
that which he has thought of will
suit his purpose or not. The inquirer
or arguer must be guided by his own
knowledge and sagacity in the choice
of the inductions out of which he will
construct his argument. But the vali-
dity of the argument when constructed
depends on principles and must be
tried by tests which are the same for
all descriptions of inquiries, whether
the result be to give A an estate, or
to enrich science with a new general
truth. In the one case and in the
other, the senses, or testimony, must
decide on the individual facts ; the
rules of the syllogism will determine
whether, those facts being supposed
correct, the case really falls within
the formulae of the different induc-
tions under which it has been suc-
cessively brought ; and finally, the
legitimacy of the inductions them-

INDUCTION IN GENERAL.

t87

selves must be decided by other rules,
and these it is now our purpose to in-
vestigate. If this thira part of the
operation be, in many of the ques-
tions of practical life, not the most,
but the least arduous portion of it,
we have seen that this is also the case
in some great departments of the field
of science ; in all those which are
principally deductive, and most of all
in mathematics, where the inductions
themselves are few in number, and so
obvious and elementary that they seem
to stand in no need of the evidence of
experience, while to combine them so
OS to prove a given theorem or solve
a problem may call for the utmost
powers of invention and contrivance
with which our species is gifted.

If the identity of the logical pro-
cesses which prove particular facts
and those which establish general
scientific truths required any addi-
tional confirmation, it would be suf-
ficient to consider that in many
branches of science single facts have
to be proved, as well as principles ;
facts as completely individual as any
that are debated in a court of justice,
but which are proved in the same
manner as the other truths of the
science, and without disturbing in
any degree the homogeneity of its
method. A remarkable example of
this is afforded by astronomy. The
individual facts on which that science
grounds its most important deduc-
tions, such facts as the magnitudes
of the bodies of the solar system,
their distances from one another, the
figure of the earth, and its rotation,
are scarcely any of them accessible to
our means of direct observation : they
are proved indirectly by the aid of in-
ductione founded on other facts which
we can more easily reach. For ex-
ample, the distance of the moon from
the earth was determined by a very
circuitous process. The share which
direct observation had in the work
consisted in ascertaining, at one and
the same instant, the zenith distances
of the moon, as seen from two points
very remote from one another on the

earth's surface. The ascertainment
of these angular distances ascertained
their supplements ; and since the angle
at the earth's centre subtended by the
distance between the two places of ob-
servation was deducible by spherical
trigonometry from the latitude and
longitude of those places, the angle
at the moon subtended by the same
line became the fourth angle of a
quadrilateral of which the other three
angles were known. The four angles
being thus ascertained, and two sides
of the quadrilateral being radii of the
earth ; the two remaining sides and
the diagonal, or in other words, the
moon's distance from the two places
of observation, and from the centre
of the earth, could be a.scertained, at
least in terms of the earth's radius,
from elementary theorems of geo-
metry. At each step in this demon-
stration a new induction is taken in,
represented in the aggregate of its
results by a general proposition.

Not only is the process by which
an individual astronomical fact was
thus ascertained exactly similar to
those by which the same science
establishes its general truths, but also
(as we have shown to be the case in
all legitimate reasoning) a general
proposition might have been con-
cluded instead of a single fact In
strictness, indeed, the result of the
reasoning is a general proposition ; a
theorem respecting the distance, not
of the moon in particular, but of any
inaccessible object ; showing in what
relation that distance stands to cer-
tain other quantities. And although
the moon is almost the only heavenly
body the distance of which from the
earth can really be thus ascertained,
this is merely owing to the accidental
circumstances of the other heavenly
bodies, which render them incapable
of affording such data as the applica-
tion of the theorem requires ; for the
theorem itself is as true of them as it
is of the moon.*

• Dr. Whewell thinks it improper to
apply the term Induction to any operation
not terminating in the establishment of a

188

INDUCTION.

We shall fall into no error, then,
if, in treating of Induction, we limit
our attention to tlie establishment of
general propositions. The principles
and rules of Induction as directed to
this end, are the principles and rules
of all Induction ; and the logic of
Science is the universal Logic, appli-
cable to all inquiries in which man can
engage.

CHAPTER II.

OP INDUCTIONS IMPROPERLY SO
CALLED.

§ I. Induction, then, is that opera-
tion of the mind by which we infer
that what we know to be true in a
particular case or cases, will be true
in all cases which resemble the for-
mer in certain assignable respects.
In other words, Induction is the pro-
cess by which we conclude that what
is true of certain individuals of a
class is true of the whole, class, or

/general tnith. Induction, he says, (Philo-
sophy of Discovery, p. 245,) " is not the same
thing as experience and observation. In-
duction is experience or observation con-
sciously looked, at in 3i,gen(raliorm. This
consciousness and generality are necessary
parts of that knowledge which is science. "
And he objects (p. 241) to the mode in
vi'hich the word Induction is employed in
this work, as an undue extension of that
term "not only to the cases in which the
general induction is consciously applied to
a particular instance, but to the cases in
which the particular instance is dealt with
by means of experience in that rude sense
in which experience can be asserted of
brutes, and in which of course we can in
no way imagine that the law is possessed
or understood as a general proposition."
This use of the term he deems a "con-
fusion of knowledge with practical ten-
dencies."

I disclaim, as strongly as Dr. Whewell
can do, the application of such terms as
induction, inference, or reasoning to opera-
tions performed by mere instinct, that is,
from an animal impulse, without the exer-
tion of any intelligence. But I perceive
no ground for confining the use of those
terms to cases in which the inference is
drawn in the forms and with the precau-
tions reqiiired by scientific propriety. To
the idea of science, an express recognition
and distinct apprehension of general laws,

that what is true sJb certain times
will be true in similar circumstances
at all times.

This definition excludes from the
meaning of the term Induction, vari-
ous logical operations, to which it is
not unusual to apply that name.

Induction, as above defined, is a
process of inference ; it proceeds from
the known to the unknown ; and any
operation involving no inference, any
process in which what seems the con-
clusion is no wider than the premises
from which it is drawn, does not fall
within the meaning of the term. Yet
in the common books of Logic we
find this laid down as the most per-
fect, indeed the only quite perfect,
form of induction. In those books,
every process which sets out from
a less general and terminates in a
more general expression, — which ad-
mits of being stated in the form,
" This and that A are B, therefore
every A is B," — is called an induc-
tion, whether anything be really con-
as such, is essential ; but nine-tenths of
the conclusions drawn from experience in
the course of practical life are drawn with-
out any such recognition : they are direct
inferences from known cases to a case
supposed to be similar. I have endeavoured
to show that this is not only as legitimate
an operation, but substantially the same
operation as that of ascenoing from known
cases to a general proposition ; except that
the latter process has one great security
for correctness which the former does not
possess. In science the inference must
necessarily pass through the intermediate
stage of a general proposition, becau.sc
Science wants its conclusions for record, and
not for instantaneous use. But the infer-
ences drawn for the guidance of practical
affairs, by persons who would often be quite
incapable of expressing in unexceptional
terms the corresponding generalisations
may, and frequently do, exhibit intellectual
powers quite equal to any which have ever
been displayed in science : and if these
inferences are not inductive, what are
they? The limitation imposed on the
term by Dr. Whewell seems perfectly arbi-
trary ; neither justified by any fundamen-
tal distinction between what he includes
and what he desires to exclude, nor sanc-
tioned by usage, at least from the time of
Reid and Stewart, the principal legislators
(as far as the English language is concerned)
of modern metaphysical terminology.

INDUCTIONS IMPROPERLY SO CALLED.

189

eluded or not : and the induction is
asserted not to be perfect, imless
every single individual of the class
A is included in the antecedent, co-
premise : that is, unless what we
affirm of the class has already been
ascertained to be true of every in-
dividual in it, so that the nominal
conclusion is not really a conclusion,
but a mere reassertion of the pre-
mises. If we were to say, All the
planets shine by the sun's light, from
observation of each separate planet,
or all the Apostles were Jews, be-
cause this is true of Peter, Paul, John,
and every other apostle, — these, and
such as these, would, in the phrase-
ology in question, be called perfect,
and the only perfect, Inductions.
This, however, is a totally different
kind of induction from ours ; it is
not an inference from facts known to
facts unknown, ' but a mere short-
hand registration of facts known.
The two sinmlated arguments which
we have quoted are not generalisa-
tions ; the propositions purporting to
be conclusions from them are not
really general propositions. A general
proposition is one in which the pre-
dicate is affirmed or denied of an
unlimited number of individuals ;
namely, all, whether few or many,
existing or capable of existing, which
possess the properties connoted by the
subject of tlie proposition. " All men
are mortal " does not mean all now
living, but all men past, present, and
to come. When the signification of
the term is limited so as to render it
a name not for any and every indi-
vidual falling under a certain general
description, but only for each of a
number of individusds designated as
such, and as it were counted off in-
dividually, the proposition, though it
may be general in its language, is no
general proposition, but merely that
number of singulai* propositions, writ-
ten in an abridged character. The
operation may be very useful, as most
forms of abridged notation are ; but
it is no part of the investigation of
truth, though often bearing an im-

portant port in the preparation of the
materials for that investigation.

As we may sum up a definite num-
ber of singular propositions in one
proposition, which will be apparently,
out not really, general, so we may
sum up a definite number of general
propositions in one proposition, which
will be apparently, but not really,
more general If by a separate in-
duction applied to every distinct
species of animals, it has been estab-
lished that each possesses a nervous
system, and we affirm thereupcm that
all animals have a nervous system ;
this looks like a generalisation, though
as the conclusion merely affirms of
all what has already been affirmed of
each, it seems to tell us nothing but
what we knew before. A distinction
however must be made. If in con-
cluding that all animals have a ner-
vous system, we mean the same thing
and no more as if we had said "all
known animals," the proposition is
not general, and the process by which
it is arrived at is not induction. But
if our meaning is that the observa-
tions made of the various species of
animals have discovered to us a law
of animal nature, and that we are in
a condition to say that a nervous
system will be found even in animals
yet undiscovered, this indeed is an
induction ; but in this case the general
proposition contains more than the
sum of the special propositions from
which it is inferred. The distinction
is still more forcibly brought out
when we consider, that if this real
generalisation be legitimate at all,
its legitimacy probably does not re-
quire that we should have examined
withoutexception every knownspecies.
It is the number and nature of the
instances, and not their being the
whole of those which happen to be
known, that makes them sufficient
evidence to prove a general law :
while the more limited assertion,
which stops at all known animals,
cannot be made unless we have rigor-
ously verified it in every species. In
like manner (to return to a former

190

INDUCTION.

example) we miffht have inferred, not
that all the planets, but that all
planets, shine by reflected light : the
former is no induction ; the latter
is an induction, and a bad one,
being disproved by the case of double
stars — self-luminous bodies which are
properly planets, since they revolve
round a centre.

§ 2. There are several processes
used in mathematics which require
to be distinguished from Induction,
being not unfrequently called by that
name, and being so far similar to In-
duction properly so called, that the
propositions they lead to are really
general propositions. For example,
when we have proved with respect to
the circle that a straight line cannot
meet it in more than two points, and
when the same thing has been suc-
cessively proved of the ellipse, the
parabola, and the hyperbola, it may
be laid down as an universal property
of the sections of the cone. The dis-
tinction drawn in the two previous
exaiDples can have no place here,
there being no difference between all
known sections of the cone and aU
sections, since a cone demonstrably
cannot be intersected by a plane ex-
cept in one of these four lines. It
would be difficult, therefore, to refuse
to the proposition arrived at the name
oi a generalisation, since there is no
room for any generalisation beyond
it. But there is no induction, because
there is no inference : the conclusion
is a mere summing up of what was
asserted in the various propositions
from which it is drawn. A case some-
what, though not altogether, similar,
is the proof of a geometrical theorem
by means of a diagram. Whether
the diagram be on paper or only in
the imagination, the demonstration
(as formerly observed*) does not prove
directly the general theorem ; it proves
only that the conclusion, which the
theorem asserts generally, is true of
the particular triangle or circle ex-

* Supra, p. 125.

hibited in the diagram ; but since we
perceive that in the same way in
which we have proved it of that
circle, it might also be proved of any
other circle, we gather up into one
general expression all the singular
propositions susceptible of being thus
proved, and embody them in an uni-
versal proposition. Having shown
that the three angles of the triangle
ABC are together equal to two right
angles, we conclude that this is true
of every other triangle, not because
it is true of ABC, but for the same
reason which proved it to be true of
ABC. If this were to be called In-
duction, an appropriate name for it
would be, induction by parity of rea-
soning. But the term cannot properly
belong to it ; the characteristic quality
of Induction is wanting, since the
truth obtained, though really general,
is not beloved on the evidence of par-
ticular instances. We do not conclude
that all triangles have the property
because some triangles have, but from
the ulterior demonstrative evidence
which was the ground of our convic-
tion in the particular instances.

There are, nevertheless, in mathe-
matics, some examples of so-called
Induction, in which the conclusion
does bear the appearance of a gene-
ralisation grounded on some of the
particular cases included in it. A
mathematician, when he has calcu-
lated a sufficient number of the terms
of an algebraical or arithmetical series
to have ascertained what is called the
law of the series, does not hesitate to
fill up any number of the succeeding
terms without repeating the calcula-
tions. But I apprehend he only does
so when it is apparent from a priori
considerations (which might be ex-
hibited in the form of demonstration)
that the mode of formation of the sub-
sequent terms, each from that which
preceded it, must be similar to the
formation of the terms which have
been already calculated. And when
the attempt has been hazarded with-
out the sanction of such general con-.,
siderationsi, there are instances on

INDUCTIONS IMPROPERLY SO CALLED.

191

record in which it has led to false
results.

It is said that Newton discovered
the binomial theorem by induction ;
by raising a binomial successively to
a certain number of powers, and com-
paring those powers with one another
until he detected the relation in which
the algebraic formula of each power
stands to the exponent of that power,
and to the two terms of the binomial.
The fact is not improbable, but a
mathematician like Newton, who
seemed to arrive per saltum at prin-
ciples and conclusions that ordinary
mathematicians only reached by a
succession of steps, certainly could
not have performed the comparison
in question without being led by it to
the d priat^i ground of the law ; since
any one who understands sufficiently
the nature of multiplication to ven-
ture upon multiplying several lines of
symbols at one operation, cannot but
perceive that in raising a binomial to
a power, the co-efficients must depend
on the laws of permutation and com-
bination, and as soon as this is recog-
nised, the theorem is demonstrated.
Indeed, when once it was seen that
the law prevailed in a few of the
lower powers, its identity with the
law of permutation would at once
suggest the considerations which prove
it to obtain universally. Even, there-
fore such cases as these, are but ex-
amples of what I have called Induc-
tion by parity of reasoning, that is,
not really Induction, because not
involving inference of a general pro-
position from particular instances.

§ 3. There remains a third impro-
per use of the term Induction, which
it is of real importance to clear up,
because the theory of Induction has
been, in no ordinary degiee, confused
by it, and because tlie confusion is
exemplified in the most recent and
elaborate treatise on the inductive
philosophy which exists in our lan-
guage. The error in question is that
of confounding a mere description, by
general terms, of a set of observed

phenomena, with an induction from
them.

Suppose that a phenomenon con-
sists of parts, and that these parts
are only capable of being observed
separately, and as it were piecemeal.
When the observations have been
made, there is a convenience (amount-
ing for many purposes to a necessity)
in obtaining a representation of the
phenomenon as a whole, by combining,
or, as we may say, piecing these de-
tached fragments together. A navi-
gator sailing in the midst of the ocean
discovers land : he cannot at first, or
by any one observation, determine
whether it is a continent or an island ;
but he coasts along it, and after a few
days finds himself to have sailed com-
pletely round it : he then pronounces
it an island. Now there was no par-
ticular time or place of observation
at which he could perceive that this
land was entirely surrounded by
water ; he ascertained the fact by a
succession of partial observations, and
then selected a general expression
which summed up in two ot three
words the whole of what he so ob-
served. But is there anything of the
nature of an induction in this process?
Did he infer anything that had not
been observed, from something else
which had ? Certainly not. He had
observed the whole of what the pro-
position asserts. That the land in
question is an island, is not an infer-
ence from the partial facts which the
navigator saw in the course of his
circumnavigation ; it is the facts
themselves ; it is a summary of those
facts ; the description of a complex
fact, to which those simpler ones are
as the parte of a whole.

Now there is, I conceive, no differ-
ence in kind between this simple
operation, and that by which Kepler
ascertained the nature of the plane-
tary orbite ; and Kepler's operation,
all at least that was characteristic in
it, was not more an inductive act
than that of our supposed navigator.

The object of Kepler was to deter-
mine the real path described by each

192

INDUCTION.

of the planets, or let us say by the
planet Mars (since it was of that body
that he fii^t established the two of
his three laws which did not require
a comparison of planets). To do this
there was no other mode than that of
direct observation ; and all which ob-
servation could do was to ascertain a
great number of the successive places
of the planet, or rather, of its ap-
parent places. That the planet occu-
pied successively all these positions,
or at all events, positions which pro-
duced the same impressions on the
eye, and that it passed from one of
these to another insensibly, and with-
out any apparent breach of continuity ;
thus much the senses, with the aid of
the proper instruments, could ascer-
tain. What Kepler did more than
this, was to find what sort of a curve
these different points would make,
supposing them to be all joined to-
gether. He expressed the whole
series of the observed places of Mars
by what Dr. Whewell calls the gene-
ral conception of an ellipse. This
operation was far from being as easy
as that of the navigator who expressed
the series of his observations on suc-
cessive ])oints of the coast by the
general conception of an island. But
it is the very same sort of operation ;
and if the one is not an induction but
a description, this must also be true
of the other.

The only real induction concerned
in the case consisted in inferring that
because the observed places of Mars
were correctly represented by points
in an imaginary ellipse, therefore
Mars would continue to revolve in
that same ellipse ; and in concluding
(before the gap had been filled up by
further observations) that the posi-
tions of the planet during the time
which intervened between two obser-
vations, must have coincided with the
intermediate points of the curve. For
these were facts which had not been
directly observed. They were in-
ferences from the observations ; facts
inferred, as distinguished from facts
seen. But these inferences were so

far from being a part of Kepler's
philosophical operation, that they had
been drawn long before he was bom.
Astronomers had long known that
the planets periodically returned to
the same places. Wlien this had been
ascertained, there was no induction
left for Kepler to make, nor did he
make any further induction. He
merely applied his new conception to
the facts inferred, as he did to the
facts observed. Knowing already
that the planets continued to move in
the same paths ; when he found that
an elli]^)se correctly represented the
past path he knew that it would repre-
sent the future path. In finding a com-
pendious expression for the one set
of facts he found one for the other :
but he found the expression only, not
the inference ; nor did he (which is
the true test of a general truth) add
anything to the power of predictioxi
already possessed

§4. The descriptive operation which
enables a number of details to be
summed up in a single proposition,
Dr. Whewell, by an aptly chosen ex-
pression, has termed the Colligation
of Facts. In most of his observations
concerning that mental process I full}'
agree, and would gladly transfer all
that portion of his book into my own
pages. I only think him mistaken
in setting up this kind of operation,
which, according to the old and re-
ceived meaning of the term, is not in-
duction at all, as the type of induction
generally ; and laying down, through-
out his work, as principles of induction,
the principles of mere colligation.

Dr. Whewell maintains that the
general proposition which binds to-
gether the particular facts, and makes
them, as it were, one fact, is not the
mere sum of those facts, but some-
thing more, since there is introduced
a conception of the mind, which did
not exist in the facts themselves.
"The particular facts," says he,* " are
not merely brought together, but there

* Novum Orffanuvi Renovatuvi, pp. 72, 73.

INDUCTIONS IMPROPERLY SO CALLED.

193

is a new element added to the com-
bination by the very act of thought
by which they are combined. . . .
When the Greeks, after long observing
the motions of the planets, saw that
these motions might be rightly con-
sidered as produced by the motion of
one wheel revolving in the inside of
another wheel, these wheels were crea-
tions of their minds, added to the
facts which they perceived by sense.
And even if the wheels were no longer
supposed to be material, but were re-
duced to mere geometrical spheres or
circles, they were not the less pro-
ducts of the mind alone, — something
additional to the facts observed. The
same is the case in all other dis-
coveries. The facts are known, but
they are insulated and unconnected,
till the discoverer supplies from his
own store a principle of connection.
The pearls are there, but they will
not hang together till some one pro-
vides the string."

Let me first remark that Dr. Whe-
well, in this passage, blends together,
indiscriminately, examples of both
the processes which I am endeavour-
ing to distinguish from one another.
When the Greeks abandoned the
supposition that the planetar}' mo-
tions were produced by the revolu-
tions of material wheels, and fell
back upon the idea of "mere geo-
metrical spheres or circles," there
was more in this change of opinion
than the mere substitution of an
ideal curve for a physical one. There
was the abandonment of a theory,
and the replacement of it by a mere
description. No one would think of
calling the doctrine of material wheels
a mere description. That doctrine
was an attempt to point out the
force by which the planets were
acted upon, and compelled to move
in their orbits. But when, by a
great step in philosophy, the mate-
riality of the wheels was discarded,
and the geometrical forms alone re-
tained, the attempt to account for
the motions was given up, and what
was left of the theory was a, mere

description of the orbits. The
tion that the planets were carried
round by wheels revolving in the
inside of other wheels, gave place to
the proposition that they moved in
the same lines which would be traced
by bodies so carried : which was a
mere mode of representing the sum
of the observed facts ; as Kepler's
was another and a better mode of
representing the same observations.

It is true that for these simply
descriptive operations, as well as for
the erroneous inductive one, a con-
ception of the mind was required.
The conception of an ellipse must
have presented itself to Kepler's mind
before he could identify the planetary
orbits with it. According to Dr.
Whewell, the conception was some-
thing added to the facts. He ex-
presses himself as if Kepler had put
something into the facts by his mode
of conceiving them. But Kepler did
no such thing. The ellipse was in
the facts before Kepler recognised it ;
just as the island was an island before
it had been sailed round. Kepler did
not put what he had conceived into
the facts, but saw it in them. A con-
ception implies, and corresponds to,
something conceived : and though the
conception itself is not in the facts,
but in our mind, yet if it is to convey
any knowledge relating to them it
must be a conception of something
which really is in the facts, some
property which they actually possess,
and which they could manifest to our
senses if our senses were able to take
cognisance of it. If, for instance, the
planet left behind it in space a visible
track, and if the observer were in a
fixed position at such a distance from
the plane of the orbit as would en-
able him to see the whole of it at
once, he would see it to be an ellipse ;
and if gifted with appropriate instru-
ments and f)Owers of locomotion, he
would prove it to be such by measur-
ing its different dimensions. Nay,
further : if the track were visible, and
he were so placed that he could see
all parts of it in succession, but not

194

INDUCTION.

all of them at once, he might be able,
by piecing together his successive
observations, to discover both that
it was an ellipse and that th^ planet
moved in it. The case would then
exactly resemble that of the naviga-
tor who discovers the land to be an
island by sailing round it. If the
path was visible, no one I think
would dispute that to identify it
with an ellipse is to describe it :
and I cannot see why any differ-
ence should be made by its not being
directly an object of sense, when
every point in it is as exactly ascer-
tained as if it were so.

Subject to the indispensable con-
dition which has just been stated,
I do not conceive that the part which
conceptions have in the operation of
studying facts has ever been over-
looked or undervalued. No one ever
disputed that in order to reason about
anything we must have a conception
of it ; or that when we include a
multitude of things under a general
expression, there is implied in the
expression a conception of something
commoii to those things. But it by
no means follows that the conception
u necessarily pre-existent, or con-
structed by the mind out of its own
materials. If the facts are rightly
classed under the conception, it is
because there is in the facts them-
selves something of which the con-
ception is itself a copy ; and which
if we cannot directly perceive, it is
because of the limited power of our
organs, and not because the thing
itself is not there. The conception
itself is often obtained by abstraction
from the very facts which, in Dr.
Whewell's language, it is afterwards
called in to connect. This he himself
admits, when he observes, (which he
does on several occasions,) how great
a service would be rendered to the
science of physiology by the philoso-
pher ** who should establish a precise,
tenable, and consistent conception of
life." * Such a conception can only

* Novum Orffanum Jienovatuvi, p. 32.

be abstracted from the phenomena of
life itself ; from the very facts which
it is put in requisition to connect.
In other cases, no doubt, instead of
collecting the conception from the
very phenomena which we are at-
temptmg to colligate, we select it
from among those which have been
previously collected by abstraction
from other facts. In the instance of
Kepler's laws, the latter was the case.
The facts being out of the reach of
being observed in any such manner
as would have enabled the senses to
identify directly the path of the
planet, the conception requisite for
framing a general description of that
path could not be collected by abstrac-
tion from the observations themselves ;
the mind had to supply hypotheti-
cally, from among the conceptions it
had obtained from other portions of
its experience, some one which would
correctly represent the series of the
observed facts. It had to frame a
supposition respecting the general
course of the phenomenon, and ask
itself. If this be the general descrip-
tion, what will the details be ? and
then compare these with the details
actually observed. If they agreed,
the hypothesis would serve for a de-
scription of the phenomenon : if not,
it was necessarily abandoned, and
another tried. It is such a case as
this which gives rise to the doctrine
that the mind, in framing the de-
scriptions, adds something of its own
which it does not find in the facts.

Yet it is a fact surely that the
planet does describe an ellipse ; and
a fact which we could see if we had
adequate visual organs and a suitable
position. Not having these advan-
tages, but possessing the conception
of an ellipse, or (to express the mean-
ing in less technical language) know-
ing what an ellipse was, Kepler tried
whether the observed places of the
planet were conwstent with such a
path. He found they were so ; and
he, consequently, asserted as a fact
that the planet moved in an ellipse.
But this fact, which Kepler did not

INDUCTIONS IMPROPERLY SO CALLED.

'95

add to, but found in, the motions of
the planet, namely, that it occupied
in succession the various points in the
circumference of a given ellipse, was
the very fact the separate parts of
which had been separately observed ;
it was the sum of the different obser-
vations.

Having stated this fundamental
difference between my opinion and
that of Dr. Whewell, I must add,
that his account of the manner in
which a conception is selected suit-
able to express the facts appears to
me perfectly just. The experience of
all thinkers will, I believe, testify
that the process is tentative ; that it
consists of a succession of guesses ;
many being rejected, until one at last
occurs fit to be chosen. We know
from Kepler himself that before hit-
ting upon the " conception " of an
ellipse, he tried nineteen other ima-
ginary paths, which, finding them in-
consistent with the observations, he
was obliged to reject. But, as Dr.
Whewell truly says, the successful
hypothesis, though a guess, ought
generally to be called, not a lucky,
but a skilful guess. The guesses
which serve to give mental unity and
wholeness to a chaos of scattered par-
ticulars are accidents which rarely
occur to any minds but those abound-
ing in knowledge and disciplined in
intellectual combinations.

How far this tentative method, so
indispensable as a means to the col-
ligation of facts for purposes of de-
scription, admits of application to In-
duction itself, and what functions
belong to it in that department, will
be considered in the chapter of the
present Book which relates to Hypo-
theses. On the present occasion we
have chiefly to distinguish this pro-
cess of Colligation from Induction
properly so called ; and that the dis-
tinction may be made clearer, it is
well to advert to a curious and in-
teresting remark, which is as strik-
ingly true of the former operation, as
it appears to me unequivocally false
of the latter.

In different stages of the progress
of knowledge, philosophers have em-
ployed, for the colligation of the same
order of facts, different conceptions.
The early rude observations of the
heavenly bodies, in which minute pre-
cision was neither attained nor sought,
presented nothing inconsistent with
the itepresentation of the path of a
planet as an exact circle, having the
earth for its centre. As observations
increased in accuracy, facts were dis-
closed which were not reconcilable
with this simple supposition : for the
colligation of those additional facts,
thesuppo-sition was varied ; and varied
again and again as facts became more
immerous and precise. The earth
was removed from the centre to some
other point within the circle ; the
planet was supposed to revolve in a
smaller circle called an epicycle, round
an imaginary point which revolved in
a circle round the earth : in proportion
as observation elicited fresh facts con-
tradictory to these representations,
other epicycles and other excentrics
were added, producingadditional com-
plications ; until at last Kepler swept
all these circles away, and substituted
the conception of an exact ellipse.
Even this is found not to represent
with complete correctness the accurate
observations of the present day, which
disclose many slight deviations from
an orbit exactly elliptical. Now Dr.
Whewell has remarked that these
successive general expressions, though
apparently so conflicting, were all
correct : they all answered the purpose
of colligation ; they all enabled the
mind to represent to itself with facility,
and by a simultaneous glance, the
whole body of facts at the time ascer-
tained : each in its turn served as a
correct description of the phenomena,
so far as the senses had up to that
time taken cognisance of them. If a
necessity afterwards arose for discard-
ing one of these general descriptions
of the planet's orbit, and framing a
different imaginary line, by which to
express the series of observed positions,
it was because a number of new factp

196

INDUCTION.

had now been added, which it was
necessary to combine with the old facts
into one general description. But
this did not aflfect the correctness of
the former expression, considered as
a general statement of the only facts
which it was intended to represent.
And so true is this, that, as is well
remarked by M. Comte, these ancient
generalisations, even the rudest and
most imperfect of them, that of uni-
form movement in a circle, are so far
from being entirely false, that they
are even now habitually employed by
astronomers when only a rough ap-
proximation to correctness is required.
" L'astronomie modeme, en detruisant
sans retour les hypotheses primitives,
envisag^es comme lois reelles du
monde, a soigneusement maintenu
leur valeur positive et permanente, la
propriety de representor commod^-
ment les ph^nomenes quand il s'agit
d'une premiere ebauche. Nos res-
sources a cet ^gard sont meme bien
plus etendues, pr^cisdment h cause que
nous ne nous faisonsaucune illusion sur
la r^alitd des hypotheses ; ce qui nous
permet d'employer sans scrupule, en
chaque cas, celle que nous jugeons la
plus avantageuse."*

Dr. Whewell's remark, therefore, is
philosophically correct. Successive
expressions for the colligation of ob-
served facts, or, in other words, suc-
cessive descriptions of a phenomenon
as a whole, which has been observed
only in parts, may, though conflicting,
be all correct as far as they go. But
it would surely be absurd to assert
this of conflicting inductions.

The scientific study of facts may be
undertaken for three different pur-
poses : the simple description of the
facts ; their explanation ; or their
prediction : meaning by prediction,
the determination of the conditions
under which similar facts may be ex-
pected again to occur. To the first of
these three operations the name of
Induction does not properly belong :
to the other two it does. Now Dr.

* Oour$ de Fhiloiophit Potitive, vol. ii. p.
999,

Whewell's observation is true of the
first alone. (Considered as a mere
description, the circular theory of the
heavenly motions represents perfectly
well their general features : and by
adding epicycles without limit, those
motions, even as now known to us,
might be expressed with any degree
of accuracy that might be required.
The elliptical theory, as a mere de-
scription, would have a great advan-
tage in point of simplicity, and in the
consequent facility of conceiving it
and reasoning about it ; but it would
not really be more true than the other.
Different descriptions, therefore, may
be all true : but not, surely, different
explanations. The doctrine that the
heavenly bodies moved by a virtue
inherent in their celestial nature ; the
doctrine that they were moved by im-
pact, (which led to the h3rpothesi8 of
vortices as the only impelling force
capable of whirling bodies in circles,)
and the Newtonian doctrine that they
are moved by the composition of a
centripetal with an original projectile
force ; all these are explanations col-
lected by real induction from supposed
parallel cases ; and they were all
successively received by philosophers,
as scientific truths on the subject of
the heavenly bodies. Can it be said
of these, as was said of the different
descriptions, that they sore all true as
far as they go ? Is it not clear that
only one can be true in any degree,
and the other two must be altogether
false ? So much for explanations :
let us now compare different predic-
tions : the first, that eclipses will occur
when one planet or satellite is so
situated as to cast its shadow upon
another ; the second, that they will
occur when some great calamity is
impending over mankind. Do these
two doctrines only differ in the degree
of their truth as expressing real facts
with unequal degrees of accuracy ?
Assuredly the one is true, and the
other absolutely false.*

* Dr. Whewell, in his reply, contests the
distinction here drawn, and maintains,
that not oul^ different descriptions, but

INDUCTIONS IMPROPERLY SO CALLED.

197

In every way, therefore, it is evident
that to explain induction as the col-
ligation of facts by means of appro-
priate conceptions, that is, conceptions
which will really express them, is to
confound mere descriptions of the

different explanations of a phenomenon,
may all be true. Of the three theories
respecting the motions of the heavenly
bodies, he says {Philotophy of Discovery,
p. 231) : " Undoubtedly all these explana-
tions may be true and consistent with
each other, and would be so if each had
been followed out so as to show iu what
manner it could be made consistent with
the facts. And this was in reality in a
great measure done. The doctrine that the
heavenly bodies were moved by vortices
was successfully modified, so that it came
to coincide in its results witii the doctrine
of an inverse-quadratic centripetal force.
.... When this point was reached, the
vortex was merely a machinery, well or
ill devised, for producing sucli a centripetal
force, and therefore did not contradict the
doctrine of a centripetal force. Newton
himself does not appear to have been averse
to explaining gravity by impulse. So little
is it true that if one theory be true the
other must bo false. The attempt to ex-
plain gravity by the impulse of streams of
particles flowing tiirough the universe in
all directions, which I have mentioned in
the Philosophy, is so fur from being incon-
sistent with the Newtonian theory, that it
is founded entirely upon it. And even with
regard to the doctrine that the heavenly
bodies move by an inherent virtue, if this
doctrine had been maintained in any such
way that it was brought to agree with the
facts, the inherent virtue must have had
its laws determined; and then it would
have been found that the virtue had a
reference to the central body ; and so the
I inherent virtue ' must have coincided in
its effect with the N ewtonian force ; and
then the two explanations would agree,
except so far as the word ' inherent ' was
concerned. And if such a part of an earlier
theory as this word inherent indicates is
found to be untenable, it is of course re-
jected in the transition to later and more
exact theories, in Inductions of this kind,
as well as in what Mr. Mill calls Descrip-
tions. There is, therefore, still no validity
discoverable in the distinction which Mr.
Mill attempts to draw between descriptions
like Kepler's law of elliptical orbits, and
other examples of induction."

If the doctrine of vortices had meant,
not that vortices existed, but only that the
planets moved in the same vianner as if
they had been whirled by vortices ; if the
hypothesis had been merely a mode of
representing the facts, not an attempt to
account for them ; if, in short, it had been
only a Description, it would, no doubt.

observed facts with inference from
those facts, and ascribe to the latter
what is a characteristic property of
the former.

There is, however, between Colliga-
tion and Induction a real correlation,

have been reconcilable with the Newtonian
theory. The vortices, however, were not a
mere aid to conceiving the motions of the
planets, but a supposed physical agent,
actively impelling them ; a material fact
which might be true or not true, but could
not be both true and not true. According
to Descartes' theory it was true, according
to Newton's it was not true. Dr. Whewell
probably means that since the phrases,
centripetal and projectile force, do not
declare the nature but only the direction
of the forces, the Newtonian theory does
not absolutely contradict any hypothesis
which may be framed respecting the mode
of theirproduction. The Newtonian theory,
regarded as a mere description of the
planetary motions, does not ; but the
Newtonian theory as an explanation of them
does. For in wliat does the explanation
consist? In ascribing those motions to a
general law which obtains between all
particles of matter, and in identifying this
with the law by which bodies fall to the
ground. If the planets are kept in their
orbits by a force which draws the particles
composing them towards every other par-
ticle of matter in the solar system, they are
not kept in those orbits by the impulsive
force of certain streams of matter which
whirl them round. The one explanation
absolutely excludes the other. Either the
planets are not moved by vortices, or they
do not move by a law common to all matter.
It is impossible that both opinions can be
true. As well might it be said that there
is no conti-adiction between the assertions,
that a man died because somebody kUled
him, and that he died a natural death.

So, again, the theory that the planets
move by a virtue inherent in their celestial
nature, is incompatible with either of the
two others: either that of their being
moved by vortices, or that which regards
them as moving by a property which they
have in common with the earth and all
terrestrial bodies. Dr. Whewell says that
the theory of an inherent virtue agrees
with Newton's when the word inherent is
left out, which of course it would be (he
says) if "found to be untenable." But
leave that out, and where is the theory?
The word inherent is the theory. When
that is omitted, there remains nothing ex-
cept that the heavenly bodies move '' by a
virtue," i.e. by a power of some sort, or by
virtue of their celestial nature, which
directly contradicts the doctrine that ter-
restrial bodies fall by the same law.

If Dr. Whewell is not yet satisfied, any
other subject will serve equally well to test

!98

INBtrCTlON.

which it is important to conceive
correctly. Colligation is not always
induction ; but induction is always
colligation. The assertion that the
planets move in ellipses was but a
mode of representing observed facts ;
it was but a colligation ; while the
assertion that they are drawn or tend
towards the sun was the statement of
a new fact, inferred by induction.
But the induction, once made, accom-
plishes the purposes of colligation
likewise. It brings the same facts,
which Kepler had connected by his
conception of an ellipse, under the
additional conception of bodies acted
upon by a central force, and serves
therefore as a new bond of connection
for those facts ; a new principle for
their classification.

Further, the descriptions which are
improperly confounded with induction
are nevertheless a necessary prepara-
tion for induction ; no less necessary
than correct observation of the facts
themselves. Without the previous
colligation of detached observations
by means of one general conception,
we could never have obtained any
basis for an induction, except in the
case of phenomena of very limited
compass. We should not be able to
aflirm any predicates at all of a sub-

his doctrine. He will hardly say that there
is 110 contradiction between the emission
theory and the undulatory theory of light ;
or that there can be both one and two
electricities ; or that the hypothesis of
the production of the higher organic
forms by development from the lower, and
the supposition of separate and successive
acts of creation, are quite reconcilable ;
or that the theory that volcanoes are fed
from a central fire, and the doctrines
which ascribe them to ciiemical action at
a comparatively small depth below the
earth's surface, are consistent with one
another, and all true as far as they go.

If different explanations of the same fact
cannot both be true, still less, surely, can
different predictions. Dr. WheweU quar-
rels (on what ground it is not necessary
here to consider) with the example I had
chosen on this point, and thinks an objec-
tion to an illustration a sufl&cient answer
to a theory. Examples not liable to his
objection are easily found, if the proposi-
tion that conflicting predictions cannot
both be true can be made clearer by any

ject incapable of being observed other-
wise than piecemeal : much less could
we extend those predicates by induc-
tion to other similar subjects. Induc-
tion, therefore, always presupposes,
not only that the necessary observa-
tions are made with the necessary
accuracy, but also that the results of
these observations are, so far as prac-
ticable, connected together by general
descriptions, enabling the mind to-
represent to itself as wholes whatever
phenomena are capable of being so
represented-

§ 5. Dr. WheweU has replied at
some length to the preceding observa-
;ions, re -stating his opinions, but with-
out (as far as I can perceive) adding
anything material to his former argu-
ments. Since, however, mine have not
had the good fortune to make any
impression upon him, I will subjoin a
few remarks, tending to show more
clearly in what our difference of
opinion consists, as well as, in some
measure, to account for it.

Nearly all the definitions of induc-
tion, by writers of authority, make it
consist in drawing inferences from
known cases to unknown ; affirming
of a class a predicate which has been
found true of some cases belonging to

examples. Suppose the phenomenon to
be a newly discovered comet, and that one
astronomer predicts its return once in every
300 years — another once in every. 400 : can'
they both be right ? When Columbus pre-
dicted that by sailing constantly westward
he should in time return to the point from
which he set out, while others asserted that
he could never do so except by turning
back, were both he and his opponents true
prophets ? Were the predictions which fore-
told the wonders of railways and steam-
ships, and those which averred that the
Atlantic could never be crossed by steam
navigation, nor a railway train propelled
ten miles an hour, both (in Dr. Whewell's
words) "true and consistent with one
another ? "

Dr. WheweU sees no distinction between
holding contradictory opinions of a ques-
tion of fact, and merely employing differ-
ent analogies to facilitate the conception
of the same fact. The case of different
Inductions belongs to the former class,
that of diffeient Descriptions to the
latter.

INDUCTIONS IMPROPERLY SO CALLED.

199

the class ; concluding, because some
things have a certain property, that
other things which resemble them
have the same property — or because a
thing has manifested a property at a
certain time, that it has and will have
that property at other times.

It can scarcely be contended that
Kepler's operation was an Induction
in this sense of the term. The state-
ment that Mars moves in an ellipti-
cal orbit was no generalisation from
individual cases to a class of cases.
Neither was it an extension to all
time of what had been found true at
some particular time. The whole
amount of generalisation which the
case admitted of was already com-
pleted, or might have been so. Long
before the elliptic theory was thought
of, it had been ascertained that the
planets returned periodically to the
same apparent places ; the series of
these places was, or might have been,
completely determined, and the ap-
parent course of each planet marked
out on the celestial globe in an unin-
terrupted line. Kepler did not ex-
tend an observed truth to other cases
than those in which it had been ob-
served : he did not widen the subject
of the proposition which expressed the
observed facts. The alteration he
made was in the predicate. Instead
of saying, the successive places of
Mars are so and so, he summed them
up in the statement, that the succes-
sive places of Mars are points in an
ellipse. It is true this statement, as
Dr. Whewell says, was not the sum of
the observations merely; it was the
sum of the observations seen under a
new point of view.* But it was not
the sum of more than the observations,
as a real induction is. It took in no
cases but those which had been actu-
ally observed, or which could have
been inferred from the observations
before the new point of view presented
itself. There was not that transition
from known cases to unknown which
constitutes Induction in the original

* Phil, of Discov., p. 256.

and acknowledged meaning of the
term.

Old definitions, it is true, cannot
prevail against new knowledge : and
if the Keplerian operation, as a logi-
cal process, be really identical with
what takes place in acknowledged in-
duction, the definition of induction
ought to be so widened as to take it
in ; since scientific language ought to
adapt itself to the true relations which
subsist between the things it is em-
ployed to designate. Here then it is
that I am at issue with Dr. Whewell.
He does think the operations identi-
cal. He allows of no logical process
in any case of induction other than
what there was in Kepler's case,
namely, guessing until a guess is found
which tallies with the facts ; and ac-
cordingly, as we shall see hereafter,
he rejects all canons of induction, be-
cause it is not by means of them that
we guess. Dr. Whewell's theory of
the logic of science would be very per-
fect if it did not pass over altogether
the question of Proof. But in my ap-
prehension there is such a thing as
proof, and inductions differ altogether
from descriptions in their relation to
that element. Induction is proof ;
it is inferring something imol»erved
from something observed : it requires,
therefore, an appropriate test of proof ;
and to provide that test is the special
purpose of inductive logic. When,
on the contrary, we merely collate
known observations, and, in Dr. Whe-
well's phraseology, connect them by
means of a new conception ; if the
conception does serve to connect the
observations, we have all we want.
As the proposition in which it is em-
bodied pretends to no other truth than
what it may share with many other
modes of representing the same facts,
to be consistent with the facts is all
it requires : it neither needs nor ad-
mits of proof ; though it may serve
to prove other things, inasmuch as,
by placing the facts in mental con-
nection with other facts not previously
seen to resemble them, it assimilates'
the case to another class of phenomena,

200

INDTTCJTION.

concerning which real Inductions have
already been made. Thus Kepler's
so-called law brought the orbit of Mars
into the class ellipse, and by doing so,
proved all the properties of an ellipse
to be true of the orbit : but in this
proof Kepler's law supplied the minor
premise, and not (as is the case with
real Inductions) the major.

Dr. Whewell calls nothing Induc-
tion where there is not a new mental
conception introduced, and everything
induction where there is. But this
is to confound two very different
things, Invention and Proof. The
introduction of a new conception be-
longs to Invention : and invention
may be required in any operation, but
is the essence of none. A new concep-
tion may be introduced for descriptive
purposes, and so it may for inductive
purposes. But it is so far from con-
stituting induction, that induction
does not necessarily stand in need of
it. Most inductions require no con-
ception but what was present in every
one of the particular instances on
which the induction is grounded.
That all men are mortal is surely an
inductive conclusion ; yet no new
conception is introduced by it. Who-
ever knows that any man has died,
has all the conceptions involved in
the inductive generalisation. But
Dr. Whewell considers the process of
invention, which consists in framing
a new conception consistent with the
facts, to be not merely a necessary
part of all induction, but the whole
of it.

The mental operation which ex-
tracts from a number of detached ob-
servations certain general characters
in which the observed phenomena re-
semble one another, or resemble other
known facts, is what Bacon, Locke,
and most subsequent metaphysicians,
have understood by the word Abstrac-
tion, A general expression obtained
by abstraction, connecting known facts
by means of common characters, but
without concluding from them to
unknown, may, I think, with strict
logical correctness, be termed a De-

scription ; nor do I know in what othef
way things can ever be described.
My position, however, does not depend
on the employment of that particular
word : I am quite content to use Dr,
Whewell's term Colligation, or the
more general phrases, "mode of re-
presenting, or of expressing, pheno-
mena ; " provided it be clearly seen
that the process is not Induction, but
something radically different.

What more may usefully be said on
the subject of Colligation, or of the
correlative expression invented by
Dr. Whewell, the Explication of Con-
ceptions, and generally on the subject
of ideas and mental representations
as connected with the study of facts,
will find a more appropriate place in
the Fourth Book, on the Operations
Subsidiary to Induction : to which I
must refer the reader for the removal
of any difficulty which the present
discussion may have left

CHAPTER III.

OP THE GROUND OP INDUCTION.

§ I. Induction, properly so called,
as distinguished from those mental
operations, sometimes though impro-
perly designated by the name, which
I have attempted in the preceding
chapter to characterise, may, then, be
summarily defined as Generalisation
from Experience. It consists in infer-
ring from some individual instances
in which a phenomenon is observed to
occur, that it occurs in all instances of
a certain class ; namely, in all which
resemlle the former, in what are re-
garded as the material circumstances.

In what way the material circum-
stances are to be distinguished from
those which are immaterial, or why
some of the circumstances are material
and others not so, we are not yet
ready to point out. We must first
observe that there is a principle im-
plied in the very statement of what
Induction is ; an assumption with re-
gard to the coiirse of nature and the

GROUND OF INDUCTION.

201

order of the universe ; namely, that
there are such things in nature as
parallel cases ; that what happens
once will, under a sufiicient degree of
similarity of circumstances, happen
again, and not only again, but as often
as the san>e circumstances recur.
This, I say, is an assumption involved
in every case of induction. And if
we consult the actual course of nature,
we find that the assumption is war-
ranted. The universe, so far as known
to us, is so constituted, that whatever
is true in any one case, is true in all
cases of a certain description ; the
only difficulty is, to find what de-
scription. ,

This universal fact, which is our
warrant for all inferences from ex-
perience, has been described by dif-
ferent philosophers in difiFerent forms
of language ; that the course of nature
is uniform ; that the universe is gov-
erned by general laws ; and the like.
One of the most usual of those modes
of expression, but also one of the most
inadequate, is that which has been
brought into familiar use by the
metaphysicians of the school of Reid
and Stewart. The disposition of the
human mind to generalise from ex-
perience,— a propensity considered by
these philosophers as an instinct of our
nature, — they usually describe under
some such name as " our intuitive con-
viction that the future will resemble
the past." Now it has been well
pointed out by Mr. Bailey,* that
(whether the tendency be or not an
original and ultimate element of our
nature) Time, in its modifications of
past, present, and future, has no con-
cern either with the belief itself, or
with the grounds of it. We believe
that fire will burn to-morrow, because
it burned to-day and yesterday ; but
we believe, on precisely the same
grounds, that it burned before we were
born, and that it burns this very day
in Cochin-China. It is not from the
past to the future, as past and future,
that we infer, but from the known to

* Euayt on the Purtuit qf TrvXh.

the unknown ; from facta observed to
facts unobserved ; from what we have
perceived, or been directly conscious
of, to what has not come within our
experience. In this last predicament
is the whole region of the future ; but
also the vastly greater portion of the
present and of the past.

Whatever be the most proper mode
of expressing it, the proposition that
the course of nature is uniform is
the fundamental principle, or general
axiom, of Induction. It would yet
be a great error to offer this large
generalisation as any explanation of
the inductive process. On the con-
trary, I hold it to be itst If an instance
of induction, and induction by no
means of the most obvious kind. Far
from being the first induction we
make, it is one of the last, or at all
events one of those wliich are latest
in attaining strict philosophical accu-
racy. As a general maxim, indeed, it
has scarcely entered into the minds
of any but philosophers ; nor even by
them, as we shall have many oppor-
tunities of remarking, have its extent
and limits been always very justly
conceived. The truth is, that this
great generalisation is itself founded
on prior generalisations. The obscurer
laws of nature were discovered by
means of it, but the more obvious
ones must have been understood and
assented to as general truths before it
was ever heard of. We shotdd never
have thought of affirming that all
phenomena take place according to
general laws, if we had not first
arrived, in the case of a great multi-
tude of phenomena, at some know-
ledge of the laws themselves ; which
could be done no otherwise than by
induction. In what sense, then, can
a principle, which is so far from being
our earliest induction, be regarded as
our warrant for all the others ? In
the only sense in which (as we have
already seen) the general propositions
which we place at the head of our
reasonings when we throw them into
syllogisms ever really contribute to
their validity. As Archbishop Whately

ao2

INDtTCTION.

remarks, every induction is a syllogism
with the major premise suppressed ;
or (as I prefer expressing it) every
induction may be thrown into the
form of a syllogism by supplying a
major premise. If this be actually
done, the principle which we are now
considering, that of the uniformity of
the course of nature, will appear as
the ultimate major premise of all in-
ductions, and will, therefore, stand to
all inductions in the relation in which,
as has been shown at so much length,
the major proposition of a syllogism
always stands to the conclusion ; not
contributing at all to prove it, but
being a necessary condition of its
being proved ; since no conclusion is
proved for which there cannot be
found a true major premise.*

* In the first edition a note was appended
at this place, containing some criticism on
Archbishop Whately's mode of conceiving
the relation between Syllogism and Induc-
tion. In a subsequent issue of his Logic,
the Archbishop made a reply to the criti-
cism, which induced me to cancel part of
the note, incorporating tlie remainder in
the text. In a still later edition, the Arch-
bishop observes in a tone of something
like disapprobation, that the objections,
"doubtless from their being fully answered
and found untenable, were silently sup-
pressed," and that hence he might appear
to some of his readers to be combating a
shadow. On this latter point, the Arch-
bishop need give himself no uneasiness.
His readers, I make bold to say, will fully
credit his mere afl&rmation that the objec-
tions have actually been made.

But as he seems to think that what he
terms the suppression of the objections
ought not to have been made "silently," I
now break that silence, and state exactly
what it is that I suppressed, and why. I
suppressed that alone which might be re-
garded as personal criticism on the Arch-
bishop. I had imputed to him the having
omitted to ask himself a particular ques-
tion. I found that he had asked himself
the question, and could give it an answer
consistent with his own theory. I had
also, within the compass of a parenthesis,
hazarded some remarks on certain general
characteristics of Archbishop Whately as a
philosopher. These remarks, though their
tone, I hope, was neither disrespectful nor
arrogant, I felt, on reconsideration, that I
was hardly entitled to make ; least of all,
when the instance which I had regarded
as an illustration of them failed, as I now
■aw, to bear them out. The real matter at
the bottom of the whole dispute, tho dif-

The statement that the uniformity
of the course of nature is the ultimate
major premise in all cases of induc-
tion may be thought to require some
explanation. The immediate major
premise in every inductive argument
it certainly is not. Of that Arch-
bishop Whately's must be held to be
the correct account. The induction,
"John, Peter, &c., are mortal, there-
fore all mankind are mortal," may, as
he justly says, be thrown into a syl-
logism by prefixing asa major premise,
{what is at any rate a necessary con-
dition of the validity of the argument,)
namely, that what is true of John,
Peter, &c., is true of all mankind.
But how came we by this major pre-
mise ? It is not self-evident ; nay, in
all cases of unwarranted generalisation
it is not true. How, then, is it arrived
at ? Necessarily either by induction
or ratiocination ; and if by induction,
the process, like all other inductive
arguments, may be thrown into the
form of a syllogism. This previous
syllogism it is, therefore, necessary to
construct. There is, in the long-run,
only one possible construction. The
real proof that what is true of John,
Peter, &c., is true of all mankind, can
only be, that a different supposition
would be inconsistent with the uni-
formity which we know to exist in
the course of nature. Whether there
would be this inconsistency or not,
may be a matter of long and delicate
inquiry ; but unless there would, we

ferent view we take of the function of the
major premise, remains exactly where it
was ; and so far was I from thinking that
my opinion had been fully "answered"
and was "untenable," that in the same
edition in which I cancelled the note, I
not only enforced the opinion by further
arguments, but answered (though without
naming him) those of the Archbishop.

For not having made this statement be-
fore, I do not think it needful to apologise.
It would be attaching very great import-
ance to one's smallest sayings to think a
formal retraction requisite every time that
one falls into an error. Nor is Archbishop
Whately's well-earned fame of so tender a
quality as to require that in withdrawing
a slight criticism on him I should have
been bound to offer a public amende for
having made it.

I

GROUND OF INDUCTION.

^

have no sufficient ground for the major
of the inductive syllogism. It hence
appears, that if we throw the whole
course of any inductive argument into
a series of syllogisms, we shall arrive
by more or fewer steps at an ultimate
syllogism, which will havefor its major
premise the principle or axiom of the
uniformity of the course of nature.*

It was not to be expected that in
the case of this axiom, any more than
of other axioms, there should be unani-
mity among thinkers Avith respect
to the ground on which it is to be
received as true. I have already
stated that I regard it as itself a gene-
ralisation from experience. Others
hold it to be a principle which, ante-
cedently to any verification by experi-
ence, we are compelled by the con-
stittition of our thinking faculty to
assume as true. Having so recently,
and at so much length, combated a
similar doctrine as applied to the
axioms of mathematics by arguments
which are in a great measure appli-

* But though it is a condition of the
validity of every induction that there be
xiniforniity in the course of nature, it is
not a necessary condition that the uni-
formity should pervade all nature. It is
enough that it pervades the particular
class of phenomena to which the induction
relates. An induction concerning the
motions of the planets, or the properties
of the magnet, would not be vitiated
though we were to suppose that wind and
weather are the sport of chance, provided
it be assumed that astronomical and mag-
netic phenomena are under the dominion of
general laws. Otherwise the early experi-
ence of mankind would have rested on a
very weak fovmdation ; for in the infancy
of science it could not be known that all
phenomena are regular in their course.

Neither would it be correct to say that
every induction by which we infer any
truth implies the general fact of unifor-
mity as foreknown, even in reference to
the kind of phenomena concerned. It im-
plies, either that this general fact is already
known, oi- that we may now know it : as
the conclusion, the Duke of Wellington is
mortal, drawn from the instances A, B,
and C, implies either that we have already
concluded all men to be mortal, or that we
are now entitled to do so from the same
evidence. A vast amoimt of confusion
.•md paralogism respecting the grounds of
Induction would be dispelled by keeping
in view these simple considerations.

cable to the present case, 1 shall defer
the more particular discussion of this
controverted point in regard to the
fundamental axiom of induction un-
til a more advanced period of our
inquiry.* At present, it is of more
importance to understand thoroughly
the import of the axiom itself. For
the proposition, that the course of
nature is uniform, possesses rather the
brevity suitable to popular, than the
precision requisite in philosophical
language : its terms require to be ex-
plained, and a stricter than their
ordinary signification given to them,
before the truth of the assertion can
be admitted.

§ 2. Every person's consciousness
as-sures him that he does not always
expect uniformity in the course of
events ; he does not always believe
that the unknown will be similar to
the known, that the future will re-
semble the past. Nobody believes
that the succession of rain and fine
weather will be the same in every
future year as in the present. No-
body expects to have the same dreams
repeated every night. On the con-
trary, everybody mentions it as some-
thing extraordinary if the course of
nature is constant, and resembles it-
self in these particulars. To look
for constancy where constancy is not
to be expeoted, as, for instance, that a
j day which has once brought good
j fortune will always be a fortunate
day, is justly accounted superstition.
The course of nature, in truth, is
not only uniform, it is also infinitely
various. Some phenomena are always
seen to recur in the very same com-
binations in which we met with them
at first ; others seem altogether capri-
cious ; while some, which we had been
accustomed to regard as bound down
exclusively to a particular set of com-
binations, we unexpectedly find de-
tached from some of the elements with
which we had hitherto found them
conjoined, and united to others of

* lofra, chap. zzl.

504

INDUCTION.

quite a contrary description. To an
inhabitant of Central Africa fifty
years ago, no fact probably appeared
to rest on naore uniform experience
than this, that all human beings are
black. To Europeans not many years
ago, the proposition, All swans are
white, appeared an equally unequi-
vocal instance of uniformity in the
course of nature. Further experience
has proved to both that they were
mistaken ; but they had to wait fifty
centuries for this experience. Dur-
ing that long time, mankind believed
in an uniformity of the course of na-
ture where no such uniformity really
existed.

According to the notion which the
ancients entertained of induction, the
foregoing were cases of as legitimate
inference as any inductions whatever.
In these two instances, in which, the
conclusion being false, the ground of
inference must have been insufficient,
there was, nevertheless, as much
ground for it as this conception of
induction admitted of. The induc-
tion of the ancients has been well
described by Bacon, under the name
of " Inductio per enumerationem sim-
plicem, ubi non reperitur instantia
contradictoria." It consists in ascrib-
ing the character of general truths
to all propositions which are true in
every instance that we happen to
know of. This is the kind of induc-
tion which is natural to the mind
when unaccustomed to scientific
methods. The tendency, which some
call an instinct, and which others
account for by association, to infer
the future from the past, the unknown
from the known, is simply a habit
of expecting that what has been found
true once or several times, and never
yet found false, will be found true
again. Whether the instances are
few or many, conclusive or inconclu-
sive, does not much affect the matter :
these are considerations which occur
only on reflection ; the unprompted
tendency of the mind is to generalise
its experience, provided this points all
in one direction ; provided no other

experience of a conflicting character
comes unsought. The notion of seek-
ing it, of experimenting for it, of in-
terrogating nature (to use Bacon's ex-
pression) is of much later growth.
The observation of nature by uncul-
tivated intellects is purely passive:
they accept the facts which present
themselves, without taking the trouble
of searching for more : it is a superior
mind only which asks itself what facts
are needed to enable it to come to a
safe conclusion, and then looks out for
these.

But though we have always a pro-
pensity to generalise from unvarying
experience, we are not always war-
ranted in doing so. Before we can be
at liberty to conclude that something
is universally true because we have
never known an instance to the con-
trary, we must have reason to be-
lieve that if there were in nature
any instances to the contrary, we
should have known of them. This
assurance, in the great majority of
cases, we cannot have, or can have
only in a very moderate degree. The
possibility of having it is the founda-
tion on which we shall see hereafter
that induction by simple enumeration
may in some remarkable cases amount
practically to proof.* No such assur-
ance, however, can be had on any of
the ordinary subjects of scientific in-
quiry. Popular notions are usually
founded on induction by simple enu-
meration ; in science it carries us but
a little way. We are forced to begin
with it ; we must often rely on it
provisionally, in the absence of means
of more searching investigation. But,
for the accurate study of nature, we
require a surer and a more potent in-
strument.

It was, above all, by pointing out
theinsufiiciencyof /this rude and loose
conception of Induction that Bacon
merited the title so generally awarded
to him of Founder of the Inductive
Philosophy, The value of his own
contributions to a more philosophical

* lufra, chap. xxi. xxii.

GROUND OF INDUCTION.

205

fcheory of the subject has certainly
been exaggerated. Although (along
with some fundamental errors) his
writings contain, more or less fully
developed, several of the most im-
portant principles of the Inductive
Method, physical investigation has
now far outgrown the Baconian con-
ception of Induction. Moral and
political inquiry, indeed, are as yet
far behind that conception. The cur-
rent and improved modes of reason-
ing on these subjects are still of the
same vicious description against which
Bacon protested ; the method almost
exclusively employed by those pro-
fessing to treat such matters induc-
tively, is the very inductio per enu-
nierationem simplicem which he con-
demns ; and the experience which we
hear so confidently appealed to by all
sects, parties, and interests is still, in
his own emphatic words, mera palpatio.

§ 3. In order to a better under-
standing of the problem which the
logician must solve if he would estab-
lish a scientific theory of Induction,
let us compare a few cases of incorrect
inductions with others which are ac-
knowledged to be legitimate. Some,
we know, which were believed for
centuries to be correct, were never-
theless incorrect. That all swans are
white, cannot have been a good in-
duction, since the conclusion has
turned out erroneous. The experi-
ence, however, on which the conclu-
sion rested was genuine. From the
earliest records, the testimony of the
inhabitants of the known world was
unanimous oii the point. The uniform
experience, therefore, of the inhabi-
tants of the known world, agreeing
in a common result, without one
known instance of deviation from
that result, is not always suflBcient to
establish a general conclusion.

But let us now turn to an instance
apparently not very dissimilar to this.
Mankind were WTX)ng, it seems, in
concluding that all swans were white ;
are we also wrong when we conclude
tl^at (^1 mep's beads grow above their

shoulders, and never below, in spite
of the conflicting testimony of the
naturalist Pliny? As there were
black swans, though civilised people
had existed for three thousand years
on the earth without meeting with
them, may there not also be "men
whose heads do grow beneath their
shoulders," notwithstanding a rather
less perfect unanimity of negative
testimony from observers ? Most
persons would answer No ; it was
more credible that a bird should vary
in its colour than that men should
vary in the relative position of their
principal organs. And there is no
doubt that in so saying they would
be right ; but to say why they are
right would be impossible, without
entering more deeply than is usually
done into the true theory of Induction.
Again, there are cases in which we
reckon with the most unfailing con-
fidence upon uniformity, and other
cases in which we do not count upon
it at alL In some we feel complete
assurance that the future will resem-
ble the past, the unknown be precisely
similar to the known. In others,
however invariable may be the result
obtained from the instances which
have been observed, we draw from
them no more than a very feeble pre-
sumption that the like result will hold
in aJl other cases. That a straight
line is the shortest distance between
two points, we do not doubt to be
true even in the region of the fixed
stars.* When a chemist announces
the existence and properties of a
newly discovered substance, if we
confide in his accuracy, we feel as-
sured that the conclusions he has
arrived at will hold universally, though
the induction be founded but on a
single instance. We do not withhold
our assent, waiting for a repetition of
the experiment ; or if we do, it is
from a doubt whether the one experi-
ment was properly made, not whether,

* In strictness, wherever the present
constitution of space exists ; which we
have ample reason to believe that it does
in-the region of the fixed stars.

206

INDUCTION.

if properly made, it would be conclu-
sive. Here, then, is a general law of
nature, inferred without hesitation
from a single instance ; an universal
proposition from a singular one. Now
mark another case, and contrast it
with this. Not all the instances
which have been observed since the
beginning of the world in support of
the general proposition that all crows
are black would be deemed a suffi-
cient presumption of the truth of the
proposition, to outweigh the testimony
of one unexceptionable witness who
should affirm that in some region of
the earth not fully explored he had
caught and examined a crow, and
had found it to be grey.

Why is a single instance, in some
cases, sufficient for a complete induc-
tion, while in others myriads of con-
curring instances, without a single ex-
ception known or presumed, go such
a very little way towards establish-
ing an universal proposition? Who-
ever can answer this question knows
more of the philosophy of logic than
the wisest of the ancients, and has
solved the problem of Induction.

CHAPTER IV.

OF LAWS OP NATURE.

§ I. In the contemplation of that
uniformity in the course of nature
which is assumed in every inference
from experience, one of the first ob-
servations that present themselves is,
that the uniformity in question is not
properly uniformity, but uniformities.
The general regularity results from
the co-existence of partial regularities.
The course of nature in general is
constant, because the course of each
of the various phenomena that com-
pose it is so. A certain fact invari-
ably occurs whenever certain circum-
stances are present, and does not
occur when they are absent ; the like
is true of another fact ; and so on.
From these separate threads of con-
nection between parts of the great
whole which we term nature a gene-

ral tissue of connection unavoidably
weaves itself, by which the whole is
held together. If A is always ac-
companied by D, B by E, and C by
F, it follows that A B is accompanied
by D E, A C by D F, B C by E F,
and finally A B O by D E F ; and
thus the general character of regula-
rity is produced, which, along with
and in the midst of infinite diversity,
pervades all nature.

The first point, therefore, to be
noted in regard to what is called the
uniformity of the course of nature
is, that it is itself a complex fact,
compounded of all the separate uni-
formities which exist in respect to
single phenomena. These various
uniformities, when ascertained by
what is regarded as a sufficient in-
duction, we call in common parlance,
Laws of Nature. Scientifically speak-
ing, that title is employed in a more
restricted sense to designate the uni-
formities when reduced to their most
simple expression. Thus in the illus-
tration already employed, there were
seven uniformities : all of which, if
considered sufficiently certain, would,
in the more lax application of the
term, be called laws of nature. But
of the seven, three alone are properly
distinct and independent : these being
pre-supposed, the others follow of
course. The three first, therefore,
according to the stricter acceptation,
are called laws of nature ; the re-
mainder not ; because they are in
truth mere cases of the three first :
virtually included in them ; said,
therefore, to result from them : who-
ever affirms those three has already
affirmed all the rest.

To substitute real examples for sym-
bolical ones, the following are three uni-
formities, or call them laws of nature :
th e 1 aw that air has weight, the law that
pressure on a fluid is propagated equally
in all directions, and the law that pres-
sure in one direction, not opposed by
equal pressure in the contrary direction,
produces motion, which does not cease
until equilibrium is restored. From
these three unifonnities we should

LAWS OF NATURE.

207

be able to predict another uniformity,
namely, the rise of the mercury in the
Torricellian tube. This, in the stricter
use of the phrase, is not a law of nature.
It is the result of laws of nature. It
is a case of each and every one of the
three laws ; and is the only occurrence
by which they could all be fulfilled.
If the mercury were not sustained in
the barometer, and sustained at such
a height that the column of mercury
were equal in weight to a column of
the atmosphere of the same diameter ;
here would be a case, either of the air
not pressing upon the surface of the
mercury with the force which is called
its weight, or of the downward pres-
sure on the mercury not being propa-
gated equally in an upper direction,
or of a body pressed in one direction
and not in the direction opposite,
either not moving in the direction in
which it is pressed, or stopping before
it had attained equilibrium. If we
knew, therefore, the three simple laws,
but had never tried the Torricellian
experiment, we might deduce its re-
sult from those laws. The known
weight of the air, combined with the
position of the apparatus, would bring
the mercury within the first of the
three inductions ; the first induction
would bring it within the second, and
the second within the third, in the
manner which we characterised in
treating of Ratiocination, We should
thus come to know the more complex
uniformity, independently of specific
experience, through our knowledge of
the simpler ones from which it results ;
though, for reasons which will appear
hereafter, verification by specific expe-
rience would still be desirable, and
might possibly be indispensable.

Complex uniformities which, like
this, are mere cases of simpler ones,
and have, therefore, been virtually
affirmed in aflarming those, may with
propriety be called laws, but can
scarcely, in the strictness of scientific
speech, be termed Laws of Nature.
It is the custom in science, wherever
regularity of any kind can be traced,
to call the general proposition which

expresses the nature of that regularity
a law ; as when, in mathematics, we
speak of the law of decrease of the
successive terms of a converging
series. But the expression law of
nature has generally been employed
with a sort of tacit reference to the
original sense of the word law, namely,
the expression of the will of a superior.
When, therefore, it appeared that any
of the uniformities which were ob-
served in nature would result spon-
taneously from certain other unifor-
mities, no separate act of creative
will being supposed necessary for the
production of the derivative unifor-
mities, these have not usually been
spoken of as laws of nature. Accord-
ing to one mode of expression, the
question. What are the laws of nature ?
may be stated thus : What are the
fewest and simplest assumptions,
which being granted, the whole exist-
ing order of nature would result?
Another mode of stating it would be
thus : What are the fewest general
propositions from which all the uni-
formities which exist in the universe
might be deductively inferred ?

Every great advance which marks
an epoch in the progress of science
has consisted in a step made towards
the solution of this problem. Even a
simple colligation of inductions already
made, without any fresh extension
of the inductive inference, is already
an advance in that direction. When
Kepler expressed the regularity which
exists in the observed motions of the
heavenly bodies by the three general
propositions called his laws, he, in so
doing, pointed out three simple sup-
positions, which, instead of a much
greater number, would suffice to con-
struct the whole scheme of the hea-
venly motions so far as it was known
up to that time. A similar and still
greater step was made when these
laws, which at first did not seem to
be included in any more general
ti-uths, were discovered to be cases of
the three laws of motion, as obtain-
ing among bodies which mutually
tend towards oae another with » cer-

208

INDUCTION.

tain force, and have had a certain
instantaneous impulse originally im-
pressed upon them. After this great
discover^', Kepler's three propositions,
though still called laws, would hardly,
by any person accustomed to use
language with precision, be termed
laws of nature : that phrase would
be reserved for the simpler and more
general laws into which Newton is
said to have resolved them.

According to this language, every
well-grounded inductive generalisa-
tion is either a law of nature or a
result of laws of nature, capable, if
those laws are known, of being pre-
dicted from them. And the problem
of Inductive Logic may be summed
up in two questions : how to ascertain
tihe laws of nature ; and how, after
having ascertained them, to follow
them into their results. On the other
hand, we must not suffer ourselves to
imagine that this mode of statement
amounts to a real analysis, or to any-
thing but a mere verbal transforma-
tion of the problem ; for the expression,
Laws of Nature, means nothing but
the uniformities which exist among
natural phenomena (or, in other
words, the results of induction) when
reduced to their simplest expression.
It is, however, something to have ad-
vanced so far as to see that the study
of nature is the study of laws, not a
law ; of uniformities in the plural
number ; that the different natural
phenomena have their separate rules
or modes of taking place, which,
though much intermixed and en-
tangled with one another, may, to a
certain extent, be studied apart ; that
(to resTime our former metaphor) the
regularity which exists in nature is
a web composed of distinct threads,
and only to be understood by tracing
each of the threads sepai-ately ; for
which purpose it is often necessary to
unravel some portion of the web, and
exhibit the fibres apart The rules
of experimental inquiry are the con-
trivances for unravelling the web.

§ 2. In thus attempting to ascertain

the general order of nature by ascer-
taining the particular order of the
occurrence of each one of the pheno-
mena of nature, the most scientific
proceeding can be no more than an
improved form of that which was
primitively pursued by the human
understanding while undirected by
science. When mankind first formed
the idea of studying phenomena ac-
cording to a stricter and surer method
than that which they had in the first
instance spontaneously adopted, they
did not, conformably to the well-meant
but impracticable precept of Des-
cartes, set out from the supposition
that nothing had been already ascer-
tained. Many of the uniformities
existing among phenomena are so
constant, and so open to observation,
as to force themselves upon involun-
tary recognition. Some facts are
so perpetually and familiarly accom-
panied by certain others, that man-
kind learnt, as children learn, to
expect the one where they found the
other, long before they knew how to
put their expectation into words by
asserting, in a proposition, the exist-
ence of a connection between those
phenomena. No science was needed
to teach that food nourishes, that
water drowns, or quenches thirst,
that the sun gives light and heat,
that bodies fall to the ground. The
first scientific inquirers assumed these
and the like as known truths, and
set out from them to discover others
which were unknown : nor were they
wrong in so doing, subject, however,
as they afterwards began to see, to
an ulterior revision of these spon-
taneous generalisations themselves,
when the progress of knowledge
T-iointed out limits to them, or showed
their truth to be contingent on some
circumstance not originally attended
to. It will appear, I think, from the
subsequent part of our inquiry, that
there is no logical fallacy in this
mode of proceeding ; but we may see
already that any other mode is rigor-
ously impracticable : since it is im-
possible to frame any scientific method

LAWS OF NATURE.

209

of induction, or test of the correctness
of inductions, unless on the hypothesis
that some inductions deserving of re-
liance have been already made.

Let us revert, for instance, to one
of our former illustrations, and con-
sider why it is that, with exactly the
eame amount of evidence, both nega-
tive and positive we did not reject
the assertion that there are black
swans, while we should refuse credence
to any testimony which asserted that
there were men wearing their heads
underneath their shoulders. The first
assertion was more credible than the
latter. But why more credible ? So
long as neither phenomenon had been
actually witnessed, what reason was
there for finding the one harder to be
believed than the other ? Apparently
because there is less constancy in the
colours of animals than in the general
structure of their anatomy. But how
do we know this ? Doubtless, from
experience. It appears, then, that we
need experience to inform us in what
degree, and in what cases, or sorts of
cases, experience is to be relied on.
Experience must be consulted in order
to learn from it under what circum-
stances arguments from it will be
valid. We have no ulterior test to
which we subject experience in gene-
ral ; but we make experience its own
test. Experience testifies that among
the uniformities which it exhibits or
seems to exhibit, some are more to be
relied on than others ; and uniformity,
therefore, may be presumed, from any
given number of instances, with a
greater degree of assurance, in pro-
portion as the case belongs to a class
in which the uniformities have hitherto
been found more uniform.

This mode of correcting one genera-
lisation by means of another, a nar-
rower generalisation by a wider, which
common sense suggests and adopts in
practice, is the real type of scientific
Induction. All that art can do is
but to give accuracy and precision
to this process, and adapt it to all
varieties of cases, without any
tial alteration in its pi'inciple.

There are of course no means of
applying such a test as that above
described, unless we already possess
a general knowledge of the prevalent
character of the uniformities existing
throughout nature. The indispen-
sable foundation, therefore, of a scien-
tific formula of induction must be a
survey of the inductions to which
mankind have been conducted in un-
scientific practice, with the special
purpose of ascertaining what kinds
of uniformities have been found per-
fectly invariable, pervading all nature,
and what are those which have been
found to vary with difference of time,
place, or other changeable circum«
stances.

§ 3. The necessity of such a survey
is confirmed by the consideration that
the stronger inductions are the touch-
stone to which we always endeavour
to bring the weaker. If we find any
means of deducing one of the less
strong inductions from stronger ones,
it acquires, at once, all the strength of
those from which it is deduced ; and
even adds to that strength ; since the
independent experience on which the
weaker induction previously rested
becomes additional evidence of the
truth of the better established law in
which it is now found to be included.
We may have inferred, from historical
evidence, that the uncontrolled power
of a monarch, of an aristocracy, or of
the majority, will often be abused ;
but we are entitled to rely on this
generalisation with much greater as-
surance when it is shown to be a
corollary from still better established
facts ; the very low degree of eleva-
tion of character ever yet attained by
the average of mankind, and the little
efficacy, for the most part, of the
modes of education hitherto practised,
in maintaining the predominance of
reason and conscience over the sel-
fish propensities. It is at the same
time obvious that even these more
general facts derive an accession of
evidence from the testimony which
history bears to the effects of des-

0

210

INDUCTION.

potism. The strong induction becomes
still stronger when a weaker one has
been bound up with it.

On the other hand, if an induction
conflicts with stronger inductions, or
with conclusions capable of being
correctly deduced from them, then,
unless on reconsideration it should
appear that some of the stronger
inductions have been expressed with
greater universality than their evi-
dence warrants, the weaker one must
give way. The opinion so long pre-
valent that a comet or any other
unusual appearance in the heavenly
regions was the precursor of calami-
ties to mankind, or to those at least
who witnessed it ; the belief in the
veracity of the oracles of Delphi or
Dodona ; the reliance on astrology,
or on the weather-prophecies in al-
manacks, were doubtless inductions
supposed to be grounded on experi-
ence ; * and faith in such delusions
seems quite capable of holding out
against a great multitude of failures,
provided it be nourished by a reason-
able number of casual coincidences
between the prediction and the event.
What has really put an end to these
insufficient inductions is their incon-
sistency with the stronger inductions
subsequently obtained by scientific in-
quiry, respecting the causes on which

* Dr. Whewell (Phil, of Discov., p. 246)
will not allow these and similar erroueous
judgments to be called inductions, inas-
much as such superstitious fancies "were
not collected from the facts by seeking a
law of their occurrence, but were suggested
by an imagination of the anger of superior
powers, sliown by such deviations from
the ordinary course of nature. ' I conceive
the question to be, not in what manner
these notions were at first suggested, but
by what evidence they have, from time to
time, been supposed to be substantiated.
If the believers in these erroneous opinions
had been put on their defence, they would
have referred to experience : to the comet
which preceded the assjissination of Julius
Csesar, or to oracles and other prophecies
known to have been fulfilled. It is by
such appeals to facts that all analogous
superstitions, even in our day, attempt to
justify tliemselves ; the supposed evidence
of experience is necessary to their hold on
the mind. I quite admit that the influence
of such coincidences would not be. what it

terrestrial events really depend ; and
where those scientific truths have not
yet penetrated, the same or similar
delusions still prevail.

It may be affirmed as a general
principle, that all inductions, whether
strong or weak, which can be con-
nected by ratiocination, are confirma-
tory of one another ; while any which
lead deductively to consequences that
are incompatible become mutually
each other's test, showing that one
or other must be given up, or at
least more guardedly expressed. In
the case of inductions which confirm
each other, the one which becomes a
conclusion from ratiocination rises to
at least the level of certainty of the
weakest of those from which it is
deduced ; while in general all are
more or less increased in certainty.
Tjjus the Torricellian experiment,
though a mere case of three more
general laws, not only strengthened
greatly the evidence on which those
laws rested, but converted one of
them (the weight of the atmosphere)
from a still doubtful generalisation
into a completely established doctrine.

If, then, a survey of the uniformi-
ties which have been ascertained to
exist in nature should point out some
which, as far as any human purpose
requires certainty, may be considered

is if strength were not lent to it by an
antecedent presumption ; but this is not
peculiar to such cases; preconceived no-
tions of probability form part of the ex-
planation of many other cases of belief on
insuflacient evidence. The a priori pre-
judice does not prevent the erroneous
opinion from being sincerely regarded as a
legitimate conclusion from experience ;
though it improperly predisposes the mind
to that interpretation of experience.

Thus much in defence of the sort of
examples objected to. But it would be
easy to produce instances, equally adapted
to the purpose, and in which no antecedent
prejudice is at all concerned. " For many
ages," says Archbishop Whately, "all far-
mers and gardeners were firmly convinced
— and convinced of their knowing it by
experience — that the crops would never
turn out good unless the seed were sown
during the increase of the moon." This
was induction, but bad induction ; just as
a vicious syllogism is reasoning, but bad
reasoning.

LAW OF CAUSATION.

2X1

quite certain and quite universal,
tnen by means of these uniformities
we may be able to raise multitudes
of other inductions to the same point
in the scale. For if we can show,
with respect to any inductive infer-
ence, that either it must be true, or
one of these certain and universal
inductions must admit of an excep-
tion, the former generalisation will
attain the same certainty, and inde-
feasibleness within the bounds as-
signed to it, which are the attributes
of the latter. It will be proved to
be a law ; and if not a result of other
and simpler laws, it Mrill be a law of
nature.

There are such certain and uni-
versal inductions ; and it is because
there are such, that a Logic of In-
duction is possible.

CHAPTER V.

OF THE LAW OF UNIVERSAL CAUSATION.

§ I, The phenomena of nature
exist in two distinct relations to one
another ; that of simultaneity, and
that of succession. Every pheno-
menon is related, in an uniform man-
ner, to some phenomena that co-exist
with it, and to some that have pre-
ceded and ^vill follow it.

Of the uniformities which exist
among synchronous phenomena, the
most important, on every account,
are the laws of number ; and next
to them those of space, or, in other
words, of extension and figure. The
laws of number are common to syn-
chronous and successive phenomena.
That two and two make four, is
equally true whether the second two
follow the first two or accompany
them. It is as true of days and
yeare as of feet and inches. The
laws of extension and figure (in other
words, the theorems of geometry, from
its lowest to its highest branches) are,
on the contrary, laws of simultaneous
phenomena only. The various parts
of space, and of the objects which are

said to fill space, co-exist; and the
unvarying laws which are the subject
of the science of geometry are an
expression of the mode of their co-
existence.

This is a class of laws, or, in other
words, of uniformities, for the com-
prehension and proof of which it is
not necessary to suppose any lapse of
time, any variety of facts or events
succeeding one another. The pro-
positions of geometry are indepen-
dent of the succession of events. All
things which possess extension, or,
in other words, which fill space, are
subject to geometrical laws. Pos-
sessing extension, they possess figure;
possessing figure, they must possess
some figure in particular, and have
all the properties which geometry
assigns to that figure. If one body
be a sphere and another a cylinder,
of equal height and diameter, the
one will be exactly two-thirds of the
other, let the nature and quality of
the material be what it wilL Again,
each body, and each point of a body,
must occupy some place or position
among other bodies ; and the position
of two bodies relatively to each other,
of whatever nature the bodies be,
may be unerringly inferred from the
position of each of them relatively to
any third body.

In the laws of number, then, and
in those of space, we recognise in the
most unqualified manner the rigorous
universality of which we are in quest.
Those laws have been in all ages the
type of certainty, the standard of
comparison for all inferior degrees of
evidence. Their invariability is so
perfect, that it renders us unable even
to conceive any exception to them ;
and philosophers have been led, though
(as I have endeavoured to show)
erroneously, to consider their evi-
dence as lying not in experience, but
in the original constitution of the in-
tellect. If, therefore, from the laws
of space and number we were able
to deduce uniformities of any other
description, this would be conclusive
evidence to us that those other uni-

212

INDUCTION.

formities possessed the same rigorous
certainty. But this we cannot do.
From laws of space and number alone,
nothing can be deduced but laws of
space and number.

Of all truths relating to phenomena,
the most valuable to us are those
which relate to the order of their suc-
cession. On a knowledge of these is
founded every reasonable anticipation
of future facts, and whatever power
we possess of influencing those facts
to our advantage. Even the laws of
geometry are chiefly of practical im-
portance to us as being a portion of
the premises from which the order of
the succession of phenomena may be
inferred. Inasmuch as the motion of
bodies, the action of forces, and the
propagation of influences of all sorts,
take place in certain lines and over
definite spaces, the properties of those
lines and spaces are an important part
of the laws to which those pheno-
mena are themselves subject. Again,
motions, forces, or other influences,
and times are numerable quantities ;
and the properties of number are ap-
plicable to them as to all other things.
But though the laws of number and
space are important elements in the
ascertainment of uniformities of suc-
cession, they can do nothing towards
it when taken by themselves. They
can only be made instrumental to that
purpose when we combine with them
additional premises, expressive of uni-
formities of succession already known.
By taking, for instance, as premises
these propositions, that bodies acted
upon by an instantaneous force move
with uniform velocity in straight
lines ; that bodies acted upon by a
continuous force move with accele-
rated velocity in straight lines ; and
that bodies acted upon by two forces
in different directions move in the
diagonal of a parallelogram, whose
sides represent the direction and quan-
tity of those forces ; we may by com-
bining these truths with propositions
relating to the properties of straight
lines and of parallelograms (as that a
triangle is half a parallelogram of the

same base and altitude), deduce an-
other important uniformity of suc-
cession, viz., that a body moving
round a centre of force describes
areas proportional to the times. But
unless there had been laws of succes-
sion in our premises, there could have
been no truths of succession in our
conclusions. A similar remark might
be extended to every other class of
phenomena really peculiar ; and, had
it been attended to, would have pre-
vented many chimerical attempts at
demonstrations of the indemonstrable,
and explanations which do not explain.

It is not, therefore, enough for us
that the laws of space, which are only
laws of simultaneous phenomena, and
the laws of number, which though true
of successive phenomena do not relate
to their succession, possess the rigorous
certainty and universality of which
we are in search. We must endeavour
to find some law of succession which
has those same attributes, and is there-
fore fit to be made the foundation of
processes for discovering, and of a test
for verifying, all other uniformities of
succession. This fundamental law
must resemble the truths of geometry'
in their most remarkable peculiarity,
that of never being, in any instance
whatever, defeated or suspended by
any change of circumstances.

Now among all those uniformities
in the succession of phenomena which
common observation is sufficient to
bring to light, there are very few which
have any, even apparent, pretension
to this rigorous indefeasibility ; and
of those few, one only has been found
capable of completely sustaining it.
In that one, however, we recognise a
law which is imiversal also in another
sense ; it is co-extensive with the entire
field of successive phenomena, all
instances whatever of succession being
examples of it. This law is the Law
of Causation. The truth that everj'
fact which has a beginning has a
cause, is co-extensive with human ex-
perience.

This generalisation may appear to
some minds not to amount to much.

LAW OF CAUr ATION.

4t3

since after all it asserts only this :
*'it is a law that every event depends
on some law : " " it is a law that there
is a law for everything," We must
not, however, conclude that the gene-
rality of the principle is merely verbal ;
it will be found on inspection to be no
vague or unmeaning assertion, but a
most important and really fundamen-
tal truth.

§ 2. The notion of Cause being the
root of the whole theory of Induction,
it is indispensable that this ideashould,
at the very outset of our inquiry, be,
with the utmost practicable degree
of precision, fixed and determined.
If, indeed, it Avere necessary for the
purpose of inductive logic that the
strife should be quelled which has
so long raged among the dififerent
schools of metaphysicians respecting
the origin and analysis of our idea of
causation, the promulgation, or at
least the general reception, of a true
theory of induction might be con-
sidered, desperate for a long time to
come. But the science of the Investi-
gation of Truth by means of Evidence
is happily independent of many of the
controversies which perplex the science
of the ultimate constitution of the
human mind, and is under no neces-
sity of pushing the analysis of mental
phenomena to that extreme limit
which alone ought to satisfy a meta-
phvsician.

I premise, then, that when in the
course of this inquiry I speak of the
cause of any phenomenon, I do not
mean a cause which is not itself a
phenomenon ; I make no research into
the ultimate or ontological cause of
anything. To adopt a distinction
familiar in the writings of the Scotch
metaphysicians, and especially of Reid,
the causes with which I concern my-
self are not efficient, hut physical causes.
They are causes in that sense alone
in which one physical fact is said to
be the cause of another. Of the effi-
cient causes of phenomena, or whether
any such causes exist at all, I am not
called upon to give an opinion. The

notion of causation is deemed by the
schools of metaphysics most in vogue
at the present moment to imply a
mysterious and most powerful tie,
such as cannot, or at least does not,
exist between any physical fact and
that other physical fact on which it is
invariably consequent, and which is
popularly termed its cause : and thence
is deduced the supposed necessity of
ascending higher, into the essences
and inherent constitution of things, to
find the true cause, the cause which
is not only followed by, but actually
produces, the effect. No such neces-
sity exists for the purposes of the pre-
sent inquiry, nor will any such doctrine
be found in the following pages. The
only notion of a cause which the
theory of induction requires is such
a notion as can be gained from experi-
ence. The Law of Causation, the
recognition of which is the main pillar
of inductive science, is but the familiar
truth that invariability of succession
is found by observation to obtain
between every fact in nature and
some other fact which has preceded
it, independently of all considerations
respecting the ultimate mode of pro-
duction of phenomena, and of every
other question regarding the nature of
"Things in themselves."

Between the phenomena, then,
which exist at any instant, and the
phenomena which exist at the succeed-
ing instant, there is an invariable order
of succession ; and, as we said in
speaking of the general uniformity of
the course of nature, this web is com-
posed of separate fibres ; this collective
order is made up of particular se-
quences, obtaining invariably among
the separate parts. To certain facts,
certain facts always do, and, as we
believe, will continue to, succeed. The
invariable antecedent is termed the
cause ; the invariable consequent, the
effect. And the universality of the
law of causation consists in this, that
every consequent is connected in this
manner with some particular ante-
cedent or set of antecedents. Let
the fact be what it may, if it has begun

214

INDUCTION.

to exist, it was preceded by some fact
or facts with which it is invariably
connected. For every event there
exists some combination of objects or
events, some given concurrence of
circumstances, positive and negative,
the occurrence of which is always fol-
lowed by that phenomenon. We
may not have found out what this
concurrence of circumstances may be;
but we never doubt that there is such
a one, and that it never occurs with-
out having thephenomenon in question
as its effect or consequence. On the
universality of this truth depends the
possibility of reducing the inductive
process to rules. The undoubted as-
surance we have that there is a law to
be found if we only knew how to find
it, will be seen presently to be the
source from which the canons of the
Inductive Logic derive their validity.

§ 3. It is seldom, if ever, between
a consequent and a single antecedent
that this invariable sequence subsists.
It is usually between a consequent
and the sum of several antecedents ;
the concurrence of all of them being
requisite to produce, that is, to be
certain of being followed by, the con-
sequent. In such cases it is very com-
mon to single out one only of the ante-
cedents under the denomination of
Cause, calling the others merely Con-
ditions. Thus, if a person eats of a
particulardish,anddiesinconsequence,
that is, would not have died if he had
not eaten of it, people would be apt to
say that eating of that dish was the
cause of his death. There needs not,
however, be any invariable connection
between eating of the dish and death ;
but there certainly is, among the cir-
cumstances which took place, some
combination or other on which death
is invariably consequent : as, for in-
stance, the act of eating of the dish,
combined with a particular bodily
constitution, a particular state of pre-
sent health, and perhaps even a certain
state of the atmosphere ; the whole of
which circumstances perhaps consti-
tuted in this particular case the con-

ditions of the phenomenon, or, m othei*
words, the set of antecedents which
determined it, and but for which it
would not have happened. The real
Cause is the whole of these antece-
dents ; and we have, philosophically
speaking, no right to give the name of
cause to one of them exclusively of
the others. What, in the case we have
supposed, disguises the incorrectness
of the expression is this : that the
various conditions, except the single
one of eating the food, were not events
(that is, instantaneous changes, or suc-
cessions of instantaneous changes) but
states possessing more or less of per-
manency ; and might therefore have
preceded the effect by an indefinite
length of duration, for want of the
event which was requisite to complete
the required concurrence of condi-
tions : while as soon as that event,
eating the food, occurs, no other cause
is waited for, but the effect begins im-
mediately to take place ; and hence
the appearance is presented of a
more immediate and close connection
between the effect and that one ante-
cedent, than between the effect and
the remaining conditions. Butthough
we may think proper to give the name
of cause to that one condition, the ful-
filment of which completes the tale,
and brings about the effect without
further delay ; this condition has really
no closer relation to the effect than
any of the other conditions has. All
the conditions were equally indispens-
able to the production of the conse-
quent ; and the statement of the cause
is incomplete, unless in some shape or
other we introduce them alL A man
takes mercury, goes out of doors, and
catches cold. We say, perhaps, that
the cause of his taking cold was ex-
posure to the air. It is clear, how-
ever, that his having taken mercury
may have been a necessary condition
of his catching cold ; and though it
might consist with usage to say that
the cause of his attack was exposure
to the air, to be accurate we ought to
say that the cause was exposure to the
air while under the effect of mercury.

Law of CAITSATION.

215

If we do not, when aiming at ac-
curacy, enumerate all the conditions,
it is only because some of them will
in most cases be understood without
being expressed, or because for the
purpose in view they may without de-
triment be overlooked. For example,
when we say, the cause of a man's
death was that his foot slipped in
climbing a ladder, we omit as a thing
unnecessary to be stated the circum-
stance of his weight, though quite as
indispensable a condition of the effect
which took place. When we say that
the assent of the crown to a bill makes
it law, we mean that the assent, being
never given until all the other con-
ditions are fulfilled, makes up the
sum of the conditions, though no one
now regards it as the principal one.
When the decision of a legislative
assembly has been determined by the
casting vote of the chairman, we some-
times say that this one person was
the cause of all the effects which re-
sulted from the enactment. Yet we
do not really suppose that his single
vote contributed more to the result
than that of any other person who
voted in the affirmative ; but, for the
purpose we have in view, which is to
insist on hi.s individual responsibility,
the part which any other person had
in the transaction is not material.

In all these instances the fact which
was dignified with the name of cause
was the one condition which came
last into existence. But it must not
be supposed that in the employment
of the term this or any other rule is
always adhered to. Nothing can
better show the absence of any
.scientific ground for the distinction
between the cause of a phenomenon
and its conditions, than the capricious
manner in which we select from among
the conditions that which we choose
to denominate the cause. However
numerous the conditions may be, there
is hardly any of them which may not,
according to the purpose of our im-
mediate discourse, obtain that nomi-
nal pre-eminence. This will be seen
by analysing the conditions of some

one familiar phenomenon. Tor ex-
ample, a stone thrown into water falls
to the bottom. What are the condi-
tions of this event ? In the first place,
there must be a stone and water, and
the stone must be thrown into the
water ; but these suppositions forming
part of the enunciation of the pheno-
menon itself, to include them also
among the conditions would be a
vicious tautology ; and this class of
conditions, therefore, have never re-
ceived the name of cause from any
but the Aristotelians, by whom they
were called the material cause, cama
materialis. The next condition is,
there must be an earth ; and accord-
ingly it is often said that the fall of
a stone is caused by the earth, or by
a power or property of the earth, or
a force exerted by the earth ; all of
which are merely roundabout ways of
saying tliat it is caused by the earth ;
or, lastly, the earth's attraction,
which also is only a technical mode
of saying that the earth causes the
motion, with the additional particu-
larity that the motion is towards the
earth, which is not a character of the
cause, but of the effect. Let ixs now
pass to another condition. It is not
enough that the earth should exist ;
the body must be within that dis-
tance from it in which the earth's at-
traction preponderates over that of
any other body. Accordingly we may
say, and the expression would be con-
fessedly correct, that the cause of the
stone's falling is its being iciihin the
sphere of the earth's attraction. We
proceed to a further condition. The
stone is immersed in water : it i.s
therefore a condition of its reaching
the ground that its specific gravity-
exceed that of the surrounding fluid,
or, in other words, that it sui-pass in
weight an equal volume of water.
Accordingly any one would be ac-
knowledged to speak correctly who
said that the cause of the stone's
going to the bottom is its exceeding
in specific gravity the fluid in which
it is immersed.
Thus we see that each and every con-

ii6

INDUCTION.

dition of the phenomenon may be
taken in its turn, and, with equal
propriety in common parlance, but
with equal impropriety in scientific
discourse, may be spoken of as if it
were the entire cause. And in prac-
tice that particular condition is usually
styled the cause whose share in the
matter is superficially the most con-
spicuous, or whose requisiteness to
the production of the effect we happen
to be insisting on at the moment.
So great is the force of this last con-
sideration, that it sometimes induces
us to give the name of cause even to
one of the negative conditions. We
say for example, The army was sur-
prised because the sentinel was off
his post. But since the sentinel's
absence was not what created the
enemy or put the soldiers asleep,
how did it cause them to be surprised?
All that is really meant is, that the
event would not have happened if he
had been at his duty. His being off
his post was no producing cause, but
the mere absence of a preventing
cause : it was simply equivalent to
his non-existence. From nothing,
from a mere negation, no conse-
quences can proceed. All effects are
connected, by the law of causation,
with some set of positive conditions ;
negative ones, it is true, being almost
always required in addition. In other
words, every fact or phenomenon which
has a beginning invariably arises when
some certain combination of positive
facts exists, provided certain other
positive facts do not exist.

There is, no doubt, a tendency
(which our first example, that of death
from taking a particular food, suffici-
ently illustrates) to associate the idea
of causation with the proximate ante-
cedent event, rather than with any of
the, antecedent states, or permanent
facts, which may happen also to be
conditions of the phenomenon ; the
reason being that the event not only
exists, but begins to exist immediately
previous ; while the other conditions
may have pre-existed for an indefinite
time. And this tendency shows itself

very visibly in the different logical
fictions which are resorted to, even by
men of science, to avoid the necessity
of giving the name of cause to anything
which had existed for an indetermi-
nate length of time before the effect.
Thus, rather than say that the earth
causes the fall of bodies, they ascribe
it to a force exerted by the earth, or an
attraction by the earth, abstractions
which they can represent to them-
selves as exhausted by each effort,
and therefore constituting at each
successive instant a fresh fact, simul-
taneous with or only immediately pre-
ceding the effect. Inasmuch as the
coming of the circumstance which
completes the assemblage of condi-
tions, is a change or event, it thenc«
happens that an event is always
the antecedent in closest apparent
proximity to the consequent : and
this may account for the illusicn
which disposes us to look upon the
proximate event as standing more
peculiarly in the position of a cause
than any of the antecedent states.
But even this peculiarity, of being in
closer proximity to the effect than
any other of its conditions, is, as we
have already seen, far from being
necessary to the common notion of a
cause ; with which notion, on the
contrary, any one of the conditions,
either positive or negative, is found,
on occasion, completely to accord.*

* The assertion that any and every one
of the conditions of a phenomenon may
be and is, on some occasions and for some
purposes, spoken of as the cause, has been
disputed by an intelligent reviewer of this
work in the Prospective Review, (the pre-
decessor of the justly esteemed National
Review,) who maintains that "we always
apply the word cause rather to that ele-
ment in the antecedents which exercises
force, and which would tend at all times
to produce the same or a similar effect to
that which, under certain conditions, it
would actually produce." And he says,
that "every one would feel" the expres-
sion, that the cause of a surprise was
the sentinel's being off his post, to be in-
correct ; but that the "allurement or force
which drew him off his post might be so
called, because in doing so it removed a
resisting power which would have pre-
vented the surprise." I cannot think that.

LAW OF CAUSATION.

217

The cause, then, philosophically
gpeaking, is the sum total of the con-
ditions positive and negative taken
together ; the whole of the contin-
gencies of every description, which
being realised, the consequent in-

it would be wrong to say that the event
took place because the sentinel was absent,
and yet right to say that it took place be-
cause he was bribed to be absent. Since
the only direct effect of the bribe was his
absence, the bribe could be called the re-
mote cause of the surprise, only on the
supposition that the absence was the proxi-
mate cause ; nor does it seem to me that
any one (who had not a theory to support)
would use the one expression and reject
the other.

The reviewer observes, that when a per-
son dies of poison, his possession of bodily
organs is a necessary condition, but that
no one would ever speak of it as the cause.
I admit the fact ; but I believe the reason
to be, that the occasion could never arise
for so speaking of it ; for when in the
accuracy of common discourse we are led
to speak of some one condition of a pheno-
menon as its cause, the condition so spoken
of is always one which it is at 1 .ast possible
that the hearer may require to be informed
of. The possession of bodily organs is a
known condition, and to give that as the
answer, when asked the cause of a person's
death, would not supply the information
sought. Once conceive that a doubt could
exist as to his having bodily organs, or
tliat he were to be compared with some
being who had them not, and cases may
be imagined in which it might be said that
his possession of them was the cause of his
death. If Faust and Mephistopheles to-
gether took poison, it might be said that
Faust died because he was a human being,
and had a body, while Mephistopheles sur-
vived because he was a spirit.

It is for the same reason that no one (as
the reviewer remarks) " calls the cause of
a leap, the muscles or sinews of the body,
thou^'h they are necessary conditions ; nor
the cause of a self-sacrifice, the knowledge
which was necessary for it ; nor the cause
of writing a book, tiiat a man has time for
it, which is a necessary condition." These
condition 8 (besides that they are antecedent
states, and not proxiinate antecedent events,
and are therefore never the conditions in
closest apparent proximity to the effect)
are all of them so obviously implied, that
it is hardly possible there should exist
that necessity for insisting on them, which
alone gives occasion for speaking of a single
condition as if it were the cause. Where-
evei- this necessity exists in regard to some
one condition, and does not exist in re-
gard to any other, I conceive that it is
consistent with usage, when scientific accu-
racy is not aimed at, to apply the name

variably follows. The negative con-
ditions, however, of any phenomenon,
a special enumeration of which would
generally be very prolix, may be all
summed up under one head, namely,
the absence of preventing or counter-
cause to that one condition. If the only
condition which can be supix)sed to be un-
known is a negative condition, the nega-
tive condition may be spoken of as tho
cause. It might be said that a person died
for want of medical advice, though this
would not be likely to be said unless the
person was already understood to be ill,
and in order to indicate that this negative
circumstance was what made the illness
fatal, and not the weakness of his con-
stitution, or tlie original virulence of the
disease. It might be said that a person
was drowned because he could not swim ;
the positive condition, namely, that he fell
into the water, being already implied in
the word drowned. And here let me re-
mark, that his falling into the water is in
this case the only positive condition : all
the conditions not expressly or virtually
included in this (as that he could not
swim, that nobody helped him, and so
forth) are negative. Yet, if it were simply
said that the cause of a man's death was
falling into the water, there would be quite
as great a sense of impropriety in the ex-
pression, as there would be if it were said
that the cause was his inability to swim :
because, though the one condition is posi-
tive and the other negative, it would be
felt that neither of them was sufficient,
without the other, to produce death.

With regard to the assertion that nothing
is termed the cause except the element
which exerts active force, I- waive the
question as to the meaning of active force,
and accepting the phrase in its popular
sense, I revert to a former example, and I
ask, would it be more agreeable to custom
to say that a man fell because his foot
slipped in climbing a ladder, or that he
fell because of his weight ? for his weight,
and not the motion of his foot, was the
active force which determined his fall. If
a person walking out on a frosty day
stumbled and fell, it might be said that he
stumbled because the ground was slippery,
or because he was not sufficiently careful ;
but few people, I suppose, would say that he
stumbled because he walked. Yet the only
active force concerned was that which he
exerted in walking : the others were mere
negative conditions ; but they happened to
be the only ones which there could be any
necessity to state ; for he walked, most
likely, in exactly his usual manner, and
the negative conditions made all the differ-
ence. Again, if a person were asked why
the army of Xerxes defeated that of Leoni-
das, he would probably say, because they
were a thousand times the number : but I

2lS

INDUCTION.

acting causes. The convenience of
this mode of expression is mainly
grounded on the fact, that the effects
of any cause in counteracting another
cause may in most cases be, with
strict scientific exactness, regarded
as a mere extension of its own proper
and separate effects. If gravity re-
tards the upward motion of a projec-
tile, and deflects it into a parabolic
trajectory, it produces, in so doing,
the very same kind of effect, and
even (as mathematicians know) the
same quantity of effect, as it does in
its ordinary operation of causing the
fall of bodies when simply deprived
of their support If an alkaline solu-
tion mixed with an acid destroys its
sourness, and prevents it from redden-
ing vegetable blues, it is because the
specific effect of the alkali is to com-
bine with the acid, and form a com-
pound with totally different qualities.
This property, which causes of all
descriptions possess, of preventing the
effects of other causes by virtue (for
the most part) of the same laws ac-
cording to which they produce their
own,* enables us, by establishing the

do not think be would say it was because
they fought, though that was the element
of active force. To borrow another example,
used by Mr. Grove and by Mr. Baden Po-
well, the opening of floodgates is said to
be the cause of the flow of water ; yet the
active force is exerted by the water itself,
and opening the floodgates merely supplies
a negative condition. The reviewer adds,
" There are some conditions absolutely pas-
sive, and yet absolutely necessary to phy-
sical phenomena, viz. the relations of space
and time ; and to these no one ever applies
the word cause without being immediately
arrested by those who hear him." Even
from this statement I am compelled to
dissent. Few persons would feel it incon-
gruous to say (for example) that a secret
became known because it was spoken of
when A. B. was within hearing ; which is
a condition of space; or that the cause
why one of two particular trees is taller
than the other is that it has been longer
planted ; which is a condition of time.

* There are a few exceptions ; for there
are some properties of objects which seem
to be purely preventive ; as the property
of opaque bodies by which they intercept
the passage of light. This, as far as we
are able to understand it, appears an in-
stance not of one cause counteracting an-

general axiom that all causes ai*G
liable to be counteracted in their
effects by one another, to dispense
with the consideration of negative
conditions entirely, and limit the
notion of cause to the assemblage of
the positive conditions of the pheno-
menon : one negative condition in-
variably understood, and the same in
all instances (namely, the absence of
counteracting causes) being sufficient,
along with the sum of the positive
conditions, to make up the whole set
of circumstances on which the pheno-
menon is dependent.

§ 4. Among the positive conditions,
as we have seen that there are some
to which, in common parlance, the
term cause is more readily and fre-
quently awarded, so there are others
to which it is, in ordinary circum-
stances, refused. In most cases of
causation a distinction is commonly
drawn between something which acts,
and some other thing which is acted
upon ; between an agent and a. patient.
Both of these, it would be universally
allowed, are conditions of the pheno-
menon ; but it would be thought
absurd to call the latter the cause,
that title being reserved for the
former. The distinction, however,
vanishes on examination, or rather
is found to be only verbal, arising
from an incident of mere expression,
namely, that the object said to be
acted upon, and which is considered
as the scene in which the effect takes

other by the same law whereby it produces
its own effects, but of an agency which
manifests itself in no other way than in
defeating the effects of another agency. If
we knew on what other relations to light,
or on what peculiarities of structure,
opacity depends, we might find that this
is only an apparent, not a real exception
to the general proposition in the text. In
any case it needs not affect the practical
application. The formula v^^hich includes
all the negative conditions of an effect in
the single one of the absence of counter-
acting causes, is not violated by such cases
as this ; though if all counteracting agen-
cies were of this description, there would
be no purpose served by employing the for-
mula.

LAW OF CAUSATION.

2t$

place, IS commonly j included in the
phrase by which the effect is spoken
of, so that if it were also reckoned as
part of the cause, the seeming incon-
gruity would arise of its being sup-
posed to cause itself. In the instance
which we have already had, of falling
bodies, the question was thus put :
What is the cause which makes a
stone fall ? and if the answer had
been "the stone itself," the expression
would have been in apparent contra-
diction to the meaning of the word
cause. The stone, therefore, is con-
ceived as the patient, and the earth (or,
according to the common and most
unphilosophical practice, an occult
quality of the earth) is represented as
the agent or cause. But that there
is nothing fundamental in the dis-
tinction may be sctu from this, that
it is quite possible to conceive the
stone as causing it^s own fall provided
the language employed be such as
to save the mere verbal incongruity.
We might say that the stone moves
towards the earth by the properties
of the matter composing it ; and ac-
cording to this mode of presenting the
phenomenon, the stone itself might
without impropriety be called the
agent ; though to save the established
doctrine of the inactivity of matter,
men usually prefer here also to ascribe
the effect to an occult quality, and
say that the cause is not the stone
itself, but the weight or gravitation of
the stone.

Those who have contended for a
radical distinction between agent and
patient, have generally conceived the
agent as that which causes some state
of, or some change in the state of,
another object which is called the
patient. But a little reflection will
show that the license we assume of
speaking of phenomena as states of
the various objects which take part
in them (an artifice of which so much
use has been made by some philo-
sophers, Brown in particular, for the
apparent explanation of phenomena)
is simply a sort of logical fiction, use-
ful sometimes as one among several

modes of expression, but which should
never be supposed to be the enuncia-
tion of a scientific truth. Even those
attributes of an object which might
seem with greatest propriety to be
called states of the object itself, its
sensible qualities, its colour, hardness,
shape, and the like, are in reality (as
no one has pointed out more clearly
than Brown himself) phenomena of
causation, in which the substance is
distinctly the agent or producing
cause, the patient being our own or-
gans, and those of other sentient
beings. What we call states of ob-
jects, are always sequences into which
the objects enter, generally as an-
tecedents or causes ; and things are
never more active than in the pro-
duction of those phenomena in which
they are said to be acted upon. Thus,
in the example of a stone falling to
the earth, according to the theory of
gravitation the stone is as much an
agent as the earth, which not only
attracts, but is itself attracted by,
the stone. In the case of a sensation
produced in our organs, the laws of
our organisation, and even those of
our minds, are as directly operative
in determining the effect produced,
as the laws of the outward object.
Though we call prussic acid the agent
of a person's death, the whole of the
vital and organic properties of the
patient are as actively instrumental
as the poison in the chain of effects
which so rapidly terminates his sen-
tient existence. In the process of
education, we may call the teacher
the agent and the scholar only the
material acted upon ; yet in truth all
the facts which pre-existed in the
scholar's mind exert either cooperat-
ing or counteracting agencies in rela-
tion to the teacher's efforts. It is
not light alone which is the agent in
vision, but light coupled with the
active properties of the eye and brain,
and with those of the visible object.
The distinction between agent and
patient is merely verbal : patients
are always agents ; in a great propor-
tion, indeed, of all natural pheno-

220

INDUCTION.

mena, they are so to such a degree as
to react forcibly on the causes which
acted upon them : and even when
this is not the case, they contribute,
in the same manner as any of the
other conditions, to the production of
the effect of which they are vulgarly
treated as the mere theatre. All the
positive conditions of a phenomenon
are alike agents, alike active ; and in
any expression of the cause which
professes to be complete, none of them
can with reason be excluded, except
such as have already been implied in
the words used for describing the
effect ; nor by including even these
would there be incurred any but a
merely verbal impropriety.

§ 5. There is a case of causation
which calls for separate notice, as it
possesses a peculiar feature, and pre-
sents a greater degree of complexity
than the common case. It often hap-
pens that the effect, or one of the
effects, of a cause is, not to produce
of itself a certain phenomenon, but to
fit something else for producing it.
In other words, there is a case of
causation in which the effect is to
invest an object with a certain pro-
perty. When sulphur, charcoal, and
nitre are put together in certain pro-
portions and in a certain manner, the
effect is, not an explosion, but that
the mixture acquires a property by
which, in given circumstances, it will
explode. The various causes, natural
and artificial, which educate the hu-
man body or the human mind, have
for their principal effect, not to make
the body or mind immediately do
anything, but to endow it with cer-
tain properties — in other words, to
give assurance that in given circum-
stances certain results will take place
in it, or as consequences of it. Phy-
siological agencies often have for the
chief part of their operation to pre-
dispose the constitution to some mode
of action. To take a simpler in-
stance than all these : putting a coat
of white paint upon a wall does not
merely produce in those who see it

done the sensation of white ; it con-
fers on the wall the permanent pro-
perty of giving that kind of sensation.
Regarded in reference to the sensa-
tion, the putting on of the paint is a
condition of a condition ; it is a con-
dition of the wall's causing that par-
ticular fact. The wall may have
been painted years ago, but it has
acquired a property which has lasted
till now and will last longer ; the
antecedent condition necessary to en-
able the wall to become in its turn a
condition has been fulfilled once for
all. In a case like this, where the
immediate consequent in the sequence
is a property produced in an object,
no one now supposes the property to
be a substantive entity "inherent"
in the object. What has been pro-
duced is what, in other language,
may be called a state of preparation
in an object for producing an effect.
The ingredients of the gunpowder
have been brought into a state of
preparation for exploding as soon as
the other conditions of an explosion
shall have occurred. In the case of
the gunpowder, this state of prepara-
tion consists in a certain collocation
of its particles relatively to one an-
other. In the example of the wall,
it consists in a new collocation of two
things relatively to each other — the
wall and the paint. In the example
of the moulding influences on the
human mind, its being a collocation
at all is only conjectural ; for, even
on the materialistic hypothesis, it
would remain to be proved that the
increased facility with which the brain
sums up a column of figures when it
has been long trained to calculation,
is the result of a permanent new
arrangement of some of its material
particles. We must, therefore, con-
tent ourselves with what we know,
and must include among the effects
of causes the capacities given to ob-
jects of being causes of other effects.
This capacity is not a real thing
existing in the objects ; it is but a
name for our conviction that they
will act in a particular manner when

LAW OF CAUSATION.

221

certain new circumstances arise. We
may invest this assurance of future
events with a fictitious objective ex-
istence, by calling it a state of the
object. But unless the state consists,
as in the case of the gunpowder it
does, in a collocation of particles, it
expresses no present fact ; it is but
the contingent future fact brought
back under another name.

It may be thought that this form
of causation requires us to admit an
exception to the doctrine that the
conditions of a phenomenon — the
antecedents required for calling it
into existence — must all be found
among the facts immediately, not
remotely, preceding its commence-
ment. But what we have arrived
at is not a correction, it is only an
explanation, of that doctrine. In the
enumeration of the conditions required
for the occurrence of any phenomenon,
it always has to be included that
objects must be present, possessed of
given properties. It is a condition
of the phenomenon explosion that an
object should be present, of one or
other of certain kinds, which for that
reason are called explosive. The pre-
sence of one of these objects is a con-
dition immediately precedent to the
explosion. The condition which is
not immediately precedent is the
cause which produced, not the ex-
plosion, but the explosive property.
The conditions of the explosion itself
were all present immediately before
it took place, and the general law,
therefore, remains intact.

§ 6. It now remains to advert to a
distinction which is of first-rate im-
portance both for clearing up the
notion of cause, and for obviating a
very specious objection often made
against the view which we have taken
of the subject.

When we define the cause of any-
thing (in the only sense in which the
present inquiry has any concern with
causes) to be " the antecedent which
it invariably follows," we do not use
this phrase as exactly synonymous

I with "the antecedent which it in-
1 variably has followed in our past ex-
perience." Such a mode of conceiving
I causation would be liable to the ob-
jection very plausibly urged by Dr.
Reid, namely, that according to this
doctrine night must be the cause of
day, and day the cause of night ;
since these phenomena have invari-
i ably succeeded one another from the
beginning of the world. But it is
necessary to our using the word cause
that we should believe not only that
the antecedent always has been fol-
lowed by the consequent, but that as
long as the present constitution of
things * endures it always ivill be so.
And this would not be true of day
and night. We do not believe that
night will be followed by day under
I all imaginable circumstances, but only
' that it will be so provided the sun
j rises above the horizon. If the sun
I ceased to rise, which, for aught we
; know, may be perfectly compatible
i with the general laws of matter, night
I would be, or might be, eternal. On
i the other hand, if the sun is above
I the horizon, his light not extinct, and
I no opaque body between us and him,
I we believe firmly that unless a change
i takes place in the properties of matter,
I this combination of antecedents will
be followed by the consequent day ;
I that if the combination of antecedents
could be indefinitely prolonged, it
would be always day ; and that if
the same combination had always
existed, it would always have been
I day, quite independently of night as
I a previous condition. Therefore is it
I that we do not call night the cause,
nor even a condition, of day. The
existence of the sun (or some such
luminous body), and there being no
: opaque medium in a straight Unef

* I mean by this expression, the ultimate
laws of nature (whatever they may be) as
distinguished from the derivative laws and
from the collocations. The diurnal revolu-
tion of the earth (for example) is not a
part of the constitution of things, because
nothing can be so called which might pos-
sibly be terminated or altered by natural
causes.

t I use the words "straight line" foi

222

INDUCTION.

between that body and the part of
the earth where we are situated, are
the sole conditions ; and the union
of these, without the addition of any
superfluous circumstance, constitutes
the causa This is what writers mean
when they say that the notion of
cause involves the idea of necessity.
If there be any meaning which con-
fessedly belongs to the term necessity,
it is unconditionatness. That which
is necessary, that which must be,
means that which will be, whatever
supposition we may make in regard
to all other things. The succession
of day and night evidently is not
necessary in this sense. It is con-
ditional on the occurrence of other
antecedents. That which will be fol-
lowed by a given consequent when,
and only when, some third circum-
stance also exists, is not the cause,
even though no case should ever have
occurred in which the phenomenon
took place without it.

Invariable sequence, therefore, is
not synonymous with causation, un-
less the sequence, besides being in-
variable, is unconditional. There are
sequences, as uniform in past experi-
ence as any others whatever, which
yet we do not regard as cases of
causation, but as conjunctions in some
sort accidental. Such, to an accurate
thinker, is that of day and night.
The one might have existed for any
length of time, and the other not have
followed the sooner for its existence ;
it follows only if certain other ante-
cedents exist ; and where those ante-
cedents existed, it would follow in
any case. No one, probably, ever
called night the cause of day ; man-
kind must BO soon have arrived at
the very obvious generalisation, that
the state of general illumination which
we call day would follow from the pre-

brevity and simplicity. In reality the line
in question is not exactly straight, for,
from the effect of refraction, we actually
see the sun for a short interval during
which the opaque mass of the earth is
interposed in a direct line between the sun
and our eyes ; thus realising, though but
to a limited extent, the coveted desidera-
tum of seeing round a corner.

eence of a sufficiently luminous body,
whether darkness had preceded or not.

We may define, therefore, the cause
of a phenomenon to be the ante-
cedent, or the concurrence of antece-
dents, on which it is invariably and
unconditionally consequent. Or if we
adopt the convenient modification of
the meaning of the word cause which
confines it to the assemblage of positive
conditions without the negative, then
instead of "unconditionally," we must
say, "subject to no other than nega-
tive conditions."

To some it may appear, that the
sequence between night and day being
invariable in our experience, we have
as much ground in this case as ex-
perience can give in any case for
recognising the two phenomena as
cause and effect ; and that to say
that more is necessary — to require a
belief that the succession is uncon-
ditional, or, in other words, that it
would be invariable under all changes
of circumstances — is to acknowledge
in causation an element of belief not
derived from experience. The answer
to this is, that it is experience itself
which teaches us that one uniformity
of sequence is conditional and another
unconditional. When we judge that
the succession of night and day is a
derivative sequence, depending on
something else, we proceed on grounds
of experience. It is the evidence of
experience which convinces us that
day could equally exist without being
followed by night, and that night
could equally exist without being fol-
lowed by day. To say that these
beliefs are "not generated by our
mere observation of sequence," * is
to forget that twice in every twenty-
four hours, when the sky is clear, we
have an experimentum crucis that the
cause of day is the sun. We have an
experimental knowledge of the sun
which justifies us on experimental
grounds in concluding, that if the
sun were always above the horizon
there would be day, though there had

* Second Burnet Prize Essay, by Principal
TuUoch, p. 25,

LAW OF CAUSATION.

233

been no night, and that if the sun
were always below the horizon there
would be night, though there had
been no day. We thus know from
experience that the succession of night
and day is not unconditional. Let
me add, that the antecedent, which
is only conditionally invariable, is not
the invariable antecedent. Though a
fact may, in experience, have always
been followed by another fact, yet
if the remainder of our experience
teaches us that it might not always
be so followed, or if the experience
itself is such as leaves room for a
possibility that the known cases may
not correctly represent all possible
cases, the hitherto invariable ante-
cedent is not accounted the cause ;
but why ? Because we are not sure
that it is the invariable antecedent.

Such cases of sequence as that of
day and night not only do not con-
tradict the doctrine which resolves
causation into invariable sequence,
but are necessarily implied in that
doctrine. It is evident, that from
a limited number of unconditional
sequences, there will result a much
greater number of conditional ones.
Certain causes being given, that is,
certain antecedents which are uncon-
ditionally followed by certain conse-
quents, the mere co-existence of these
causes will give rise to an unlimited
number of additional uniformities. If
two causes exist together, the effects
of both will exist together ; and if
many causes co-exist, these causes (by
what we shall term hereafter the in-
termixture of their laws) will give rise
to new effects, accompanying or suc-
ceeding one another in some particular
order, which order will be invariable
while the causes continue to co-exist,
but no longer. The motion of the
earth in a given orbit round the sun
is a series of changes which follow
one another as antecedent and conse-
quents, and will continue to do so
while the sun's attraction, and the
force with which the earth tends to
advance in a direct line through space,
continue to co-exist in the same quan-

tities as at present. But vary either
of these causes, and this particular
succession of motions would cease to
take place. The series of the earth's
motions therefore, though a case of
sequence invariable within the limits
of human experience, is not a case of
causation. It is not unconditional.

This distinction between the rela-
tions of succession which, so far as we
know, are unconditional, and those
relations, whether of succession or of
co-existence, which, like the earth's
motions or the succession of day and
night, depend on the existence or on
the co-existence of other antecedent
facts, corresponds to the great divi-
sion which Dr. Whewell and other
writers have made of the field of
science into the investigation of what
they term the Laws of Phenomena
and the investigation of causes ; a
phraseology, as I conceive, not philo-
sophically sustainable, inasmuch as
the ascertainment of causes, such
causes as the human faculties can
ascertain, namely, causes which are
themselves phenomena, is, therefore,
merely the ascertainment of other and
more universal Laws of Phenomena.
Ar I let me here observe, that Dr.
Whewell, and in some degree even
Sir John Herschel, seem to have
misunderstood the meaning of those
writers who, like M. Comte, limit
the sphere of scientific investigation
to Laws of Phenomena, and speak of
the inquiry into causes as vain and
futile. The causes which M. Cocnte
designates as inaccessible are efficient
causes. The investigation of physical,
as opposed to efficient, causes (includ-
ing the study of all the active forces
in Nature, considered as facts of ob-
j servation) is as important a part of
I M. Comte's conception of science as
of Dr. Whewell's. His objection to
the ivord cause is a mere matter of
nomenclature, in which, as a matter
of nomenclature, I consider him to be
entirely wrong. "Those," it is justly
remarked by Mr. Bailey,* " who, like

* Letters on the Philosophy of the Human
Mind, First Series, p. 219. .

224

INDUCTION.

M. Comte, object to designate events
as causes, are objecting without any
real ground to a mere but extremely
convenient generalisation, to a very
useful common name, the employment
of which involves, or needs involve,
no particular theory." To which it
may be added, that by rejecting this
form of expression, M. Comte leaves
himself without any term for marking
a distinction which, however incor-
rectly expressed, is not only real, but
is one of the fundamental distinctions
in science ; indeed, it is on this alone,
as we shall hereafter find, that the
possibility rests of framing a rigorous
Canon of Induction. And as things
left without a name are apt to be for-
gotten, a Canon of that description is
not one of the many benefits which
the philosophy of Induction has re
ceived from M. Comte's great powers.

§ 7. Does a cause always stand with
its effect in the relation of antecedent
and consequent? Do we not often
say of two simultaneous facts that
they are cause and effect — as when
we say that fire is the cause of warmth,
the sun and moisture the cause of
vegetation, and the like? Since a
cause does not necessarily perish be-
cause its effect has been produced,
the two things do very generally co-
exist ; and there are some appearances,
and some common expressions, seem-
ing to imply not only that causes may,
but that they must, be contempo-
raneous with their effects, Cessante
causd cessat et effectus has been a dogma
of the schools : the necessity for the
continued existence of the cause in
order to the continuance of the effect,
seems to have been once a generally
received doctrine. Kepler's numerous
attempts to account for the motions
of the heavenly bodies on mechanical
principles were rendered abortive by
his always supposing that the agency
which set those bodies in motion must
continue to operate in order to keep
up the motion which it at first pro-
duced. Yet there were at all times
many familiar instances of the con-

tinuance of effects long after their
causes had ceased. A coup de soleil
gives a person brain-fever: will the
fever go off as soon as he is moved
out of the sunshine ? A sword is run
through his body : must the sword
remain in his body in order that he
may continue dead ? A ploughshare
once made, remains a ploughshare,
without any continuance of heating
and hammering, and even after the
man who heated and hammered it
has been gathered to his fathers. On
the other hand, the pressure which
forces up the mercury in an exhausted
tube must be continued in order to
sustain it in the tube. This (it may
be replied) is because another force is
acting without intermission, the force
of gravity, which would restore it to
its level, unless counterpoised by a
force equally constant. But again :
a tight bandage causes pain, which
pain will sometimes go off as soon as
the bandage is removed. The illumi-
nation which the sun diffuses over the
earth ceases when the sun goes down.
There is, therefore, a distinction to
be drawn. The conditions which are
necessary for the first production of
a phenomenon are occasionally also
necessary for its continuance ; though
more commonly its continuance re-
quires no condition except negative
ones. Most things, once produced,
continue as they are, until something
changes or destroys them ; but some
require the permanent presence of
the agencies which produced them at
first. These may, if we please, be
considered as instantaneous pheno-
mena, requiring to be renewed at each
instant by the cause by which they
were at first generated. Accordingly,
the illumination of any given point of
space has always been looked upon as
an instantaneous fact, which perishes
and is perpetually renewed as long as
the necessary conditions subsist. If
we adopt this language we avoid the
necessity of admitting that the con-
tinuance of the cause is ever required
to maintain the effect. We may say,
it is not required to maintain, but to

LAW OF CAUSATION.

225

reproduce, the effect, or else to coun-
teract some force tending to destroy
it. And this may be a convenient
phraseology ; but it is only a phrase-
ology. The fact remains, that in some
cases (though these are a minority)
the continuance of the conditions
which produced an effect is necessary
to the continuance of the effect.

As to the ulterior question, whether
it is strictly necessary that the cause,
or assemblage of conditions should
precede, by ever so short an instant,
the production of the effect, (a question
raised and argued with much ingenuity
by Sir John Herschel in an Essay
already quoted,*) the inquiry is of no
consequence for our present purpose.
There certainly are cases in which the
effect follows without any interval per-
ceptible by our faculties ; and when
there is an interval, we cannot tell by
how many intermediate links imper-
ceptible to us that interval may really
be filled up. But even granting that
an effect may commence simultane-
ously with its cause, the view I have
taken of causation is in no way practi-
cally affected. Whether the cause and
its effect be necessarily succes.sive or
not, the beginning of a phenomenon
is what implies a cause, and causation
is the law of the succession of phe-
nomena. If these axioms be granted,
we can afford, though I see no neces-
sity for doing so, to drop the words
antecedent and consequent as applied
to cause and effect I have no objec-
tion to define a cause, the assemblage
of phenomena, which occurring, some
other phenomenon invariably com-
mences, or has its origin. Whether
the effect coincides in point of time
with, or immediately follows, the
hindmost of its conditions, is im-
material. At all events, it does not
precede it ; and when we are in doubt,
between two co-existent phenomena,
which is cause and which effect, we
rightly deem the question solved if we
can ascertain which of them preceded
the other.

• ^way«, pp. ag^-aeS-

§ 8. It continually happens that
several different phenomena, which
are not in the slightest degree de-
pendent or conditional on one another,
are found all to depend, as the phrase
is, on one and the same agent ; in
other words, one and the same phe-
nomenon is seen to be followed by
several sorts of effects quite hetero-
geneous, but which go on simultane-
ously one with another ; provided,
of course, that all other conditions
requisite for each of them also exist.
Thus, the sun produces the celestial
motions, it produces daylight, and it
produces heat The earth causes the
fall of heavy bodies, and it also, in its
capacity of a great magnet, causes the
phenomena of the magnetic needle.
A crystal of galena causes the sensa-
tions of hardness, of weight, of cubical
form, of grey colour, and many others
between which we can trace no inter-
dependence. The purpose to which the
phraseology of Properties and Powers
is specially adapted is the expression
of this sort of cases. When the same
phenomenon is followed (either subject
or not to the presence of other con-
ditions) by effects of different and
dissimilar orders, it is usual to say
that each different sort of effect is
produced by a different property of
the cause. Thus we distinguish the
attractive or gravitative property of
the earth, and its magnetic property :
the gravitative, luminiferous, and ca-
lorific properties of the sun : the
colour, shape, weight, and hardness
of a crystal. These are mere phrases,
which explain nothing, and add no-
thing to our knowledge of the subject,
but considered as abstract names
denoting the connection between the
different effects produced and the
object which produces them, they are
a very powerful instrument of abridg-
ment, and of that acceleration of the
process of thought which abridgment
accomplishes.

This class of considerations leads to
a conception which we shall find to be
of great importance, that of a Perma-
nent Cause, or original natural agent.

226

INDUCTION.

There exist in nature a number of
permanent causes, which have sub-
sisted ever since the human race has
been in existence, and for an indefi-
nite and probably an enormous length
of time previous. The sun, the earth,
and planets, with their various con-
stituents, air, water, and other distin-
guishable substances, whether simple
or compound, of which nature is made
up, are such Permanent Causes. These
have existed, and the effects or con-
sequences which they were fitted to
produce have taken place (as often as
the other conditions of the production
met) from the very beginning of our
experience. But we can give no ac-
count of the origin of the Permanent
Causes themselves. Why these par-
ticular natural agents existed origi-
nally and no others, or why they are
commingled in such and such propor-
tions, and distributed in such and
such a manner throughout space, is a
question we cannot answer. More
than this : we can discover nothing
regular in the distribution itself ; we
can reduce it to no uniformity, to no
law. There are no means by which,
from the distribution of these causes
or agents in one part of space we
could conjecture whether a similar
distribution prevails in another. The
co-existence, therefore, of Primeval
Causes ranks, to us, among merely
casual concurrences ; and all those
sequences or co-existences among the
effects of several such causes, which,
though invariable while those causes
co-exist, would, if the co-existence ter-
minated, terminate along with it, we
do not class as cases of causation, or
Jaws of nature : we can only calculate
on finding these sequences or co-
existences where we know by direct
evidence that the natural agents on
the properties of which they ulti-
mately depend are distributed in the
requisite manner. These Permanent
Causes are not always objects ; they
are sometimes events, that is to say,
periodical cycles of events, that being
the only mode in which events can
possess the property of permanence,

Not only, for instance, is the earth
itself a permanent cause, or primitive
natvu-al agent, but the earth's rota-
tion is so too : it is a cause which has
produced, from the earliest period,
(by the aid of other necessary condi-
tions,) the succession of day and night,
the ebb and flow of the sea, and many
other effects, while, as we can assign
no cause (except conjecturally) for the
rotation itself, it is entitled to be
ranked as a primeval cause. It is,
however, only the origin of the rota-
tion which is mysterious to us : once
begun, its continuance is accounted
for by the first law of motion (that
of the permanence of rectilinear mo-
tion once impressed) combined with
the gravitation of the parts of the
earth towards one another.

All phenomena without exception
which begin to exist, that is, all ex-
cept the primeval causes, are effects
either immediate or remote of those
primitive facts, or of some combina-
tion of them. There is no Thing
produced, no event happening, in the
known universe, which is not con-
nected by an uniformity, or invari-
able sequence, with some one or more
of the phenomena which preceded it ;
insomuch that it will happen again
as often as those phenomena occur
again, and as no other phenomenon
having the character of a counteract-
ing cause shall co-exist. These ante-
cedent phenomena, again, were con-
nected in a similar manner with some
that preceded them ; and so on, until
we reach, as the ultimate step attain-
able by us, either the properties of
some one primeval cause, or, the con-
junction of several. The whole of
the phenomena of nature were there-
fore the necessary, or, in other wwds,
the unconditional, consequences of
some former collocation <rf the Per-
manent Causes.

The state of the whole universe at
any instant we believe to be the con-
sequence of its state at the previous
instant ; insomuch that one who knew
all the agents which exist at the
present moment, their opllocation in

LAW OF CAUSATION.

227

space, and all their properties, in
other words, the laws of their agency,
could predict the whole subsequent
history of the universe, at least unless
some new volition of a power capable
of controlling the universe should
supervene.* And if any particular
state of the entire universe could
ever recur a second time, all subse-
quent states would return too, and
history would, like a circulating deci-
mal of many figures, periodically re-
peat itself : —

Jam redit et virgo, redeunt Satumia

regna, . . .
Alter erit turn Tiphys, et altera qiise

vehat Argo
Delectus heroas ; erunt quoque altera

bella,
Atque iieriim ad Trojam magnus mitte-

tur Achillea.

And though things do not really re-
volve in this eternal round, the whole

* To the universality which mankind are
agreed in ascribing to the Law of Causa-
tion there is one claim of exception, one
disputed case, that of the Human Will ;
the determinations of which, a large class
of metaphysicians are not willing to regard
as following the causes called motives, ac-
cording to as strict laws as those which
they suppose to exist in the world of mere
matter. This controverted point will un-
dergo a special examination when we come
to treat particularly of the Logic of the
Moral Sciences (Book vi. ch. 2). In the
meantime I may remark, that these me-
taphysicians, who, it must be obsefved,
ground the main part of their objection on
the supposed repugnance of the docti-ine
in question to our consciousness, seem to
me to mistake the fact which conscious-
ness testifies against. What is really in
contradiction to consciousness they would,
I think, on strict self-examination, find to
be the application to human actions and
volitions of the ideas involved in the com-
mon use of the term Necessity ; which I
agree with them in objecting to. But if
they would consider that by saying that a
person's actions necessarily follow from his
character, all that is really meant (for no
more is meant in any case whatever of
causation) is that he invariably does act in
conformity to his character, and that any
one who thoroughly knew his character
could certainly predict how he would act
in any supposable case ; they probably
would not find this doctrine either con-
trary to their experience or revolting to
their feeUnga. And no more than this is
contended for by any one but an Asiatic
fatalist: ' ^

series of events in the history of the
universe, past and future, is not the
less capable, in its own nature, of
being constructed d pinori by any one
whom we can suppose acquainted
with the original distribution of all
natural agents, and with the whole of
their properties, that is, the law of
succession existing between them and
their eflFects : saving the far more
than human powers of combination
and calculation which would be re-
quired, even in one possessing the
data, for the actual perfornjance of
the task.

§ 9. Since everything which occurs
is detennined by laws of causation
and collocations of the original causes,
it follows that the co-existences which
are observable among effects cannot
be themselves the subject of any
similar set of laws, distinct from laws
of causation. Uniformities there are,
as well of co-existence as of succession,
among effects ; but these must in all
cases be a mere result either of the
identity or of the co-existence of their
causes : if the causes did not co-exist,
neither could the effects. And these
causes being also effects of prior
causes, and these of others, until we
reach the primeval causes, it follows
that (except in the case of effects
which can be traced immediately 01
remotely to one and the same cause)
the co-existences of phenomena can in
no case be universal, unless the co-
existences of the primeval causes to
which the effects are ultimately trace-
able, can be reduced to an universal
law : but we have seen that they
cannot. There are, accordingly, no
original and independent, in other
words no unconditional, uniformities
of co-existence — between effects of
different causes ; if they co-exist, it is
only because the causes have casually
co-existed. The only independent and
unconditional co-existences which are
sufficiently invariable to have any
claim to the character of laws, are
between different and mutually inde-
pendent effects of the same cause ; in

228

INDUCTION.

other words, between different pro-
perties of the same natural agent.
This portion of the Laws of Nature
will be treated of in the latter part of
the present Book, under the name of
the Specific Properties of Kinds.

§ lO. Since the first publication of
the present treatise, the sciences of
physical nature have made a great
advance in generalisation through
the doctrine known as the Conserva-
tion or Persistence of Force. This
imposing edifice of theory, the build-
ing and laying out of which has for
some time been the principal occupa-
tion of the most systematic minds
among physical inquirers, consists of
two stages : one, of ascertained fact,
the other containing a large element
of hypothesis.

To begin with the first. It is
proved by numerous facts, both natu-
ral and of artificial production, that
agencies which had been regarded as
distinct and independent sources of
force — heat, electricity, chemical ac-
tion, nervous and muscular action,
momentum of moving bodies — are
interchangeable, in definite and fixed
quantities, with one another. It had
long been known that these dissimilar
phenomena had the power, luider
certain conditions, of producing one
another : what is new in the theory
is a more accurate estimation of what
this production consists in. What
happens is, that the whole or part of
the one kind of phenomena disappears,
and is replaced by phenomena of one
of the other descriptions, and that
there is an equivalence in quantity
between the phenomena that have
disappeared and those which have
been produced, insomuch that if the
process be reversed, the very same
quantity which had disappeared will
reappear, without increase or diminu-
tion. Thus, the amount of heat
which will raise the temperature of a
pound of water one degree of the
thermometer, will, if expended, say
in the expansion of steam, lift a
"height of 772 pounds one foot, or a

weight of one pound 772 feet : and
the same exact quantity of heat can,
by certain means, be recovered,
through the expenditure of exactly
that amount of mechanical motion.

The establishment of this compre-
hensive law has led to a change in the
language in which the scientific world
had been accustomed to speak of what
are called the Forces of Nature. Be-
fore this correlation between pheno-
mena most unlike one another had
been ascertained, their unlikeness had
caused them to be referred to so many
distinct forces. Now that they are
known to be convertible into one
another without loss, they are spoken
of as all of them results of one and
the same force, manifesting itself in
different modes. This force (it is said)
can only produce a limited and defi-
nite quantity of effect, but always
does produce that definite quantity ;
and produces it, according to circum-
stances, in one or another of the
forms, or divides it among several,
but so as (according to a scale of
numerical equivalents established by
experiment) always to make up the
same sum : and no one of the mani-
festations can be produced save by
the disappearance of the equivalent
quantity of another, which in its turn,
in appropriate circumstances, will re-
appear undiminished. This mutual
interchangeability of the forces of
nature, according to fixed numerical
equivalents, is the part of the new
doctrine which rests on irrefragable
fact.

To make the statement true, how-
ever, it is necessary to add, that an
indefinite and perhaps immense inter-
val of time may elapse between the
disappearance of the force in one form
and its reappearance in another. A
stone thrown up into the air with a
given force, and falling back im-
mediately, will, by the time it reaches
the earth, recover the exact amount
of mechanical momentum which was
expended in throwing it up, deduction
being made of a small portion of
motion which has beeii communicate<J

LAW OF CAUSATION.

229

to the air. But if the stone has lodged
on a height, it may not fall back for
years, or perhaps ages, and until it does,
the force expended in raising it is tem-
porarily lost, being represented only
by what, in the language of the new
theory, is called potential energy. The
coal imbedded in the earth is con-
sidered by the theory as a vast reser-
voir of force, which has remained
dormant for many geological periods,
and will so remain until, by being
burnt, it gives out the stored-up force
in the form of heat. Yet it is not
supposed that this force is a material
thing which can be confined by bounds,
as used to be thought of latent heat
when that important phenomenon was
first discovered. What is meant is
that when the coal does at last, by
combustion, generate a quantity of
heat, (transformable like all other heat
into mechanical momentimi and the
other forms of force,) this extrication
of heat is the reappearance of a force
derived from the sun's rays, expended
myriads of ages ago in the vegetation
of the organic substances which were
the material of the coal.

Let us now pass to the higher stage
of the theory of Conservation of Force;
the part which is no longer a gene-
ralization of proved fact, but a com-
Innation of fact and hypothesis.
Stated in a few words, it is as follows :
That the Conservation of Force is
really the Conservation of Motion ;
that in the various interchanges be-
tween the forms of force, it is always
motion that is transformed into mo-
tion. To establish this, it is necessary
to assume motions which are hypo-
thetical. The supposition is, that there
are motions which manifest themselves
to our senses only as heat, electricity,
&c., being molecular motions ; oscilla-
tions, invisible to us, among the minute
particles of bodies ; and that these
molecular motions are transmutable
into molarmotions (motions of masses)
and molar motions into molecular.
Now there is a real basis of fact for
this supposition : we have positive
evidence of the existence of molecular

motion in these manifestations of
force. In the case of chemical action,
for instance, the particles separate
and form new combinations, often
with a great visible disturbance of the
mass. In the case of heat, the evi-
dence is equally conclusive, since heat
expands bodies (that is, causes their
particles to move froni one another) ;
and if of sufficient amount, changes
their mode of aggregation from solid
to liquid, or from liquid to gaseous.
Again, the mechanical actions which
produce heat — friction, and the col-
lision of bodies — must from the nature
of the case produce a shock, that is,
an internal motion of particles, which
indeed, we find, is often so violent as
to break them permanently asunder.
Such facts are thought to warrant the
inference that it is not, as was sup-
posed, heat that causes the motion of
particles, but the motion of particles
tliat catiscs heat ; the original cause
of both being the previous motion
(whether molar or molecular — col-
lision of bodies or combustion of fuel)
which fOTmed the heating agency.
This inference already contains hypo-
thesis : but at least the supposed
cause, the intestine motion of mole-
cules, is a vein causa. But in order
to reduce the Conservation of Force
to Conservation of Motion, it was
necessary to attribute to motion the
heat propagated, through apparently
empty space, from the sim. This re-
quired the supposition (already made
for the explanation of the laws of
light) of a subtle ether pervading
space, which, though impalpable to us,
must have the property which consti-
tutes matter, that of resistance, since
waves are propagated through it by
an impulse from a given point. The
ether must be supposed (a supposition
not required by the theory of light)
to penetrate into the minute inter-
stices of all bodies. The vibratory
motion supposed to be taking place in
the heated mass of the sun, is con-
sidered as imparted from that mass
to the particles of the surrounding
ether, and through them to the par-

230

INDUCTION.

tides of the same ether in the inter-
stices of terrestrial bodies ; and this,
too, with a sufficient mechanical force
to throw the particles of those bodies
into a state of similar vibration, pro-
ducing the expansion of their mass,
and the sensation of heat in sentient
creatures. All this is hypothesis,
though of its legitimacy as hypothesis
I do not mean to express any doubt.
It would seem to follow as a conse-
quence from this theory, that Force
may and should be defined, matter
in motion. This definition, however,
will not stand, for, as has already
been seen, the matter needs not be
in actual motion. It is not necessary
to suppose that the motion afterwards
manifested is actually taking place
among the molecules of the coal dur-
ing its sojourn in the earth;* certainly
not in the stone which is at rest on
the eminence to which it has been
raised. The true definition of Force
must be, not motion, but Potentiality
of Motion ; and what the doctrine,
if established, amounts to is, not that
there is at all times the same quantity
of actual motion in the universe ; but
that the possibilities of motion are
limited to a definite quantity, which
cannot be added to, but which cannot
be exhausted ; and that all actual
motion which takes place in Nature is
a draft upon this limited stock. It
needs not all of it have ever existed
as actual motion. There is a vast
amount of potential motion in the
universe in the form of gravitation,
which it would be a great abuse of
hypothesis to suppose to have been
stored up by the expenditure of an
equal amount of actual motion in some
former state of the universe. Nor

* I believe, however, the accredited
authorities do suppose that molecular
motion, equivalent in amount to that
which will be manifested in the combus-
tion of the coal, is actually taking place
during the whole of the long interval, if
not in the coal, yet in the oxygen which
will then combine with it. But how purely
hypothetical this supposition is, need
hardly be remarked ; I venture to say, un-
necessarily and extravagantly hypotheti-
cal.

does the motion produced by giravity
take place, so far as we know, at the
expense of any other motion, either
molar or molecular.

It is proper to consider whether the
adoption of this theory as a scientific
truth, involving as it does a change
in the conception hitherto entertairxed
of the most general physical agencies,
requires any modification in the view
I have taken of Causation as a law of
nature. As it appears to me, none
whatever. The manifestations which
the theory regards as modes of motion
are as much distinct and separate
phenomena when referred to a single
force as when attributed to several.
Whether the phenomenon is called a
transformation of force or the genera-
tion of one, it has its own set or sets
of antecedents, with which it is con-
nected by invariable and uncondi-
tional sequence ; and that set, or
those sets, of antecedents are its
cause. The relation of the Conser-
vation theory to the principle of
Causation is discussed in much de-
tail, and very instructively, by Pro-
fessor Bain, in the second volume of
his Logic. The chief practical con-
clusion drawn by ' him bearing on
Causation is, that we must distinguish
in the assemblage of conditions which
constitutes the Cause of a pheno-
menon two elements : one, the pre-
sence of a force ; the other, the col-
location or position of objects which
is required in order that the force
may undergo the particular transmu-
tation which constitutes the pheno-
menon. Now, it might always have
been said with acknowledged correct-
ness, that a force and a collocation
were both of them necessary to pro-
duce any phenomenon. The law of
causation is, that change can only be
produced by change. Along with any
number of stationary antecedents,
which are collocations, there must
be at least one changing antecedent,
which is a force. To produce a bon-
fire, there must not only be fuel, and
air, and a spark, which are colloca-
tions, but chemical action between

LAW OF CAUSATION.

231

the air and the materials, which is
a force. To grind com, there must
be a certain collocation of the parts
composing a mill, relatively to one
another and to the com ; but there
must also be the gravitation of water,
or the motion of wind, to supply a
force. But as the force in these cases
was regarded as a property of the
objects in which it is embodied, it
seemed tautology to say that there
must be the collocation and the force.
As the collocation must be a colloca-
tion of objects possessing the force-
giving property, the collocation, so
understood, included the force.

How, then, shall we have to express
these facts, if the theory be finally
substantiated that all Force is redu-
cible to a previous Motion ? We shall
have to say that one of the conditions
of every phenomenon is an antecedent
Motion. But it will have to be ex-
plained that this needs not be actual
motion. The coal which supplies the
force exerted in combustion is not
shown to have been exerting that force
in the form of molecular motion in the
pit ; it was not even exerting pressure.
The stone on the eminence is exerting
a pressure, but only equivalent to its
weight, not to the additional momen-
tum it would acquire by falling. The
antecedent, therefore, is not a force in
action ; and we can still only call it
a property of the objects, by which
they would exert a force on the occur-
rence of a fresh collocation. The col-
location, therefore, still includes the
force. The force said to be stored up,
is simply a particular property which
the object has acquired. The cause
we are in search of is a collocation
of objects possessing that particular
property. When indeed we inquire
further into the cause from which they
derive that property, the new concep-
tion introduced by the Conservation
theory comes in : the property is itself
an effect, and its cause, according to
the theory, is a former motion of
exactly equivalent amount, which has
been impressed on the particles of the
body, perhaps at some very distant

period. But the casfe is simply one
of those we have already considered,
in which the efficacy of a cause con-
sists in its investing an object with a
property. The force said to be laid
up, and merely potential, is no more
a really existing thing than any other
properties of objects are really exist-
ing things. The expression is a mere
artifice of language, convenient for
describing the phenomena : it is un-
necessary to suppose that anything
has been in continuous existence ex-
cept an abstract potentiality. A force
suspended in its operation, neither
manifesting itself by motion nor by
pressure, is not an existing fact, but
a name for our conviction that in ap-
propriate circumstances a fact would
take place. We know that a pound
weight, were it to fall from the earth
into the sun, would acquire in falling
a momentum equal to millions of
pounds ; but we do not credit the
pound weight with more of actually
existing force than is equal to the
pressure it is now exerting on the
earth, and that is exactly a pound.
We might as well say that a force of
millions of pounds exists in a pound,
as that the force which will manifest
itself when the coal is burnt is a real
thing existing in the coal. What is
fixed in the coal is only a certain pro-
perty : it has become fit to be the ante-
cedent of an effect called combustion,
which partly consists in giving out,
under certain conditions, a given de-
finite quantity of heat.

We thus see that no new general
conception of Causation is introduced
by the Conservation theory. The in-
destructibility of Force no more inter-
feres with the theory of Causation
than the indestructibility of Matter,
meaning by matter the element of
resistance in the sensible world. It
only enables us to understand better
than before the nature and laws of
some of the sequences.

This better understanding, how-
ever, enables us, with Mr. Bain, to
admit, as one of the tests for distin-
guishing causation from mere con-

232

INDUCTION.

comitance, the expenditure or transfer
of energy. If the effect, or any part
of the effect, to be accounted for, con-
sists in putting matter in motion, then
any of the objects present which has
lost motion has contributed to the
effect ; and this is the true meaning
of the proposition that the cause is
that one of the antecedents which
exerts active force.

§ II. It is proper in this place to
advert to a rather ancient doctrine re-
specting causation, which has been re-
vived during the last few years in
many quarters, and at present gives
more signs of life than any other
theory of causation at variance with
that set forth in the preceding pages.

According to the theory in question,
Mind, or, to speak more precisely, Will
is the only cause of phenomena. The
type of Causation, as well as the ex-
clusive source from which we derive
the idea, is our own voluntary agency.
Here, and here only (it is said) we
have direct evidence of causation. We
know that we can move our bodies.
Respecting the phenomena of inani-
mate nature, we have no other direct
knowledge than that of antecedence
and sequence. But in the case of our
voluntary actions, it is affirmed that
we are conscious of power before we
have experience of results. An act
of volition, whether followed by an
effect or not, is accompanied by a con-
sciousness of effort, " of force exerted,
of power in action, which is necessarily
causal or causative." This feeling of
energy or force inherent in an act of
will is knowledge ci pj'ioi'i ; assurance
prior to experience that we have the
power of causing effects. Volition,
therefore, it is asserted, is something
more than an unconditional antece-
dent ; it is a cause in a different sense
from that in which physical pheno-
mena are said to cause one another :
it is an Efficient Cause. From this
the transition is easy to the further
doctrine, that Volition is the sole
Efficient Cause of all phenomena.
** It is inconceivable that dead force

could continue unsupported for a mo-
ment beyond its creation. We can-
not even conceive of change of pheno-
mena without the energy of a mind."
" The word action " itself, says another
writer of the same school, "has no
real significance except when applied
to the doings of an intelligent agent.
Let any one conceive, if he can, of
any power, energy, or force, inherent
in a lump of matter." Phenomena
may have the semblance of being pro-
duced by physical causes, but they
are in reality produced, say these
writers, by the immediate agency of
mind. All things which do not pro-
ceed from a human (or, I suppose, an
animal) will, proceed, they say,
directly from divine will. The earth
is not moved by the combination of a
centripetal and a projectile force ;
this is but a mode of speaking, which
serves to facilitate our conceptions.
It is moved by the direct volition of
an Omnipotent Being, in a path coin-
ciding with that which we deduce
from the hypothesis of these two
forces.

As I have so often observed, the
general question of the existence of
Efficient Causes does not fall within
the limits of our subject : but a theory
which represents them as capable of
being subjects of human knowledge,
and which passes off as efficient causes
what are only physical or phenomenal
causes, belongs as much to Logic as
to Metaphysics, and is a fit subject
for discussion here.

To my apprehension, a volition is
not an efficient, but simply a physical
cause. Our will causes our bodily
actions in the same sense, and in no
other, in which cold causes ice, or a
spark causes an explosion of gun-
powder. The volition, a state of our
mind, is the antecedent ; the motion
of our limbs in conformity to the voli-
tion is the consequent. This sequence
I conceive to be not a subject of direct
consciousness, in the sense intended
by the theory. The antecedent, in-
deed, and the consequent, are subjects
of consciousness. But the connection

LAW OF CAUSATION.

233

between them ia a subject of experi-
ence. I cannot admit that our con-
sciousness of the volition contains in
itself any d priori knowledge that the
muscular motion will foUow. If our
nerves of motion were paralysed, or
our muscles stiff and inflexible, and
had been so all our lives, I do not see
the slightest ground for supposing that
we should ever (unless by information
from other people) have known any-
thing of volition as a physical power,
or been conscious of any tendency in
feelings of our mind to produce mo-
tions of our body, or of other bodies.
I will not undertake to say whether
we should in that case have had the
physical feeling which I suppose is
meant when these writers speak of
" consciousness of effort : " I see no
reason why we should not ; since that
physical feeling is probably a state of
nervous sensation beginning and end-
ing in the brain, without involving the
motory apparatus : but we certainly
should not have designated it by any
term equivalent to effort, since effort
implies consciously aiming at an end,
which we should not only in that case
have had no reason to do, but could
not even have had the idea of doing.
If conscious at all of this peculiar
sensation, we should have been con-
scious of it, I conceive, only as a kind
of uneasiness, accompanying our feel-
ings of desire.

It is well ai^ed by Sir William
Hamilton against the theory in ques-
tion, that it " is refuted by the con-
sideration that between the overt fact
of corporeal movement of which we
are cognisant, and the internal act of
mental determination of which we
are also cognisant, there intervenes
a numerous series of intermediate
agencies of which we have no know-
ledge ; and, consequently, that we
can have no consciousness of any
casual connection between the ex-
treme links of this chain, the volition
to move and the limb moving, as this
hypothesis asserts. No one is im-
mediately conscious, for example, of
moving his arm through his volition.

Previously to this ultimate movement,
muscles, nerves, a multitude of solid
and fluid parts, must be set in motion
by the will, but of this motion we
know, from consciousness, absolutely
nothing. A person struck with para-
lysis is conscious of no inability in
his limb to fulfil the determinations
of his will ; and it is only after hav.
ing willed, and finding that his linibs
do not obey his volition, that he learns
by this experience that the external
movement does not follow the inter-
nal act. But as the paralytic learns
after the volition that his limbs do not
obey his mind, so it is only after
volition that the man in health learns
that his limbs do obey the mandates
of his will. " *

Those against whom I am contend-
ing have never produced, and do not
pretend to produce, any positive evi-
dence f that the power of our will to

* Lectures on Metaphysics, vol. ii. Lect.
xxxix. pp. ^91-392.

I regret that I cannot invoke the autho-
rity of Sir William Hamilton in favour of
my own opinions ou Causation, as I can
against the particular theory which I am
now combating. But that acute thinker
has a theory of Causation peculiar to him-
self, which has never yet, as far as I know,
been analytically examined, but which, I
venture to think, admits of as complete
refutation as any one of the false or insuf-
ficient psychological theories which strew
the ground in such numbers under his
potent metaphysical scythe. (Since exa-
mined and controverted in the sixteenth
chapter of An Examination of Sir William
Hamilton's Philosophy.)

t Unless we are to consider as such the
following statement by one of the writers
quoted in the text : " In the case of mental
exertion, the result to be accompHshed is
preconsidered or meditated, and is therefore
known a priori, or before experience." —
Bowen's Lowell Lectures on the Application
of Metaphysical and Ethical Science to the
Evidence of Religion, Boston, 1849. This
is merely saying that when we will a thing
we have an idea of it. But to have an idea
of what we wish to happen does not imply
a prophetic knowledge that it will happen.
Perhaps it will be said that the first time
we exerted our will, when we had of course
no experience of any of the powers resid-
ing in us, we nevertheless must already
have known that we possessed them, since
we cannot will that which we do not be-
lieve to be in our power. But the impos-
sibility is perhaps in the words only, and

234

INDUCTION.

move our bodies would be known to
U3 independently of experience. What
they have to say on the subject is,
that the production of physical events
by a will seems to carry its own ex-
planation with it, while the action of
matter upon matter seems to require
something else to explain it ; and is
even, according to them, " inconceiv-
able" on any other supposition than
that some will intervenes between
the apparent cause and its apparent
effect. They thus rest their case on
an appeal to the inherent laws of our
conceptive faculty ; mistaking, as I
apprehend, for the laws of that faculty
its acquired habits, grounded on the
spontaneous tendencies of its uncul-
tured state. The succession between
the will to move a limb and the actual
motion is one of the most direct and
instantaneous of all sequences which
come under our observation, and is
familiar to every moment's experi-
ence from our earliest infancy ; more
familiar than any succession of events
exterior to our bodies, and especially
more so than any other case of the
apparent origination (as distinguished
from the mere communication) of mo-
tion. Now, it is the natural ten-
dency of the mind to be always at-
tempting to facilitate its conception
of unfamiliar facts by assimilating
them to others which are familiar.
Accordingly, our voluntary acts, being
the most familiar to us of all cases of
causation, are, in the infancy and
early youth of the human race, spon-
taneously taken as the type of causa-
tion in general, and all phenomena
are supposed to be directly produced

not in the facts; for we may desire what
we do not know to be in our power ; and
finding by experience that our bodies move
according to our desire, we may then, and
only then, pass into the more complicated
mental state which is termed will.

After all, even if we had an instinctive
knowledge that our actions would follow
our will, this, as Brown remarks, would
prove nothing as to the nature of Causa-
tion. Our knowing, previous to experi-
ence, that an antecedent will be followed
by a certain consequent, would not prove
the relation between them to be anything
more than antecedence and consequence.

by the will of some sentient being.
This original Fetichism I shall not
characterise in the words of Hume,
or of any follower of Hume, but in
those of a religious metaphysician. Dr.
Reid, in order more effectually to show
the unanimity which exists on the sub-
ject among all competent thinkers.

"When we turn our attention to
external objects, and begin to exercise
our rational faculties about them, we
find that there are some motions and
changes in them which we have power
to produce, and that there are many
which must have some other cause.
Either the objects must have life and
active power, as we have, or they must
be moved or changed by something
that has life and active power, as ex-
ternal objects are moved by us.

" Our first thoughts seem to be, that
the objects in which we perceive such
motion have understanding and active
power as we have. 'Savages,' says the
Abb^ Raynal, * wherever they see mo-
tion which they cannot account for,
there they suppose a soul. ' All men
may be considered as savages in this
respect, until they are capable of in-
struction, and of using their faculties in
a more perfect manner than savages do.

" The Ahh6 Raynal's observation is
sufficiently confirmed both from fact
and from thestructure of all languages.

"Rude nations do really believe sun,
moon, and stars, earth, sea, and air,
fountains and lakes, to have under-
standing and active power. To pay
homage to them, and implore their
favour, is a kind of idolatry natural
to savages.

" All languages carry in their struc-
ture the marks of their being formed
when this belief prevailed. The dis-
tinction of verbs and participles into
active and passive, which is found in
all languages, must have been origin-
ally intended to distinguish what is
really active from what is merely pas-
sive ; and in all languages we find
active verbs applied to those objects
in which, according to the Abb^ Ray-
nal's observations, savages suppose a
souL

LAW OF CAUSATION.

23s

"Thus we say the sun rises and
sets, and comes to the meridian, the
moon changes, the sea ebbs and flows,
the winds blow. Languages were
formed by men who believed these
objects to have life and active power
in themselves. It was therefore pro-
jier and natural to express their mo-
tions and changes by active verbs.

" There is no surer way of tracing
the sentiments of nations before they
have records than by the structure
of their language, which, notwith-
standing the changes produced in it
by time, will always retain some sig-
natures of the thoughts of those by
whom it was invented. When we
find the same sentiments indicated in
the structure of all languages, those
sentiments must have been common
to the human species when languages
were invented.

" When a few, of superior intellec-
tual abilities, find leisure for specu-
lation, they begin to philosophise, and
soon discover that many of those
objects which at first they believed
to be intelligent and active are really
lifeless and passive. This is a very
important discovery. It elevates the
mind, emancipates from many vidgar
superstitions, and invites to further
discoveries of the same kind.

" As philosophy advances, life and
activity in natural objects retires, and
leaves them dead and inactive. In-
stead of moving voluntarily, we find
them to be moved necessarily ; in-
stead of acting, we find them to be
acted upon ; and Nature appears as
one great machine, where one wheel
is turned by another, that by a third;
and how far this necessary succession
may reach, the philosopher does not
know." *

There is, then, a spontaneous ten-
dency of the intellect to account to
itself for all cases of causation by
assimilating them to the intentional
acts of voluntary agents like itself.
This is the instinctive philosophy of
the human mind in its earliest stage,

* Reid's Estays on iht Active Powers, Easay
iv. chap. 3.

before it has become familiar with
j any other invariable sequences than
those between its own volitions or
I those of other human beings and their
I voluntary acts. As the notion of
fixed laws of succession among ex-
ternal phenomena gradually esta-
blishes itself, the propensity to refer
all phenomena to voluntary agency
slowly gives way before it. The sug-
gestions, however, of daily life con-
tinuing to be more powerful than
those of scientific thought, the original
instinctive philosophy maintains its
ground in the mind, underneath the
growths obtained by cultivation, and
keeps up a constant resistance to their
throwing their roots deep into the
soil. The theory against which I am
contending derives its nourishment
from that substratum. Its strength
does not lie in argument, but in its
affinity to an obstinate tendency of
the infancy of the human mind.

That this tendency, however, is not
the result of an inherent mental law,
is proved by superabundant evidence.
The history of science, from its ear-
liest davni, shows that mankind have
not been unanimous in thinking either
that the action of matter upon mat-
ter was not conceivable, or that the
action of mind upon matter was. To
some thinkers, and some schools of
thinkers, both in ancient and in
modem times, this last has appeared
much more inconceivable than the
former. Sequences entirely physical
and material, as soon as they had
become sufficiently familiar to the
human mind, came to be thought
perfectly natural, and were regarded
not only as needing no explanation
themselves, but as being capable of
affording it to others, and even of
serving as the ultimate explanation
of things in general.

One of the ablest recent supporters
of the Volitional theory has furnished
an explanation, at once historically
true and philosophically acute, of the
failure of the Greek philosophers in
physical inquiry, in which, as I con-
4.ceive, he unconsciously depicts his

236

INDUCTION.

own state of mind. " Their stum-
bling-block was one as to the nature
of the evidence they had to expect
for their conviction. . . . They had
not seized the idea that they must
not expect to understand the processes
of outward causes, but only their
results : and consequently, the whole
physical philosophy of the Greeks was
an attempt to identify mentally the
effect with its cause, to feel after some
not only necessary but natural con-
nection, where they meant by natural
that which would per se carry some
presumption to their own mind. . . .
They wanted to see some reason why
the physical antecedent should pro-
duce this particular consequent, and
their only attempts were in directions
where they could find such reasons." *
In other words, they were not content
merely to know that one phenomenon
was always followed by another ; they
thought that they had not attained
the true aim of science unless they
could perceive something in the nature
of the one phenomenon from which it
might have been known or presumed
previous to trial that it would be
followed by the other ; just what the
writer, who has so clearly pointed out
their error, thinks that he perceives
in the nature of the phenomenon
Volition. And to complete the state-
ment of the case, he should have
added that these early speculators
not only made this their aim, but
were quite satisfied with their success
in it ; not only sought for causes
which should carry in their mere
statement evidence of their efficiency,
but fully believed that they had found
such causes. The reviewer can see
plainly that this was an error, because
Tie does not believe that there exist
any relations between material phe-
nomena which can account for their
producing one another ; but the very
fact of the persistency of the Greeks
in this error shows that their minds
were in a very different state : they
were able to derive from the assimi-

* Prospective Revieie for February 1850.

lation of physical facts to other
physical facts the kind of mental
satisfaction which we connect with
the word explanation, and which the
reviewer would have us think can
only be found in referring phenomena
to a will. When Thales and Hippo
held that moisture was the universal
cause and external element of which
all other things were but the infinitely
various sensible manifestations ; when
Anaximenes predicted the same thing
of air, Pythagoras of numbers, and
the like, they all thought that they
had found a real explanation, and
were content to rest in this explana-
tion as ultimate. The ordinary se-
quences of the external universe
appeared to them, no less than to
their critic, to be inconceivable with-
out the supposition of some universal
agency to connect the antecedents
with the consequents ; but they did
not think that Volition, exerted by
minds, was the only agency which
fulfilled this requirement. Moisture,
or air, or numbers, carried to their
minds a precisely similar impression
of making intelligible what was other-
wise inconceivable, and gave the same
full satisfaction to the demands of
their conceptive faculty.

It was not the Greeks alone who
** wanted to see some reason why the
physical antecedent should produce
this particular consequent," some con-
nection "which would per se carry
some presumption to their own mind."
Among modem philosophers, Leibnitz
laid it down as a self-evident principle
that all physical causes without excep-
tion must contain in their own nature
something which makes it intelligible
that they should be able to produce
the effects which they do produce.
Far from admitting Volition as the
only kind of cause which carried inter-
nal evidence of its own power, and as
the real bond of connection between
physical antecedents and their conse-
quents, he demanded some naturally
and per se efficient physical antece-
dent as the bond of connection be-
tween Volition itself and its effects.

LAW OF CAUSATION.

237

He distinctly refused to admit the
will of God as a sufficient explanation
of anything except miracles ; and in-
sisted upon finding something that
would account better for the pheno-
mena of nature than a mere reference
to divine volition.*

Again, and conversely, the action
of mind upon matter (which, we are
now told, not only needs no explana-
tion itself, but is the explanation of
all other effects) has appeared to
some thinkers to be itself the grand
inconceivability. It was to get over
this very difficulty that the Cartesians
invented the system of Occasional
Causes. They could not conceive that
thoughts in a mind could produce
movements in a body, or that bodily
movements could produce thoughts.
They could see no necessary connec-
tion, no relation d priori, between a
motion and a thought. And as the
Cartesians, more than any other school
of philosophical speculation before or
since, made their own minds the mea-
sure of all things, and refused, on
principle, to believe that Nature had
done what they were unable to see
any reason why she must do, they
affirmed it to be impossible that a
material and a mental fact could be
causes one of 'another. They regarded
them as mere Occasions on which the
real agent, God, thought fit to exert
his power as a Cause. When a man
wills to move his foot, it is not his
will that moves it, but God (they
said) moves it on the occasion of his
will. God, according to this system,
is the only efficient cause, not qua
mind, or qud endowed with volition,
but qud omnipotent. This hypothe-
sis was, as I said, originally suggested
by the supposed inconceivability of
any real mutual action between Mind
and Matter ; but it was afterwards ex-
tended to the action of Matter upon
Matter, for on a nicer examination
they found this inconceivable too, and
therefore, according to their logic, im-
possible. The deus ex machind was
ultimately called in to produce a spark
* Vide supra, p. 157, note,

on the occasion of a flint and steel
coming together, or to break an egg
on the occasion of its falling on the
ground.

All this, undoubtedly, shows that
it is the disposition of mankind in
general not to be satisfied with know-
ing that one fact is invariably ante-
cedent and another consequent, but
to look out for something which may
seem to explain their being sa But
we also see that this demand may be
completely satisfied by an agency
purely physical, provided it be much
more familiar than that which it is
invoked to explain. To Thales and
Anaximenes it appeared inconceiv-
able that the antecedents which we
see in nature should produce the con-
sequents, but perfectly natural that
water or air should produce them.
The writers whom I oppose declare
this inconceivable, but can conceive
that mind, or volition, is per se an
efficient cause ; while the Cartesians
could not conceive even that, but
peremptorily declared that no mode
of production of any fact whatever
was conceivable, except the direct
agency of an omnipotent being. Thus
giving additional proof of what finds
new ct)nfirmation in every stage of
the history of science, that both what
persons can, and what they cannot,
conceive is very much an affair of
accident, and depends altogether on
their experience and their habits of
thought ; that by cultivating the re-
quisite associations of ideas, people
may make themselves unable to con-
ceive any given thing ; and may make
themselves able to conceive most
things, however inconceivable these
may at first appear : and the same
facts in each person's mental his-
tory which determine what is or is
not conceivable to him, determine
also which among the various se-
quences in nature will appear to him
so natural and plausible as to need
no other proof of their existence ; to
be evident by their own light, inde-
pendent equally of experience and of
ezplanatioD,

238

INDUCTION.

By what rule is any one to decide
between one theory of this descrip-
tion and another ? The theorists do
not direct us to any external evidence;
they appeal each to his own subjective
feelings. One says, The succession C,

B, appears to me more natural, con-
ceivable, and credible per se, than the
succession A, B ; you are therefore
mistaken in thinking that B depends
upon A ; I am certain, though I can
give no other evidence of it, that C
comes in between A and B, and is
the real and only cause of B. The
other answers, The successions C, B,
and A, B, appear to me equally natu-
ral and conceivable, or the latter more
so than the former : A is quite cap-
able of producing B without any other
intervention. A third agrees with the
first in being unable to conceive that
A can produce B, but finds the se-
quence D, B, still more natural than

C, B, or of nearer kin to the subject-
matter, and prefers his D theory to
the C theory. It is plain that there
is no universal law operating here,
except the law that each person's con-
ceptions are governed and limited by
his individual experiences and habits
of thought. We are warranted in
saying of all three, what each of
them already believes of the other
two, namely, that they exalt into an
original law of the human intellect
and of outward nature, one particular
sequence of phenomena, which appears
to them more natural and more con-
ceivable than other sequences, only
because it is more familiar. And
from this judgment I am unable to
except the theory that Volition is an
Efficient Cause.

I am unwilling to leave the subject
without adverting to the additional
fallacy contained in the corollary from
this theory ; in the inference that be-
cause Volition is an efficient cause,
therefore it is the only cause, and the
direct agent in producing even what
is apparently produced by something
else. Volitions are not known to pro-
duce anything directly except nervous
action, for the will influences eyeu

the muscles only through the nerves.
Though it were granted, then, that
every phenomenon has an efficient,
and not merely a phenomenal cause,
and that volition, in the case of the
peculiar phenomena which are known
to be produced by it, is that efficient
cause, are we therefore to say, with
these writers, that since we know of
no other efficient cause, and ought
not to assume one without evidence,
there is no other, and volition is the
direct cause of all phenomena ? A
more outrageous stretch of infer-
ence could hardly be made. Because
among the infinite variety of the
phenomena of nature there is one,
namely, a particular mode of action
of certain nerves, which has for its
cause, and, as we are now supposing,
for its efficient cause, a state of our
mind ; and because this is the only
efficient cause of which we are con-
scious, being the only one of which
in the nature of the case we can be
conscious, since it is tlie only one
which exists within ourselves ; does
this justify us in concluding that all
other phenomena must have the same
kind of efficient cause with that one
eminently special, narrow, and pecu-
liarly human or animal phenomenon?
The nearest parallel to this specimen
of generalisation is suggested by the
recently revived controversy on the
old subject of Plurality of Worlds, in
which the contending parties have
been so conspicuously successful in
overthrowing one another. Here also
we have experience only of a single
case, that of the world in which we
live, but that this is inhabited we
know absolutely, and without possi-
bility of doubt. Now if on this evi-
dence any one were to infer that
every heavenly body without excep-
tion, sun, planet, satellite, comet, fixed
star or nebula, is inhabited, and must
be so from the inherent constitution
of things, his inference would exactly
resemble that of the writers, who con-
clude that because volition is the effi-
cient cause of our own bodily motions,
it must be the efficient cause of every.

LAW OF CAUSATION.

239

thing else in the universe. It is true
there are cases in which, with acknow-
ledged propriety, we generalise from
a single instance to a multitude of in-
stances. But they must be instances
which resemble the one known in-
stance, and not such as have no cir-
cumstance in common with it except
that of being instances. I have, for
example, no direct evidence that any
creature is alive except myself ; yet I
attribute, with full assurance, life and
sensation to other human beings and
animals. But I do not conclude that
all other things are alive merely be-
cause I am. I ascribe to certain other
creatures a life like my own, because
they manifest it by tlie same sort of
indications by which mine is mani-
fested. I find that their phenomena
and mine conform to the same laws,
and it is for this reason that I believe
both to arise from a similar cause.
Accordingly I do not extend the con-
clusion beyond the grounds for it.
Earth, fire, mountains, trees, are re-
markable agencies, but their pheno-
mena do not conform to the same
laws as my actions do, and I there
fore do not believe earth or fire, moun-
tains or trees, to possess animal life.
But the supporters of the Volition
Theory ask us to infer that volition
causes everything, for no reason ex-
cept that it causes one particular
thing ; although that one pheno-
menon, far from being a type of all
natural phenomena, is eminently pecu-
liar, its laws bearing scarcely any
resemblance to those of any other
phenomenon, whether "of inorganic or
of organic nature.

NOTE SUPPLEMENTARY TO THE
PRECEDING CHAPTER.

The author of the Second Burnett Prize
Essay (Dr. Tulloch), who has employed a
considerable number of jKiges in contro-
verting the doctrines of the preceding
chapter, has somewhat surprised me by
denying a fact which I imagined too well
known to require proof — that there have
been philosophers who found in physical
?xplauatiop,3 of phenoqiena tl^e same com-

plete mental satisfaction which we are told
is only given by volitional explanation, and
others who denied the VoUtional Theory
on the same ground of inconceivability on
which it is defended. The assertion of the
Essayist is countersigned still more posi-
tively by an able reviewer of the Essay : *
" Two illustrations," says the reviewer,
"are advanced by Mr. Mill: the case of
Thales and Anaximenes, stated by him to
have maintained, the one Moisture, and
the other Air to be the origin of all things ;
and that of Descartes and Leibnitz, whom
he asserts to have found the action of
Mind upon Matter the grand inconceiv-
ability. In counter-statement as to the first
of these cases the author shows — what we
believe now hardly admits of doubt— that
the Greek philosophers distinctly recog-
nised as beyond and above their primal
material source, the vovi, or Divine In-
telligence, as the efficient and originating
Source of all ; and as to the second, by
proof that it was the mode, not the fact, of
that action on matter, which was repre-
sented as inconceivable."

A greater quantity of historical error
has seldom been comprised in a single
sentence. With regard to Thales, the as-
sertion that he considered water as a mere
material in the bands of vav^ rests on a
pa.ssage of Cicero de Naturd Deorum: and
whoever will refer to any of the accurate
historians of philosophy, will find that
they treat this as a mere fancy of Cicero,
resting on no authority, opposed to all the
evidence ; and make sui-mises as to the
manner in which Cicero may have been
led into the error. (See Ritter, vol. i. p.
211, 2<1 ed. ; Brandis, vol. i. pp. 118-119, ist
ed. ; Preller, Historia Philosophia Graco-
Romana, p. 10. " Schiefe Ansicht, dur-
chaus zu verwerfen;" " augenscheinlich
folgemd statt zu berichten :" "quibus vera
sententia Thaletis plane detorquetur ; " are
the expressions of these writers.) As for
Anaximenes, he, even according to Cicero,
maintained, not that air was the material
out of which God made the world, but that
the air was a god : " Anaximenes aera deum
statuit ; " or, according to St. Augustine,
that it was the material out of which the
gods were made: "non tamen ab ipsis
[Diisjaerem factum, sed ipsos ex aereortos
credidit." Those who are not familiar with
the metaphysical terminology of antiquity
must not be misled by finding it stated
that Anaximenes attributed «//vx»? (trans-
lated soul or life) to his universal element,
the air. The Greek philosophers acknow-
ledged several kinds of i/n;xT», the nutritive,
the sensitive, and the intellective, f Even
the modems, with admitted correctness,
attribute life to plants. As far as we can

* Westminster Review for October 1855.

t See the whole doctrine in Aristotle de
Aiiimd. where the Optnnicir} ifrux^l is treated
as exactly equivalent to dpcirriKii Svvofii^.

240

INDUCTION.

make out the meaning of Anaximenes, he
made choice of Air as the universal agent,
on the ground that it is perpetually in
motion, without any apparent cause ex-
ternal to itself : so that he conceived it as
exercising spontaneous force, and as the
principle of life and activity in all things,
men and gods inclusive. If this be not
representing it as the Eflficient Cause, the
dispute altogether has no meaning.

If either Anaximenes, or Thales, or any
of their cotemporaries, had held the doc-
trine that j'oOs was the Efl&cient Cause,
that doctrine could not have been reputed,
as it was throughout antiquity, to have
originated with Anaxagoras. The testi-
mony of Aristotle, in the first book of his
Metaphysics, is perfectly decisive with
respect to these early speculations. After
enumerating four kinds of causes, or rather
four different meanings of the word Cause,
viz. the Essence of a thing, the Matter of
it, the Origin of Motion (Efficient Cause),
and the End or Final Cause, he proceeds
to say, that most of the early philosophers
recognised onlv the second kind of Cause,
the Matter of a thing, tos ev vAijs elSei
fxova^ (iriOi}crav dp^a; elvai TravruiV. As his
first example he specifies Thales, whom he
describes as taking the lead in this view
of the subject, 6 rff; TOtauTrj? dpxrjyo? <^tAo-
<ro(/)ias, and goes on to Hippon, Anaxi-
menes, Diogenes (of ApioUonia), Hippasus
of Metapontum, Heraclitus, and Empe-
docles. Anaxagoras, however, (he proceeds
to say,) taught a different doctrine, as we
know, and it is alleged that Hermotimus of
Clazomense taught it before him. Anaxa-
goras represented that even if these various
theories of the universal material were
true, there would be need of some other
cause to account for the transformations
of the material, since the material cannot
originate its own changes : ov yap 5tj to ye
viTOKeifxevo¥ avrb noiel ixerapdWeiv eavTO"
keyui S" olov oure to ^vKov ovre o xa^KOs aiTio?
ToO ixerapdWeiv eKarepov avTuJv, ovSe noiel
TO nev $v\ov kKLvtiv o 8e xaA*cbs avhptavTa,
oAA' eVepoj' ti ttjs jueTa/3o\rjs oLtiov, viz.
the other kind of cause, oOev i) apxri t^s
Kiv^o-ews — an Efl&cient Cause. Aristotle
expresses great approbation of this doc-
trine, (which he says made its author appear
the only sober man among persons raving,
olov vrjffxtiP e<t>dvr) irap elitri XeyovTa? tovs
wpoTepov ;) but while describing the influ-
ence which it exercised over subsequent
speculation, he remarks that the philo-
sophers against whom this, as he thinks,
insuperable difficulty was urged, had not
felt it to be any diflBculty : ov8ev eSv<rxe-
pdvav ev eavTois. It is surely unnecessaiy
to say more in proof of the matter of fact
which Dr. Tulloch and his reviewer dis-
believe.

Having pointed out what he thinks the
error of these early speculators in not re-
cognising the need of an eflScient cause,
^ristotle goes on to mention two ocher

efficient causes to which they might have
had recourse, instead of intelligence : Tvx*?f
chance, and to avr tiaTov, spontaneity. He
indeed puts these aside as not sufficiently
vvorthy causes for the order in the universe,
ou6' ay to> avTop-drot Kal Tfj tvx*? TOaouToi'
intTp€\pai, npayfia koAm? elxev ; but he does
not reject them as incapable of producing
ani/ effect, but only as incapable of pro-
ducing that effect. He himself recognises
Tvxr) and t6 auToju-dToi/ as co-ordinate agents
with Mind in producing the phenomena of
the universe ; the department allotted to
them being composed of all the classes of
phenomena which are not supposed to fol-
low any uniform law. By thus including
Chance among efficient causes, Aristotle
fell into an error which philosophy has
now outgrown, but which is by no means
so alien to the spirit even of modern specu-
lation as it may at first sight appear. Up to
quite a recent period philosophers went on
ascribing, and many of them have not yet
ceased to ascribe, a real existence to the
results of abstraction. Chance could make
out as good a title to that dignity as many
other of the mind's abstract creations : it
had had a name given to it, and why should
it not be a reality? As for Tb avTOfidrov,
it is recognised even yet as one of the
modes of origination of phenomena, by all
those thinkers who maintain what is called
the Freedom of the Will. The same self-
determining power which that doctrine
attributes to volitions was supposed by
the ancients to be possessed also by some
other natural phenomena : a circumstance
which throws considerable light on more
than one of the supposed invincible neces-
sities of belief. I have introduced it here
because this belief of Aristotle, or rather
of the Greek philosophers generally, is as
fatal as the doctrines of Thales and the
Ionic school to the theory that the human
mind is compelled by its constitution to
conceive volition as the origin of all force,
and the efficient cause of all phenomena.*

* It deserves notice that the parts of
nature which Aristotle regards as present-
ing evidence of design are the Uniformi-
ties : the phenomena in so far as reducible
to law. Tuxi? and to avTO/uiaToi' satisfy him
as explanations of the variable element in
phenomena, but their occurring according
to a fixed rule can only, to his conceptions,
be accounted for by an Intelligent Will.
The common, or what may be called the
instinctive, religious interpretation of na-
ture, is the reverse of this. The events in
which men spontaneously see the hand of
a supernatural being are those which can-
not, as they think, be reduced to a physical
law. What they can distinctly connect
with physical causes, and especially what,
they can predict, though of course ascribed
to an Author of Nature if tliey already
recognise such an author, might be con-
ceived,, they think, to arise from ^ blin^

LAW OF CAUSATION.

241

With regard to the modem philosophers
(Leibnitz and the Cartesians) whom I had
cited as having maintained that the action
of mind upon matter, 80 far from being
the only conceivable origin of material
phenomena, is itself inconceivable ; the
atten)pt to rebut this argument by assert-
ing that the mode, not the fuct, of the
action of mind on matter was represented
as inconceivable, is an abuse of the privi-
lege of writing confidently about authors
without reading them ; for any knowledge
whatever of Leibnitz would have taught
those who thus bpeak of him, that the in-
conceivability of the mode and the im-
possibility of the thing were in his mind
convertible expressions. What was his
famous Principle of the Sufficient Reason,
the very corner-stone of his Philosophy,
from which the Pre-established Harmony,
the doctrine of Monads, and all the opinions
most characteristic of Leibnitz were corol-
laries? It was, that nothing exists the
existence of which is not capable of being
proved and explained d priori : the proof
and explanation in the case of contingent
facts being derived from the nature of their
causes ; which could not be the causes unless
there was something in their nature siiow-
ing them to be capable of producing those
particular effects. And this " something"
which accounts for the production of phy-
sical effects he was able to find in many
physical causes, but could not find it in
any finite minds, which therefore he un-
hesitatingly asserted to be incapable of
producing any physical effects whatever.
" On ne saurait concevoir," he says, "une
fiction reciproque de la mati&re et de I'in-
telligence I'une sur I'autre," and there
is therefore (he contends) no choice but
between the Occasional Causes of the Carte-
sians and his own Pre-established Har-
mony, according to which there is no more
connection between our volitions and our
muscular actions than there is between
two clocks which are wound up to strike
at the same instant. But he felt no simi-
lar difficulty as to physical causes; and

fatality, and in any case do not appear to
them to bear so obviously the mark of a
divine will. And this distinction has been
countenanced by eminent writers on Natu-
ral Theology, in particular by Dr. Chalmers,
who thinks that though design is present
everywhere, the irresistible evidence of it
is to be found not in the laws of nature,
but in the collocations, i.t. in the part of
nature in which it is impossible to trace
any law. A few properties of dead matter
might, he thinks, conceivably account for
the regular and invariable succession of
effects and causes ; but that the different
kinds of matter have been so placed as to
promote beneficent ends, is what he re-
gards as the proof of a Divine Providence.
Mr. Baden Powell, in his Essay entitled

throughout his speculations, as in the pas-
sage I have already cited respecting gravi-
tation, he distinctly refuses to consider as
part of the order of nature any fact which
i.s not explicable from the nature of its
physical cause.

Witli regard to the Cartesians, (not Des-
cartes; I did not make that mistake,
though the reviewer of Dr. Tulloch's Essay
attributes it to me,) 1 take a passage almost
at random from Malebranche, who is the
best known of the Cartesians, and, though
not the inventor of the system of Occa-
sional Causes, is its principal expositor.
In Part 2, chap. 7, of his Sixth Book,
having first said that matter cannot have
the power of moving itself, he proceeds
to argue that neither can mind have the

Power of moving it. " Quand on examine
id6e que Ton a de tons les esprits finis, on
ne voit point de liaison n^cessaire entre
leur volonte et le mouvement de quelque
corps que ce soit, on voit au contraire qu'il
n'y en a point, et qu'il n'y en peut avoir,"
(there is nothing in the idea of finite
mind which can account for its causing
the motion of a body;) "on doit aussi
conclure, si on veut raisonner selon ses
lumieres, qu'il n'y a aucun esprit cr66 qui
puisse remuer quelque corps que ce soit
comme cause veritable ou principale, de
mfeme que Ton a dit qu'aucun corps ne
se pouvait remuer soi-m6me:" thus the
idea of Mind is, according to him, as in-
compatible as the idea of Matter with the
exercise of active force. But when, he
continues, we consider not a created but
a Divine Mind, the case is altered ; for tlie
idea of a Divine Mind includes omnipo-
tence ; and the idea of omnipotence does
contain the idea of being able to move
bodies. Thus it is the nature of omnipo-
tence which renders the motion of bodies
even by the Divine Mind credible or con-
ceivable, while, so far as depended on the
mere nature of mind, it would have been
inconceivable and incredible. If Male-
branche had not believed in an omnipotent
being, he would have held all action of

"Philosophy of Creation," has returned
to the point of view of Aristotle and the
ancients, and vigorously reasserts the doc-
trine that the indication of design in the
universe is not special adaptations, but
Uniformity and Law, these being the evi-
dences of mind, and not what appears to
us to be a provision for our uses. While I
decline to express any opinion here on this
vexata qucestio, I ought not to mention Mr.
Powell's volume without the acknowledg-
ment due to the philosophic spirit which
pervades generally the three Essays com-
posing it, forming in the case of one of them
(the " Unity of Wo rids ') an honourable con-
trast with the other dissertations, so far as
they have come under my notice, which have
appeared on either side of that controversy.

^42

INDUCTION.

mind on body to be a demonstrated im-
possibility.*

A doctrine more precisely the reverse
of the Volitional theory of causation can-
not well be imagined. The Volitional
theory is, that we know Ijy intuition or
by direct experience the action of our own
mental volitions on matter ; that we may
hence infer all other action upon matter
to be that of volition, and might thus
know, without any other evidence, that
matter is under the governmentof a divine
mind. Leibnitz and the Cartesians, on the
contrary, maintain that our volitions do
not and cannot act upon matter, and that
it is only the existence of an all-governing
Being, and that Being omnipotent, which
can account for the sequence between our
volitions and our bodily actions. When
we consider that each of these two theories,
which, as theories of causation, stand at
the opposite exti-emes of possible diver-
gence from one another, invokes not only
as its evidence, but as its sole evidence,
the absolute inconceivability of any theory
but itself, we are enabled to measure the
worth of this kind of evidence ; and when
we find the Volitional theory entirely built
upon the assertion that by our mental
constitution we are compelled to recognise
our volitions as eflficient causes, and then
find other thinkers maintaining that we
know that they are not and cannot be
such causes, and cannot conceive them to
be so, I think we have a right to say that
this supposed law of our mental constitu-
tion does not exist.

Dr.Tulloch (pp. 45-47)thinksita sufficient
answer to this that Leibnitz and the Car-
tesians were Tbeists, and believed the will
of God to be an efficient cause. Doubtless
they did, and the Cartesians even believed
(though Leibnitz did not) that it is the only
surh cause. Dr. TuUoch mistakes the na-
ture of the question. I was not writing
on Theism, as Dr. Tulloch is, biit against a
particular theory of causation, which, if it
be unfounded, can give no effective support
to Theism or to anything else. I found it
asserted that volition is the only efficient
cause, on the ground that no other efficient
cause is conceivable. To this assertion I
oppose the instances of Leibnitz and of the
Cartesians, who affirmed with equal posi-
tiveness that volition as an efficient cause
is itself not conceivable, and that omnipo-

* In the words of Fontenelle, another
celebrated Cartesian, " Les philosophes
aussi bien que le peuple avaient cru que
Time et le corps agissaient r^ellement et
physiquement i'un sur I'autre. Descartes
Vint, qui prouva que leur nature ne per-
mettait point cette sorte de communication
veritable, et qu'ils n'en pouvaient avoir
qu'uiie apparente, dont Dieu ^taitle M6dia-
teur." — (Envreade Fontenelle, ed. 1767, torn,
v. p. 534.

tence, which renders all things conceivable,
can alone take away the impossibility.
This I thought, and think, a conclusive
answer to the argument on which this
theory of causation avowedly depends.
But I certainly did not imagine that Theism
w;i8 bound up with that theory ; nor ex-
pected to be charged with denying Leibnitz
and the Cartesians to be Theists because I
denied that they held the ttieory

CHAPTER VI.

ON THE COMPOSITION OF CAUSES.

§ I. To complete the general notion
of causation on which the rules of ex-
perimental inquiry into the laws of
nature must be founded, one distinc-
tion still remains to be pointed out :
a distinction so radical, and of so
much importance, as to require a
chapter to itself.

The preceding discussions have ren-
dered us familiar with the case in
which several agents, or causes, con-
cur as conditions to the production of
an effect ; a case, in truth, almost uni-
versal, there being very few effects to
the production of which no more than
one agent contributes. Suppose, then,
that two different agents, operating
jointly, are followed, under a certain
set of collateral conditions, by a given
effect. If either of these agents, in-
stead of being joined with the other,
had operated alone, under the same
set of conditions in all other respects,
some effect would probably have fol-
lowed ; which would have been diffe-
rent from the joint effect of the two,
and more or less dissimilar to it. Now,
if we happen to know what would be
the effect of each cause when acting
separately from the other, we are often
able to arrive deductively, or d priori,
at a correct prediction of what will
arise from their conjunct agency. To
render this possible, it is only neces-
sary that the same law which expresses
the effect of each cause acting by it-
self shall also correctly express the
part due to that cause of the effect
which followt from the two together.

COMPOSITION OF CAUSES.

243

This condition is realised in the ex-
tensive and important class of pheno-
mena commonly called mechanical,
namely, the phenomena of the com-
munication of motion (or of pressure,
which is tendency to motion) from
one body to another. In this impor-
tant class of cases of causation, one
cause never, properly speaking, defeats
or frustrates another ; both have their
full effect. If a body is propelled in
two directions by two forces, one tend-
ing to drive it to the north and the
other to the east, it is caused to move
in a given time exactly as far in both
directions as the two forces would
separately have carried it ; and is left
precisely where it would have arrived
if it had been acted upon first by one
of the two forces, and afterwards by
the other. This law of nature is
called, in dynamics, the principle of
the Composition of Forces : and, in
imitation of that well-chosen expres-
sion, I shall give the name of the
Composition of Causes to the prin-
ciple which is exemplified in all cases
in which the joint efifect of several
causes is identical with the sum of
their separate effects.

This principle, however, by no
means prevails in all departments of
the field of nature. The chemical
combination of two substances pro-
duces, as is well known, a third sub-
stance with properties different from
those of either of the two substances
separately, or of both of them taken
together. Not a trace of the proper-
ties of hydrogen or of oxygen is ob-
servable in those of their compound,
water. The taste of sugar of lead is
not the sum of the tastes of its com-
ponent elements, acetic acid and lead
or its oxide ; nor is the colour of blue
vitriol a mixture of the colours of sul-
phuric acid and copper. This ex-
plains why mechanics is a deductive
or demonstrative science, and chemis-
try not. In the one, we can com-
pute the effects of combinations of
causes, whether real or h3rpothetical,
from the laws which we know to
govern those causes when acting sepa-

rately, because they continue to ob-
serve the same laws when in combina-
tion which they observed when sepa-
rate : whatever would have happened
in consequence of each cause taken by
itself, happens when they are together,
and we have only to cast up the
results. Not so in the phenomena
which are the peculiar subject of the
science of chemistry. There, most of
the uniformities to which the causes
conformed when separate cease alto-
gether when they are conjoined ; and
we are not, at least in the present
state of our knowledge, able to fore-
see what result will follow from any
new combination, until we have tried
the specific experiment.

If this be true of chemical com-
binations, it is still more true of those
far more complex combinations of
elements which constitute organised
bodies, and in which those extra-
ordinary new uniformities arise which
are called the laws of life. All orga-
nised bodies are composed of parts
similar to those composing inorganic
nature, and which have even them-
selves existed in an inorganic state ;
but the phenomena of life which
result from the juxtaposition of those
parts in a certain manner bear no
analogy to any of the effects which
would be produced by the action of
the component substances considered
as mere physical agents. To whatever
degree we might imagine our know-
ledge of the properties of the several
ingredients of a living body to be
extended and perfected, it is certain
that no mere summing up of the
separate actions of those elements will
ever amount to the action of the living
body itself. The tongue, for instance,
is, like all other parts of the animal
frame, composed of gelatine, fibrin,
and other products of the chemistry
of digestion, but from no knowledge
of the properties of those substances
could we ever predict that it could
taste, unless gelatine or fibrin could
themselves taste ; for no elementary
fact can be in the conclusion which
was not in the premises.

244

INDUCTION.

There are thus two different modes
of the conjunct action of causes, from
which arise two modes of conflict, or
mutual interference, between laws of
nature. Suppose, at a given point of
time and space, two or more causes,
which, if they acted separately, would
produce effects contrary, or at least
conflicting with each other, one of
them tending to undo, wholly or
partially, what the other tends to do.
Thus, the expansive force of the gases
generated by the ignition of gun-
powder tends to project a bullet
towards the sky, while its gravity
tends to make it fall to the ground.
A stream running into a reservoir at
one end tends to fill it higher and
higher, while a drain at the other
extremity tends to empty it. Now,
in such cases as these, even if the
two causes which are in joint action
exactly annul one another, still the
laws of both are fulfilled : the effect
is the same as if the drain had been
open for half an hour first,* and the
stream had flowed in for as long
afterwards. Each agent produced
the same amotmt of effect as if it had
acted separately, though the contrary
effect which was taking place during
the same time obliterated it as fast
as it was produced. Here then are
two causes, producing by their joint
operation an effect which at first
seems quite dissimilar to those which
they produce separately, but which on
examination proves to be really the
sum of those separate effects. It will
be noticed that we here enlarge the
idea of the sum of two effects, so as
to include what is commonly called
their difference, but which is in reality
the result of the addition of opposites ;
a conception to which mankind are
indebted for that admirable extension

* I omit, for simplicity," to take into
account the effect iu this latter case of the
diminution of pressure, in diminishing the
flow of water through the drain ; which
evidently in no way affects the truth or
applicabiUty of the principle, since when
the two causes act simultaneously the con-
ditions of that diminution of pressure do
Mot arise.

of the algebraical calculus which has
so vastly increased its powers as an
instrument of discovery, by introduc-
ing into its reasonings (with the sign
of subtraction prefixed, and under the
name of Negative Quantities) every
description whatever of positive phe-
nomena, provided they are of such a
quality in reference to those previ-
ously introduced, that to add the one
is equivalent to subtracting an equal
quantity of the other.

There is, then, one mode of the
mutual interference of laws of nature,
in which, even when the concurrent
causes annihilate each other's effects,
each exerts its full efficacy according
to its own law — its law as a separate
agent. But in the other description
of cases, the agencies which are
brought together cease entirely, and
a totally different set of phenomena
arise : as in the experiment of two
liquids which, when mixed in certain
proportions, instantly become, not a
larger amount of liquid, but a solid

§ 2. This difference between the
case in which the joint effect of causes
is the sum of their separate effects,
and the case in which it is hetero-
geneous to them ; between laws which
work together without alteration, and
laws which, when called upon to work
together, cease and give place to
others ; is one of the fundamental
distinctions in nature. The former
case, that of the Composition of
Causes, is the general one ; the other
is always special and exceptional.
There are no objects which do not, as
to some of their phenomena, obey the
principle of the Composition of Causes;
none that have not some laws which
are rigidly fulfilled in every combina-
tion into which the objects enter.
The weight of a body, for instance,
is a property which it retains in all
the combinations in which it is placed.
The weight of a chemical compound,
or of an organised body, is equal to
the sum of the weights of the ele-
ments which compose it. The weight

COMPOSITION OF CAUSES.

245

either of the elements or of the com-
pound will vary, if they be carried
farther from their centre of attraction,
or brought nearer to it ; but whatever
affects the one affects the other. They
always remain precisely equal. So
again, the component parts of a
vegetable or animal substance do not
lose their mechanical and chemical
properties as separate agents, when,
by a peculiar mode of juxtaposition,
they, as an aggregate whole, acquire
physiological or vital properties in
addition. Those bodies continue, as
before, to obey mechanical and chemi-
cal laws, in so far as the operation of
those laws is not counteracted by the
new laws which govern them as
organised beings. When, in short, a
concurrence of causes takes place
which calls into action new laws
bearing no analogy to any that we
can trace in the separate operation of
the causes, the new laws, while they
supersede one portion of the previous
laws, may co-exist with another por-
tion, and may even compound the effect
of those previous laws with their own.
Again, laws which were themselves
generated in the second mode, may
generate others in the first. Though
there are laws which, like those of
chemistry and physiology, owe their
existence to a breach of the principle
of Composition of Causes, it does not
follow that these peculiar, or, as they
might be termed, hcteropathic laws,
are not capable of composition with
one another. The causes which by
one combination have had their laws
altered, may carry their new laws
with them unaltered into their ulterior
combinations. And hence there is no
reason to despair of ultimately raising
chemistry and physiology to the con-
dition of deductive sciences ; for though
it is impossible to deduce all chemical
and physiological truths from the laws
or properties of simple substances or
elementary agents, they may possibly
be deducible from laws which com-
mence when these elementary agents
are brought together into some mode-
rate number of not very complex com-

binations. The Laws of Life will
never be deducible from the mere
laws of the ingredients, but the pro-
digiously complex Facts of Life may
all be deducible from comparatively
simple laws of life ; which laws (de-
pending indeed on combinations, but on
comparatively simple combinations, of
antecedents) may, in more complex cir-
cumstances, be strictly compounded
with one another, and with the physical
and chemical laws of the ingredients.
Thedetailsof the vital phenomena, even
now, afford innumerable exemplifica-
tions of the Composition of Causes ; and
in proportion as these phenomena are
more accurately studied, there appears
more reason to believe that the same
laws which operate in the simpler
combinations of circumstances, do, in
fact, continue to be observed in the
more complex. This will be found
equally true in the phenomena of
mind ; and even in social and political
phenomena, the results of the laws of
mind. It is in the case of chemical
phenomena that the least progress
has yet been made in bringing the
special laws under general ones from
which they may be deduced ; but
there are even in chemistry many
circumstances to encourage the hope
that such general laws will hereafter
be discovered. The different actions
of a chemical compound will never,
undoubtedly, be found to be the sums
of the actions of its separate elements ;
but there may exist, between the pro-
perties of the compound and those of
its elements, some constant relation,
which, if discoverable by a sufficient
induction, would enable us to foresee
the sort of compound which will result
from a new combination before we
have actually tried it, and to judge of
what sort of elements some new sub-
stance is compounded before we have
analysed it. The law of definite pro-
portions, first discovered in its full
generality by Dalton, is a complete
solution of this problem in one, though
but a secondary aspect, that of quan-
tity: and in respect to quality, we
have already aome partial generalisa-

246

INDUCTION.

tions, sufficient to Indicate the possi-
bility of ultimately proceeding farther.
We can predicate some common proper-
ties of the kind of compounds which re-
sult from the combination in each of the
small numberof possible proportions, of
any acid whatever with any base. We
have also the curious law, discovered
by Berthollet, that two soluble salts
mutually decompose one another when-
ever the new combinations which re-
sult produce an insoluble compound,
or one less soluble than the two for-
mer. Another uniformity is that
called the law of isomorphism ; the
identity of the crystalline forms of
substances which possess in common
certain peculiarities of chemical com-
position.* Thus it appears that even
heteropathic laws, such laws of com-
bined agency as are not compounded
of the laws of the separate agencies,
are yet, at least in some cases, derived
from them according to a fixed prin-
ciple. There may, therefore, be laws
of the generation of laws from others
dissimilar to them ; and in chemistry,
these undiscovered laws of the depend-
ence of the properties of the compound
on the properties of its elements, may,
together with the laws of the elements
themselves, furnish the premises b}'
which the science is perhaps destined
one day to be rendered deductive.

It would seem, therefore, that there
is no class of phenomena in which
the Composition of Causes does not
obtain: that, as a general rule, causes in
combination produce exactly the same
effects as when acting singly ; but
that this rule, though general, is not
universal : that in some instances, at
some particular points in the transi-
tion from separate to united action,
the laws change, and an entirely new
set of effects are either added to, or

* Professor Bain adds several other well-
established chemical generalisations : " The
laws that simple substances exhibit the
strongest affinities ; that compounds are
more fusible than their elements ; that
combination tends to a lower state of mat-
ter from gas down to solid ; " and aome
general propositions concerning the cir-
cumstances which facilitate or resist che-
mical combination {Logic, ii. 254).

take the place of, those which arise
from the separate agency of the same
causes : the laws of these new effects
being again susceptible of composi-
tion to an indefinite extent, like the
laws which they superseded.

§ 3. That effects are proportional
to their causes is laid down by some
writers as an axiom in the theory of
causation ; and great use is sometimes
made of this principle in reasonings
respecting the laws of nature, though
it is encumbered with many diffi-
culties and apparent exceptions, which
much ingenuity has been expended in
showing not to be real ones. This
proposition, in so far as it is true,
enters as a particular case into the
general principle of the Composition
of Causes ; the causes compounded
being, in this instance, homogeneous;
in which case, if in any, their joint
effect might be expected to be identi-
cal with the sum of their separate
effects. If a force equal to one
hundredweight will raise a certain
body along an inclined plane, a force
equal to two hundredweight will raise
two bodies exactly similar, and thus
the effect is proportional to the cause.
But does not a force equal to two
hundredweight actually contain in
itself two forces each equal to one
hundredweight, which, if employed
apart, would separately raise the two
bodies in question ? The fact, there-
fore, that when exerted jointly they
raise both bodies at once, results from
the Composition of Causes, and is a
mere instance of the general fact that
mechanical forces are subject to the
law of Composition. And so in every
other case which can be supposed.
For the doctrine of the proportionality
of effects to their causes cannot of
course be applicable to cases in which
the augmentation of the cause alters
the kind of effect ; that is, in which
the surplus quantity superadded to the
cause does not become compounded
with it, but the two together generate
an altogether new phenomenon. Sup-
pose that the application of a certain

OBSERVATION AKd EXPERIMENT.

Ml

fc|Uantity of heat to a body merely in-
creases its bulk, that a double quantity
melts it, and a triple quantity decom-
poses it : these three eflFects being
heterogeneous, no ratio, whether cor-
responding or not to that of the
quantities of heat applied, can be
established between them. Thus the
supposed axiom of the proportionality
of effects to their causes fails at the
precise point where the principle of
the Composition of Causes also fails,
viz. where the concurrence of causes
is such as to determine a change in
the properties of the body generally,
and render it subject to new laws,
more or less dissimilar to those to
which it conformed in its previous
state. The recognition, therefore, of
any such law of proportionality, is
superseded by the more comprehen-
sive principle, in which as much of it
as is true is implicitly asserted.*

The general remarks on causation,
which seemed necessary as an intro-
duction to the theory of the inductive
process, may here terminate. That
process is essentially an inquiry into
cases of causation. All the uniformi-
ties which exist in the succession of
phenomena, and most of the uni-
formities in their co-existence, are
either, as we have seen, themselves
laws of causation, or consequences

* Professor Rtin (Logic, ii. 39) points out
a class of cases, other tlian that spoken of
in the t«xt, which he thinks raust be re-
g-.irded as an exception to the Composition
of Causes. "Causes that merely make
good the collocation for bringing a prime
mover into action, or that release a poten-
tial force, do not follow any such rule.
One man may direct a gun upon a fort as
well as three : two sjarks are not more
effecttial than one in exploding a barrel of
gunpowder. In medicine there is a certain
dose that answers the end, and adding to
it does no more good."

I am not sure that these cases are really
exceptions. The law of Composition of
Causes, I think, is really fulfilled, and the
appearance to the contrary is poduced by
attending to the remote instead of the im-
mediate effect of the causes. In the cases
mentioned, the immediate effect of the
causes in action is a collocation, and the
duplication of th« cause does double the
quantity of collocation. Two men could
raise the gun to the required angle twice

resulting from, and corollaries cap-
able of being deduced from, such
laws. If we could determine what
causes are correctly assigned to what
effects, and what effects to what
causes, we should be virtually ac-
quainted with the whole course of
nature. All those uniformities which
are mere results of causation might
then be explained and accounted for ;
and every individual fact or event
might be predicted, provided we had
the requisite data, that is, the requisite
knowledge of the circumstances which,
in the particular instance, preceded it.
To ascertain, therefore, what are
the laws of causation which exist in
nature ; to determine the effect of
every cause, and the causes of all
effects, is the main business of In-
duction ; and to point out how this
is done is the chief object of Inductive
Logia

CHAPTER VII.

OF OBSERVATION AND EXPERIMENT.

§ I. It results from the preceding
exposition, that the process of as-
certaining what consequents in na-
ture are invariably connected with
what antecedents, or, in other words,
what phenomena are related to each

as quickly as one, though one is enough.
Two sparks put two sets of particles of
the gunpowder into the state of intes-
tine motion which make them explode,
though one is suflBcient. It is the colloca-
tion itself that does not, by being doubled,
always double the effect ; because in many
cases a certain collocation, once obtained,
is all that is required for the production of
the whole amount of effect which can be
produced at all at the given time and place.
Doubling the collocation with difference of
time and place, as by pointing two guns,
or explodinjj a second barrel after the first,
does double the effect. This remark appliei*
still more to Mr. Bun's third example, that
of a double dose of medicine ; for a double
dose of an aperient does purge more vio-
lently, and a double dose of laudanum does
produce longer and sounder sleep. But a
double purging, or a double amount of
narcotism, may have remote effects dif-
ferent in kind from the effect of the smaller
amo«mt, reducing the case to that of hete-
ropathic laws, discussed in the text.

248

INDUCTION.

other as causes and effects, is in some
sort a process of analysis. That every
fact which begins to exist has a cause,
and that this cause must be found in
some fact or concourse of facts which
immediately preceded the occurrence,
may be taken for certain. The whole
of the present facts are the infallible
result of all past facts, and more im-
mediately of all the facts which ex-
isted at the moment previous. Here,
then, is a great sequence, which we
know to be uniform. If the whole
prior state of the entire universe could
again recur, it would again be fol-
lowed by the present state. The
question is, how to resolve this com-
plex uniformity into the simpler uni-
formities which compose it, and assign
to each portion of the vast antecedent
the portion of the consequent which
is attendant on it.

This operation, which we have called
analytical, inasmuch as it is the resolu-
tion of a complex whole into the com-
ponent elements, is more than a merely
mental analysis. No mere contempla-
tion of the phenomena, and partition
of them by the intellect alone, will of
itself accomplish the end we have now
in view. Nevertheless, such a mental
partition is an indispensable first step.
The order of nature, as perceived at a
first glance, presents at every instant a
chaos followed by another chaos. We
must decompose each chaos into single
facts. We must learn to see in the
chaotic antecedent a multitude of dis-
tinct antecedents, in the chaotic con-
sequent a multitude of distinct conse-
quents. This, supposing it done, will
not of itself tell us on which of the ante-
cedents each consequent is invariably
attendant. To determine that point, we
must endeavour to effect a separation
of the facts from one another, not in
our minds only, but in nature. The
mental analysis, however, must take
place first. And every one knows
that in the mode of performing it,
one intellect differs immensely from
another. It is the essence of the act
of observing, for the observer is not
he who merely sees the thing which

is before his 6yes, but he who sees
what parts that thing is composed of.
To do this well is a rare talent. One
person, from inattention, or attending
only in the wrong place, overlooks
half of what he sees ; another sets
down much more than he sees, con-
founding it with what he imagines,
or with what he infers ; another takes
note of the kind of all the circum-
stances, but being inexpert in estimat-
ing their degree, leaves the quantity
of each vague and uncertaiii ; another
sees indeed the whole, but makes such
an awkward division of it into parts,
throwing things into one mass which
require to be separated, and separat-
ing others which might more con-
veniently be considered as one, that
the result is much the same, some-
times even worse, than if no analysis
had been attempted at all. It would
be possible to point out what qualities
of mind, and modes of mental culture
fit a person for being a good observer :
that, however, is a question not of
Logic, but of the Theory of Educa-
tion, in the most enlarged sense of
the term. There is not properly an
Art of Observing. There may be
rules for observing. But these, like
rules for inventing, are properly in-
structions for the preparation of one's
own mind ; for putting it into the
state in which it will be most fitted
to observe, or most likely to invent.
They are, therefore, essentially rules
of self -education, which is a different
thing from Logic. They do not teach
how to do the thing, but how to make
ourselves capable of doing it. They
are an art of strengthening the limbs,
not an art of using them.

The extent and minuteness of ob-
servation which may be requisite, and
the degree of decomposition to which
it may be necessary to carry the
mental analysis, depend on the par-
ticular purpose in view. To ascer^
tain the state of the whole universe
at any particular moment is impos-
sible, but would also be useless. In
making chemical experiments, we do
not think it necessary to note the

OBSERVATION AND EXPERIMENT.

249

position of the planets ; because ex-
perience has shown, as a very super-
ficial experience is sufficient to show,
that in such cases that circumstance
is not material to the result : and
accordingly, in the ages when men
believed in the occult influences of
the heavenly bodies, it might have
been unphilosophical to omit ascer-
taining the precise condition of those
bodies at the moment of the experi-
ment. As to the degree of minute-
ness of the mental subdivision, if we
were obliged to break down what we
observe into its very simplest elements,
that is, literally into single facts, it
would be difficult to say where we
should find them : we can hardly
ever affirm that our divisions of any
kind have reached the ultimate unit.
But this, too, is fortunately unneces-
sary. The only object of the mental
separation is to suggest the requisite
physical separation, so that we may
either accomplish it ourselves, or seek
for it in nature ; and we have done
enough when we have carried the
subdivision as far as the point at
which we are able to see what obser-
vations or experiments we require.
It is only essential, at whatever point
our mental decomposition of facts may
for the present have stopped, that we
should hold ourselves ready and able
to carry it farther as occasion requires,
and should not allow the freedom of
our discriminating faculty to be im-
prisoned by the swathes and bands of
ordinary classification, as was the case
with all early speculative inquirers,
not excepting the Greeks, to whom it
seldom occurred that what was called
by one abstract name might, in reality,
be several phenomena, or that there
was a possibility of decomposing the
facts of the universe into any ele-
ments but those which ordinary lan-
guage already recognised.

§ 2. The different antecedents and
consequents being, then, supposed to
be, so far as the case requires, ascer-
tained and discriminated from one
another, we are to inquire which is

connected with which. In every in-
stance which comes under our obser-
vation, there are many antecedents
and many consequents. If those
antecedents could not be severed
from one another except in thought,
or if those consequents never were
found apart, it would be impossible
for us to distinguish (d posteriori at
least) the real laws, or to assign to
any cause its effect, or to any effect
its cause. To do so, we must be able
to meet with some of the antecedents
apart from the rest, and observe what
follows from them ; or some of the
consequents, and observe by what they
are preceded. We must, in short, fol-
low the Baconian rule of varying the
circumstances. This is, indeed, only
the first rule of physical inquiry, and
not, as some have thought, the sole rule;
but it is the foundation of all the rest.
For the purpose of varying the cir-
cumstances, we may have recourse
(according to a distinction commonly
made) either to observation or to ex-
periment ; we may either Jind an
instance in nature suited to our pur-
poses, or, by an artificial arrangement
of circumstances, viake one. The
value of the instance depends on
what it is in itself, not on the mode
in which it is obtained : its employ-
ment for the purposes of induction
depends on the same principles in the
one case and in the other, as the
uses of money are the same whether
it is inherited or acquired. There is,
in short, no difference in kind, no
real logical distinction, between the
two processes of investigation. There
are, however, practical distinctions to
which it is of considerable import-
ance to advert.

§ 3. The first and most obvious
distinction between Observation and
Experiment is, that the latter is an
immense extension of the former. It
not only enables us to produce a much
greater number of variations in the
circumstances than nature spontane-
ously offers, but, also, in thousands of
cases, to produce the precise sort of

250

INDUCTION.

variation which we are in want of for
discovering the law of the pheno-
menon, — a service which nature,
being constructed on a quite different
scheme from that of facilitating our
studies, i« seldom so friendly as to
bestow upon us. Yor example, in
order to ascertain what principle in
the atmosphere enables it to sustain
life, the variation we require is that
a living animal should be immersed
in each component element of the
atmosphere separately. But nature
does not supply either oxygen or azote
in a separate state. We are indebted
to artificial experiment for our know-
ledge that it is the former, and not
the latter, which supports respiration;
and for our knowledge of the very
existence of the two ingredients.

Thus far the advantage of experi-
mentation over simple observation is
universally recognised : all are aware
that it enables us to obtain innume-
rable combinations of circumstances
which are not to be found in nature,
and so add to nature's experiments a
multitude of experiments of our own.
But there is another superiority (or,
as Bacon would have expressed it,
another prerogative) of instances arti-
ficially obtained over spontaneous
instances, — of our own experiments
over even the same experiments when
made by nature, — which is not of less
importance, and which is far from
being felt and acknowledged in the
same degree.

When we can produce a pheno-
menon artificially, we can take it, as
it were, home with us, and observe it
in the midst of circumstances with
which in all other respects we are
accurately acquainted. If we desire
to know what are the effects of the
cause A, and are able to produce A
by means at our disposal, we can
generally determine at our own dis-
cretion, so far as is compatible with
the nature of the phenomenon A, the
whole of the circumstances which
shall be present along with it : and
thus, knowing exactly the simulta-
neous state of everything else which

is within the reach of A's influence,
we have only to observe what altera-
tion is made in that state by the pre-
sence of A.

For example, by the electric machine
we can produce, in the midst of known
circumstances, the phenomena which
nature exhibits on a grander scale in
the form of lightning and thunder.
Now let any one consider what amount
of knowledge of the effects and laws
of electric agency mankind could have
obtained from the mere observation
of thunderstorms, and compare it with
that which they have gained, and may
expect to gain, from electrical and
galvanic experiments. This example
is the more striking, now that we
have reason to believe that electric
action is of all natural phenomena
(except heat) the most pervading and
universal, which, therefore, it might
antecedently have been supposed
could stand least in need of artificial
means of production to enable it to
be studied ; while the fact is so much
the contrary, that without the electric
machine, the Leyden jar, and the
voltaic battery, we probably should
never have suspected the existence
of electricity as one of the great
agents in nature : the few electric
phenomena we should have known
of would have continued to be re-
garded either as supernatural, or as
a sort of anomalies and eccentricities
in the order of the universe.

When we have succeeded in insu-
lating the phenomenon which is the
subject of inquiry by placing it
among known circumstances, we may
produce further variations of circum-
stances to any extent, and of such
kinds as we think best calculated to
bring the laws of the phenomenon
into a clear light. By introducing
one well-defined circumstance after
another into the experiment, we ob-
tain assurance of the manner in which
the phenomenon behaves under an
indefinite variety of possible circum-
stances. Thiis, chemists, after having
obtained some newly-discovered sub-
stance in a pure state, (that is,, having

OBSERVATION AND EXPERIMENT.

251

made sure that there is nothing pre-
sent which can interfere with and
modify its agency,) introduce various
other substances, one by one, to ascer-
tain whether it will combine with
them, or decompose them, and with
what result ; and also apply heat, or
electricity, or pressure, to discover
what will happen to the substance
under each of these circumstances.

But if, on the other hand, it is out
of our power to produce the pheno-
menon, and we have to seek for in-
stances in which nature produces it,
the task before us is very different.

Instead of. being able to choose
what the concomitant circumstances
shall be, we now have to discover
what they are, which, when we go
beyond the simplest and most acces-
sible cases, it is next to impossible to
do with any precision and complete-
ness. Let us take, as an exemplifica-
tion of a phenomenon which we have
no means of fabricating artificially,
a human mind. Nature produces
many ; but the consequence of our
not being able to produce them by
art is, that in every instance in which
we see a human mind developing
itself, or acting upon other things, we
see it surrounded and obscured by an
indefinite multitude of unascertain-
able circumstances, rendering the use
of the common experimental methods
almost delusive. We may conceive
to what extent this is true, if we
consider, among other things, that
whenever nature produces a human
mind, she produces, in close connection
with it, a body, that is, a vast com-
plication of physical facts, in no two
cases perhaps exactly similar, and
most of which (except the mere struc-
ture, which we can examine in a sort
of coarse way after it has ceased to
act) are radically out of the reach of
our means of exploration. If, instead
of a human mind, we suppose the sub-
ject of investigation to be a human
society or itate, all the same difficul-
ties recur in a greatly augmented
degree.

We have thus already come within

sight of a conclusion which the pro-
gress of the inquiry will, I think,
bring before us with the clearest evi-
dence, namely, that in the sciences
which deal with phenomena in which
artificial experiments are impossible,
(as in the case of astronomy,) or in
which they have a very limited range,
(as in mental philosophy, social science,
and even physiology,) induction from
direct experience is practised at a dis-
advantage in most cases equivalent to
impracticability : from which it fol-
lows that the methods of those sciences,
in order to accomplish anything wor-
thy of attainment, must be to a great
extent, if not principally, deductive.
This is already known to be the case
with the first of the sciences we have
mentioned, astronomy ; that it is not
generally recognised as true of the
others is probably one of the reasons
why they are not in a more advanced
state.

§ 4. If what is called pure observa-
tion is at so great a disadvantage,
compared with artificial experimenta-
tion, in one department of the direct
exploration of phenomena, there is
another branch in which the advan-
tage is all on the side of the former.

Inductive inquiry having for its ob-
ject to ascertain what causes are con-
nected with what effects, we may begin
this search at either end of the road
which leads from the one point to the
other : we may either inquire into the
effectsofagivencause,orintothecau8es
of a given effect. The fact that light
blackens chloride of silver might have
been discovered either by experiments
on light, trying what effect it would
produce on various substances, or by
observing that portions of the chloride
had repeatedly become black, and in-
quiring into the circumstances. The
effect of the urali poison might have
become known either by administer-
ing it to animals, or by examining
how it ha.ppened that the wounds
which the Indians of Guiana inflict
with their arrows prove so uniformly
mortal. Now it is manifest from the

252

INDtrCTlON.

mere statement of the examples, with-
out any theoretical discussion, that
artificial experimentation is applicable
only to the former of these modes of
investigation. We can take a cause,
and try what it will produce : but we
cannot take an effect, and try what it
will be produced by. We can only
watch till we see it produced, or are
enabled to produce it by accident.

This would be of little importance, if
it always depended on our choice from
which of the two ends of the sequence
we would undertake our inquiries.
But we have seldom any option. As
we can only travel from the known to
the unknown, we are obliged to com-
mence at whichever end we are best
acquainted with. If the agent is
more familiar to us than its effects,
we watch for, or contrive, instances
of the agent, under such varieties of
circumstances as are open to us, and
observe the result. If, on the con-
trary, the conditions on which a
phenomenon depends are obscure, but
the phenomenon itself familiar, we
must commence our inquiry from the
effect. If we are struck with the
fact that chloride of silver has been
blackened, and have no suspicion of
the cause, we have no resource but to
compare instances in which the fact
has chanced to occur, until by that
comparison we discover that in all
those instances the substances had
been exposed to light. If we knew
nothing of the Indian arrows but
their fatal effect, accident alone could
turn our attention to experiments on
the urali ; in the regular course of
investigation, we could only inquire,
or try to observe, what had been done
to the arrows in particular instances.

Wherever, having nothing to guide
us to the cause, we are obliged to set
out from the effect, and to apply the
rule of varying the circumstances to
the consequents, not the antecedents,
we are necessarily destitute of the
resource of artificial experimentation.
We cannot, at our choice, obtain con-
sequents as we can antecedents, under
any set of circumstances compatible

with their nature. There are mo
means of producing effects but through
their causes, and by the sxipposition
the causes of the effect in question
are not known to us. We have,
therefore, no expedient but to study
it where it offers itself spontaneously.
If nature happens to present us with
instances sufficiently varied in their
circumstances, and if we are able to
discover, either among the proximate
antecedents or among some other
order of antecedents, something which
is always found when the effect is
found, however various the circum-
stances, and never found when it is
not ; we may discover, by mere ob-
servation without experiment, a real
uniformity in nature.

But though this is certainly the
most favourable case for sciences of
pure observation, as contrasted with
those in which artificial experiments
are possible, there is in reality no case
which more strikingly illustrates the
inherent imperfection of direct induc-
tion when not founded on experimen-
tation. Suppose that, by a comparison
of cases of the effect, we have found
an antecedent which appears to be,
and perhaps is, invariably connected
with it : we have not yet proved that
antecedent to be the cause until we
have reversed the process and pro-
duced the effect by means of that
antecedent. If we can produce the
antecedent artificially, and if, when
we do so, the effect follows, the in-
duction is complete ; that antecedent
is the cause of that consequent.*
But we have then added the evidence
of experiment to that of simple obser-
vation. Until we have done so, we
had only proved invariable antece-
dence within the limits of experience,
but not unconditional antecedence or
causation. Until it had been shown

* Unless, indeed, the consequent was
generated, not by the antecedent, but by
the means employed to produce the ante-
cedent. As, however, these means are
under our power, there is so far a proba-
bility that they are also stiflBciently with-
in our knowledge to enable us to judge
whether that could be the case or not.

THE FOUR EXPERIMENTAL METHODS.

253

by the actual production of the ante-
cedent under known circumstances,
and the occurrence thereupon of the
consequent, that the antecedent was
really the condition on which it de-
pended ; the uniformity of succession
which was proved to exist between
them might, for aught we knew, be
(like the succession of day and night)
not a case of causation at all ; both
antecedent and consequent might be
successive stages of the effect of an
ulterior cause. Observation, in short,
without experiment (supposing no aid
from deduction) can ascertain se-
quences and co-existences, but cannot
prove causation.

In order to see these remarks veri-
fied by the actual state of the sciences,
we have only to think of the condition
of natural history. In zoology, for
example, there is an immense number
of uniformities ascertained, some of
co-existence, others of succession, to
many of which, notwithstanding con-
siderable variations of the attendant
circumstances, we know not any ex-
ception ; but the antecedents, for the
most part, are such as we caimot arti-
ficially produce ; or if we can, it is
only by setting in motion the exact
process by which nature produces
them ; and this being to us a myste-
rious process, of which the main cir-
cumstances are not only unknown but
unobservable, we do not succeed in ob-
taining the antecedents under known
circumstances. What is the result?
That on this vast subject, which
affords so much and such varied scope
for observation, we have made most
scanty progress in ascertaining any
laws of causation. We know not with
certainty, in the case of most of the
phenomena that we find conjoined,
which is the condition of the other ;
which is cause, and which effect, or
whether either of them is so, or they
are not rather conjunct effects of
causes yet to be discovered, complex
results of laws hitherto unknown.

Although some of the foregoing
observations may be, in technical
•trictness of arrangement, premature

in this place, it seemed that a few
general remarks on the difference
between sciences of mere observation
and sciences of experimentation, and
the extreme disadvantage under which
directly inductive inquiry is neces-
sarily carried on in the former, were
the best preparation for discussing
the methods of direct induction ; a
preparation rendering superfluous
much that must otherwise have been
introduced, with some inconvenience,
into the heart of that discussion. To
the consideration of these methods we
now proceed.

CHAPTER VIII.

OP THE FOUR METHODS OP EXPERI-
MENTAL INQUIRY.

§ I, The simplest and most obvious
modes of singling out from among the
circumstances which precede or follow
a phenomenon those with which it is
really connected by an invariable law
are two in number. One is, by com-
paring together different instances in
which the phenomenon occurs. The
other is, by comparing instances in
which the phenomenon does occur,
with instances in other respects simi-
lar in which it does not. These two
methods may be respectively denomi-
nated the Method of Agreement and
the Method of Difference.

In illustrating these methods, it
will be necessary to bear in mind the
twofold character of inquiries into the
laws of phenomena, which may be
either inquiries into the cause of a
given effect, or into the effects or pro-
perties of a given cause. We shall
consider the methods in their applica-
tion to either order of investigation,
and shall draw our examples equally
from both.

We shall denote antecedents by the
large letters of the alphabet, and the
consequents corresponding to them by
the small. Let A, then, be an agent
or cause, and let the object of our in-
quiry be to ascertain what arc the

254

INDUCTION.

effects of this cause. If we can either
find or produce the agent A in such
varieties of circumstances that the
different cases have no circumstance
in common except A, then whatever
effect we find to be produced in all
our trials is indicated as the effect of
A. Suppose, for example, that A is
tried along with B and C, and that
the effect is a 6 c ; and suppose that
A is next tried with D and E, but
without B and C, and that the effect
is a d e. Then we may reason thus :
b and c are not effects of A, for they
were not produced by it in the second
experiment ; nor are d and e, for they
were not produced in the first. What-
ever is really the effect of A must have
been produced in both instances ; now
this condition is fulfilled by no cir-
cumstance except a. The phenomenon
a cannot have been the effect of B or
C, since it was produced where they
were not ; nor of D or E, since it
was produced where they were not.
Therefore it is the effect of A.

For example, let the antecedent A
be the contact of an alkaline sub-
stance and an oil. This combination
being tried under several varieties of
circumstances, resembling each other
in nothing else, the results agree in
the production of a greasy and deter-
sive or sapmaceous substance: it. is
therefore concluded that the combina-
tion of an oil and an alkali causes the
production of a soap. It is thus we
inquire, by the Method of Agreement,
into the effect of a given cause.

In a similar manner we may in-
quire into the cause of a given effect.
Let a be the effect. Here, as shown
in the last chapter, we have only the
resource of observation without ex-
periment : we cannot take a pheno-
menon of which we know not the
origin, and try to find its mode of
production by producing it : if we
succeeded in such a random trial it
could only be by accident. But if
■we can observe a in two different
combinations, ab c and a d e ; and if
we know, or can discover, that the
antecedent circumstances in these

cases respectively were ABC and A
D E, we may conclude by a reason-
ing similar to that in the preceding
example, that A is the antecedent
connected with the consequent a by
a law of causation. B and C, we
may say, cannot be causes of a, since
on its second occurrence they were
not present ; nor are D and E, for
they were not present on its first
occurrence. A, alone of the five cir-
cumstances, was found among the
antecedents of a in both instances.

For example, let the effect a be
crystallisation. We compare instances
in which bodies are known to assume
crystalline structure, but which have
no other point of agreement ; and we
find them to have one, and, as far as
we can observe, only one, antecedent
in common : the deposition of a solid
matter from a liquid state, either a
state of fusion or of solution. We con-
clude, therefore, that the solidifica-
tion of a substance from a liquid
state is an invariable antecedent of
its crystallisation.

In this example we may go farther,
and say, it is not only the invariable
antecedent, but the cause, or at least
the proximate event which completes
the cause. For in this case we are
able, after detecting the antecedent
A, to produce it artificially, and by
finding that a follows it, verify the
result of our induction. The import-
ance of thus reversing the proof was
strikingly manifested when by keep-
ing a phial of water charged with
siliceous particles undisturbed for
years, a chemist (I believe Dr. Wol-
laston) succeeded in obtaining crystals
of quartz ; and in the equally interest-
ing experiment in which Sir James
Hall produced artificial marble by the
cooling of its materials from fusion
under immense pressure ; two admir-
able examples of the light which may
be thrown upon the most secret pro-
cesses of Nature by well-contrived
interrogation of her.

But if we cannot artificially pro-
duce the phenomenon A, the conclu-
Bion that it is the cause of a remains

THE FOUR EXPERIMENTAL METHODS.

255

subject to very considerable doubt.
Though an invariable, it may not be
the unconditional antecedent of a,
but may precede it as day precedes
night or night day. This uncertainty
arises from the impossibility of assur-
ing ourselves that A is the only imme-
diate antecedent common to both the
instances. If we could be certain of
having ascertained all the invariable
antecedents, we might be sure that
the unconditional invariable ante-
cedent or cause must be found some-
where among them. Unfortunately
it is hardly ever possible to ascertain
all the antecedents, unless the pheno-
menon is one which we can produce
artificially. Even then, the difficulty
is merely lightened, not removed :
men knew how to raise water in
pumps long before they adverted to
what was really the operating cir-
cumstance in the means they em-
ployed, namely, the pressure of the
atmosphere on the open surface of
the water. It is, however, much
easier to analyse completely a set
of arrangements matle by ourselves,
than the whole complex mass of the
agencies which nature happens to be
exerting at the moment of the pro-
duction of a given phenomenon. We
may overlook some of the material
circumstances in an experiment with
an electrical machine ; but we shall,
at the worst, be better acquainted
with them than with those of a
thunderstorm.

The mode of discovering and prov-
ing laws of nature, which we have
now examined, proceeds on the follow-
ing axiom. Whatever circumstances
can be excluded, without prejudice to
the phenomenon, or can be absent
notwithstanding its presence, is not
connected with it in the way of causa-
tion. The casual circumstance being
thus eliminated, if only one remains,
that one is the cause which we are
in search of : if more than oiie, they
either are, or contain among them,
the cause ; and so, mutatis mutandis,
of the effect. As this method pro-
ceeds by comparing different instances

to ascertain in what they agree, I have
termed it the Method of Agreement ;
and we may adopt as its regulating
principle the following canon : —

First Canon.

If two or more instances of the phe-
nomenon under investigation have only
one circumstance in common,the circum-
stance in which alone all the instances
agree is the cause {or effect) of the given
phenomenon.

Quitting for the present the Method
of Agreement, to which we shall
almost immediately return, we pro-^
ceed to a still more potent instrument
of the investigation of nature, the
Method of Difference.

§ 2. In the Method of Agreement,
we endeavoured to obtain instances
which agreed in the given circum-
stance but differed in every other : in
the present method we require, on the
contrary, two instances resembling
one another in every other respect,
but differing in the presence or
absence of the phenomenon we wish
to study. If our object be to discover
the effects of an agent A, we must
prcxsure A in some set of ascertained
circumstances, as A B C, and having
noted the effects produced, compare
them with the effect of the remaining
circumstances B C, when A is absent
If the effect of A B C is a 6 c, and the
effect of B C, 6 c, it is evident that the
effect of A is a. So again, if we be-
gin at the other end, and desire to
investigate the cause of an effect a,
we must select an instance, as a 6 c, in
which the effect occurs, and in which
the antecedents were ABC, and we
must look out for another instance in
which the remaining circumstances,
h c, occur without a. If the antece-
dents, in that instance, are B C, we
know that the cause of a must be A :
either A alone, or A in conjunction
with some of the other circumstances
present.

It is scarcely necessary to give ex-
amples of a logical process to which
we owe almost all the inductive con-

2$6

INDUCTION.

elusions we draw in early life. When
a man is shot through the heart, it is
by this method we know that it was
the gunshot which killed him : for he
was in the fulness of life immediately
before, all circumstances being the
same, except the wound.

The axioms implied in this method
are evidently the following. What-
ever antecedent cannot be excluded
without preventing the phenomenon,
is the cause, or a condition of that
phenomenon : Whatever consequent
can be excluded, with no other dif-
ference in the antecedents than the
absence of a particular one, is the
effect of that one. Instead of com-
paring different instances of a phe-
nomenon, to discover in what they
agree, this method compares an in-
stance of its occurrence with an
instance of its non-occurrence, to dis-
cover in what they differ. The canon
which is the regulating principle of
the Method of Difference may be ex-
pressed as follows : —

Second Canon.
If an instance in which the phe-
nomenon under investigation occurs,
and an instance in which it does not
occur, have every circumstance in com-
mon save one, that one occurring only
in the former; the circumstance in
which alone the two instances differ is
the effect, or the cause, or an indis-
pensable part of the cause, of the phe-
nomenon.

§ 3. The two methods which we
have now stated have many features
of resemblance, but there are also
many distinctions between them.
Both are methods of elimination. Thi^
term (employed in the theory of equa-
tions to denote the process by which
one after another of the elements
of a question is excluded, and the
solution made to depend on the re-
lation between the remaining ele-
ments only) is well suited to express
the operation, analogous to this,
which has been understood since the
time of Bacon to be the foundation of

experimental inquiry, namely, the
successive exclusion of the various
circumstances which are found to ac-
company a phenomenon in a given
instance, in order to ascertain what
are those among them which can be
absent consistently with the existence
of the phenomenon. The Method of
Agreement stands on the ground that
whatever can be eliminated is not
connected with the phenomenon by
any law. The Method of Difference
has for its foundation, that whatever
cannot be eliminated is connected
with the phenomenon by a law.

Of these methods, that of Differ-
ence is more particularly a method of
artificial experiment ; while that of
Agreement is more especially the re-
source employed where experimenta-
tion is impossible. A few reflections
will prove the fact, and point out the
reason of it.

It is inherent in the peculiar char-
acter of the Method of Difference
that the nature of the combinations
which it requires is much more strictly
defined than in the Method of Agree-
ment. The two instances which are
to be compared with one another
must be exactly similar in all circum-
stances except the one which we are
attempting to investigate : they must
be in the relation of A B C and B C,or
oi a b c and b c. It is true that this
similarity of circumstances needs not
extend to such as are already known
to be immaterial to the result. And
in the case of most phenomena we
learn at once, from the commonest
experience, that most of the co-existent
phenomena of the universe may be
either present or absent without affect-
ing the given phenomenon ; or, if pre-
sent, are present indifferently when
the phenomenon does not happen and
when it does. Still, even limiting the
identity which is required between
the two instances, ABC and B C, to
such circumstances as are not already
known to be indifferent ; it is very
seldom that nature affords two in-
stances, of which we can be assured
that they stand in this precise rela-

11

THE FOUR EXPERIMENTAL METHODS.

257

tion to one another. In the spon-
taneous operations of nature there is
generally such complication and such
obscurity, they are mostly either on
so overwhelmingly large or on so in-
accessibly minute a scale, we are liO
ignorant of a great part of the facts
which really take place, and even
those of which we are not ignorant
are so multitudinous, and therefore so
seldom exactly alike in any two cases,
that a spontaneous experiment, of the
kind required by the Method of Dif-
ference, is commonly not to be found.
When, on the contrary, we obtain a
phenomenon by an artificial experi-
ment, a pair of instances such as the
method requires is obtained almost as
a matter of course, provided the pro-
cess does not last a long time. A
certain state of surrounding circum-
stances existed before we commenced
the experiment ; this is B C. We
then introduce A ; say, for instance,
by merely bringing an object from
another part of the room, before there
has been time for any change in the
other elements. It is, in short,J(as M.
Comte observes,) the very nature of
an experiment to introduce into the
pre-existing state of circumstances a
change perfectly definite. We choose
a previous state of things with which
we are well acquainted, so that no
unforeseen alteration in that state is
likely to pass unobserved ; and into
this we introduce, as rapidly as pos-
sible, the phenomenon which we wish
to study ; so that in general we are
entitled to feel complete assurance
that the pre-existing state, and the
state which we have produced, differ
in nothing except the presence or ab-
sence of that phenomenon. If a bird
is taken from a cage, and instantly
plunged into carbonic acid gas, the
experimentalist may be fully assured
(at all events after one or two repeti-
tions) that no circumstance capable of
causing suffocation had supervened
in the interim, except the change
from immersion in the atmosphere to
immersion in carbonic acid gas. There
js one doubt, indeed, which may re-

main in some cases of this descrip-
tion ; the effect may have been pro-
duced not by the change, but by the
means employed to produce the
change. The possibility, however, of
this last supposition generally admits
of being conclusively tested by other
experiments. It thus appears that in
the study of the various kinds of
phenomena which we can, by our
voluntary agency, modify or control,
we can in general satisfy the requisi-
tions of the Method of Difference ;
but that by the spontaneous opera-
tions of nature those requisitions are
seldom fulfilled.

The reverse of this is the case with
the Method of Agreement. We do
not here require instances of so special
and determinate a kind. Any in-
stances whatever, in which nature
presents us with a phenomenon, may
be examined for the purposes of this
method ; and if all such instances
agree in anything, a conclusion of
considerable value is already attained.
We can seldom, indeed, be sure that
the one point of agreement is the only
one ; but this ignorance does not, as
in the Method of Difference, vitiate
the conclusion ; the certainty of the
rtisult, as far as it goes, is not affected.
We have ascertained one invariable
antecedent or consequent, however
many other invariable antecedents or
consequents may still remain unascer-
tained. If A B C, A D E, A F G,
are all equally followed by a, then a
is an invariable consequent of A. If
abc,ad€, afg, all number A among
their antecedents, then A is connected
as an antecedent, by some invariable
law, with a. But to determine whe-
ther this invariable antecedent is a
cause, or this invariable conseqtient
an effect, we must be able, in addition,
to produce the one by means of the
other ; or, at least, to obtain that
which alone constitutes our assurance
of having produced anything, namely,
an instance in which the effect, a, has
come into existence, with no other
change in the pre-existing circum-
stances than the addition of A. And

258

INDUCTION.

this, if we can do it, is an application
of the Method of Difference, not of
the Method of Agreement.

It thus appears to be by the Method
of Difference alone that we can ever,
in the way of direct experience, arrive
with certainty at causes. The Method
of Agreement leads only to laws of
phenomena, (as some writers call them,
but improperly, since laws of causation
are also laws of phenomena,) that is,
to uniformities, which either are not
laws of causation, or in which the
question of causation must for the
present remain undecided. The
Method of Agreement is chiefly to
be resorted to as a means of suggest-
ing applications of the Method of
Difference, (as in the last example the
comparison of A B C, A D E, A F G,
suggested that A was the antecedent
on which to try the experiment
whether it could produce a,) or as
an inferior resource in case the
Method of Difference is impracti-
cable ; which, as we before showed,
generally arises from the impossibility
of artificially producing the pheno-
mena. And hence it is that the
Method of Agreement, though appli-
cable in principle to either case, is
more emphatically the method o£
investigation on those subjects where
artificial experimentation is impos-
sible ; because on those it is generally
our only resource of a directly induc-
tive nature ; while, in the phenomena
which we can produce at pleasure,
the Method of Difference generally
affords a more efl&cacious process,
which will ascertain causes as well as
mere laws.

§ 4. There are, however, many
cases in which, though our power of
producing the phenomenon is com-
plete, the Method of Difference either
cannot be made available at all, or
not without a previous employment
of the Method of Agreement. This
occurs when the agency by which we
can produce the phenomenon is not
that of one single antecedent, but a
combination of antecedents, which we

have no power of separating from
each other and exhibiting apart. For
instance, suppose the subject of in-
quiry to be the cause of the double
refraction of light. "We can produce
this phenomenon at pleasure by em-
ploying any one of the many sub-
stances which are known to refract
light in that peculiar manner. But
if, taking one of those substances, as
Iceland spar, for example, we wish to
determine on which of the properties
of Iceland spar this remarkable phe-
nomenon depends, we can make no
use for that purpose of the Method
of Difference ; for we cannot find
another substance precisely resem-
bling Iceland spar except in some
one property. The only mode, there-
fore, of prosecuting this inquiry is
that afforded by the Method of Agree-
ment; by which, in fact, through a
comparison of all the known sub-
stances which have the property of
doubly refracting light, it was ascer-
tained that they agree in the circum-
stance of being crystalline substances ;
and though the converse does not hold,
though all crystalline substances have
not the property of double refraction,
it was concluded, with reason, that
there is a real connection between
these two properties ; that either
crystalline structure, or the cause
which gives rise to that structure,
is one of the conditions of double
refraction.

Out of this employment of the
Method of Agreement arises a pecu-
liar modification of that method, which
is sometimes of great avail in the
investigation of nature. In cases
similar to the above, in which it is
not possible to obtain the precise pair
of instances which our second canon
requires — instances agreeing in every
antecedent except A, or in every con-
sequent except a — we may yet be able,
by a double employment of the Me-
thod of Agreement, to discover in
what the instances which contain A
or a differ from those which do not.

If we compare various instances in
which a occurs, and find that they

THE FOUR EXPERIMENTAL METHODS.

259

all have in common the circumstance
A, and (as far as can be observed) no
other circumstance, the Method of
Agreement, so far, bears testimony
to a connection between A and a.
In order to convert this evidence of
connection into proof of causation by
the direct Method of Difference, we
ought to be able, in some one of these
instances, as, for example, A B C, to
leave out A, and observe whether by
doing so a is prevented. Now suj)-
posing (what is often the case) that
we are not able to try this decisive
experiment, yet, provided we can by
any means discover what would be
its result if we could try it, the ad-
vantage will be the same. Suppose,
then, that as we previously examined
a variety of instances in which a oc-
curred, and found them to agree in
containing A, so we now observe a
variety of instances in which a does
not occur, and find them agree in not
containing A ; which establishes, by
the Method of Agreement, the same
connection between the absence of A
and the absence of a, which was before
established between their presence.
As, then, it had been shown that
whenever A is present a is present,
so it being now shown that when A
is taken away a is removed along
with it, we have by the one proposi-
tion A B C, a 6 c, by the other B C,
b c, the positive and negative in-
stances which the Method of Differ-
ence requires.

This method may be called the
Indirect Method of Difference, or
the Joint Method of Agreement and
Difference, and consists in a double
employment of the Method of Agree-
ment, each proof being independent
of the other, and corroborating it.
But it is not equivalent to a pioof by
the direct Method of Difference. For
the requisitions of the Method of Dif-
ference are not satisfied unless we
can be quite sure either that the in-
stances affirmative of a agree in no
antecedent whatever but A, or that
the instances negative of a agree in
potbing but the nefication of A, Now

if it were possible, which it never is,
to have this assurance, we should not
need the joint method ; for either of
the two sets of instances separately
would then be sufficient to prove
causation. This indirect method,
therefore, can only be regarded as a
great extension and improvement of
the Method of Agreement, but not
as participating in the more cogent
nature of the Method of Difference.
The following may be stated as its
canon : —

Third Canon.
If two or more instances in which
the phenomenon occurs have only one
circumstance in common, while two or
more instances in which it does not
occur have nothing in common save the
absence of that circumstance, the cir-
cumstance in which alone the two sets
of instances differ is the effect, or the
cause, or an indispensable part of the
cause, of the phenomenon.

We shall presently see that the Joint
Method of Agreement and Difference
constitutes, in another respect not yet
adverted to, an improvement upon
the common Method of Agreement,
namely, in being unaffected by a
characteristic imperfection of that
method, the nature of which still
remains to be pointed out. But as
we cannot enter into this exposition
without introducing a new element
of complexity into this long and in-
tricate discussion, I shall postpone it
to a subsequent chapter, and shall at
once proceed to a statement of two
other methods, which will complete
the enumeration of the means which
mankind possess for exploring the laws
of nature by specific observation and
experience.

§ 5. The first of these has been
aptly denominated the Method of Re-
sidues. Its principle is very simple.
Subducting from any given pheno-
menon all the portions which, by
virtue of preceding inductions, can
be assigned to known causes, the re-
maii^der will be the effect of the

26o

INDUCTION.

antecedents which had been over-
looked, or of which the effect was as
yet an unknown quantity.

Suppose, as before, that we have
the antecedents ABC, followed by
the consequents a b c, and that by
previous inductions (founded, we will
suppose, on the Method of Difference)
we have ascertained the causes of some
of these effects, or the effects of some
of these causes ; and are thence ap-
prised that the effect of A is a, and
that the effect of B is b. Subtracting
the sum of these effects from the total
phenomenon, there remains c, which
now, without any fresh experiments,
we may know to be the effect of C.
This Method of Residues is in truth
a peculiar modification of the Method
of Difference. If the instance ABC,
ab c, could have been compared with
a single instance A B, a b, we should
have proved C to be the cause of c,
by the common process of the Method
of Difference. In the present case,
however, instead of a single instance
A B, we have had to study separately
the causes A and B, and to infer from
the effects which they produce separ-
ately what effect they must produce
in the case ABC where they act to-
gether. Of the two instances, there-
fore, which the Method of Difference
requires, — the one positive, the other
negative, — the negative one, or that
in which the given phenomenon is
absent, is not the direct result of
observation and experiment, but has
been arrived at by deduction. As
one of the forms of the Method of
Difference, the Method of Residues
partakes of its rigorous certainty, pro-
vided the previous inductions, those
which gave the effects of A and B,
were obtained by the same infallible
method, and provided we are certain
that C is the only antecedent to which
the residual phenomenon c can be re-
ferred ; the only agent of which we
had not already calculated and sub-
ducted the effect. But as we can
never be quite certain of this, the
evidence derived from the Method of
Residues is not complete unless we

can obtain C artificially and try it sepal
rately, or unless its agency, when once
suggested, can be accounted for, and
proved deductively, from known laws.
Even with these reservations, the
Method of Residues is one of the most
important among our instruments of
discovery. Of all the methods of in-
vestigating laws of nature, this is the
most fertile in unexpected result* :
often informing us of sequences in
which neither the cause nor the effect
were sufficiently conspicuous to at-
tract of themselves the attention of
observers. The agent C may be an
obscure circumstance, not likely to
have been perceived unless sought
for, nor likely to have been sought
for until attention had been awakened
by the insufficiency of the obvious
causes to account for the whole of
the effect. And c may be so dis-
guised by its intermixture with a and
b, that it would scarcely have pre-
sented itself spontaneously as a sub-
ject of separate study. Of these uses
of the method we shall presently cite
some remarkable examples. The canon
of the Method of Residues is as fol-
lows : —

Fourth Canon.

Subduct from any phenomenon such
part as is knoivn by previous induc-
tions to be the effect of certain ante-
cedents, and the residue of the pheno-
menon is the effect of the remaining
antecedents.

§ 6. There remains a class of laws
which it is impracticable to ascertain
by any of the three methods which
I have attempted to characterise,
namely, the laws of those Permanent
Causes, or indestructible natural
agents, which it is impossible either
to exclude or to isolate ; which we
can neither hinder from being pre-
sent, nor contrive that they shall be
present alone. It would appear at
first sight that we could by no means
separate the effects of these agents
from the effects of those other pheno-
mena with which they cannot be pre-

THE FOUR EXPERIMENTAL METHODS.

261

Vented from co-existing. In respect,
indeed, to most of the permanent
causes, no such difficulty exists ; since,
though wecannoteliminate them as co-
existing facts, we can eliminate them
as influencing agents, by simply trying
our experiment in a local situation
beyond the limits of their influence.
The pendulum, for example, has its
oscillations disturbed by the vicinity
of a mountain : we remove the pen-
dulum to a sufficient distance from
the mountain, and the disturbance
ceases : from these data we can de-
termine by the Method of Difference
the amount of effect due to the moun-
tain ; and beyond a certain distance
everything goes on precisely as it
would do if the mountain exercised
no influence whatever, which, accord-
ingly, we, with sufficient reason, con-
clude to be the fact.

The difficulty, therefore, in apply-
ing the methods already treated of to
determine the effects of Permanent
Causes, is confined to the cases in
which it is impossible for us to get
out of the local limits of their influ-
ence. The pendulum can be removed
from the influence of the mountain,
but it cannot be removed from the
influence of the earth : we cannot
take away the earth from the pen-
dulum, nor the pendulum from the
earth, to ascertain whether it would
continue to vibrate if the action which
the earth exerts upon it were with-
drawn. On what evidence, then, do
we ascribe its vibrations to the earth's
influence? Not on any sanctioned
by the Method of Difference ; for
one of the two instances, the negative
instance, is wanting. Nor by the
Method of Agreement ; for though
all pendulums agree in this, that dur-
ing their oscillations the earth is al-
ways present, why may we not as
well ascribe the phenomenon to the
sun, which is equally a co-existent
fact in all the experiments? It is
evident that to establish even so simple
a fact of causation as this, there was
required some method over and above
those which we have yet examined.

As another example, let us take
the phenomenon Heat. Indepen-
dently of all hypothesis as to the real
nature of the agency so called, this
fact is certain, that we are unable
to exhaust any body of the whole of
its heat. It is equally certain that
no one ever perceived heat not eman-
ating from a body. Being unable,
then, to separate Body and Heat, we
cannot effect such a variation of cir-
cumstances as the foregoing three
methods require ; we cannot ascer-
tain, by those methods, what portion
of the phenomena exhibited by any
body is due to the heat contained in
it. If we could observe a body with
its heat, and the same body entirely
divested of heat, the Method of
Difference would show the effect due
to the heat, apart from that due to
the body. If we could observe heat
under circumstances agreeing in no-
thing but heat, and therefore not char-
acterised also by the presence of a
bod}', we could ascertain the effects
ci heat, from an instance of heat with
p body and an instance of heat with-
out a body, by the Method of Agree-
ment ; or we could determine by the
Method of Difference what effect was
due to the body, when the remainder
which was due to the heat would be
given by the Method of Residues.
But we can do none of these things ;
and without them the application of
any of the three methods to the solu-
tion of this problem would be illusory.
It would be idle, for instance, to at-
tempt to ascertain the effect of heat
by subtracting from the phenomena
exhibited by a body all that is due
to its other properties ; for as we
have never been able to observe any
bodies without a portion of heat in
them, effects due to that heat might
form a part of the very results which
we were affecting to subtract in order
that the effect of heat might be shown
by the residue.

If, therefore, there were no other
methods of experimental investiga-
tion than these three, we should be
unable to determine the effects due

262

INDUCTION.

to heat as a cause. But we have
still a resource. Though we cannot
exclude an antecedent altogether, we
may be able to produce, or nature
may produce for us, some modification
in it. By a modification is here
meant a change in it, not amounting
to its total removal. If some modi-
fication in the antecedent A is always
followed by a change in the conse-
quent a, the other consequents 6 and
c remaining the same ; or vice versd,
if every change in a is found to have
been preceded by some modification
in A, none being observable in any
of the other antecedents ; we may
safely conclude that a is, wholly or
in part, an effect traceable to A, or
at least in some way connected with
it through causation. For example,
in the case of heat, though we can-
not expel it altogether from any
body, we can modify it in quantity,
we can increase or diminish it ; and
doing so, we find by the various
methods of experimentation or obser-
vation already treated of, that such
increase or diminution of heat is fol-
lowed by expansion or contraction of
the body. In this manner we arrive
at the conclusion, otherwise unattain-
able by us, that one of the effects of
heat is to enlarge the dimensions of
bodies ; or what is the same thing in
other words, to widen the distances
between their particles.

A change in a thing, not amounting
to its total removal, that is, a change
which leaves it still the same thing
it was, must be a change either in its
quantity, or in some of its variable
relations to other things, of which
variable relations the principal is its
position in space. In the previous
example, the modification which was
produced in the antecedent was an
alteration in its quantity. Let us
now suppose the question to be, what
influence the moon exerts on the sur-
face of the earth. We cannot try an
experiment in the absence of the
moon, so as to observe what terrestrial
phenomena her annihilation would
put an end to j but when we find that

all the variations in the position of
the moon are followed by correspond-
ing variations in the time and place
of high water, the place being always
either the part of the earth which is
nearest to, or that which is most re-
mote from, the moon, we have ample
evidence that the moon is, wholly or
partially, the cause which determines
the tides. It very commonly happens,
as it does in this instance, that the
variations of an efiEect are correspon-
dent, or analogous, to those of its
cause ; as the moon moves farther
towards the east, the high -water point
does the same : but this is not an in-
dispensable condition, as may be seen
in the same example ; for along with
that high-water point there is at the
same instant another high-water point
diametrically opposite to it, and which,
therefore, of necessity, moves towards
the west, as the moon, followed by
the nearer of the tide-waves, advances
towards the east : and yet both these
motions are equally effects of the
moon's motion.

That the oscillations of the pendu-
lum are caused by the earth is proved
by similar evidence. Those oscillations
take place between equidistant points
on the two sides of a line, which,
being perpendicular to the earth,
varies with every variation in the
earth's position, either in space or
relatively to the object. Speaking
accurately, we only know by the
method now characterised that all
terrestrial bodies tend to the earth,
and not to some unknown fixed point
lying in the same direction. In every
twenty-four hours, by the earth's
rotation, the line drawn from the
body at right angles to the earth
coincides successively with all the
radii of a circle, and in the course of
six months the place of that circle
varies by nearly two hundred millions
of miles ; yet in all these changes of
the earth's position, the line in which
bodies tend to fall continues to be
directed towards it : which proves
that terrestrial gravity is directed
to the earth, and not, as was once

THE FOUR EXPERIMENTAL METHODS.

263

fancied by some, to a fixed point of
space.

The method by which these re-
su^s were obtained may be termed
the Method of Concomitant Varia-
tions : it is regulated by the following
canor. : —

Fifth Canon.
Whaiever phenomenon varies in any
manner whenever another phenomenon
varies i% some particular manner, is
either a cause or an effect of that pheno-
menon, 07 is connected with it through
some fact of causation.

The last clause is subjoined because
it by no means follows, when two
phenomena accompany each other in
their variations, that the one is cause
and the other effect. The same thing
may, and indeed must happen, sup-
posing them to be two different effects
of a common cause : and by this
method alone it would never be pos-
sible to ascertain which of the sup-
positions is the true one. The only
way to solve the doubt would be that
which we have so often adverted to,
viz. by endeavouring to ascertain
whether we can produce the one set
of variations by means of the other.
In the case of heat, for example, bj'
increasing the temperature of a body
we increase its bulk, but by increas-
ing its bulk we do not increase its
temperature ; on the contrary, (as in
the rarefaction of air under the re-
ceiver of an air-pump,) we generally
diminish it : therefore heat is not an
effect, but a cause, of increase of bulk.
If we cannot ourselves produce the
variations, we must endeavour, though
it is an attempt which is seldom suc-
cessful, to find them produced by
nature in some case in which the pre-
existing circumstances are perfectly
known to us.

It is scarcely necessary to say, that
in order to ascertain the uniform con-
comitants of variations in the effect
with variations in the cause, the same
precautions must be used as in any
other case of the determination of
an invariable sequence. We must

endeavour to i-etain all the other
antecedents unchanged, while that
particular one is subjected to the
requisite series of variations ; or, in
other words, that we may be war-
ranted in inferring causation from
concomitance of variations, the con-
comitance itself must be proved by
the Method of Difference.

It might at first appear that the
Method of Concomitant Variations
assumes a new axiom, or law of
causation in general, namely, that
every modification of the cause is
followed by a change in the effect.
And it does usually happen that when
a phenomenon A causes a phenomenon
a, any variation in the quantity or in
the various relations of A is uniformly
followed by a variation in the quan-
tity or relations of a. To take a
familiar instance, that of gravitation.
The sun causes a certain tendency to
motion in the earth ; here we have
cause and effect ; but that tendency
is towards the sun, and therefore
varies in direction as the sun varies
in the relation of position ; and more-
over the tendency varies in intensity,
in a certain numerical correspondence
to the sun's distance from the earth,
that is, according to another relation
of the sun. Thus we see that there
is not only an invariable connection
between the sun and the earth's
gravitation, but that two of the rela-
tions of the sun, its position with
respect to the earth and its distance
from the earth, are invariably con-
nected as antecedents with the quan-
tity and direction of the earth's gravi-
tation. The cause of the earth's
gravitating at aU is simply the sun ;
but the cause of its gravitating with
a given intensity and in a given
direction is the existence of the sun
in a given direction and at a given
distance. It is not strange that a
modified cause, which is in truth a
different cause, should produce a dif-
ferent effect.

Although it is for the most part
true that a modification of the cause
is followed by a modification of the

264

INDUCTION.

effect, the Method of Concomitant
"Variations does not, however, pre-
suppose this as an axiom. It only
requires the converse proposition,
that anything on whose modifications,
modifications of an effect are invari-
ably consequent, must be the cause
(or connected with the cause) of that
effect ; a proposition, the truth of
which is evident ; for if the thing
itself had no influence on the effect,
neither could the modifications of the
thing have any influence. If the
stars have no power over the fortunes
of mankind, it is implied in the very
terms that the conjunctions or oppo-
sitions of different stars can have no
such power.

Although the most striking applica-
tions of the Method of Concomitant
Variations take place in the cases
in which the Method of Difference,
strictly so called, is impossible, its
use is not confined to those cases ; it
may often usefully follow after the
Method of Difference, to give addi-
tional precision to a solution which
that has found . When by the Method
of Difference it has first been ascer-
tained that a certain object produces
a certain effect, the Method of Con-
comitant Variations may be usefully
called in to determine according to
what law the quantity or the different
relations of the effect follow those
of the cause.

§ 7. The case in which this method
admits of the most extensive employ-
ment is that in which the variations
of the cause are variations of quan-
tity. Of such variations we may in
general affirm with safety that they
will be attended not only with varia-
tions, but with similar variations of
the effect : the proposition, that more
of the cause is followed by more of
the effect, being a corollary from
the principle of the Composition of
Causes, which, as we have seen, is the
general rule of causation ; cases of
the opposite description, in which
causes change their properties on
being conjoined with one another.

being, on the contrary, special and ex-
ceptional. Suppose, then, that when
A changes in quantity, a also changes
in quantity, and in such a manuer
that we can trace the numerical rela-
tion which the changes of the one bear
to such changes of the other as take
place within our limits of observation.
We may then, with certain precau-
tions, safely conclude that the same
numerical relation will hold beyond
those limits. If, for instance, we find
that when A is double, a is double ;
that when A is treble or quadruple,
a is treble or quadruple ; we may
conclude that if A were a half or a
third, a would be a half or a third ;
and finally, that if A were annihi-
lated, a would be annihilated ; and
that a is wholly the effect of A, or
wholly the effect of the same cause
with A And so with any other
numerical relation according to which
A and a would vanish simultaneously ;
as, for instance, if a were proportional
to the square of A. If, on the other
hand, a is not wholly the effect of A,
but yet varies when A varies, it is
probably a mathematical function not
of A alone, but of A and something
else ; its changes, for example, may
be such as would occur if part of it
remained constant, or varied on some
other principle, and the remainder
varied in some numerical relation ta
the variations of A. In that case,
when A diminishes, a will be seen to
approach not towards zero, but to-
wards some other limit ; and when
the series of variations is such as to
indicate what that limit is, if con-
stant, or the law of its variation if
variable, the limit will exactly mea-
sure how much of a is the effect of
some other and independent cause,
and the remainder will be the effect
of A (or of the cause of A).

These conclusions, however, must
not be drawn without certain precau-
tions. In the first place, the possi-
bility of drawing them at all mani-
festly supposes that we are acquainted
not only with the variations, but with
the absolute quantities both of A and

THE FOUR EXPERIMENTAL METHODS.

26s

a. If we do not know the total quan-
tities, we cannot, of course, determine
the real numerical relation according
to which those quantities vary. It
is therefore an error to conclude, as
some have concluded, that because
increase of heat expands bodies, that
is, increases the distance between
their particles, therefore the distance
is wholly the effect of heat, and that
if we could entirely exhaust the body
of its heat, the particles would be in
complete contact. This is no more
than a guess, and of the most hazard-
ous sort, not a legitimate induction ;
for since we neither know how much
heat there is in any body, nor what
is the real distance between any two
of its particles, we cannot judge
whether the contraction of the dis-
tance does or does not follow the
diminution of the quantity of heat
according to such a numerical rela-
tion that the two quantities would
vanish simultaneously.

In contrast with this, let us consider
a case in which the absolute quan-
tities are known — the case contem-
plated in the first law of motion,
viz. that all bodies in motion con-
tinue to move in a straight line with
uniform velocity until acted upon by
some new force. This assertion is in
open opposition to first appearances ;
all terrestrial objects, when in motion,
gradually abate their velocity and
at last stop ; which accordingly the
ancients, with their inductio per enu-
mcrationem simplicem, imagined to be
the law. Every moving body, how-
ever, encounters various obstacles, as
friction, the resistance of the atmos-
phere, &c., which we know by daily
experience to be causes capable of
destroying motion. It was suggested
that the whole of the retardation
might be owing to these causes. How
was this inquired into? If the ob-
stacles could have been entirely re-
moved, the case would have been
amenable to the Method of Differ-
ence. They could not be removed,
they could only be diminished, and
the case therefore admitted only of

the Method of Concomitant Varia-
tions. This accordingly being em-
ployed, it was found that every dimi-
nution of the obstacles diminished
the retardation of the motion ; and
inasmuch as in this case (unlike the
case of heat) the total quantities both
of the antecedent and of the conse-
quent were known, it was practicable
to estimate, with an approach to ac-
curacy, both the amount of the re-
tardation and the amount of the
retarding causes or resistances, and
to judge how near they both were
to being exhausted ; and it appeared
that the effect dwindled as rapidly,
and at each step was as far on the road
towards annihilation, as the cause
was. The simple oscillation of a
weight suspended from a fixed point,
and moved a little out of the perpen-
dicular, which in ordinary circum-
stances lasts but a few minutes, was
prolonged in Borda's experiments to
more than thirty hours, by diminish-
ing as much as possible the friction
at the point of suspension, and by
making the body oscillate in a space
exhausted as nearly as possible of its
air. There could therefore be no hesi-
tation in assigning the whole of the
retardation of motion to the influence
of the obstacles ; and since, after sub-
ducting this retardation from the total
phenomenon, the remainder was an
uniform velocity, the result was the
proposition known as the first Law
of Motion.

There is also another characteristic
uncertainty affecting the inference
that the law of variation, which the
quantities observe within our limits
of observation, will hold beyond those
limits. There is, of course, in the first
instance, the possibility that beyond
the limits, and in circumstances there-
fore of which we have no direct ex-
perience, some counteracting cause
might develop itself ; either a new
agent, or a new property of the agents
concerned, which lies dorn\ant in the
circumstances we are able to observe.
This is an element of uncertainty
which enters largely into all our pre-

266

INDUCTION.

dictions of effects ; but it is not
peculiarly applicable to the Method
of Concomitant Variations. The un-
certainty, however, of which I am
about to speak is characteristic of
that method, especially in the cases
in which the extreme limits of our
observation are very narrow in com-
parison with the possible variations
in the quantities of the pheno-
mena. Any one who has the slightest
acquaintance with mathematics is
aware that very different laws of
variation may produce numerical re-
sults which differ but slightly from
one another within narrow limits ;
and it is often only when the absolute
amounts of variation are considerable
that the difference between the re-
sults given by one law and by another
becomes appreciable. When, there-
fore, such variations in the quantity
of the antecedents as we have the
means of observing are small in com-
parison with the total quantities, there
is much danger lest we should mis-
take the numerical law, and be led
to miscalculate the variations which
would take place beyond the limits ;
a miscalculation which would vitiate
any conclusion respecting the de-
pendence of the effect upon the cause,
that could be founded on those varia-
tions. Examples are not wanting of
such mistakes. " The formulae," says
Sir John Herschel,* ''which have been
empirically deduced for the elasticity
of steam, (till very recently,) and those
for the resistance of fluids, and other
similar subjects," when relied on be-
yond the limits of the observations
from which they were deduced, "have
almost invariably failed to support
the theoretical structures which have
been erected on them,"

In this uncertainty, the conclusion
we may draw from the concomitant
variations of a and A, to the existence
of an invariable and exclusive con-
nection between them, or to the per-
manency of the same numerical rela-
tion between their variations when

* Discourse on the Study of Natural Philo-
tophy, p. 179.

the quantities are much greater or
smaller than those which we have had
the means of observing, cannot be
considered to rest on a complete in-
duction. All that in such a case can
be regarded as proved on the subject
of causation is, that there is some
connection between the two pheno-
mena ; that A, or something which
can influence A, must be one of the
causes which collectively determine a.
We may, however, feel assured that
the relation which we have observed
to exist between the variations of A
and a, will hold true in all cases which
fall between the same extreme limits ;
that is, wherever the utmost increase
or diminution in which the result has
been found by observation to coincide
with the law, is not exceeded.

The four methods which it has now
been attempted to describe are the
only possible modes of experimental
inquiry — of direct induction a pos-
teriori, as distinguished from deduc-
tion : at least, I know not, nor am
able to imagine, any others. And
even of these, the Method of Resi-
dues, as we have seen, is not inde-
pendent of deduction ; though, as it
also requires specific experience, it
may, without impropriety, be included
among methods of direct observation
and experiment.

These, then, with such assistance
as can be obtained from Deduction,
compose the available resources of the
human mind for ascertaining the laws
of the succession of phenomena. Be-
fore proceeding to point out certain
circumstances by which the employ-
ment of these methods is subjected to
an immense increase of complication
and of difficulty, it is expedient to
illustrate the use of the methods by
suitable examples drawn from actual
physical investigations. These, ac-
cordingly, will form the subject of
the succeeding chapter.

EXAMPLES OF THE FOUR METHODS.

267

CHAPTER XI.

MISCELLANEOUS EXAMPLES OF THE
FOUR METHODS.

§ r. I SHALL select, as a first ex-
ample, an interesting speculation of
one of the most eminent of theoretical
chemists, Baron Liebig. The object
in view is to ascertain the immediate
cause of the death produced by metal-
lic poisons.

Arsenious acid and the salts of lead,
bismuth, copper, and mercury, if in-
troduced into the animal organism,
except in the smallest doses, destroy
life. These facts have long been
known, as insulated truths of the
lowest order of generalisation ; but
it was reserved for Liebig, by an apt
employment of the first two of our
methods of experimental inquiry, to
connect these truths together by a
higher induction, pointing out what
property, common to all tliese dele-
terious substances, is the really operat-
ing cause of their fatal effect.

When solutions of these substances
are placed in sufficiently close contact
with many animal products, albumen,
milk, muscular fibre, and animal mem-
branes, the acid or salt leaves the
water in which it was dissolved, and
enters into combination with the ani-
mal substance : which substance, after
being thus acted upon, is found to
have lost its tendency to spontaneous
decomposition or putrefaction.

Observation also shows, in cases
where death has been produced by
these poisons, that the parts of the
body with which the poisonous sub-
stances have been brought into con-
tact do not afterwards putrefy.

And, finally, when the poison has
been supplied in too small a quantity
to destroy life, eschars are produced,
that is, certain superficial portions of
the tissues are destroyed, which are
afterwards thrown off by the repara-
tive process taking place in the healthy
parts.

These three sets of instances admit
of being treated according to the

Method of Agreement. In all of
them the metallic compounds are
brought into contact with the sub-
stances which compose the human
or animal body ; and the instances do
not seem to agree in any other cir-
cumstance. The remaining antece-
dents are as different, and even oppo-
site, as they coiild possibly be made ;
for in some the animal substances
exposed to the action of the poisons
are in a state of life, in others only
in a state of organisation, in others
not even in that. And what is the
result which follows in all the cases ?
The conversion of the animal sub-
stance (by combination with the
poison) into a chemical compound,
held together by so powerful a force
as to resist the subsequent action of
the ordinary causes of decomposition.
Now, organic life (the necessary con-
dition of sensitive life) consisting in
a continual state of decomposition
and recomposition of the different
organs and tissues, whatever inca-
pacitates them for this decomposition
destroys life. And thus the proxi-
mate cause of the death produced by
this description of poisons is ascer-
tained, as far as the Method of Agree-
ment can ascertain it.

Let us now bring our conclusion to
the test of the Method of Difference.
Setting out from the cases already
mentioned, in which the antecedent
is the presence of substances forming
with the tissues a compound incap-
able of putrefaction, (and a fortiori
incapable of the chemical actions
which constitute life,) and the con-
sequent is death, either of the whole
organism, or of some portion of it ;
let us compare with these cases other
cases, as much resembling them as
possible, but in which that effect is
not produced. And, first, " many in-
soluble basic salts of arsenious acid
are known not to be poisonous. The
substance called alkargen, discovered
by Bunsen, which contains a very
large quantity of arsenic, and ap-
proaches very closely in composition
to the organic arsenious compoundi

26S

INDUCTION.

found in the body, has not the slightest
injurious action upon the organism,"
Now when these substances are brought
into contact with the tissues in any
way, they do not combine with them ;
they do not arrest their progress to
decomposition. As far, therefore, as
these instances go, it appears that
when the effect is absent, it is by
reason of the absence of that ante-
cedent which we had already good
ground for considering as the proxi-
mate cause.

But the rigorous conditions of the
Method of Difference are not yet
satisfied ; for we cannot be sure that
these unpoisonous bodies agree with
the poisonous substances in every pro-
perty, except the particular one of
entering into a difficultly decompos-
able compound with the animal tis-
sues. To render the method strictly
applicable, we need an instance, not
of a different substance, but of one of
the very same substances, in circum-
stances which would prevent it from
forming, with the tissues, the sort of
compound in question ; and then, if
death does not follow, our case is made
out. Now such instances are afforded
by the antidotes to these poisons.
For example, in case of poisoning by
arsenious acid, if hydrated peroxide
of iron is administered, the destructive
agency is instantly checked. Now this
peroxide is known to combine with
the acid, and form a compound, which,
being insoluble, cannot act at all on
animal tissues. So, again, sugar is
a well-known antidote to poisoning
by salts of copper ; and sugar reduces
those salts either into metallic copper,
or into the red sub-oxide, neither of
which enters into combination with
animal matter. The disease called
painter's colic, so common in manu-
factories of white lead, is unknown
where the workmen are accustomed
to take, as a preservative, sulphuric
acid lemonade (a solution of sugar
rendered acid by sulphuric acid).
Now diluted sulphuric acid has the
property of decomposing all com-
pounds of lead with organic matter,

or of preventing them from being
formed.

There is another class of instances,
of the nature required by the Method
of Difference, which seem at first
sight to conflict with the theory.
Soluble salts of silver, such, for in-
stance, as the nitrate, have the same
stiffening antiseptic effect on decom-
posing animal substances as corro-
sive sublimate and the most deadly
metallic poisons ; and when applied
to the external parts of the body, the
nitrate is a powerful caustic, depriv-
ing those parts of all active vitality,
and causing them to be thrown off by
the neighbouring living structures, in
the form of an eschar. The nitrate
and the other salts of silver ought,
then, it would seem, if the theory be
correct, to be poisonous ; yet they
may be administered internally with
perfect impunity. From this apparent
exception arises the strongest confir-
mation which the theory has yet
received. Nitrate of silver, in spite
of its chemical properties, does not
poison when introduced into the
stomach ; but in the stomach, as in
all animal liquids, there is common
salt ; and in the stomach there is also
free muriatic acid. These substances
operate as natural antidotes com-
bining with the nitrate, and, if its
quantity is not too great, immediately
converting it into chloride of silver ;
a substance very slightly soluble, and
therefore incapable of combining with
the tissues, although to the extent of
its solubility it has a medicinal influ-
ence, through an entirely different class
of organic actions.

The preceding instances have afford-
ed an induction of a high order of
conclusiveness, illustrative of the two
simplest of our four methods, though
not rising to the maximum of cer-
tainty which the Method of Differ-
ence, in its most perfect exemplifi-
cation, is capable of affording. For
(let us not forget) the positive in-
stance and the negative one which the
rigour of that method requires, ought
to differ only in the presence or ab>-

EXAMPLES OF THE FOUR METHODS.

269

sence of one single circumstance.
Now, in the preceding argument, they
differ in the presence or absence not
of a single circumstance, but of a single
substance ; and as every substance has
innumerable properties, there is no
knowing what number of real differ-
ences are involved in what is nomi-
nally and apparently only one differ-
ence. It is conceivable that the
antidote, the peroxide of iron, for
example, may counteract the poison
through some other of its properties
than that of forming an insoluble
compound with it ; and if so, the
theory would fall to the ground, so
far as it is supported by that instance.
This source of uncertainty, which is a
serious hindrance to all extensive
generalisations in chemistry, is how-
ever reduced in the present case to
almost the lowest degree possible,
when we find that not only one sub-
stance, but many substances, possess
the capacity of acting as antidotes to
metallic poisons, and that all these
agree in the property of forming in-
soluble compounds with the poisons,
while they cannot be ascertained to
agree in any other property whatso-
ever. We have thus, in favour of the
theory, all the evidence which can be
obtained by what we termed the In-
direct Method of Difference, or the
Joint Method of Agreement and Dif-
ference ; the evidence of which, though
it never can amount to that of the
Method \ of Difference properly so
called, may approach indefinitely near
to it.

§ 2, Let the object be * to ascertain
the law of what is termed induced
electricity ; to find under what condi-
tions any electrified body, whether
positively or negatively electrified,
gives rise to a contrary electric state
in some other body adjacent to it.

The most familiar exemplification

■* For this speculation, as for many other
of my scientific illustration*, I am indebted
to Professor Bain, whose subsequent trea-
tise on Logfic abounds with apt illustra-
tions of all the inductive methods,

of the phenomenon to be investigated
is the following. Around the prime
conductors of an electrical machine,
the atmosphere to some distance, or
any conducting surface suspended in
that atmosphere, is found to be in an
electric condition opposite to that of
the prime conductor itself. Near and
around the positive prime conductor
there is negative electricity, and near
and around the negative prime con-
ductor there is positive electricity.
When pith balls are brought near to
either of the conductors, they become
electrified with the opposite electri-
city to it ; either receiving a share
from the already electrified atmos-
phere by conduction, or acted upon
by the direct inductive influence of
the conductor itself ; they are then
attracted by the conductor to which
they are in opposition ; or, if with-
drawn in their electrified state, they
will be attracted by any other oppo-
sitely charged body. In like manner
the hand, if brought near enough to
the conductor, receives or gives an
electric discharge. Now we have no
evidence that a charged conductor
can be suddenly discharged unless by
the approach of a body oppositely
electrified. In the case, therefore, of
the electric machine, it appears that
the accumulation of electricity in an
insulated conductor is always accom-
panied by the excitement of the con-
trary electricity in the surrounding
atmosphere, and in every conductor
placed near the former conductor. It
does not seem possible, in this case,
to produce one electricity by itself.

Let us now examine all the other
instances which we can obtain re-
sembling this instance in the given
consequent, namely, the evolution of
an opposite electricity in the neigh-
bourhood of an electrified body. As
one remarkable instance we have the
Leyden jar; and after the splendid
experiments of Faraday in complete
and final establishment of the sub-
stantial identity of magnetism and
electricity, we may cite the magnet,
both the natural and the electrq-

270

INDUCTION.

magnet, in neither of which it is
possible to produce one kind of elec-
tricity by itself, or to charge one pole
without charging an opposite pole with
the contrary electricity at the same
time. We cannot have a magnet
with one pole : if we break a natural
loadstone into a thousand pieces, each
piece will have its two oppositely elec-
trified poles complete within itself. In
the voltaic circuit, again, we cannot
have one current without its opposite.
In the ordinary electric machine, the
glass cylinder or plate, and the rubber,
acquire opposite electricities.

From all these instances, treated
by the Method of Agreement, a gene-
ral law appears to result. The in-
stances embrace all the known modes
in which a body can become charged
with electricity ; and in all of them
there is found, as a concomitant or
consequent, the excitement of the
opposite electric state in some other
body or bodies. It seems to follow
that the two facts are invariably con-
nected, and that the excitement of
electricity in any body has for one of
its necessar}' conditions the possibility
of a simultaneous excitement of the
opposite electricity in some neigh-
bouring body.

As the two contrary electricities
can only be produced together, so
they can only cease together. This
may be shown by an application of
the Method of Difference to the ex-
ample of the Leyden jar. It needs
scarcely be here remarked that in
the Leyden jar electricity can be ac-
cumulated and retained in consider-
able quantity, by the contrivance of
having two conducting surfaces of
equal extent, and parallel to each
other through the whole of that ex-
tent, with a non-conducting substance
such as glass between them. When
one side of the jar is charged posi-
tively, the other is charged nega-
tively, and it was by virtue of this
^ fact that the Leyden jar served just
now as an instance in our employ-
ment of the Method of Agreement.
Now it is impossible to discharge one

of the coatings unless the other can
be discharged at the same time. A
conductor held to the positive side
cannot convey away any electricity
unless an equal quantity be allowed
to pass from the negative side : if
one coating be perfectly insulated,
the charge is safe. The dissipation
of one must proceed pari passu with
that of the other.

The law thus strongly indicated ad-
mits of corroboration by the Method
of Concomitant Variations. The Ley-
den jar is capable of receiving a much
higher charge than can ordinarily be
given to the conductor of an electrical
machine. Now in the case of the
Leyden jar, the metallic surface which
receives the induced electricity is a
conductor exactly similar to that
which receives the primary charge,
and is therefore as susceptible of re-
ceiving and retaining the one elec-
tricity as the opposite surface of re-
ceiving and retaining the other ; but
in the machine, the neighbouring
body which is to be oppositely elec-
trified is the surrounding atmosphere,
or any body casually brought near to
the conductor ; and as these are gene-
rally much inferior in their capacity
of becoming electrified to the conduc-
tor itself, their limited power imposes
a corresponding limit to the capacity
of the conductor for being charged.
As the capacity of the neighbouring
body for supporting the opposition
increases, a higher charge becomes
possible : and to this appears to be
owing the great superiority of the
Leyden jar.

A further and most decisive confir-
mation tby the Method of Difference
is to be found in one of Faraday's
experiments in the course of his re-
searches on the subject of Induced
Electricity.

Since common or machine electri-
city and voltaic electricity may be
considered for the present purpose to
be identical, Faraday wished to know
whether, as the prime conductor de-
velops opposite electricity upon a con-
ductor in its vicinity, so a vpltaiq

EXAMPLES OF THE FOUR METHODS.

271

current nnining along a wire would
induce an opposite current upon an-
other wire laid parallel to it at a short
distance. Now this case is similar
to the cases previously examined, in
every circumstance except the one to
which we have ascribed the effect. We
found in the former instances that
whenever electricity of one kind was
excited in one body, electricity of the
opposite kind must be excited in a
neighbouring bod}'. But in Faraday's
experiment this indispensable opposi-
tion exists within the wire itself. From
the nature of a voltaic charge, the two
opposite currents necessary to the ex-
istence of each other are both accom-
modated in one wire ; and there is no
need of another wire placed beside it
to contain one of them, in the same
way as the Leyden jar must have a
positive and a negative surface. The
exciting cause can and does produce
all the effect which its laws require,
independently of any electric excite-
ment of a neighbouring body. Now
the result of the experiment with the
second wire was, that no opposite
current was produced. There was
an instantaneous effect at the closing
and breaking of the voltaic circuit ;
electric inductions appeared when the
two wires were moved to and from
one another ; but these are pheno-
mena of a different class. There was
no induced electricity in the sense in
which this is predicated of the Ley-
den jar ; there was no sustained cur-
rent running up the one wire while
an opposite current ran down the
neighbouring wire ; and this alone
would have been a true parallel case
to the other.

It thus appears by the combined
evidence of the Method of Agreement,
the Method of Concomitant Varia-
tions, and the most rigorous form of
the Method of Difference, that neither
of the two kinds of electricity can be
excited without an equal excitement
of the other and opposite kind ; that
both are effects of the same cause ;
that the possibility of the one is a
pouditiuu uf the possibility of the

other, and the quantity of the one an
impassable limit to the quantity of
the other. A scientific result of con-
siderable interest in itself and illus-
trating those three methods in a
manner both characteristic and easily
intelligible.*

§ 3. Our third example shall be
extracted from Sir John Herschel's
Discourse on the Study of Natural
Philosophy, a work replete with hap-
pily selected exemplifications of in-
ductive processes from almost every
department of physical science, and
in which alone, of all books which I
have met with, the four methods of
induction are distinctly recognised,
though not so clearly characterised
and defined, nor their correlation so
fully shown, as has appeared to me
desirable. The present example is
described by Sir John Herschel as
"one of the most beautiful speci-
mens " which can be cited " of induc-
tive experimental inquiry lying within
a moderate compass;" the theory of
dew, first promiilgated by the late Dr.
Wells, and now universally adopted
by scientific authorities. The pas-
sages in inverted commas are ex-
tracted verbatim from the Discourse.f

"Suppose dew wei-e the phenomenon
proposed whose cause we would know.
In the first place " we must determine

* This view of the necessary co-existence
of opposite excitements involves a great
extension of the original doctrine of two
electricities. The early theorists assumed
that, when amber was rubbed, the amber
was made positive and the rubber negative
to the same degree ; but it never occurred
to them to suppose that the existence of
the amber charge was dependent on an
opposite charge in the bodies with which
the amber was contiguous, while the exist-
ence of the negative charge on the rubber
was equally dependent on a contrary state
of the surfjices that might accidentally be
confronted with it ; that, in fact, in a case
of electrical excitement by friction, four
charges were the minimum that could
exist. But this double electrical action
is essentially implied in the explanation
now universally adopted in regard to the
phenomena of the common electric mv
chine.

272

INDUCTION.

precisely what we mean by dew ; what
the fact really is, whose cause we
desired to investigate, "We must
separate dew from rain, and the
moisture of fogs, and limit the appli-
cation of the term to what is really
meant, which is the spontaneous
appearance of moisture on substances
exposed in the open air when no
rain or visible wet is falling." This
answers to a preliminary operation
which will be characterised in the
ensuing book, treating of operations
subsidiary to induction.*

" Now, here we have analogous
phenomena in the moisture which
bede\vs a cold metal or stone when
we breathe upon it ; that which ap-
pears on a glass of water fresh from
the well in hot weather ; that which
appears on the inside of windows
when sudden rain or hail chills the
external air ; that which runs down
our walls when, after a long frost, a
warm moist thaw comes on." Com-
paring these cases, we find that they
all contain the phenomenon which
was proposed as the subject of in-
vestigation. Now '* all these instances
agree in one point, the coldness of the
object dewed, in comparison with the
air in contact with it." But there
still remains the most important case
of all, that of nocturnal dew : does
the same circumstance exist in this
case ? " Is it a fact that the object
dewed is colder than the air? Cer-
tainly not, one would at first be in-
clined to say ; for what is to maJce it
so? But .... the experiment is
easy : we have only to lay a thermo-
meter in contact with the dewed
substance, and hang one at a little
distance above it, out of reach of its
influence. The experiment has been
therefore made, the question has been
asked, and the answer has been in-
variably in the affirmative. When-
ever an object contracts dew, it is
colder than the air."

Here then is a complete application
of the Method of Agreement, esta-

• Infra, book iv. cb. ii. On Abstraction.

blishing the fact of an invariable con-
nection between the deposition of dew
on a surface and the coldness of that
surface compared with the external
air. But which of these is cause and
which effect ? or are they both effects
of something else? On this subject
the Method of Agreement can afford
us no light : we must call in a more
potent method. "We must collect
more facts, or, which comes to the
same thing, vary the circumstances ;
since every instance in which the cir-
cumstances differ is a fresh fact : and
especially we must note the contrary
or negative cases, i.e. where no dew
is produced : " a comparison between
instances of dew and instances of no
dew being the condition necessary to
bring the Method of Difference into
play.

" Now, first, no dew is produced on
the surface of polished metals, but it
is very copiously on glass, both ex-
posed with their faces upwards, and
in some cases the under side of a
horizontal plate of glass is also dewed."
Here is an instance in which the effect
is produced, and another instance in
which it is not produced ; but we
cannot yet pronounce, as the canon
of the Method of Difference requires,
that the latter instance agrees with
the former in all its circumstances
except one ; for the differences be-
tween glass and polished metals are
manifold, and the only thing we can
as yet be sure of is, that the cause of
dew will be found among the circum-
stances by which the former substance
is distinguished from the latter. But
if we could be sure that glass, and the
various other substances on which
dew is deposited, have only one quality
in common, and that polished metals
and the other substances on which
dew is not deposited have also nothing
in common but the one circumstance
of not having the one quality which
the others have ; the requisitions of
the Method of Difference would be
completely satisfied, and we should
recognise, in that quality of the sub-
stances, the cause of dew. This,

EXAMPLES OF THE FOUR METHODS.

273

accordingly, is the path of inquiry
which is next to be pursued.

*' In the cases of polished metal
and polished glass, the contrast shows
evidently that the substance has much
to do with the phenomenon ; therefore
let the substance alone be diversified
as much as possible, by exposing
polished surfaces of various kinds.
This done, a scale of intensity becomes
obvious. Those polished surfaces are
found to be most strongly dewed
which conduct heat worst, while
those which conduct well resist dew
most effectually." The complication
increases ; here is the Method of
Concomitant Variations called to our
assistance ; and no other method was
practicable on this occasion ; for the
quality of conducting heat could not
be excluded, since all substances con-
duct heat in some degree. The
conclusion obtained is, that ccttens
paribus the deposition of dew is in
some proportion to the power which
the body possesses of resisting the
passage of heat ; and that this, there-
fore, (or something connected with
this,) must be at least one of the
causes which assist in producing the
deposition of dew on the surface.

" But if we expose rough surfaces
instead of polished, we sometimes
find this law interfered with. Thus,
roughened iron, especially if painted
over or blackened, becomes dewed
sooner than varnished paper ; the kind
of surface, therefore, has a great in-
fluence. Expose, then, the same
material in very diversified states as
to surface," (that is, employ the
Method of Difference to ascertain
concomitance of variations,) •' and
another scale of intensity becomes at
once apparent ; those surfaces which
part with their heat most readily by
radiation are found to contract dew
most copiously." Here, therefore, are
the requisites for a second employment
of the Method of Concomitant Varia-
tions, which in this case also is the only
method available, since all substances
radiate heat in some degree or other.
The conclusion obtained by this new

application of the method is, that
cceteris paribus the deposition of dew
is also in some proportion to the power
of radiating heat; and that the quality
of doing this abundantly (or some
cause on which that quality depends)
is another of the causes which pro-
mote the deposition of dew on the
substance.

"Again, the influence ascertained
to exist of substance and surface leads
us to consider that of texture; and
here, again, we are presented on trial
with remarkable differences, and with
a third scale of intensity, pointing out
substances of a close, firm texture,
such as stones, metals, &c., as un-
favourable, but those of a loose one,
as cloth, velvet, wool, eider-down,
cotton, &c., as eminently favourable
to the contraction of dew." The
Method of Concomitant Variations is
here, for the third time, had recourse
to, and, as before, from necessity,
since the texture of no substance is
absolutely firm or absolutely loose.
Looseness of texture, therefore, or
something which is the cause of that
quality, is another circumstance which
promotes the deposition of dew ; but
this third course resolves itself into
the first, viz. the quality of resisting
the passage of heat ; for substances
of loose texture '* are precisely those
which are best adapted for clothing,
or for impeding the free passage of
heat from the skin into the air, so as
to allow their outer surfaces to be
very cold, while they remain warm
within ; " and this last is, therefore,
an induction (from fresh instances)
simply corroborative of a former induc-
tion.

It thus appears that the instances
in which much dew is deposited, which
are very various, agree in this, and,
so far as we are able to observe, in this
only, that they either radiate heat
rapidly or conduct it slowly : qualities
between which there is no other cir-
cumstance of agreement than that, by
virtue of either, the body tends to lose
heat from the surface more rapidly than
it can be restwed from within. Th«

S

274

INDUCTION

instances, on the contrary, in which
no dew, or but a small quantity of it,
is formed, and which are also ex-
tremely various, agree (as far as we
can observe) in nothing except in not
having this same property. We seem,
therefore, to have detected the charac-
teristic difference between the sub-
stances on which dew is produced
and those on which it is not produced.
And thus have been realised the
requisitions of what we have termed
the Indirect Method of Difference, or
the Joint Method of Agreement and
Difference. The example afforded of
this indirect method, and of the man-
ner in which the data are prepared
for it by the Methods of Agreement
and of Concomitant Variations, is the
most important of all the illustrations
of induction afforded by this interest-
ing speculation.

We might now consider the ques-
tion, on what the deposition of dew
depends, to be completely solved, if
we could be quite sure that the sub-
stances on which dew is produced
differ from those on which it is not,
in nothing but in the property of los-
ing heat from the surface faster than
the loss can be repaired from within.
And though we never can have that
complete certainty, this is not of so
much importance as might at first be
supposed ; for we have, at all events,
ascertained that even if there be any
other quality hitherto unobserved
which is present in all the substances
which contract dew, and absent in
those which do not, this other property
must be one which, in all that great
number of substances, is present or
absent exactly where the property of
being a better radiator than conductor
is present or absent ; an extent of coin-
cidence which affords a strong pre-
sumption of a community of cause,
and a consequent invariable co-exis-
tence between the two properties ; so
that the property of being a better
radiator than conductor, if not itself
the caupe, almost certainly always ac-
wmpanies the cause, and, for purposes
>{ prediction, no error is likely to be

committed by treating it as if it were
really such.

Reverting now to an earlier stage
of the inquiry, let us remember that
we had ascertained that, in every in-
stance where dew is formed, there is
actual coldness of the surface below
the temperature of the surrounding
air ; but we were not sure whether
this coldness was cause of the dew,
or its effect. This doubt we are
now able to resolve. We have found
that, in every such instance, the sub-
stance is one which, by its own pro-
perties or laws, would, if exposed in
the night, become colder than the
surrounding air. The coldness there-
fore being accounted for indepen-
dently of the dew, while it is proved
that there is a connection between
the two, it must be the dew which
depends on the coldness ; or, in other
words, the coldness is the cause of
the dew.

This law of causation, already so
amply established, admits, however,
of efficient additional corroboration
in no less than three ways. First, by
deduction from the known laws of
aqueous vapour when diffused through
air or any other gas ; and though we
have not yet come to the Deductive
Method, we will not omit what is
necessary to render this speculation
complete. It is known by direct ex-
periment that only a limited quantity
of water can remain suspended in
the state of vapour at each degree
of temperature, and that this maxi-
mum grows less and less as the tem-
perature diminishes. From this it
follows, deductively, that if there is
already as much vapour suspended as
the air will contain at its existing tem-
perature, any lowering of that tem-
perature will cause a portion of the
vapour to be condensed, and become
water. But, again, we know deduc-
tively, from the laws of heat, that the
contact of the air with a body colder
than itself will necessarily lower the
temperature of the stratum of air
immediately applied to its surface ;
and will, therefore, cause it to part

EXAMPLES OF THE FOUR METHODS.

275

with a portion of its water, which ac-
cordingly will, by the ordinary laws
of gravitation or cohesion, attach it-
self to the surface of the body, thereby
constituting dew. This deductive
proof, it will have been seen, has the
advantage of at once proving causa-
tion as well as co-existence ; and it has
the additional advantage that it also
accounts for the exceptions to the oc-
currence of the phenomenon, the cases
in which, although the body is colder
than the air, yet no dew is deposited ;
by showing that this will necessarily
be the case when the air is so under-
supplied with aqueous vapour, com-
paratively to its temperature, that
even when somewhat cooled by the
contact of the colder body it can still
continue to hold in suspension all the
vapour which was previously sus-
pended in it : thus in a very dry
summer there are no dews, in a very
dry winter no hoar-frost. Here, there-
fore, is an additional condition of the
production of dew, which the methods
we previously made use of failed to
detect, and which might have re-
mained still undetected if recourse
had not been had to the plan of de-
ducing the effect from the ascertained
properties of the agents known to be
present.

The second corroboration of the
theory is by direct experiment, ac-
cording to the canon of the Method
of Difference. We can, by cooling
the surface of any body, find in all
cases some temperature (more or less
inferior to that of the surrounding air,
according to its hygrometic condition)
at which dew will begin to be de-
posited. Here, too, therefore, the
causation is directly proved. We
can, it is true, accomplish this only
on a small scale ; but we have ample
reason to conclude that the same
operation, if conducted in Nature's
great laboratory, would equally pro-
duce the effect.

And, finally, even on that great
scale we are able to verify the result.
The case is one of those rare cases, as
we have sho\vn them to be, in which

Nature works the experiment for us
in the same manner in which we our-
selves perform it, introducing into the
previous state of things a single and
perfectly definite new circumstance,
and manifesting the effect so rapidly
that there is not time for any other
material change in the pre-existing
circumstances. " It is observed that
dew is never copiously deposited in
situations much screened from the
open sky, and not at all in a cloudy
night ; but if the clouds withdraw
even for a few minutes, and leave a
clear opening, a deposition of dew pre-
sently begins, and goes on increasing.
. . . Dew formed in clear intervals
will often even evaporate again when
the sky becomes thickly overcast."
The proof, therefore, is complete that
the presence or absence of an unin-
terrupted communication with the
sky causes the deposition or non-depo-
sition of dew. Now, since a clear
sky is nothing but the absence of
clouds, and it is a known property of
clouds, as of all other bodies between
which and any given object nothing
intervenes but an elastic fluid, that
they tend to raise or keep up the
superficial temperature of the object
by radiating heat to it, we see at
once that the disappearance of clouds
will cause the surface to cool ; so that
Nature, in this case, produces a
change in the antecedent by definite
and known means, and the conse-
quent follows accordingly : a natural
experiment which satisfies the re-
quisitions of the Method of Differ-
ence.*

* I must, however, remark, that this
example, which seems to militate against
the assertion we made of the comparative
inapplicability of the Metht.d of Difference
to cases of pure observation, is really one
of those exceptions which, according to a
proverbial expression, prove the general
rule. For in this case, in which Nature,
in her experiment, seems to have imitated
the type of the experiments made by man,
slie has only succeer.ed in producing the
hkeness of man's most imperfect experi-
ments, namely, those in which, though ho
succeeds in producing the phenomenon,
he does so by employing complex means,
which he ia unable perfectly to analyse,

2T6

INDUCTION.

The accumulated proof of which
the Theory of Dew has been found
susceptible is a striking instance of
the fulness of assurance which the
inductive evidence of laws of causa-
tion may attain in cases in which
the invariable sequence is by no means
obvious to a superficial view.

§ 4. The admirable physiological
investigations of Dr. Brown-Sequard
afford brilliant examples of the appli-
cation of the Inductive Methods to a
class of inquiries in which, for reasons
which will presently be given, direct
induction takes place under peculiar
difficulties and disadvantages. As
one of the most apt instances, I select
his speculation (in the Proceedings
of the Royal Society for May 16,
1 861) on the relations between mus-
cular irritability, cadaveric rigidity,
and putrefaction.

The law which Dr. Brown-S^quard's
investigation tends to establish is the
following : — " The greater the degree
of muscular irritability at the time of
death, the later the cadaveric rigidity
sets in, and the longer it lasts, and
the later also putrefaction appears,
and the slower it progresses." One
would say at first sight that the
method here required must be that
of Concomitant Variations. But this
is a delusive appearance, arising from
the circumstance that the conclusion
to be tested is itself a fact of con-
comitant variations. For the estab-
lishment of that fact any of the

and can form, therefore, no suflBcient judg-
ment what portion of the effects may be
due, not to the supposed cause, but to some
unknown agency <>f the means by which
that cause was produced. In the natural
experiment which we are speaking of, the
means used was the clearing off a canopy
of clouds ; and we certainly do not know
sufficiently in what this process consists,
or on what it depends, to be certain d priori
that it might not operate upon the deposi-
tion of dew independently of any ther-
mometric effect at the eartii's surface.
Even, therefore, in a case so favourable as
this to Nature's experimental talents, her
experiment is of little value except in
corroboration of a conclusion already at-
tained through other meani.

Methods may be put in requisition,
and it will be found that the fourth
Method, though really employed, has
only a subordinate place in this par-
ticular investigatioa

The evidences by which Dr. Brown -
S^quard establishes the law may be
enumerated as follows : —

1st. Paralysed muscles have greater
irritability than healthy muscles.
Now, paralysed muscles are later in
assuming the cadaveric rigidity than
healthy muscles, the rigidity lasts
longer, and putrefaction sets in later,
and proceeds more slowly.

Both these propositions had to be
proved by experiment; and for the
experiments which prove them science
is also indebted to Dr. Brown-Sdquard.
The former of the two — that paralysed
muscles have greater irritability than
healthy muscles — he ascertained in
various ways, but most decisively by
"comparing the duration of irrita-
bility in a paralysed muscle and in
the corresponding healthy one of the
opposite side, while they are both
submitted to the same excitation."
He "often found in experimenting
in that way that the paralysed muscle
remained irritable twice, three times,
or even four times as long as the
healthy one." This is a case of in-
duction by the Method of Difference.
The two limbs, being those of the
same animal, were presumed to differ
in no circumstance material to the
case except the paralysis, to the pre-
sence and absence of which, therefore,
the difference in the muscular irrita-
bility was to be attributed. This
assumption of complete resemblance
in all material circumstances save
one, evidently could not be safely
made in any one pair of experiments,
because the two legs of any given
animal might be accidentally in very
different pathological conditions ; but
if, besides taking pains to avoid any
such difference, the experiment was
repeated sufficiently often in different
animals to exclude the supposition
that any abnormal circumstance could
be present in them all, the conditions

EXAMPLES OP THE FOUR METHODS.

577

of the Method of Difference were
adequately secured.

In the same manner in which Dr.
Brown-S^quard proved that paralysed
muscles have greater irritability, he
also proved the correlative proposi-
tion respecting cadaveric rigidity and
putrefaction. Having, by section of
the roots of the sciatic nerve, and
again of a lateral half of the spinal
cord, produced paralysis in one hind-
leg of an animal while the other
remained healthy, he found that not
only did muscular irritability last
much longer in the paralysed limb,
but rigidity set in later, and ended
later, and putrefaction began later,
and was less rapid than on the healthy
side. This is a common case of the
Method of Difference, requiring no
comment. A further and very im-
portant corroboration was obtained by
the same method. When the animal
was killed, not shortly after the section
of the nerve, but a month later, the
effect was reversed ; rigidity set in
sooner, and lasted a shorter time, than
in the healthy muscles. But after
this lapse of time, the paralysed
muscles, having been kept by the
paralysis in a state of rest, had lost
a great part of their irritability, and
instead of more, had become less irri-
table than those on the healthy side.
This gives the A B C, a 6 c, and B
C, b c, of the Method of Difference.
One antecedent, increased irritability,
being changed, and the other circum-
stances being the same, the conse-
quence did not follow ; and, more-
over, when a new antecedent, contrary
to the first, was supplied, it was fol-
lowed by a contrary consequent. This
instance is attended with the special
advantage of proving that the retar-
dation and prolongation of the rigidity
do not depend directly on the paraly-
sis, since that was the same in both
the instances ; but specifically on one
•ffect of the paralysis, namely, the in-
creased irritability, since they ceased
when it ceased, and were reversed
when it was reversed.

2dly. Diminution of the tempera-

ture of muscles before death increases
their irritability. But diminution of
their temperature also retards cada-
veric rigidity and putrefaction.

Both these truths were first made
known by Dr, Brown-S^quard him-
self, through expei'iments which con-
clude according to the Method of
Difference. There is nothing in the
nature of the process requiring specific
analysis.

3dly. Muscular exercise, prolonged
to exhaustion, diminishes the muscular
irritability. This is a well-known
truth, dependent on the most general
laws of muscular action, and proved
by experiments under the Method of
Difference, constantly repeated. Now
it has been shown by observation
that overdriven cattle, if killed before
recovery from their fatigue, become
rigid and putrefy in a surprisingly
short time. A similar fact has been
observed in the case of animals hunted
to death ; cocks killed during or
shortly after a fight ; and soldiers
slain in the field of battle. These
various cases agree in no circumstance
directly connected with the muscles,
except that these have just been sub-
jected to exhausting exercise. Under
the canon, therefore, of the Method
of Agreement, it may be inferred that
there is a connection between the two
facts. The Method of Agreement,
indeed, as has been shown, is not
competent to prove causation. The
present case, however, is already
known to be a case of causation, it
being certain that the state of the
body after death must somehow de-
pend upon its state at the time of
death. We are therefore warranted
in concluding that the single circum-
stance in which all the instances
agree is the part of the antecedent
which is the cause of that particular
consequent,

4thly. In proportion at the nuti'i-
tion of muscles is in a good state,
their irritability is high. This fact
also rests on the general evidence of
the laws of physiology, grounded on
many familiar applications of the

278

INDUCTION.

Method of DiflFerence. Now, in the
case of those who died from accident
or violence, with their muscles in a
good state of nutrition, the muscular
irritability continues long after death,
rigidity sets in late, and persists long
without the putrefactive change. On
the contrary, in cases of disease in
which nutrition has been diminished
for a long time before death, all these
effects are reversed. These are the
conditions of the Joint Method of
Agreement and Difference. The cases
of retarded and long-continued rigi-
dity here in question agree only in
being preceded by a high state of
nutrition of the muscles ; the cases
of rapid and brief rigidity agree only
in being preceded by a low state of
muscular nutrition ; a connection is
therefore inductively proved between
the degree of the nutrition and the
slowness and prolongation of the rigi-
dity.

5thly. Convulsions, like exhausting
exercise, but in a still greater degree,
diminish the muscular irritability.
Now, when death follows violent and
prolonged convulsions, as in tetanus,
hydrophobia, some cases of cholera,
and certain poisons, rigidity sets in
Tery rapidly, and, after a very brief
duration, gives place to putrefaction.
This is another example of the Method
of Agreement, of the same character
with No. 3.

6thly. The series of instances which
we shall take last is of a more com-
plex character, and requires a more
minute analysis.

It has long been observed that in
some cases of death by lightning cada-
veric rigidity either does not take place
at all, or is of such extremely brief
duration as to escape notice, and that
in these cases putrefaction is very ra-
pid. In other cases, however, the usual
cadaveric rigidity appears. There
must be some difference in the cause
to account for this difference in the
•ffect Now "death by lightning
may be the result of, let, a syncope
by fright, or in consequence of a direct
or reflex influence of lightning on the

par vagum ; 2dly, hemorrhage in or
around the brain, or in the lungs, the
pericardium, &c. ; 3dly, concussion,
or some other alteration in the brain ;"
none of which phenomena have any
known property capable of account-
ing for the suppression, or almost
suppression, of the cadaveric rigidity.
But the cause of death may also be
that the lightning produces " a violent
convulsion of every muscle in the
body," of which, if of sufficient in-
tensity, the known effect would be
that " muscular irritability ceases
almost at once." If Dr. Brown-
S^quard's generalisation is a true law,
these will be the very cases in which
rigidity is so much abridged as to
escape notice ; and the cases in which,
on the contrary, rigidity takes place
as usual will be those in which the
stroke of lightning operates in some
of the other modes which have been
enumerated. How, then, is this
brought to the test ? By experiments
not on lightning, which cannot be
commanded at pleasure, but on the
same natural agency in a manageable
form, that of artificial galvanism. Dr.
Brown-S^quard galvanised the entire
bodies of animals immediately after
death. Galvanism cannot operate in
any of the modes in which the stroke
of lightning may have operated, ex-
cept the singular one of producing
muscular convulsions. If, therefore,
after the bodies have been galvanised,
the durati jn of rigidity is much short-
ened and putrefaction much accele-
rated, it is reasonable to ascribe the
same effects when produced by light-
ning to the property which galvanism
shares with lightning, and not to
those which it does not. Now this
Dr. Brown -S^quard found to be the
fact. The galvanic experiment was
tried with charges of very various
degrees of strength ; and the more
powerful the charge, the shorter was
found to be the duration of rigidity,
and the more speedy and rapid the
putrefaction. In the experiment in
which the charge was strongest and
the muscular irritability most promptly

EXAMPLES OF tHPi FOtTR METHODS.

27^

destroyed, the rigidity only lasted
fifteen minutes. On the principle,
therefore, of the Method of Concomi-
tant Variations, it may be infened
that the duration of the rigidity de-
pends on the degree of the irritability ;
and that if the charge had been
aa much stronger than Dr. Brown -
S^quard's strongest, as a stroke of
lightning must be stronger than any
electric shock which we can produce
artificially, the rigidity would have
been shortened in a corresponding
ratio, and might have disappeared
altogether. This conclusion having
been arrived at, the case of an electric
shock, whether natural or artificial,
becomes an instance, in addition to all
those already ascertained, of corre-
spondence between the irritability
of the muscle and the duration of
rigidity.

All these instances are summed iip
in the following statement : — " That
when the degree of muscular irrita-
bility at the time of death is consider-
able, either in consequence of a good
state of nutrition, as in persons who
die in full health from an accidental
cause, or in consequence of rest, as in
cases of paralysis, or on account of
the influence of cold, cadaveric rigidity
in all these cases sets in late and lasts
long, and putrefaction appears late,
and progresses slowly ; " but " that
when the degree of muscular irrita-
bility at the time of death is slight,
either in consequence of a bad state
of nutrition, or of exhaustion from
over-exertion, or from convulsions
caused by disease or poison, cadaveric
rigidity sets in and ceases soon, and
putrefaction appears and progresses
quickly." These facts present, in all
their completeness, the conditions of
the Joint Method of Agreement and
Difference. Early and brief rigidity
takes place in cases which agree only
in the circumstance of a low state of
muscular irritability. Rigidity begins
late and lasts long in cases which
agree only in the contrary circum-
stance, of a muscular irritability high
*nd "Tiusually prolonged. It follows

that there is a connection through
causation between the degree of mus-
cular irritability after death and the
tardiness and prolongation of the cada-
veric rigidity.

This investigation places in a strong
light the value and efl&cacy of the
Joint Method. For, as we have
already seen, the defect of that
Method is, that, like the Method of
Agreement, of which it is only an
improved form, it cannot prove causa-
tion. But in the present case (as in
one of the steps in the argument
which led up to it) causation is already
proved, since there could never be
any doubt that the rigidity altogether,
and the putrefaction which follows it,
are caused by the fact of death. The
observationsand experiments on which
this rests are too familiar to need
analysis, and fall under the Method
of Difference. It being, therefore,
beyond doubt that the aggregate
antecedent, the death, is the actual
cause of the whole train of conse-
quents, whatever of the circumstances
attending the death can be shown to
be followed in all its variations by
variations in the effect under investi-
gation, must be the particular feature
of the fact of death on which that
effect depends. The degree of muscu-
lar irritability at the time of death
fulfils this condition. The only point
that could be brought into question
would be whether the effect depended
on the irritability itself, or on some-
thing which always accompanied the
irritability : and this doubt is set at
rest by establishing, as the instances
do, that by whatever cause the high
or low irritability is produced, the
effect equally follows ; and cannot,
therefore, depend upon the causes of
irritability, nor upon the other effects
of those causes, which are as various
as the causes themselves, but upon
the irritability solely.

§ 5. The last two examples will
have conveyed to any one by whom
they have been duly followed so clear
a conception of the use and practical

dSo

INDUCTION.

management of three of the four
meth^s of experimental inquiry, as
to supersede the necessity of any
further exemplification of them. The
remaining method, that of Residues,
not having found a place in any of
the preceding investigations, I shall
quote from Sir John Herschel some
examples of that method, with the
remarks by which they are introduced.

" It is by this process, in fact, that
science, in its present advanced state,
is chiefly promoted. Most of the phe-
nomena which Nature presents are
very complicated ; and when the
effects of all known causes are esti-
mated with exactness, and subducted,
the residual facts are constantly ap-
pearing in the form of phenomena
altogether new, and leading to the
most important conclusions.

" For example : the return of the
comet predicted by Professor Encke,
a great many times in succession, and
the general good agreement of its
calculated with its observed place dur-
ing any one of its periods of visibility,
would lead us to say that its gravita-
tion towards the sun and planets is
the sole and sufficient cause of all the
phenomena of its orbitual motion ;
but when the effect of this cause is
strictly calculated and subducted from
the observed motion, there is found to
remain behind a residual phenomenon,
which would never have been other-
wise ascertained to exist, which is a
small anticipation of the time of its
reappearance, or a diminution of its
periodic time, which cannot be ac-
counted for by gravity, and whose
cause is therefore to be inquired into.
Such an anticipation would be caused
by the resistance of a medium dissemi-
nated through the celestial regions ;
and as there are other good reasons
for believing this to be a vera causa,"
(an actually existing antecedent,) "it
has therefore been ascribed to such a
resistance.*

• In his subsequent work, Outlinet of
Attronomy (J 570), Sir John Herschel sug-
geets another possible explanation of the
acceleration of the revolution of a comet.

"M. Arago, having suspended a
magnetic needle by a silk thread, and
set it in vibration, observed that it
came much sooner to a state of rest
when suspended over a plate of copper,
than when no such plate was beneath
it. Now, in both cases there were
two verce causae" (antecedents known
to exist) " why it should come at
length to rest, viz. the resistance of
the air, which opposes, and at length
destroys, all motions performed in it;
and the want of perfect mobility in
the silk thread. But the effect of
these causes being exactly knovn by
the observation made in the absence
of the copper, and being thus albwed
for and subducted, a residual pheno-
menon appeared, in the fact that a
retarding influence was exerted by
the copper itself ; and this fact, once
ascertained, speedily led to the know-
ledge of an entirely new and unex-
pected class of relations." This ex-
ample belongs, however, not to the
Method of Residues but to the Method
of Difference, the law being ascer-
tained by a direct comparison of the
results of two experiments, which
differed in nothing but the presence
or absence of the plate of copper. To
have made it exemplify the Method
of Residues, the effect of the resistance
of the air and that of the rigidity of
the silk should have been calculated
d priori from the laws obtained by
separate and foregone experiments.

" Unexpected and peculiarly strik-
ing confirmations of inductive laws
frequently occur in the form of re-
sidual phenomena, in the course of
investigations of a widely different
nature from those which gave rise to
the inductions themselves. A very
elegant example may be cited in the
unexpected confirmation of the law of
the development of heat in elastic
fluids by compression, which is afforded
by the phenomena of sound. The
inquiry into the cause of sound had
led to conclusions respecting its mode
of propagation, from which its velocity
in the air could be precisely calculated.
The calcvdations were performed, but,

EXAMPLES OF T*HE tOVU METHODS.

281

when compared with fact, though the
agreement was quite sufficient to show
the general correctness of the cause
and mode of propagation assigned, yet
the whole velocity could not be shown
to arise from this theory. There was
still a residual velocity to be accounted
for, which placed dynamical philoso-
phers for a long time in great dilemma.
At length Laplace struck on the happy
idea that this might arise from the heat
developed in the act of that condensa-
tion which necessarily takes place at
every vibration by which sound is
conveyed. The matter was subjected
to exact calculation, and the result
was at once the complete explanation
of the residual phenomenon, and a
striking confirmation of the general
law of the development of heat by
compression, under circumstances be-
yond artificial imitation."

"Many of the new elements of
chemistry have been detected in the
investigation of residual phenomena.
Thus Arfwedson discovered lithia by
perceiving an excess of weight in the
sulphate produced from a small por-
tion of what he considered as magnesia
present in a mineral he had analysed.
It is on this principle, too, that the
small concentrated residues of great
operations in the arts are almost sure
to be the lurking-places of new chemi-
cal ingredients : witness iodine, bro-
mine, selenium, and the new metals
accompanying platina in the experi-
ments of Wollaston and Tennant. It
was a happy thought of Glauber to
examine what everybody else threw
away." *

" Almost all the greatest discoveries
in Astronomy," says the Bameauthor,+
•' have resulted from the consideration
of residual phenomena of a quantita-
tive or ujmerical kind. ... It was
thus that the grand discovery of the
precession of the equinoxes resulted
as a residual phenomenon from the
imperfect explanation of the return of
the seasons by the return of the sun
to the same apparent place among

* Discourse, T>p. 156-158, and 171.
t Ouiliius oj Astronomy, § 856.

the fixed stars. Thus, also, aberra-
tion and nutation resulted as residual
phenomena from that portion of the
changes of the apparent places of the
fixed stars which was left unaccounted
for by precession. And thus again
the apparent proper motions of the
stars are the observed residues of
their apparent movements outstand-
ing and unaccounted for by strict
calculation of the effects of preces-
sion, nutation, and aberration. The
nearest approach which human theories
can make to perfection is to diminish
this residue, this caput mortuum of
observation, as it may be considered,
as much as practicable, and, if pos-
sible, to reduce it to nothing, either
by showing that something has been
neglected in our estimation of known
causes, or by reasoning upon it as a
new fact, and on the principle of the
inductive philosophy ascending from
the effect to its cause or causes."

The disturbing eflfects mutually pro-
duced by the earth and planets upon
each other's motions were first brought
to light as residual phenomena, by
the difference which appeared between
the observed places of those bodies
and the places calculated on a con-
sideration solely of their gravitation
towards the sun. It was this which
determined astronomers to consider
the law of gravitation as obtaining
between all bodies whatever, and
therefore between all particles of
matter ; their first tendency having
been to regard it as a force acting
only between each planet or satellite
and the central body to whose system
it belonged. Again, the catastro-
phists, in geology, be their opinion
right or wrong, support it on the
plea, that after the effect of all causes
now in operation has been allowed
for, there remains in the existing
constitution of the earth a large
residue of facts, proving the exist-
ence at former periods either of other
forces, or of the same forces in a much
greater degree of intensity. To add
one more example : those who assert,
what no one has shown any real

282

INDUCTION.

ground for believing, that there is
in one human individual, one sex, or
one race of mankind over another an
inherent and inexplicable superiority
in mental faculties, could only sub-
stantiate their proposition by sub-
tracting from the differences of in-
tellect which we in fact see all that
can be traced by known laws either
to the ascertained differences of physi-
cal organisation, or to the differences
which have existed in the outward
circumstances in which the subjects
of the comparison have hitherto been
placed. What these causes might
fail to account for would constitute
a residual phenomenon, which, and
which alone, would be evidence of an
ulterior original distinction, and the
measure of its amount. But the as-
sertors of such supposed differences
have not provided themselves with
these necessary logical conditions of
the establishment of their doctrine.

The spirit of the Method of Resi-
dues being, it is hoped, sufficiently
intelligible from these examples, and
the other three methods having al-
ready been so fully exemplified, we
may here close our exposition of the
four methods, considered as employed
in the investigation of the simpler and
more elementary order of the com-
binations of phenomena.

§ 6. Dr. Whewell has expressed
a very unfavourable opinion of the
utility of the Four Methods, as well
as of the aptness of the examples by
which I have attempted to illustrate
them. His words are these : * —

"Upon these methods the obvious
thing to remark is, that they take for
granted the very thing which is most
difficult to discover, the reduction of
the phenomena to formvdse such as
are here presented to us. When we
have any set of complex facts offered
to us, — for instance, those which were
offered in the cases of discovery which
I have mentioned, — the facts of the
planetary paths, of falling bodies, of

* PhiUf9opli^ 0/ Discoveiii, pp. 263, 264.

refracted rays, of cosmical motions,
of chemical analysis ; and when, in
any of these cases, we would discover
the law of nature which governs them,
or, if any one chooses so to term it,
the feature in which all the cases
agree, where are we to look for our
A, B, C, and a, 6, c? Nature does
not present to us the cases in this
form ; and how are we to reduce
them to this form? You say, when
we find the combination of A B C
with a b c and A B D with a b d,
then we may draw our inference.
Granted ; but when and where are
we to find such combinations ? Even
now that the discoveries are made,
who will point out to us what are the
A, B, C, and a, b, c, elements of the
cases which have just been enumer-
ated ? Who will tell us which of the
methods of inquiry those historically
real and successful inquiries exem-
plify ? Who will carry these formulae
through the history of the sciences,
as they have really grown up ; and
show us that these four methods have
been operative in their formation ; or
that any light is thrown upon the
steps of their progress by reference to
these formulae ? "

He adds that, in this work, the
methods have not been applied "to
a large body of conspicuous and un-
doubted examples of discovery, ex-
tending along the whole history of
science ; " which ought to have been
done in order that the methods might
be shown to possess the "advantage"
(which he claims as belonging to his
own) of being those "by which all
great discoveries in science have really
been made " (p. 277).

There is a striking similarity be-
tween the objections here m^de against
Canons of Induction, ana what was
alleged, in the last century, by as able
men as Dr. Whewell, against the ac-
knowledged Canon of Ratiocination.
Those who protested against the Aris-
totelian Logic said of the Syllogism,
what Dr. Whewell says of the In-
ductive Methods, that it "takes for
granted the very thing which is most

EXAMPLES OF THE FOUR METHODS.

285

difficult to discover, the reduction of
the argument to formulae such as are
here presented to us." The grand
difficulty, they said, is to obtain your
syllogism, not to judge of its correct-
ness when obtained. On the matter
of fact, both they and Dr. Whewell
are right. The greatest difficulty in
both cases is first that of obtaining
the evidence, and next, of reducing it
to the form which tests its conclusive-
ness. But if we try to reduce it with-
out knowing what it is to be reduced
to, we are not likely to make much
progress. It is a more difficult thing
to ^Kolve a geometrical problem than
to judge whether a proposed solution
is correct ; but if people were not able
to judge of the solution when found,
they would have little chance of find-
ing it. And it cannot be pretended
that to judge of an induction when
found is perfectly easy, is a thing for
which aids and instruments are super-
fluous ; for erroneous inductions, false
inferences from experience, are quite
as common, on some subjects much
commoner, than true ones. The busi-
ness of Inductive Logic is to provide
rules and models, (such as the Syllo-
gism and its rules are for ratiocina-
tion,) to which, if inductive argu-
ments conform, those arguments are
conclusive, and not otherwise. This
is what the Four Methods profess to
be, and what I believe they are uni-
versally considered to be by experi-
mental philosophers, who had prac-
tised all of them long before any
one sought to reduce the practice to
theory.

The assailants of the Syllogism had
also anticipated Dr. Whewell in the
other branch of his argument. They
said that no discoveries were ever
made by syllogism ; and Dr. Whe-
well says, or seems to say, that none
were ever made by the Four Methods
of Induction. To the former objec-
tors, Archbishop Whately very per-
tinently answered, that their argu-
ment, if good at all, was good against
the reasoning process altogether ; for
whatever cannot be reduced to syllo-

gism is not reasoning. And Dr.
Whewell's argument, if good at all,
is good against all inferences from
experience. In saying that no dis-
coveries were ever made by the Four
Methods, he affirms that none were
ever made by observation and ex-
periment ; for assuredly if any were,
it was by processes reducible to one
or other of those methods.

This difference between us accounts
for the dissatisfaction which my ex-
amples give him ; for I did not select
them with a view to satisfy any one
who required to be convinced that ob-
servation and experiment are modes
of acquiring knowledge : I confess
that in the choice of them I thought
only of illustration, and of facilitating
the conception of the Methods by con-
crete instances. If it had been my
object to justify the processes them-
selves as means of investigation, there
would have been no need to look far
off, or make use of recondite or com-
plicated instances. As a specimen of
a truth ascertained by the Method of
Agreement, I might have chosen the
proposition " Dogs bark." This dog,
and that dog, and the other dog,
answer to A B C, A D E, A F G.
The circumstance of being a dog
answers to A. Barking answers to
a. As a truth made known by the
Method of Difference, " Fire bums "
might have sufficed. Before I touch
the fire I am not burnt ; this is B C ;
I touch it, and am burnt ; this is A B
C, a B C.

Such familiar experimental pro-
cesses are not regarded as inductions
by Dr. Whewell ; but they are per-
fectly homogeneous with those by
which, even on his own showing, the
pyramid of science is supplied with
its base. In vain he attempts to
escape from this conclusion by laying
the mofet arbitrary restrictions on the
choice of examples admissible as in-
stances of Induction : they must
neither be such as are still matter of
discussion (p. 265), nor must any of
them be drawn from mental and
social subjects (p. 269), nor from

i84

INDUCTION.

ordinary observation and practical
life (pp. 241-247). They must be
taken exclusively from the generalisa-
tions by which scientific thinkers have
ascended to great and comprehensive
laws of natural phenomena. Now it
is seldom possible, in these compli-
cated inquiries, to go much beyond
the initial steps without calling in
the instrument of Deduction and the
temporary aid of hypotheses ; as I
myself, in common with Dr. Whewell,
have maintained against the purely
empirical school. Since, therefore,
such cases could not conveniently be
selected to illustrate the principles of
mere observation and experiment. Dr.
Whewell is misled by their absence
into representing the Experimental
Methods as serving no purpose in
scientific investigation ; forgetting
that if those methods had not sup-
plied the first generalisations, there
would have been no materials for his
own conception of Induction to work
upon.

His challenge, however, to point
out which of the four methods are
exemplified in certain important cases
of scientific inquiry is easily answered.
"The planetary paths," as far as they
are a case of induction at all,* fall
under the Method of Agreement.
The law of " falling bodies," namely,
that they describe spaces proportional
to the squares of the times, was his-
torically a deduction from the first
law of motion ; but the experiments
by which it was verified, and by which
it might have been discovei-ed, were
examples of the Method of Agree-
ment ; and the apparent variation
from the true law, caused by the re-
sistance of the air, was cleared up by
experiments in vacuo, constituting an
application of the Method of Differ-
ence. The law of " refracted rays "
(the constancy of the ratio between
the sines of incidence and of refrac-
tion for each refracting substance)
was ascertained by direct measure-
ment, and therefore by the Method

* See, on this point, the second chapter
of the present Book.

of Agreement. The "cosmical mo-
tions" were determined by highly
complex processes of thought, in which
Deduction was predominant, but the
Methods of Agreement and of Con-
comitant Variations had a large part
in establishing the empirical laws.
Every case without exception of
*' chemical analysis " constitutes a
well-marked example of the Method
of Difference. To any one acquainted
with the subjects — to Dr. Whewell
himself, there would not be the small-
est difficulty in setting out " the ABC
and a b c elements " of these cases.

If discoveries are ever made by
observation and experiment without
Deduction, the four methods are
methods of discovery : but even if
they were not methods of discovery,
it would not be the less true that they
are the sole methods of Proof ; and
in that character, even the results of
deduction are amenable to them. The
great generalisations which begin as
Hypotheses must end by being proved,
and are in reality (as will be shown
hereafter) proved, by the Four Me-
thods. Now it is with Proof, as such,
that Logic is principally concerned.
This distinction has, indeed, no chance
of finding favour with Dr. Whewell ;
for it is the peculiarity of his system
not to recognise, in cases of Induc-
tion, any necessity for proof. If, after
assuming an hypothesis and carefully
collating it with facts, nothing is
brought to light inconsistent with it,
that is, if experience does not disprove
it, he is content ; at least until a sim-
pler hypothesis, equally consistent
with experience, presents itself. If
this be Induction, doubtless there is
no necessity for the Four Methods.
But to suppose that it is so appears
to me a radical misconception of the
nature of the evidence of physical
truths.

So real and practical is the need of
a test for induction similar to the
syllogistic test of ratiocination, that
inferences which bid defiance to the
most elementary notions of inductive
logic are put forth without misgiv-

PLURALITY OF CAUSES.

285

ing by persons eminent in physical
science, as soon as they are off the
ground on which they are conversant
with the facts, and not reduced to
judge only by the arguments ; and as
for educated persons in general, it
may be doubted if they are better
judges of a good or a bad induction
than they were before Bacon wrote.
The improvement in the results of
thinking has seldom extended to the
processes ; or has reached, if any pro-
cess, that of investigation only, not
that of proof. A knowledge of many
laws of nature has doubtless been ar-
rived at by framing hypotheses and
finding that the facts corresponded to
them ; and many errors have been
got rid of by coming to a knowledge
of facts which were inconsistent with
them, but not by discovering that the
mode of thought which led to the
errors was itself faulty, and might
have been known to be such inde-
pendently of the facts which disproved
the specific conclusion. Hence it is
that, while the thoughts of mankind
have on many subjects worked them-
selves practically right, the thin ^
power remains as weak as ever ; and
on all subjects on which the facts
which would check the result are not
accessible, as in what relates to the
invisible world, and even, as has
been seen lately, to the visible world
of the planetary regions, men of the
greatest scientific acquirements argue
as pitiably as the merest ignoramus.
For though they have made many
sound inductions, they have not
learnt from them (and Dr. Whewell
thinks there is no necessity that they
should learn) the principles of induc-
tive evidence.

CHAPTER X

OP PLURALITY OF CATTSBS, AND OP THE
INTERMIXTURE OP EXPECTS.

§ I. In the preceding exposition of
the four methods of observation and
experiment, by which we contrive to
distinguish among a mass of co-exis-

tent phenomena the particular effect
due to a given cause, or the parti-
cular cause which gave birth to a
given effect, it has been necessary to
suppose, in the first instance, for the
sake of simplification, that this analy-
tical operation is encumbered by no
other difficulties than what are essen-
tially inherent in its nature ; and to
represent to ourselves, therefore, every
effect, on the one hand as connected
exclusively with a single cause, and
on the other hand as incapable of
being mixed and confounded with
any other co-existent effect. We
have regarded a b c d e, the aggre-
gate of the phenomena existing at
any moment, as consisting of dissi-
milar facts, a, 6, c, d, and e, for each
of which one, and only one, cause
needs be sought ; the difficulty being
only that of singling out this one
cause from the multitude of antece-
dent circumstances. A, B, C, D, and
E, The cause indeed may not be
simple ; it may consist of an assem-
blage of conditions ; but we have sup-
posed that there was only one possible
assemblage of conditions from which
the given effect could result.

If such were the fact, it would be
comparatively an easy task to inves-
tigate the laws of nature. But the
supposition does not hold in either of
its parts. In the first place, it is not
true that the same phenomenon is
always produced by the same cause ;
the effect a may sometimes arise from
A, sometimes from B. And, secondly,
the effects of different causes are
often not dissimilar, but homogeneous,
and marked out by no assignable
boundaries from one another ; A and
B may produce not a and b, but dif-
ferent portions of an effect a. The
obscurity and diflBculty of the inves-
tigation of the laws of phenomena is
singularly increased by the necessity
of adverting to these two circum-
stances— Intermixture of Effects and
Plurality of Causes. To the latter,
being the simpler of the two con-
siderations, we shall first direct our
attention.

2S6

INDUCTION.

It is not true, then, that one effect
must be connected with only one
cause, or assemblage of conditions ;
that each phenomenon can be pro-
duced only in one way. There are
often several independent modes in
which the same phenomenon could
have originated. One fact may be
the consequent in several invariable
seqiiences ; it may follow, with equal
uniformity, any one of several ante-
cedents, or collections of antecedents.
Many causes may produce mechanical
motion : many causes may produce
some kinds of sensation : many causes
may produce death. A given effect
may really be produced by a certain
cause, and yet be perfectly capable
of being produced without it.

§ 2. One of the principal conse-
quences of this fact of Plurality of
Causes is, to render the first of the
inductive methods, that of Agreement,
uncertain. To illustrate that method
we supposed two instances, ABC
followed by a b c, and A D E followed
hy a d e. From these instances it
might apparently be concluded that
A is an invariable antecedent of a,
and even that it is the unconditional
invariable antecedent or cause, if we
could be sure that there is no other
antecedent common to the two cases.
That this diflficulty may not stand in
the way, let us suppose the two cases
positively ascertained to have no
antecedent in common except A. The
moment, however, that we let in the
possibility of a plurality of causes,
the conclusion fails. For it involves
a tacit supposition that a must have
been produced in both instances by
the same cause. If there can pos-
sibly have been two causes, those two
may, for example, be C and E : the
one may have been the cause of a in
the former of the instances, the other
in the latter, A having no influence
in either case.

Suppose, for example, that two
great artists or great philosophers,
that two extremely selfish or ex-
tremely generous characters, were

compared together as t© the circum.
stances of their education and history,
and the two cases were found to
agree only in one circumstance :
would it follow that this one circum-
stance was the cause of the quality
which characterised both those indi-
viduals ? Not at all ; for the causes
which may produce any type of char-
acter are very numerous ; and the
two persons might equally have
agreed in their character, though
there had been no manner of resem-
blance in their previous history.

This, therefore, is a characteristic
imperfection of the Method of Agree-
ment ; from which imperfection the
Method of Difference is free. For if
we have two instances, ABC and
B C, of which B C gives b c, and A
being added converts it into a b c, it
is certain that in this instance, at
least, A was either the cause of a,
or an indispensable portion of its
cause, even though the cause which
produces it in other instances may
be altogether different. Plurality of
Causes, therefore, not only does not
diminish the reliance due to the
Method of Difference, but does not
even render a greater number of ob-
servations or experiments necessary :
two instances, the one positive and
the other negative, are still sufficient
for the most complete and rigorous
induction. Not so, however, with
the Method of Agreement. The con-
clusions which that yields, when the
number of instancCvH compared is
small, are of no real value, except as,
in the character of suggestions, they
may lead either to experiments bring-
ing them to the test of the Method
of Difference, or to reasonings which
may explain and verify them deduc-
tively.

It is only when the instances, being
indefinitely multiplied and varied,
continue to suggest the same result,
that this result acquires any high
degree of independent value. If there
are but two instances, ABC and
A D E, though these instances have
no antecedent in common except A,

PLURALITY OF CAUSES.

287

yet, as the effect may possibly have
been produced in the two cases by
different causes, the result is at most
only a slight probability in favour of
A ; there may be causation, but it is
almost equally probable that there
was only a coincidence. But the
oftener we repeat the observation,
varying the circumstances, the more
we advance towards a solution of this
doubt. For if we try A F G, A H
K, &c., all unlike one another except
in containing the circumstance A, and
if we find the effect a entering into
the result in all these cases, we must
suppose one of two things, either that
it is caused by A, or that it has as
many different causes as there are
instances. With each addition, there-
fore, to the number of instances, the
presumption is strengthened in favour
of A. The inquirer, of course, will
not neglect, if an opportunity present
itself, to exclude A from some one of
these combinations, from A H K for
instance, and by trying H K sepa-
rately, appeal to the Method of Dif-
ference in aid of the Method of
Agreement. By the Method of Dif-
ference alone can it be ascertained
that A is the cause of a ; but that it
is either the cause, or another effect
of the same cause, may be placed
beyond any reasonable doubt by the
Method of Agreement, provided the
instances are very numerous as well
as sufficiently various.

After how great a multiplication,
then, of varied instances, all agreeing
in no other antecedent except A, is
the supposition of a plurality of causes
sufficiently rebutted, and the conclu-
sion that a is connected with A
divested of the characteristic imper-
fection, and reduced to a virtual cer-
tainty ? This is a question which we
cannot be exempted from answering :
but the consideration of it belongs to
what is called the Theory of Proba-
bility, which will form the subject of
a chapter hereafter. It is seen, how-
ever, at once, that the conclusion
does amount to a practical certainty
»fter » tufficient number of instances,

and that the method, therefore, is not
radically vitiated by the characteristic
imperfection. The result of these
considerations is only, in the first
place, to point out a new source of
inferiority in the Method of Agree-
ment as compared with other modes
of investigation, "and new reasons for
never resting contented with the
results obtained by it, without at-
tempting to confirm them either by
the Method of Difference, or by con-
necting them deductively with some
law or laws already ascertained by
that superior method. And, in the
second place, we learn from this the
true theory of the value of a mere
mumher of instances in inductive in-
quiry. The Plurality of Causes is
the only reason why mere number
is of any importance. The tendency
of unscientific inquirers is to rely too'
much on number, without analysing
the instances ; without looking closely
enough into their nature, to ascertain
what circumstances are or are not
eliminated by means of them. Most
people hold their conclusions with a
degree of assurance proportioned to
the mere mass of the experience on
which they appear to rest ; not con-
sidering that by the addition of in-
stances to instances, all of the same
kind, that is, differing from one
another only in points already recog-
nised as immaterial, nothing whatever
is added to the evidence of the con-
clusion. A single instance eliminating
some antecedent which existed in all
the other cases is of more value than
the greatest multitude of instances
which are reckoned by their number
alone. It is necessary, no doubt, to
assure ourselves, by repetition of the
observation or experiment, that no
error has been committed concerning
the individual facts observed ; and
until we have assured ourselves of
this, instead of varying the circum-
stances, we cannot too scrupulously
repeat the same experiment or obser-
vation without any change. But
when once this assurance has been
obtained, the multiplication of in-

288

INDUCTION.

Btances which do not exclude any
more circumstances is entirely useless,
provided there have been already
enough to exclude the supposition of
Plurality of Causes.

It is of importance to remark,
that the peculiar modification of the
Method of Agreement, which, as par-
taking in some degree of the nature
of the Method of Difference, I have
called the Joint Method of Agree-
ment and Difference, is not affected
by the characteristic imperfection now
pointed out. For, in the joint method,
it is supposed not only that the in-
stances in which a is, agree only in
containing A, but also that the in-
stances in which a is not, agree only
in not containing A. Now, if this
be so, A must be not only the cause
of a, but the only possible cause : for
if there were another, as, for example,
B, then in the instances in which a is
not, B must have been absent as well
as A, and it would not be true that
these instances agree only in not con-
taining A. This, therefore, consti-
tutes an immense advantage of the
joint method over the simple Method
of Agreement. It may seem, indeed,
that the advantage does not belong
so much to the joint method as to
one of its two premises, (if they may
be so called,) the negative premise.
The Method of Agreement, when
applied to negative instances, or those
in which a phenomenon does not take
place, is certainly free from the char-
acteristic imperfection which affects
it in the affirmative case. The nega-
tive premise, it might therefore be
supposed, could be worked as a simple
case of the Method of Agreement,
without requiring an affirmative pre-
mise to be joined with it. But though
this is true in principle, it is gene-
rally altogether impossible to work
the Method of Agreement by negative
instances without positive ones : it is
so much more difficult to exhaust the
field of negation than that of affirma-
tion. For instance, let the question
be, what is the cause of the trans-
parency of bodies ; with what prospect

of success could we set ourselves to
inquire directly in what the multi-
farious substances which are not trans-
parent agree? But we might hope
much sooner to seize some point of
resemblance among the comparatively
few and definite species of objects
which are transparent ; and this being
attained, we should quite naturally
be put upon examining whether the
absence of this one circumstance be
not precisely the point in which all
opaque circumstances will be found
to resemble.

The Joint Method of Agreement
and Difference, therefore, or, as I
have otherwise called it, the Indirect
Method of Difference, (because, like
the Method of Difference properly so
called, it proceeds by ascertaining
how and in what the cases where the
phenomenon is present differ from
those in which it is absent,) is, after
the Direct Method of Difference, the
most powerful of the remaining instru-
ments of inductive investigation ; and
in the sciences which depend on pure
observation, with little or no aid from
experiment, this method, so well ex-
emplified in the speculation on the
cause of dew, is the primary resource,
so far as direct appeals to experience
are concerned-

§ 3. We have thus far treated
Plurality of Causes only as a possible
supposition, which, until removed,
renders our inductions uncertain; and
have only considered by what means,
where the plurality does not really
exist, we may be enabled to disprove
it. But we must also consider it as a
case actually occurring in nature, and
which, as often as it does occur, our
methods of induction ought to be
capable of ascertaining and establish-
ing. For this, however, there is re-
quired no peculiar method. When an
effect is really producible by two or
more causes, the process for detecting
them is in no way different from that
by which we discover single causes.
They may (first) be discovered as
separate sequences by separate seta

INTERMIXTURE OF EFFECTS.

2«9

of instances. One set of observations
or experiments shows that the sun is
a cause of heat, another that friction is
a source of it, another that percussion,
another that electricity, another that
chemical action is such a source. Or
(secondly) the plurality may come to
light in the course of collating a
number of instances, when we attempt
to find some circumstance in which
they all agree, and fail in doing so.
We find it impossible to trace, in all the
cases in which the eflfect is met with,
any common circumstance. We find
that we can eliminate all the ante-
cedents ; that no one of them is
present in all the instances, no one
of them indispensable to the eflfect.
On closer scrutiny, however, it appears
that though no one is always present,
one or other of several always is. If,
on further analysis, we can detect in
these any common element, we may
be able to ascend from them to some
one cause which is the really operative
circumstance in them all. Thus it is
now thought that in the production of
heat by friction, percussion, chemical
action, &c., the ultimate source is one
and the same. But if (as continually
happens) we cannot take this ulterior
step, the different antecedents must
be set down provisionally as distinct
causes, each sufficient of itself to pro-
duce the eflfect.

We here close our remarks on the
Plurality of Causes, and proceed to
the still more peculiar and more com-
plex case of the Intermixture of
Effects, and the interference of causes
with one another : a case constituting
the principal part of the complication
and difficulty of the study of nature ;
and with which the four only possible
methods of directly inductive investi-
gation by observation and experiment
are for the most part, as will appear
presently, quite unequal to cope. The
instrument of Deduction alone is
adequate to unravel the complexities
proceeding from this source ; and the
four methods have little more in their
power than to supply premises for,
IMid a verification of, our deductions,

§ 4. A concurrence of two or mora
causes, not separately producing each
its own eflfect, but interfering with or
modifying the effects of one another,
takes place, as has already been
explained, in two diflferent ways.
In the one, which is exemplified by
the joint operation of diflferent forces
in mechanics, the separate eflfects of all
the causes continue to be produced, but
are compounded with one another, and
disappear in one total. In the other,
illustrated by the case of chemical ac-
tion, the separate eflfects cease entirely,
and are succeeded by phenomena al-
together different, and governed by
different laws.

Of these cases the former is by far
the more frequent, and this case it is
which, for the most part, eludes the
grasp of our experimental methods.
The other and exceptional case is
essentially amenable to them. When
the laws of the original agents ceaso
entirely, and a phenomenon makes its
appearance, which, with reference to
those laws, is quite heterogeneous ;
when, for example, two gaseous sub-
stances, hydrogen and oxygen, on
being brought together, throw off
their peculiar properties, and produce
the substance called water — in such
cases the new fact may be subjected
to experimental inquiry, like any
other phenomenon ; and the elements
which are said to compose it may be
considered as the mere agents of its
production ; the conditions on which
it depends, the facts which make up
its cause.

The effects of the new phenomenon,
the properties of water, for instance,
are as easily found by experiment as
the eflfects of any other cause. But
to discover the cause of it, that is, the
particular conjunction of agents from
which it results, is often difficult
enough. In the first place, the origin
and actual production of the pheno-
menon are most frequently inacces-
sible to our observation. If we
could not have learned the composi-
tion of water until we found instances
in which it was actually produced

ago

INDUCTION.

from oxygen and hydrogen, we should
have been forced to wait until the
casual thought struck some one of
passing an electric spark through a
mixture of the two gases, or inserting
a lighted paper into it, merely to try
what would happen. Besides, many
substances, though they can be ana-
lysed, cannot by any known artificial
means be recompounded. Further,
even if we could have ascertained, by
the Method of Agreement, that oxy-
gen and hydrogen were both present
when water is produced, no experi-
mentation on oxygen and hydrogen
separately, no knowledge of their
laws, could have enabled us deduc-
tively to infer that they would pro-
duce water. We require a specific
experiment on the two combined.

Under these difficulties, we should
generally have been indebted for our
knowledge of the causes of this class
of effects, not to any inquiry directed
specifically towards that end, but
either to accident, or to the gradual
progress of experimentation on the
different combinations of which the
producing agents are susceptible ; if
it were not for a peculiarity belong-
ing to effects of this description, that
they often, under some particular com-
bination of circumstances, reproduce
their causes. If water results from
the juxtaposition of hydrogen and
oxygen whenever this can be made
sufficiently close and intimate, so, on
the other hand, if water itself be
placed in certain situations, hydrogen
and oxygen are reproduced from it :
an abrupt termination is put to the
new laws, and the agents reappear
separately with their own properties as
at first. What is called chemical ana-
lysis is the process of searching for
the causes of a phenomenon among its
effects, or rather among the effects
produced by the action of »ome other
causes upon it.

Lavoisier, by heating mercury to a
high temperature in a close vessel
containing air, found that the mercury
increased in weight, and became what
waa then called red precipitate, while

the air, on being examined after the ex-
periment, proved to have lost weight,
and to have become incapable of sup-
porting life or combustion. When
red precipitate was exposed to a
still greater heat, it became mercury
again, and gave off a gas which did
support life and flame. Thus the
agents which by their combination
produced red precipitate, namely, the
mercury and the gas, reappear as
effects resulting from that precipi-
tate when acted upon by heat. So,
if we decompose water by means of
iron filings, we produce two effects,
rust and hydrogen : now rust ia
already known, by experiments upon
the component substances, to be an
effect of the union of iron and oxy-
gen : the iron we ourselves supplied,
but the oxygen must have been
produced from the water. The re-
sult therefore is that water has dis-
appeared, and hydrogen and oxygen
have appeared in its stead : or, in
other words, the original laws of
these gaseous agents, which had been
suspended by the superinduction of
the new laws called the properties of
water, have again started into exist-
ence, and the causes of water are
found among its effects.

Where two phenomena, between the
laws or properties of which, considered
in themselves, no connection can be
traced, are thus reciprocally cause
and effect, each capable in its turn of
being produced from the other, and
each, when it produces the other,
ceasing itself to exist (as water is
produced from oxygen and hydrogen,
and oxygen and hydrogen are repro-
duced from water) ; this causation of
the two phenomena by one another,
each being generated by the other's
destruction, is properly transforma-
tion. The idea of chemical composi-
tion is an idea of transformation, but
of a transformation which is incom-
plete, since we consider the oxygen
and hydrogen to b© present in the
water at oxygen and hydrogen, and
capable of being discovered in it if our
semes were tufficiently keen ; a tup-

INTERMIXTURE OF EFFECTS.

291

position (for it is no more) grounded
solely on the fact that the weight of
the water is the sum of the separate
weights of th« two ingredients. If
there had not been this exception to
the entire disappearance in the com-
pound of the laws of the separate
ingredients; if the combined agents
had not, in this one particular of
weight, preserved their own laws, and
produced a joint result equal to the
sum of their separate results, we
should never, probably, have had the
notion now implied by the words
chemical composition ; and, in the
facts of water produced from hydro-
gen and oxygen, and hydiogen and
oxygen produced from water, as the
transformation would have been com-
plete, we should have seen only a
transformation.

In these cases, where the hetero-
pathic effect (as we called it in a
former chapter *) is but a transfor-
mation of its cause, or, in other words,
where the effect and its cause are
reciprocally such, and mutually con-
vertible into each other, the problem
of finding the cause resolves itself
into the far easier one of finding an
effect, which is the kind of inquiry
that admits of being prosecuted by
direct experiment. But there are
other cases of heteropathic effects to
which this mode of investigation is
not applicable. Take, for instance,
the heteropathic laws of mind, that
portion of the phenomena of our men-
tal nature which are analogous to
chemical rather than to dynamical
phenomena ; as when a complex pas-
sion is formed by the coalition of
several elementary impulses, or a
complex emotion by several simple
pleasures or pains, of which it is the
result without being the aggregate,
or in any respect homogeneous with
them. The product, in these cases,
is generated by its various factors ;
but the factors cannot be reproduced
from tht product ; just as a youth
can grow into an old man, but an old

* jLutm, chap. tli. 1 1.

man cannot grow into a youth. We
cannot ascertain from what simple
feelings any of our complex states of
mind are generated, as we ascertain
the ingredients of a chemical com-
pound, by making it, in its turn,
generate them. We can only, there-
fore, discover these laws by the slow
process of studying the simple feel«
ings themselves, and ascertaining
synthetically, by experimenting on
the various combinations of which
they are susceptible, what they, by
their mutual action upon one another,
are capable of generating.

§ 5. It might have been supposed
that the other, and apparently simpler
variety of the mutual interference of
causes, where each cause continues to
produce its own proper effect accord-
ing to the same laws to which it con-
forms in its separate state, would
have presented fewer diflBculties to
the inductive inquirer than that of
which we have just finished the con-
sideration. It presents, however, so
far as direct induction apart from
deduction is concerned, infinitely
greater diflBculties. When a concur-
rence of causes gives rise to a new
effect, bearing no relation to the
separate effects of those causes, the
resulting phenomenon stands forth
undisguised, inviting attention to its
peculiarity, and presenting no obstacle
to our recognising its presence or ab-
sence among any number of surround-
ing phenomena. It admits, therefore,
of being easily brought under the
canons of Induction, provided in-
stances can be obtained such as those
canons require : and the non-occur-
rence of such instances, or the want
of means to produce them artificially,
is the real and only difficulty in such
investigations ; a diflBculty not logical,
but in some sort physical. It is other-
wise with cases of what, in a preceding
chapter, has been denominated the
Composition of Causes. There, the
effects of the separate causes do not
terminate and give place to others,
thereby ceasing to form any part of

292

INDUCTION.

the phenomenon to be investigated ;
on the contrary, they still take place,
but are intermingled with, and dis-
guised by, the homogeneous and
closely allied effects of other causes.
They are no longer a, 6, c, d, e, ex-
isting side by side, and continuing
to be separately discernible ; they
are ■¥ a, a,- ^ 6, - 6, 2 6, &c. ; some
of which cancel one another, while
many others do not appear distinguish-
ably, but merge in one sum : forming
altogether a result, between which
and the causes whereby it was pro-
duced there is often an insurmount-
able difficulty in tracing by observa-
tion any fixed relation whatever.

The general idea of the Composi-
tion of Causes has been seen to be,
that though two or more laws inter-
fere with one another, and apparently
frustrate or modify one another's
operation, yet in reality all are ful-
filled, the collective effect being the
exact sum of the effects of the causes
taken separately. A familiar in-
stance is that of a body kept in
equilibrium by two equal and con-
trary forces. One of the forces if
acting alone would carry the body
in a given time a certain distance to
the west, the other if acting alone
would carry it exactly as far towards
the east ; and the result is the same
as if it had been first carried to the
west as far as the one force would
carry it, and then back towards the
east as far as the other would carry
it, that is, precisely the same dis-
tance ; being ultimately left where it
was found at first.

All laws of causation are liable to
be in this manner counteracted, and
seemingly frustrated, by coming into
conflict with other laws, the separate
result of which is opposite to theirs,
or more or less inconsistent with it.
And hence, with almost every law,
many instances in which it really is
entirely fulfilled do not, at first sight,
appear to be cases of its operation at
all. It is so in the example just
adduced : a force, in mechanics, means
neither more nor less than a cause of

motion, yet the sum of the effects of
two causes of motion may be rest.
Again, a body solicited by two forces
in directions making an angle with
one another moves in the diagonal;
and it seems a paradox to say that
motion in the diagonal is the sum of
two motions in two other lines. Mo-
tion, however, is but change of place,
and at every instant the body is in
the exact place it would have been in
if the forces had acted during alter-
nate instants instead of acting in the
same instant, (saving that if we sup-
pose two forces to act successively
which are in truth simultaneous, we
must of course allow them double the
time.) It is evident, therefore, that
each force has had, during each in-
stant, all the effect which belonged
to it ; and that the modifying influ-
ence which one of two concurrent
causes is said to exercise with respect
to the other may be considered as
exerted not over the action of the
cause itself, but over the effect after
it is completed. For all purposes of
predicting, calculating, or explaining
their joint result, causes which com-
pound their effects may be treated as
if they produced simultaneously each
of them its own effect, and all these
effects co-existed visibly.

Since the laws of causes are as
really fulfilled when the causes are
said to be counteracted by opposing
causes as when they are left to their
own undisturbed action, we must be
cautious not to express the laws in
such terms as would render the asser-
tion of their being fulfilled in those
cases a contradiction. If, for instance,
it were stated as a law of nature that
a body to which a force is applied
moves in the direction of the force,
with a velocity proportioned to the
force directly, and to its own mass
inversely ; when in point of fact some
bodies to which a force is applied do
not move at all, and those which do
move (at least in the region of our
earth) are, from the very first, re-
tarded by the action of gravity and
other resisting forces, and at last

INTERMIXTURE OF EFFECTS.

m

■topped altogether ; it is clear that
the general proposition, though it
would be true under a certain hypo-
thesis, would not express the facts as
they actually occur. To accommodate
the expression of the law to the real
phenomena, we must say, not that
the object moves, but that it tends to
move, in the direction and with the
velocity specified. We might, indeed,
guard our expression in a different
mode, by saying that the body moves
in that manner unless prevented, or
except in so far as prevented, by some
counteracting cause, but the body
does not only move in that manner
unless counteracted ; it tends to move
in that manner even when counter-
acted ; it still exerts in the original
direction the same energy of move-
ment as if its first impulse had been
undisturbed, and produces, by that
energy, an exactly equivalent quantity
of effect. This is true even when the
force leaves the body aa it found it, in
a state of absolute rest ; as when we
attempt to raise a body of three tons
weight with a force equal to one ton.
For if, while we are applying this
force, wind or water or any other
agent supplies an additional force just
exceeding two tons, the body will be
raised ; thus proving that the force
we applied exerted its full effect by
neutralising an equivalent portion of
the weight which it was insufficient
altogether to overcome. And if while
we are exerting this force of one ton
upon the object in a direction con-
trary to that of gravity, it be put into
a scale and weighed, it will be found
to have lost a ton of its weight, or, in
other words, to press downwards with
a force only equal to the difference of
the two forces.

These facts are correctly indicated
by the expression tendency. All laws
of causation, in consequence of their
liability to be counteracted, require
to be stated in words affirmative of
tendencies only, and not of actual re-
sults. In those sciences of causation
which have an accurate nomenclature,
there are special words which signify

a tendency to the particular effect
with which the science is conversant;
thus pressure, in mechanics, is synony-
mous with tendency to motion, and
forces are not reasoned on as causing
actual motion, but as exerting pres-
sure. A similar improvement in ter-
minology would be very salutary in
many other branches of science.

The habit of neglecting this neces-
sary element in the precise expres-
sion of the laws of nature has given
birth to the popular prejudice that all
general truths have exceptions ; and
much unmerited distrust has thence
accrued to the conclusions of science
when they have been submitted to
the judgment of minds insufficiently
disciplined and cultivated. The rough
generalisations suggested by common
observation usually have exceptions ;
but principles of science, or, in other
words, laws of causation, have not.
" What is thought to be an exception
to a principle," (to quote words used
on a different occasion,) "is always
some other and distinct principle
cutting into the former ; some other
force which impinges* against the
first force, and deflects it from its
direction. There are not a law and an
exception to that law, the law acting
in ninety-nine cases, and the excep-
tion in one. There are two laws, each
possibly acting in the whole hundred
cases, and bringing about a common
effect by their conjunct operation.
If the force which, being the less con-
spicuous of the two, is called the dis-
turbing force, prevails sufficiently over
the other force in some one case, to
constitute that case what is commonly
called an exception, the same disturb-
ing force probably acts as a modifying
cause in many other cases which no
one will call exceptions.

" Thus if it were stated to be a law
of nature that all heavy bodies fall to
the ground, it would probably be said

* It seetna hardly necessary to say that
the word impinge, as a general term to ex-
press collision of forces, is here used by a
figure of speech, and not as expressive of
any theory respecting the nature of force.

^94

INDUCTION.

that the resistance of the atmosphere,
which prevents a balloon from falling,
constitutes the balloon an exception
to that pretended law of nature. But
the real law is, that all heavy bodies
tend to fall ; and to this there is
no exception, not even the sun and
moon ; for even they, as every astro-
nomer knows, tend towards the earth,
with a force exactly equal to that
with which the earth tends towards
them. The resistance of the atmos-
phere might, in the particular case of
the balloon, from a misapprehension
of what the law of gravitation is, be
said to prevail over the law ; but its
disturbing effect is quite as real in
every other case, since though it does
not prevent, it retards the fall of all
bodies whatever. The rule and the
so-called exception do not divide the
cases between them ; each of them as
a comprehensive rule extending to all
cases. To call one of these concurrent
principles an exception to the other,
is superficial, and contrary to the cor-
rect principles of nomenclature and
arrangement. An effect of precisely
the same kind, and arising from the
same cause, ought not to be placed in
two different categories, merely as
there does or does not exist another
cause preponderating over it." *

§ 6. We have now to consider ac-
cording to what method these com-
plex effects, compounded of the effects
of many causes, are to be studied ;
how we are enabled to trace each
effect to the concurrence of causes in
which it originated, and ascertain the
conditions of its recurrence — the cir-
cumstances in which it may be ex-
pected again to occur. The conditions
of a phenomenon which arises from a
composition of causes may be investi-
gated either deductively or experi-
mentally.

The case, it is evident, is naturally
susceptible of the deductive mode of
investigation. The law of an effect
of this description is a result of the

* Essays on Some Unsettled Questions of
Political Economy, Essay V.

laws of the separate causes on the
combination of which it depends, and
is therefore in itself capable of being
deduced from these laws. This is
called the method d priori. The
other, or d posteriori method, pro-
fesses to proceed according to the
canons of experimental inquiry. Con-
sidering the whole assemblage of con-
current causes which produced the
phenomenon as one single cause, it
attempts to ascertain the cause in
the ordinary manner, by a compari-
son of instances. This second method
subdivides itself into two different
varieties. If it merely collates in-
stances of the effect, it is a method
of pure observation. If it operates
upon the causes, and tries different
combinations of them, in hopes of
ultimately hitting the precise com-
bination which will produce the given
total effect, it is a method of experi-
ment.

In order more completely to clear
up the nature of each of these three
methods, and determine which of
them deserves the preference, it will
be expedient (conformably to a fa-
vourite maxim of Lord Chancellor
Eldon, to which, though it has often
incurred philosophical ridicule, a
deeper philosophy will not refuse its
sanction) to " clothe them in circum-
stances." We shall select for this
purpose a case which as yet furnishes
no very brilliant example of the suc-
cess of any of the three methods,
but which is all the more suited to
illustrate the difficulties inherent in
them. Let the subject of inquiry be
the conditions of health and disease
in the human body, or (for greater
simplicity) the conditions of recovery
from a given disease ; and in order
to narrow the question still more, let
it be limited, in the first instance, to
this one inquiry, Is or is not some
particular medicament (mercury, for
instance) a remedy for the given
disease ?

Now, the deductive method would
set out from known properties of mer-
cury and known laws of the human

INTERMIXTURE OF EFFECTS.

29S

body, »nd, by reasoning from these,
would attempt to discover whether
mercury will act upon the body when
in the morbid condition supposed, in
Buch A manner as would tend to
restore health. The experimental
method would simply administer mer-
cury in as many cases as possible,
noting the age, sex, temperament,
and other peculiarities of bodily con-
stitution, the particulf^r form or variety
of the disease, the particular stage of
its progress, &c., remarking in which
of taese cases it was attended with a
•ialutary effect, and with what cir-
cumftances it was on those occasions
combined. The method of simple
observation would compare instances
of recovery, to find whether they
agreed in having been preceded by
the administration of mercury ; or
would compare instances of recovery
with instances of failure, to find cases
which, agreeing in all other respects,
differed only in the fact that mercury
had been administered or that it had
not.

§ 7. That the last of these three
modes of investigation is applicable
to the case, no one has ever seriously
contended. No conclusions of value
on a subject of such intricacy ever
were obtained in that way. The
utmost that could result would be a
vague general impression for or against
the efficacy of mercury, of no avail
for guidance unless confirmed by one
of the other two methods. Not that
the results which this method strives
to obtain would not be of the utmost
possible value if they could be obtained.
If all the cases of recovery which pre-
sented themselves, in an examination
extending to a. great number of in-
stances, were cases in which mercury
had been administered, we might
generalise with confidence from this
experience, and should have obtained
a conclusion of real value. But no
such basis for generalisation can we,
in a case of this description, hope to
obtain. The reason is that which
we have spoken of as constituting

the characteristic imperfection of the
Method of Agreement — Plurality of
Causes. Supposing even that mercury
does tend to cure the disease, so many
other causes, both natural and arti-
ficial, also tend to cure it, that there
are sure to be abundant instances ef
recovery in which mercury has not
been administered : unless, indeed,
the practice be to administer it in
all cases ; on which supposition it
will equally be found in the cases of
failure.

When an effect results from the
union of many causes, the share which
each has in the determination of the
effect cannot in general be great ; and
the effect is not likely, even in its
presence or absence, still less in its
variations, to follow, even approxi-
mately, any one of the causes. Re-
covery from a disease is an event to
which, in every case, many influences
must concur. Mercury may be one
such influence ; but from the very
fact that there are many other such,
it will necessarily happen that al-
though mercury is administered, the
patient, for want of other concurring
influences, will often not recover, and
that he often will recover when it is
not administered, the other favourable
influences being sufficiently powerful
without it. Neither, therefore, will
the instances of recovery agree in the
administration of mercury, nor will
the instances of failure agree in its
non-administration. It is much if,
by multiplied and accurate returns
from hospitals and the Hke, we can
collect that there are rather more
recoveries and rather fewer failures
when mercury is administered than
when it is not ; a result of very
secondary value even as a guide to
practice, and almost worthless as »
contribution to the theory of the sub-
ject.*

* It is justly remarked by Professor Bain,
that though the Methods of Agreement and
Difference aie not applicable to these cases,
they are not wholly inaccessible to the
Method of Concomitant Variations. " If
a cause happens to vary alone, the effect
will also vary alone : a cause and effect

296

INDUCTION.

§ 8, The inapplicability of the
method of simple observation to as-
certain the conditions of effects de-
pendent on many concurring causes
being thus recognised, we shall next
inquire whether any greater benefit
can be expected from the other branch
of the a posteriori method, that which
proceeds by directly trying different
combinations of causes, either artifici-
ally produced or found in nature, and
taking notice what is their effect :
as, for example, by actually trying
the effect of mercury, in as many
different circumstances as possible.
This method differs from the one
which we have just examined, in
turning our attention directly to the
causes or agents, instead of turning
it to the effect, recovery from the
disease. And since, as a general
rule, the effects of causes are far
more accessible to our study than the
causes of effects, it is natural to think
that this method has a much better
chance of proving successful than the
former.

may be thug singled out under the greatest
complications. Thus, when the appetite
for food increases with the cold, we have
a strong evidence of connection between
these two facts, although other circum-
stances may operate in the same direction.
The assigning of the respectire parts of the
r.\\n and moon in the action of the tides
may be effected, to a certain degree of
exactness, by the variations of the amount
according to the positions of the two at-
tractive bodies. By a series of experi-
ments of Concomitant Variations, directed
to ascertain the elimination of nitrogen
from the human body under varieties of
muscular exercise, Dr. Parkes obtained
the remarkable conclusion that a muscle
grows during exercise, and loses bulk dur-
ing the subsequent rest."— Xojric, ii. 83.

It is, no doubt, often possible to single
out the influencing causes from among a
great number of mere concomitants, by
noting what are the antecedents a varia-
tion in which is followed by a variation in
the effect. But when there are many in-
fluencing causes, no one of them greatly
predominating over the rest, and especi-
ally when some of these are continually
changing, it is scarcely ever possible to
trace such a relation between the varia-
tions of the eflfect and those of any one
cause as would enable us to assign to that
oause its real shar* in the production of
the effect.

The method now under considera-
tion is called the Empirical Method ;
and in order to estimate it fairly, we
must suppose it to be completely, not
incompletely, empirical. We musfc
exclude from it everything which par-
takes of the nature not of an experi-
mental but of a deductive operation.
If, for instance, we try experiments
with mercury upon a person in health,
in order to ascertain the general laws
of its action upon the human body,
and then reason from these la-we to
determine how it will act upon per-
sons affected with a particular disease,
this may be a really effectual method,
but this is deduction. The eicperi-
mental method does not derive the
law of a complex case from the sim-
pler laws which conspire to produce
it, but makes its experiments directly
upon the complex case. We must
make entire abstraction of all know-
ledge of the simpler tendencies, the
modi operandi, of mercury in detail.
Our experimentation must aim at
obtaining a direct answer to the speci-
fic question. Does or does not mercury
tend to cure the particular disease ?

Let us see, therefore, how far the
case admits of the observance of those
rules of experimentation, which it is
found necessary to observe in other
cases. When we devise an experi-
ment to ascertain the effect of a given
agent, there are certain precautions
which we never, if we can help it,
omit. In the first place, we introduce
the agent into the midst of a set of
circumstances which we have exactly
ascertained. It needs hardly be re-
marked how far this condition is from
being realised in any case connected
with the phenomena of life ; how far
we are from knowing what are all the
circumstances which pre-exist in any
instance in which mercury is adminis-
tered to a living being. This diffi-
culty, however, though insuperable in
most cases, may not be so in all :
there are sometimes concurrences of
many causes, in which we yet know
accurately what the causes are. More-
over, the difficulty may be attenuated

INTERMIXTURE OF EFFECTS.

297

by sufficient multiplication of experi-
ments, in circumstances rendering it
improbable that any of the unknown
causes should exist in them all. But
when we have got clear of this ob-
stacle, we encounter another still more
serious. In other cases, when we in-
tend to try an experiment, we do not
reckon it enough that there be no cir-
cumstance in the case the presence of
which is unknown to us. We require
also that none of the circumstances
which we do know shall have effects
susceptible of being confounded with
those of the agents whose properties
we wish to study. We take the utmost
pains to exclude all causes capable of
composition with the given cause ; or
if forced to let in any such causes, we
take care to make them such that we
can compute and allow for their in-
fluence, so that the effect of the given
cause may, after the subduction of
those other effects, be apparent as a
residual phenomenon.

These precautions are inapplicable
to such cases as we are now consider-
ing. The mercury of our experiment
being tried with an unknown multi-
tude (or even let it be a known mul-
titude) of other influencing circum-
stances, the mere fact of their being
influencing circumstances implies
that they disguise the effect of the
mercury, and preclude us from know-
ing whether it has any effect or not.
Unless we already knew what and
how much is owing to every other
circumstance, (that is, unless we sup-
pose the very problem solved which
we are considering the means of solv-
ing,) we cannot tell that those other
circumstances may not have produced
the whole of the effect, independently
or even in spite of the mercury. The
Method of Difference, in the ordinary
mode of its use, namely, by comparing
the state of things following the ex-
periment with the state which pre-
ceded it, is thus, in the case of inter-
mixture of effects, entirely unavailing ;
because other causes than that whose
effect we are seeking to determine
have been operating during the tran-

sition. As for the other mode of em-
ploying the Method of Difference,
namely, by comparing, not the same
case at two different periods, but
different cases, this in the present
instance is quite chimerical. In phe-
nomena so complicated it is question-
able if two cases, similar in all respects
but one, ever occurred ; and were they
to occur, we could not possibly know
that they were so exactly similar.

Anything like a scientific use of the
method of experiment, in these com-
plicated cases, is therefore out of the
question. We can generally, even in
the most favourable cases, only dis-
cover by a succession of trials that a
certain cause is very often followed by
a certain effect. For, in one of these
conjunct effects, the portion which is
determined by any one of the in-
fluencing agents, is usually, as we
before remarked, but small ; and it
must be a more potent cause than
most, if even the tendency which it
really exerts is not thwarted by other
tendencies in nearly as many cases as
it is fulfilled. Some causes indeed
there are which are more potent than
any counteracting causes to which
they are commonly exposed ; and ac-
cordingly there are some truths in
medicine which are sufficiently proved
by direct experiment. Of these the
most familiar are those that relate to
the efficacy of the substances known
as Specifics for particular diseases :
" quinine, colchicum, lime-juice, cod-
liver oil," * and a few others. Even
these are not invariably followed by
success ; but they succeed in so large
a proportion of cases, and against
such powerful obstacles, that their
tendency to restore health in the dis-
orders for which they are prescribed
may be regarded as an experimental
truth.t

* Bain's Logic, ii. 360.

t What is said in the text on the inappli-
cability of the experimental methods tore-
solve particular questions of medical treat-
ment does not detract from their eflBcacv
in ascertaining the general laws of the ani-
mal or human system. The functions, for
example, of the different classes of nervea

29S

INDUCTION.

If so little can be done by the ex-
perimental method to determine the
conditions of an eflfect of many com-
bined causes, in the case of medical
science ; still less is this method ap-
plicable to a class of phenomena more
complicated than even those of physio-
logy, the phenomena of politics and
history. There, Plurality of Causes
exists in almost boundless excess, and
effects are, for the most part, inextri-
cably interwoven veith one another.
To add to the embarrassment, most
of the inquiries in political science
relate to the production of effects of a
most comprehensive description, such
as the public wealth, public security,
public morality, and the like : results
liable to be affected directly or in-
directly either in plus or in minus by
nearly every fact which exists, or
event which occurs in human society.
The vulgar -notion that the safe me-
thods on political subjects are those
of Baconian induction — that the true
guide is not general reasoning, but
specific experience — will one day be
quoted as among the most unequivocal
marks of a low state of the speculative
faculties in any age in which it is
accredited. Nothing can be more
ludicrous than the sort of parodies on
experimental reasoning which one is
accustomed to meet with, not in popu-
lar discussion only, but in grave trea-
tises, when the affairs of nations are
the theme. " How," it is asked, " can
an institution be bad, when the
country has prospered under it ? "
" How can such or such causes have
contributed to the prosperity of one
country, when another has prospered
without them ? " "Whoever makes use
of an argument of this kind, not in-

have been discovered, and probably could
only have been discovered, by experiments
on living animals. Observation and ex-

Eeriment are the ultimate basis of all
nowledge : from them we obtain the ele-
mentary laws of life, as we obtain all other
elementary truths. It is in dealing with
the complex combinations that the ex-
perimental methods are for the most part
illusory, and the deductive mode of inves-
Mgation must be invoked to disentangle
the complexity.

tending to deceive, should be sent
back to learn the elements of some
one of the more easy physical sciences.
Such reasoners ignore the fact of
Plurality of Causes in the very case
which affords the most signal example
of it. So little could be concluded,
in such a case, from any possible col-
lation of individual instances, that
even the impossibility, in social phe-
nomena, of making artificial experi-
ments, a circumstance otherwise so
prejudicial to directly inductive in-
quiry, hardly affords, in this case,
additional reason of regret. For even
if we could try experiments upon a
nation or upon the human race, with
as little scruple as M. Magendie tried
them on dogs and rabbits, we should
never succeed in making two instances
identical in every respect except the
presence or absence of some one defi-
nite circumstance. The nearest ap-
proach to an experiment in the philo-
sophical sense, which takes place
in politics, is the introduction of a
new operative element into national
affairs by some special and assignable
measure of government, such as the
enactment or repeal of a particular
law. But where there are so many
influences at work, it requires some
time for the influence of any new
cause upon national phenomena to be-
come apparent ; and as the causes
operating in so extensive a sphere are
nofc only infinitely numerous, but in a
state of perpetual alteration, it is al-
ways certain that before the effect of
the new cause becomes conspicuous
enough to be a subject of induction,
so many of the other influencing cir-
cumstances will have changed as tc
vitiate the experiment.*

• Professor Bain, though concurring
generally in the views expressed in this
chapter, seems to estimate more highly
than I do the scope for specific experi-
mental evidence in politics (Logic, ii. 333-
337). There are, it is true, as he remarks
(p. 336), some cases "when an agent sud-
denly introduced is almost instantaneously
followed by some other changes, as when
the announcement of a diplomatic rup-
ture between two nations is followed the
same day by a derangement of the money-

THE DEDUCTIVE METHOD.

299

Two, therefore, of the three possible
methods for the study of phenomena
resulting from the composition of
many causes, being, from the very
nature of the case, inefficient and illu-
sory, there remains only the third, —
that which considers the causes sepa-
rately, and infers the effect from the
balance of the different tendencies
which produce it : in short, the de-
ductive or tt priwn method. The
more particular consideration of this
intellectual process requires a chapter
to itself.

CHAPTER XI.

OK THE DEDUCTIVE METHOD.

§ I. The mode of investigation
which, from the proved inapplicabi-
lity of direct methods of observation
and experiment, remains to us as the
main source of the knowledge we
possess or can acquire respecting the
conditions and laws of recurrence
of the more complex phenomena, is
called, in its most general expression,
the Deductive Method, and consists
of three operations — the first, one of
direct induction ; the second, of ra-
tiocination ; the third, of verification.

I call the first step in the process
an inductive operation, because there
must be a direct induction as the
basis of the whole, though in many
particular investigations the place of
the induction may be supplied by a
prior deduction ; but the premises of
this prior deduction must have been
derived from induction.

The problem of the Deductive Me-
thod is to find the law of an effect
from the laws of the dififerent ten-
market." But this experiment would be
quite inconclusive merely as an experi-
ment. It can only serve, as any experi-
ment may, to verify the conclusion of a
deduction. Unless we already knew by
our knowledge of the motives which act on
business men that the prospect of war
tends to derange the money-market, we
should never have been able to prove a
connection between the two facts, unless
after having ascertained historically that
the one followed the other in too great a

dencies of which it is the joint result.
The first requisite, therefore, is to
know the laws of those tendencies —
the law of each of the concurrent
causes ; and this supposes a previous
process of observation or experiment
upon each cause separately, or else a
previous deduction, which also must
depend for its ultimate premises on
observation or experiment. Thus, if
the subject be social or historical
phenomena, the premises of the De-
ductive Method must be the laws of
the causes which determine that class
of phenomena ; and those causes are
human actions, together with the
general outward circumstances under
the influence of which mankind are
placed, and which constitute man's
position on the earth. The Deductive
Method applied to social phenomena
must begin, therefore, by investigate
ing, or must suppose to have been
already investigated, the laws of
human action, and those propertie.s
of outward things by which the ac-
tions of human beings in society are
determined. Some of these general
truths will naturally be obtained by
observation and experiment, others
by deduction ; the more complex laws
of human action, for example, may
be deduced from the simpler ones,
but the simple or elementary laws
will always and necessarily have been
obtained by a directly inductive pro-
cess.

To ascertain, then, the laws of each
separate cause which takes a share in
producing the effect is the first de-
sideratum of the Deductive Method.
To know what the causes are which
must be subjected to this process of
study may or may not be difficult

number of instances to be consistent with
their having been recorded with due pre-
cautions. Whoever has carefully examined
any of the attempts continually made to
prove economic doctrines by such a recital
of instances, knows well )iow futile they
are. It always turns out that the circum-
stances of scarcely any of the cases have
been fully stated : and that cases, in equal
or greater numbers, have been omitted,
which would have tended to an opposite
conclusion.

300

INDUCTION.

In the case last mentioned, this first
condition is of easy fulfilment. That
social phenomena depend on the acts
and mental impressions of human be-
ings never could have been a matter
of any doubt, however imperfectly it
may have been know^n either by what
laws those impressions and actions
are governed, or to what social con-
sequences their laws naturally lead.
Neither, again, after physical science
had attained a certain development,
could there be any real doubt where
to look for the laws on which the
phenomena of life depend, since they
must be the mechanical and chemical
laws of the solid and fluid substances
composing the organised body and
the medium in which it subsists,
together with the peculiar vital laws
of the different tissues constituting
the organic structure. In other cases
really far more simple than these, it
was much less obvious in what quarter
the causes were to be looked for, as
in the case of the celestial phenomena.
Until, by combining the laws of cer-
tain causes, it was fotind that those
laws explained all the facts which ex-
perience had proved concerning the
heavenly motions, and led to predic-
tions which it always verified, man-
kind never knew that those were the
causes. But whether we are able to
put the question before or not until
after we have become capable of an-
swering it, in either case it must be
answered ; the laws of the diffei^ent
causes must be ascertained before we
can proceed to deduce from them the
conditions of the effect.

The mode of ascertaining those laws
neither is nor can be any other than
the fourfold method of experimental
inquiry, already discussed. A few
remarks on the application of that
method to cases of the Composition
of Causes are all that is requisite.

It is obvious that we cannot expect
to find the law of a tendency by an
induction from cases in which the
tendency is counteracted. The laws
of motion could never have been
brought to light from the observa-

tion of bodies kept at rest by the
equilibrium of opposing forces. Even
where the tendency is not, in the ordi-
nary sense of the word, counteracted,
but only modified, by having its
effects compounded with the effects
arising from some other tendency or
tendencies, we are still in an un-
favourable position for tracing, by
means of such cases, the law of the
tendency itself. It would have been
scarcely possible to discover the law
that every body in motion tends to
continue moving in a straight line, by
an induction from instances in which
the motion is deflected into a curve,
by being compounded with the effect
of an accelerating force. Notwith-
standing the resources afforded in this
description of cases by the Method
of Concomitant Variations, the prin-
ciples of a judicious experimentation
prescribe that the law of each of the
tendencies should be studied, if pos-
sible, in cases in which that tendency
operates alone, or in combination with
no agencies but those of which the
effect can, from previous knowledge,
be calculated and allowed for.

Accordingly, in the cases, unfortu-
nately very numerous and important,
in which the causes do not suffer
themselves to be separated and ob-
served apart, there is much difficulty
in laying down with due certainty
the inductive foundation necessary to
support the deductive method. This
difficulty is most of all conspicuous
in the case of physiological pheno-
mena : it being seldom possible to
separate the different agencies which
collectively compose an organised
body, without destroying the very phe-
nomena which it is our object to in-
vestigate :
" Following life, in creatures we dissect,

We lose it in the moment we detect."

And for this reason I am inclined to
the opinion that physiology (greatly
and rapidly progressive as it now is)
is embarrassed by greater natural
difficulties, and is probably suscep-
tible of a less degree of ultimate per-
fection than even the social sciencCj

THE DEDUCTIVE METHOD.

301

inasmuch m it is possible to study
the laws and operations of one human
mind apart from other minds much
less imperfectly than we can study
the laws of one organ or tissue of the
human body apart from the other
organs or tissues.

It has been judiciously remarked
that pathological facts, or, to speak
in comn^on language, diseases in their
different forms and degrees, afiford in
the case of physiological investigation
the most valuable equivalent to ex-
perimentation properly so called, in-
asmuch as they often exhibit to us a
definite disturbance in some one organ
or organic function, the remaining
organs and functions being, in the
first instance at least, imaifected. It
is true that from the perpetual actions
and reactions which are going on
among all parts of the organic econo-
my there can be no prolonged dis-
turbance in any one function with-
out ultimately involving many of the
others ; and when once it has done
so, the experiment for the most part
loses its scientific value. All depends
on observing the early stages of the
derangement, which, unfortunately,
are of necessity the least marked. If,
however, the organs and functions
not disturbed in the first instance,
become affected in a fixed order of
succession, some light is thereby
thrown upon the action which one
organ exercises over another, and we
occasionally obtain a series of effects
which we can refer with some con-
fidence to the original local derange-
ment ; but for this it is necessary
that we should know that the original
derangement was local. If it was
what is termed constitutional, that
is, if we do not know in what part of
the animal economy it took its rise,
or the precise nature of the disturb-
ance which took place in that part,
we are unable to determine which of
the various derangements was cause
and which effect ; which of them
were produced by one another, and
which by the direct, though perhaps
tardv, action of the original caus^

Besides natural pathological facts,
we can produce pathological facts
artificially ; we can try experiments,
even in the popular sense of the term,
by subjecting the living being to some
external agent, such as the mercury
of our former example, or the section
of a nerve to ascertain the functions of
different parts of the nervous system.
As this experimentation is not in-
tended to obtain a direct solution of
any practical question, but to dis-
cover general laws, from which after-
wards the conditions of any particular
effect may be obtained by deduction,
the best cases to select are those of
which the circumstances can be best
ascertained : and such are generally
not those in which there is any prac-
tical object in view. The experi-
ments are best tried, not in a state of
disease, which is essentially a change-
able state, but in the condition of
health, comparatively a fixed state.
In the one, unusual agencies are at
work, the results of which we have
no means of predicting ; in the other,
the course of the accustomed physio-
logical phenomena would, it may
generally be presumed, remain undis-
turbed, were it not for the disturbing
cause which we introduce.

Such, with the occasional aid of the
Method of Concomitant Variations,
(the latter not less encumbered than
the more elementary methods by the
peculiar difficulties of the subject,)
are our inductive resources for ascer-
taining the laws of the causes con-
sidered separately, when we have it
not in our power to make trial of
them in a state of actual separation.
The insufficiency of these resources is
so glaring, that no one can be sur-
prised at the backward state of the
science of physiology in which in-
deed our knowledge of causes is so
imperfect, that we can neither explain,
nor could without specific experience
have predicted, many of the facts
which are certified to us by the most
ordinary observation. Fortunately,
we are much better informed as to
the empirical laws of the phenomena,

302

INDUCTION.

that is, the uniformities respecting
which we cannot yet decide whether
they are cases of causation or mere
results of it. Not only has the order
in which the facts of organisation and
life successively manifest themselves,
from the first germ of existence to
death, been found to be uniform, and
very accurately ascertainable ; but,
by a great application of the Method
of Concomitant Variations to the en-
tire facts of comparative anatomy and
physiology, the characteristic organic
structure corresponding to each class
of functions has been determined
with considerable precision. Whether
these organic conditions are the whole
of the conditions, and in many cases
whether they are conditions at all, or
mere collateral effects of some common
cause, we are quite ignorant ; nor are
we ever likely to know, unless we
could construct an organised body,
and try whether it would live.

Under such disadvantages do we,
in cases of this description, attempt
the initial or inductive step in the
application of the Deductive Method
to complex phenomena. But such,
fortunately, is not the common case.
In general, the laws of the causes on
which the effect depends may be ob-
tained by an induction from com-
paratively simple instances, or, at the
worst, by deduction from the laws
of simpler causes, so obtained. By
simple instances are meant, of course,
those in which the action of each
cause was not intermixed or inter-
fered with, or not to any great extent,
by other causes whose laws were un-
known ; and only when the induc-
tion which furnished the premises to
the Deductive Method rested on such
instances has the application of such
a method to the ascertainment of the
laws of a complex effect been attended
with brilliant results.

§ 2. When the laws of the causes
have been ascertained, and the first
atage of the great logical operation
now under discussion satisfactorily
{«,ocomplished, the tecond part follows ;

that of determining from the laws of
the causes what effect any given
combination of those causes will pro-
duce. This is a process of calcula-
tion, in the wider sense of the term,
and very often involves processes of
calculation in the narrowest sense.
It is a ratiocination ; and when our
knowledge of the causes is so perfect
as to extend to the exact numerical
laws which they observe in producing
their effects, the ratiocination may
reckon among its premises the theo-
rems of the science of number, in the
whole immense extent of that science.
Not only are the most advanced truths
of mathematics often required to
enable us to compute an effect the
numerical law of which we already
know, but, even by the aid of those
most advanced truths, we can go but
a little way. In so simple a case as
the common problem of three bodies
gravitating towards one another, with
a force directly as their mass and in-
versely as the square of the distance,
all the resources of the calculus have
not hitherto sufficed to obtain any
general solution but an approximate
one. In a case a little more complex,
but still one of the simplest which
arise in practice, that of the motion
of a projectile, the causes which affect
the velocity and range (for example)
of a cannon-ball may be all known
and estimated ; the force of the gun-
powder, the angle of elevation, the
density of the air, the strength and
direction of the wind ; but it is one
of the most difficult of mathematical
problems to combine all these, so as
to determine the effect resulting from
their collective action.

Besides the theorems of number,
those of geometry also come in as
premises, where the effects take place
in space, and involve motion and
extension, as in mechanics, optics,
acoustics, astronomy. But when the
complication increases, and the effects
are under the influence of so many
and such shifting causes as to give no
room either for fixed numbers or for
straight lines and regular curves, (as

I

THE DEDUCTIVE METHOD.

303

in the case of physiological, to say
nothing of mental and social pheno-
mena,) the laws of number and exten-
sion are applicable, if at all, only on
that large scale on which precision of
details becomes unimportant. Al-
though these laws play a conspicuous
part in the most striking examples of
the investigation of nature by the
Deductive Method, as, for example, in
the Newtonian theory of the celestial
motions, they are by no means an
indispensable part of every such pro-
cess. All that is essential in it is
reasoning from a general law to a
particular case, that is, determining
by means of the particular circum-
stances of that case what result is
required in that instance to fulfil the
law. Thus in the Torricellian experi-
ment, if the fact that air has weight
had been previously known, it would
have been easy, without any nume-
rical data, to deduce from the general
law of equilibrium that the mercury
would stand in the tube at such a
height that the column of mercury
would exactly balance a column of
the atmosphere of equal diameter ;
because, otherwise, equilibrium would
not exist.

By such ratiocinations from the
separate laws of the causes we may,
to a certain extent, succeed in answer-
ing either of the following questions :
Given a certain combination of causes,
what effect will follow ? and, What
combination of causes, if it existed,
would produce a given effect? In
the one case, we determine the effect
to be expected in any complex cir-
cumstances of which the different
elements are known : in the other
case we learn, according to what law
— under what antecedent conditions —
a given complex effect will occur.

§ 3. But (it may here be asked) are
not the same arguments by which
the methods of direct observation and
experiment were set aside as illusory
when applied to the laws of complex
phenomena, applicable with equal
force against the Method of Deduc-

tion ? When in every single instance
a multitude, often an unknown mul
titude, of agencies, are clashing and
combining, what security have we
that in our computation d priori we
have taken all these into our reckon-
ing ? How many must we not gene-
rally be ignorant of ? Among those
which we know, how probable that
some have been overlooked ; and,
even were all included, how vain the
pretence of summing up the effects
of many causes, unless we know ac-
curately the numerical law of each,
— a condition in most cases not to be
fulfilled ; and even when it is ful-
filled, to make the calculation trans-
cends, in any but very simple cases,
the utmost power of mathematical
science with all its moet modem im-
provements.

These objections have real weight,
and would be altogether unanswer-
able, if there were no test by which,
when we employ the Deductive Me-
thod, we might judge whether an
error of any of the above descriptions
had been committed or not. Such a
test, however, there is ; and its appli-
cation forms, under the name of Veri-
fication, the third essential component
part of the Deductive Method, with-
out which all the results it can give
have little other value than that of
conjecture. To warrant reliance ou
the general conclusions arrived at by
deduction, these conclusions must be
found, on careful comparison, to ac-
cord with the results of direct obser-
vation wherever it can be had. If,
when we have experience to compare
with them, this experience confirms
them, we may safely trust to them in
othei cases of which our specific ex-
perience is yet to come. But if our
deductions have led to the conclusion
that from a particular combination of
causes a given effect would result,
then in all known cases where that
combination can be shown to have
existed, and where the effect has not
followed, we must be able to show (or
at least to make a probable surmise)
what frustrated it ; if we cannot, the

304

INDUCTION.

theory is imperfect, and not yet to be
relied upon. Nor is the verification
complete, unless some of the cases in
which the theory is borne out by the
observed result, are of at least equal
complexity with any other cases in
which its application could be called
for.

If direct observation and collation
of instances have furnished us with
any empirical laws of the effect,
(whether true in all observed cases, or
only true for the most part,) the most
effectual verification of which the
theory could be susceptible would
be, that it led deductively to those
empirical laws ; that the uniformi-
ties, whether complete or incomplete,
which were observed to exist among
the phenomena were accounted for
by the laws of the causes — were such
as could not but exist if those be really
the causes by which the phenomena
are produced. Thus it was very
reasonably deemed an essential re-
quisite of any true theory of the
causes of the celestial motions, that
it should lead by deduction to Kep-
ler's laws ; which, accordingly, the
Newtonian theory did.

In order, therefore, to facilitate the
verification of theories obtained by
deduction, it is important that as
many as possible of the empirical laws
of the phenomena should be ascer-
tained by a comparison of instances,
conformably to the Method of Agree-
ment, as well as (it must be added)
that the phenomena themselves should
be described, in the most compre-
hensive as well as accurate manner
possible, by collecting from the ob-
servation of parts the simplest possible
correct expressions for the corespond-
ing wholes : as when the series of the
observed places of a planet was first
expressed by a circle, then by a system
of epicycles, and subsequently by an
ellipse.

It is worth remarking, that com-
plex instances which would have been
of no use for the discovery of the
simple laws into which we ultimately
jknalyse their pheaomena, neverthe- ]

less, when they have served* to verify
the analysis, become additional evi-
dence of the laws themselves. Al-
though we could not have got at the
law from complex cases, still when
the law, got at otherwise, is found to
be in accordance with the result of a
complex case, that case becomes a
new experiment on the law, and helps
to confirm what it did not assist to
discover. It is a new trial of the
principle in a different set of circum-
stances ; and occasionally serves to
eliminate some circumstance not pre-
viously excluded, and the exclusion
of which might require an experiment
impossible to be executed. This was
strikingly conspicuous in the example
formerly quoted, in which the difference
between the observed and the calcu-
lated velocity of sound was ascertained
to result from the heat extricated by
the condensation which takes place in
each sonorous vibration. This was a
trial, in new circumstances, of the
law of the development of heat by com-
pression ; and it added materially to
the proof of the universality of that
law. Accordingly any law of nature
is deemed to have gained in point of
certainty by being found to explain
some compleec case which had not
previously been thought of in con-
nection with it ; and this indeed is a
consideration to which it is the habit
of scientific inquirers to attach rather
too much value than too little.

To the Deductive Method, thus
characterised in its three constituent
parts, Induction, Ratiocination, and
Verification, the human mind is in-
debted for its most conspicuous
triumphs in the investigation of
nature. To it we owe all the theories
by which vast and complicated phe-
nomena are embraced under a few
simple laws, which, considered as the
laws of those great phenomena, could
never have been detected by their
direct study. We may form some
conception of what the method has
done for us from the case of the
celestial motions, one of the simplest
among the greater instances of the

THE DEDUCTIVE METHOD.

305

Composition of Causes, since (except
in a few cases not of primary im-
portance) each of the heavenly bodies
may be considered, without material
inaccuracy, to be never at one time
influenced by the attraction of more
than two bodies, the sun and one
other planet or satellite ; making with
the reaction of the body itself, and
the force generated by the body's own
motion and acting in the direction of
the tangent, only four different agents
on the concurrence of which the mo-
tions of that body depend ; a much
smaller number, no doubt, than that
by which any other of the great phe-
nomena of nature is determined or
modified. Yet how could we ever
have ascertained the combination of
forces on which the motions of the
earth and planets are dependent by
merely comparing the orbits or veloci-
ties of different planets, or the dif-
ferent velocities or positions of the
same planet? Notwithstanding the
regularity which manifests itself in
those motions, in a degree so rare
among the effects of concurrence of
causes ; and although the periodical
recurrence of exactly the same effect
affords positive proof that all the
combinations of causes which occur
at all, recur periodically ; we should
not have known what the causes were,
if the existence of agencies precisely
similar on our own earth had not,
fortunately, brought the causes them-
selves within the reach of experimen-
tation under simple circumstances.
As we shall have occasion to analyse,
farther on, this great example of the
Method of Deduction, we shall not
occupy any time with it here, but
shall proceed to that secondary appli-
cation of the Deductive Method the
result of which is not to prove laws of
phenomena, but to explain them.

CHAPTER XII.

OF THE EXPLANATION OF LAW3 OF
NATURE.

§ I. The deductive operation by
which we derive the law of an effect
from the laws of the causes, the con-
currence of which gives rise to it,
may be undertaken either for the
purpose of discovering the law, or of
explaining a law already discovered.
The word explanation occurs so con-
tinually and holds so important a
place in philosophy, that a little time
spent in fixing the meaning of it will
be profitably employed.

An individual fact is said to be
explained by pointing out its cause,
that is, by stating the law or laws of
causation of which its production is
an instance. Thus a conflagration is
explained when it is proved to have
arisen from a spark falling into the
midst of a heap of combustibles ; and
in a similar manner, a law of uni-
formity in nature is said to be ex-
plained when another law or laws
are pointed out, of which that law
itself is but a case, and from which it
could be deduced.

§ 2. There are three distinguish-
able sets of circumstances in which a
law of causation may be explained
from, or, as it also is often expressed,
resolved into, other laws.

The first is the case already so
fully considered ; an intermixture of
laws, producing a joint effect equal
to the sum of the effects of the causes
taken separately. The law of the
complex effect is explained by being
resolved into the separate laws of the
causes which contribute to it. Thus
the law of the motion of a planet is
resolved into the law of the acquired
force which tends to produce an uni-
form motion in the tangent, and the
law of the centripetal force which
tends to produce an accelerating mo-
tion towards the sun ; the real motion
being a compound of the two.

It is necessary here to remark, that

U

306

INDUCTION.

in this resolution of the law of a com-
plex effect, the laws of which it is
compounded are not the only elements.
It is resolved into the laws of the
•eparate causes, together with the
fact of their co-existence. The one
is as essential an ingredient as the
other ; whether the object be to dis-
cover the law of the effect, or only to
explain it. To deduce the laws of
the heavenly motions, we require not
only to know the law of a rectilineal
and that of a gravitative force, but
the existence of both these forces in
the celestial regions, and even their
relative amount. The complex laws
of causation are thus resolved into
two distinct kinds of elements : the
one, simpler laws of causation, the
other (in the aptly selected expression
of Dr. Chalmers) collocations ; the
collocations consisting in the existence
of certain agents or powers, in certain
circumstances of place and time. We
shall hereafter have occasion to return
to this distinction, and to dwell on it
at such length as dispenses with the
necessity of further insisting on it
here. The first mode, then, of the
explanation of Laws of Causation, is
when the law of an effect is resolved
into the various tendencies of which
it is the result, together with the laws
of those tendencies.

§ 3. A second case is when, be-
tween what seemed the cause and
what was supposed to be its effect,
further observation detects an inter-
mediate link ; a fact caused by the
antecedent, and in its turn causing
the consequent ; so that the cause at
first assigned is but the remote cause,
operating through the intermediate
phenomenon. A seemed the cause of
C, but it subsequently appeared that
A was only the cause of B, and that
it is B which was the cause of C.
For example : mankind were aware
that the act of touching an outward
object caused a sensation. It was
subsequently discovered, that after
we have touched the object, and be-
fore we experience the sensation, some

change takes place in a kind of thread
called a nerve, which extends from our
outward organs to the brain. Touch -
mg the object, therefore, is only the re-
mote causeof oursensation ; that is, not
the cause, properly speaking, but the
cause of the cause ; — the real cause of
the sensation is the change in the
state of the nerve. Future experience
may not only give us more knowledge
than we now have of the particular
nature of this change, but may also
interpolate another link : between the
contact (for example) of the object
with our outward organs, and the
production of the change of state in
the nerve, there may take place some
electric phenomenon, or some pheno-
menon of a nature not resembling the
effects of any known agency. Hitherto,
however, no such intermediate link
has been discovered ; and the touch
of the object must be considered, pro-
visionally, as the proximate cause of
the affection of the nerve. The se-
quence, therefore, of a sensation of
touch on contact with an object is
ascertained not to be an ultimate law ;
it is resolved, as the phrase is, into
two other laws, — the law that contact
with an object produces an affection
of the nerve, and the law that an
affection of the nerve produces sensa-
tion.

To take another example : the more
powerful acids corrode or blacken or-
ganic compounds. This is a case of
causation, but of remote causation ;
and is said to be explained when it is
shown that there is an intermediate
link, namely, the separation of some
of the chemical elements of the organic
structure from the rest, and their en-
tering into combination with the acid.
The acid causes this separation of the
elements, and the separation of the
elements causes the disorganisation,
and often the charring of the structure. ,
So, again, chlorine extracts colouring
matters (whence its efficacy in bleach-
ing) and purifies the air from infec-
tion. This law is resolved into the
two following laws. Chlorine has a
powerful affinity for bases of all kinds,

EXPLANATION OF LAWS.

307

particularly metalllo bases and hydro-
gen. Such bases are essential ele-
ments of colouring matters and con-
tagions compounds, which substances,
therefore, are decomposed and de-
stroyed by chlorine.

§ 4. It is of importance to remark,
that when a sequence of phenomena
is thus resolved into other laws, they
are always laws more general than
itself. The law that A is followed by
C, is less general than either of the
laws which connect B with C and A
with B. This will appear from very
simple considerations.

All laws of causation are liable to
be counteracted or frustrated by the
non-fulfilment of some negative con-
dition : the tendency, therefore, of B
to produce C may be defeated. Now
the law that A produces B, is equally
fulfilled whether B is followed by C
or not ; but the law that A produces
C by means of B, is of course only
fulfilled when B is really followed by
C, and is therefore less general than
the law that A produces B. It is
also less general than the law that B
produces C. For B may have other
causes besides A ; and as A produces
C only by means of B, while B pro-
duces C whether it has itself been
produced by A or by anything else,
the second law embraces a greater
number of instances, covers as it
were a greater space of ground, than
the first.

Thus, in our former example, the
law that the contact of an object
causes a change in the state of the
nerve, is more general than the law
that contact with an object causes
sensation, since, for aught we know,
the change in the nerve may equally
take place when, from a counteracting
cause, as, for instance, strong mental
excitement, the sensation does not
follow ; as in a battle, where wounds
are sometimes received without any
consciousness of receiving them. And
again, the law that change in the state
of a nerve produces sensation, is more
general than the law that contact

with an object produces sensation j
since the sensation equally follows .
the change in the nerve when not
produced by contact with an object,
but by some other cause ; aa in th*
well-known case when a person who
has lost a limb feels the same sensa-
tion which he has been accustomed to
call a pain in the limb.

Not only are the laws of more im-
mediate sequence, into which the law
of a remote sequence is resolved, laws
of greater generality than that law is,
but (as a consequence of, or rather as
implied in, their greater generality)
they are more to be relied on ; there
are fewer chances of their being ulti-
mately found not to be universally
true. From the moment when the
sequence of A and C is shown not to
be immediate, but to depend on an
intervening phenomenon, then, how-
ever constant and invariable the se-
quence of A and C has hitherto been
found, possibilities arise of its failure,
exceeding those which can effect either
of the more immediate sequences. A,
B, and B, C. The tendency of A to
produce C may be defeated by what-
ever is capable of defeating either the
tendency of A to produce B, or the
tendency of B to produce C ; it is
therefore twice as liable to failure as
either of those more elementary ten-
dencies; and the generalisation that
A is always followed by C, is twice
as likely to be found erroneous. And
so of the converse generalisation, that
C is always preceded and caused by
A ; which will be erroneous not only
if there should happen to be a second
immediate mode of production of C
itself, but, moreover, if there be a
second mode of production of B, the
immediate antecedent of C in the
sequence.

The resolution of the one generalisa-
tion into the other two not only shows
that there are possible limitations of
the former, from which its two ele-
ments are exempt, but shows also
where these are to be looked for. As
soon as we know that B intervenes
between A and C, we also know that if

308

INDUCTION.

there be oases in which the sequence
of A and C does not bold, these are
most likely to be found by studying
the effects or the conditions of the
phenomenon B.

It appears, then, that in the second
of the three modes in which a law
may be resolved into other laws, the
latter are more general, that is, ex-
tend to more cases, and are also less
likely to require limitation from sub-
sequent experience, than the law
which they serve to explain. They
are more nearly unconditional ; thoy
are defeated by fewer contingencies ;
they are a nearer approach to the
universal truth of nature. The same
observations are still more evidently
true with regard to the first of the
three modes of resolution. When
the law of an effect of combined
forces is resolved into the separate
laws of the causes, the nature of the
case implies that the law of the effect
is less general than the law of any of
the causes, since it only holds when
they are combined ; while the law of
any one of the causes holds good both
then, and also when that cause acts
apart from the rest. It is also mani-
fest that the complex law is liable to
be oftener unfulfilled than any one
of the simpler laws of which it is the
result, since every contingency which
defeats any of the laws prevents so
much of the effect as depends on it,
and thereby defeats the complex law.
The mere rusting, for example, of some
small part of a great machine, often
suffices entirely to prevent the effect
which ought to result from the joint
action of all the parts. The law of
the effect of a combination of causes
is always subject to the whole of the
negative conditions which attach to
the action of all the causes severally.

There is another and an equally
strong reason why the law of a com-
plex effect must be less general than
the laws of the causes which conspire
to produce it. The same causes, act-
ing according to the same laws, and
differing only in the proportions in
which they are combined, often pro-

duce effects which differ not merely
in quantity, but in kind. The com-
bination of a centripetal with a pro-
jectile force, in the proportions which
obtain in all the planets and satel-
lites of our solar system, gives rise to
an elliptical motion ; but if the ratio
of the two forces to each other were
slightly altered, it is demonstrated
that the motion produced would be
in a circle, or a parabola, or an hyper-
bola ; and it is thought that in the
case of some comets one of these is
probably the fact. Yet the law of
the parabolic motion would be re-
solvable into the very same simple
laws into which that of the elliptical
motion is resolved, namely, the law
of the permanence of rectilineal mo-
tion and the law of gravitation. If,
therefore, in the course of ages, some
circumstance were to manifest itself
which, without defeating the law of
either of those forces, should merely
alter their proportion to one another,
(such as the shock of some solid body,
or even the accumulating effect of
the resistance of the medium in which
astronomers have been led to surmise
that the motions of the heavenly
bodies take place,) the elliptical mo-
tion might be changed into a motion
in some other conic section ; and the
complex law that the planetary mo-
tions take place in ellipses would be
deprived of its universality, though
the discovery would not at all detract
from the universality of the simpler
laws into which that complex law is
resolved. The law, in short, of each
of the concurrent causes remains the
same, however their collocations may
vary ; but the law of their joint effect
varies with every difference in the
collocations. There needs no more
to show how much more general the
elementary laws must be than any of
the complex laws which are derived
from them.

§ 5. Besides the two modes which
have been treated of, there is a third
mode in which laws are resolved into
one another ; and in thi* it is self-evi-

EXPLANATION OF LAWS.

309

dent that they are resolved into laws
more general than themselves. This
third mode is the subsumption (as it has
been called) of one law under another,
or (what comes to the same thing)
the gathering up of several laws into
one more general law which includes
them all. The most splendid ex-
ample of this operation was when
terrestrial gravity and the central
force of the solar system were brought
together under the general law of
gravitation. It had been proved an-
tecedently that the earth and the
other planets tend to the sun ; and it
had been known from the earliest
times that terrestrial bodies tend to-
wards the earth. These were similar
phenomena ; and to enable them both
to be subsumed under one law, it was
only necessary to prove that, as the
effects were similar in quality, so also
they, as to quantity, conform to the
same rules. This was first shown to
be true of the moon, which agreed
with terrestrial objects not only in
tending to a centre, but in the fact
that this centre was the earth. The
tendency of the moon towards the
earth being ascertained to vary as
the inverse square of the distance, it
was deduced from this, by direct cal-
culation, that if the moon were as
near to the earth as terrestrial objects
are, and the acquired force in the
direction of the tangent were sus-
pended, the moon would fall towards
the earth through exactly as many
feet in a second as those objects do
by virtue of their weight. Hence
the inference was irresistible that the
moon also tends to the earth by vir-
tue of its weight, and that the two
phenomena, the tendency of the moon
to the earth and the tendency of ter-
restrial objects to the earth, being
not only similar in quality, but, when
in the same circumstances, identical
in quantity, are cases of one and the
same law of causation. But the ten-
dency of the moon to the earth, and
the tendency of the earth and planets
to the sun, were already known to be
of the same law of causation :

and thus the law of all these ten-
dencies and the law of terrestrial
gravity were recognised as identical,
and were subsumed under one general
law, that of gravitation.

In a similar manner, the laws of
magnetic phenomena have more re-
cently been subsumed under known
laws of electricity. It is thus that
the most general laws of nature are
usually arrived at : we mount to them
by successive steps. For, to arrive
by correct induction at laws which
hold under such an immense variety
of circumstances, laws so general as
to be independent of any varieties of
space or time which we are able to
observe, requires for the most part
many distinct sets of experiments or
observations, conducted at different
times and by different people. One
part of the law is first ascertained,
afterwards another part : one set of
observations teaches us that the law
holds good under some conditions,
another that it holds good under
other conditions, by combining which
observations we find that it holds
good under conditions much more
general, or even universally. The
general law, in this case, is literally
the sum of all the partial ones ; it
is a recognition of the same sequence
in different sets of instances, and
may, in fact, be regarded as merely
one step in the process of elimination.
The tendency of bodies towards one
another, which we now call gravity,
had at first been observed only on the
earth's surface, where it manifested
itself only as a tendency of all bodies
towards the earth, and might, there-
fore, be ascribed to a peculiar pro-
perty of the earth itself : one of the
circumstances, namely, the proximity
of the earth, had not been eliminated.
To eliminate this circumstance re-
quired a fresh set of instances in
other parts of the universe : these
we could not ourselves create ; and
though nature had created them for
us, we were placed in very unfavour-
able circumstances for observing them.
To make these observations fell natur-

p<^

INDUCTION.

ally to the lot of a different set of
persons from those who studied ter-
restrial phenomena, and had, indeed,
been a matter of great interest at a
time when the idea of explaining
celestial facts by terrestrial laws was
looked upon as the confounding of an
indefeasible distinction. When, how-
ever, the celestial motions were ac-
curately ascertained, and the deduc-
tive processes performed, from which
it appeared that their laws and those
of terrestrial gravity corresponded,
those celestial observations became a
Bet of instances which exactly elimin-
ated the circumstance of proximity to
the earth, and proved that in the
original case, that of terrestrial ob-
jects, it was not the earth, as such,
that caused the motion or the pres-
sure, but the circumstance common
to that case with the celestial in-
stances, namely, the presence of some
great body within certain limits of
distance.

§ 6. There are, then, three modes
of explaining laws of causation, or,
which is the same thing, resolving
them into other laws. First, when
the law of an effect of combined
causes is resolved into the separate
laws of the causes, together with the
fact of their combination. Secondly,
when the law which connects any two
links, not proximate, in a chain of
causation, is resolved into the laws
which connect each with the inter-
mediate links. Both of these are
cases of resolving one law into two
or more ; in the third, two or more
are resolved into one : when, after
the law has been shown to hold good
in several different classes of cases,
we decide that what is true in each
of these classes of cases is true under
some more general supposition, con-
sisting of what all those classes of
cases have in common. We may
here remark that this last operation
involves none of the uncertainties at-
tendant on induction by the Method
of Agreement, since we need not sup-
pose the result to be extended by way

of inference to any new class of cases
different from those by the compari-
son of which it was engendered.

In all these three processes, laws
are, as we have seen, resolved into
laws more general than themselves ;
laws extending to all the cases which
the former extended to, and others
besides. In the first two modes they
are also resolved into laws more cer-
tain, in other words, more universally
true than themselves ; they are, in
fact, proved not to be themselves
laws of nature, the character of which
is to be universally true, but results
of laws of nature, which may be only
true conditionally, and for the most
part. No difference of this sort exists
in the third case, since here the
partial laws are, in fact, the very
same law as the general one, and any
exception to them would be an excep-
tion to it too.

By all the three processes, the
range of deductive science is extended;
since the laws, thus resolved, may be
thenceforth deduced demonstratively
from the laws into which they are
resolved. As already remarked, the
same deductive process which proves
a law or fact of causation if unknown,
serves to explain it when known.

The word explanation is here used
in its philosophical sense. What is
called explaining one law of nature by
another, is but substituting one mys-
tery for another, and does nothing
to render the general coiirse of nature
other than mysterious : we can no
more assign a why for the most exten-
sive laws than for the partial ones.
The explanation may substitute a
mystery which has become familiar,
and has grown to seem not mysterious,
for one which is still strange. And
this is the meaning of explanation, in
common parlance. But the process
with which we are here concerned
often does the very contrary : it re-
solves a phenomenon with which we
are familiar into one of which we
previously knew little or nothing ; as
when the common fact of the fall of
heavy bodies was resolved into the

tJXAMPLES OF TSl! l5Xt*LANATI0N OF LAWS.

311

tendency of all particles of matter to-
wards one another. It must be kept
constantly in view, therefore, that in
science, those who speak of explain-
ing any phenomenon mean (or should
mean) pointing out not some more
familiar, but merely some more gene-
ral phenomenon, of which it is a par-
tial exemplification ; or some laws of
causation which produce it by their
joint or successive action, and from
which, therefore, its conditions may
be determined deductively. Every
such operation brings us a step nearer
towards answering the question which
was stated in a previous chapter as
comprehending the whole problem of
the investigation of nature, viz. What
are the fewest assumptions, which
being granted, the order of nature as
it exists would be the result ? What
are the fewest general propositions
from which all the uniformities exist-
ing in nature could be deduced ?

The laws, thus explained or re-
solved, are sometimes said to be ac-
counted for ; but the expression is
incorrect, if taken to mean anything
more than what has been already
stated. In minds not habituated to
accurate thinking, there is often a
confused notion that the general laws
are the causes of the partial ones ;
that the law of general gravitation,
for example, causes the phenomenon
of the fall of bodies to the earth. But
to assert this would be a misuse of
the word cause : terrestrial gravity is
not an effect of general gravitation,
but a case of it ; that is, one kind of
the particular instances in which that
general law obtains. To account for
a law of nature means, and can mean,
nothing more than to assign other
laws more general, together with col-
locations, which laws and collocations
being supposed, the partial law fol-
lows without any additional supposi-
tion.

CHAPTER XIII.

MISCELLANEOUS EXAMPLES OF TH« EX-
PLANATION OF LAWS OF NATURE.

§ I. The most striking example
which the history of science presents
of the explanation of laws of causa-
tion and other uniformities of sequence
among special phenomena, by resolv-
ing them into laws of greater sim-
plicity and generality, is the great
Newtonian generalisation : respecting
which typical instance so much having
already been said, it is sufficient to
call attention to the great number
and variety of the special observed
uniformities which are in this case
accounted for, either as particular
cases, or as consequences of one very
simple law of universal nature. The
simple fact of a tendency of every
particle of matter towards every other
particle, varying inversely as the
square of the distance, explains the
fall of bodies to the earth, the revolu-
tions of the planets and satellites, the
motions (so far as known) of comets,
and all the various regularities which
have been observed in these special
phenomena ; such as the elliptical
orbits, and the variations from exact
ellipses ; the relation between the
solar distances of the planets and the
duration of their revolutions ; the
precession of the equinoxes ; the
tides, and a vast number of minor
astronomical truths.

Mention has also been made in the
preceding chapter of the explanation
of the phenomena of magnetism from
laws of electricity ; the special laws
of magnetic agency having been aflfi-
liated by deduction to observed laws
of electric action, in which they have
ever since been considered to be in-
cluded as special cases. An example
not so complete in itself, but even
more fertile in consequences, having
been the starting-point of the really
scientific study of physiology, is the
affiliation, commenced by Bichat, and
carried on by subsequent biologists,
of the properties of the bodily organs

3J^

INDUCTION.

to the elementary properties of the
tissues into which they are anatomi-
cally decomposed.

Another striking instance is af-
forded by Dalton's generalisation,
commonly known as the atomic theory.
It had been known from the very
commencement of accurate chemical
observation, that any two bodies com-
bine chemically with one another in
only a certain number of proportions ;
but those proportions were in each case
expressed by a percentage — so many
parts (by weight) of each ingredient,
in lOO of the compound, (say 35 and
a fraction of one element, 64 and a
fraction of the other :) in which mode
of statement no relation was per-
ceived between the proportion in
which a given element combines with
one substance, and that in which it
combines with others. The great
step made by Dalton consisted in
perceiving, that a unit of weight
might be established for each sub-
stance, such that by supposing the
substance to enter into all its com-
binations in the ratio either of that
unit, or of some low multiple of that
unit, all the different proportions,
previously expressed by percentages,
were found to result. Thus i being
assumed as the unit of hydrogen, if 8
were then taken as that of oxygen,
the combination of one unit of hydro-
gen with one unit of oxygen would
produce the exact proportion of weight
between the two substances which is
known to exist in water ; the com-
bination of one unit of hydrogen vi^ith
two units of oxygen would produce
the proportion which exists in the
other compound of the same two ele-
ments, called peroxide of hydrogen ;
and the combinations of hydrogen
and of oxygen with all other sub-
stances would correspond with the
supposition that those elements enter
into combination by single units, or
twos, or threes, of the numbers as-
signed to them, I and 8, and the other
substances by ones or twos or threes
of other determinate numbers proper
to each. The result is that a table i

of the equivalent numbers, or, A6
they are called, atomic weights, of all
the elementary substances, comprises
in itself, and scientifically explains,
all the proportions in which any sub-
stance, elementary or compound, is
found capable of entering into chemi-
cal combination with any other sub-
stance whatever.

§ 2. Some interesting cases of the
explanation of old uniformities by
newly ascertained laws are afforded by
the researches of Professor Graham.
That eminent chemist was the first
who drew attention to the distinction
which may be made of all substances
into two classes, termed by him crys-
talloids and colloids ; or rather, of all
states of matter into the crystalloid
and the colloidal states, for many
substances are capable of existing in
either. When in the colloidal state,
their sensible properties are very dif-
ferent from those of the same sub-
stance when crystallised, or when in
a state easily susceptible of crystal-
lisation. Colloid substances pass with
extreme difficulty and slowness into
the crystalline state, and are ex-
tremely inert in all the ordinary
chemical relations. Substances in
the colloid state are almost always,
when combined with water, more or
less viscous or gelatinous. The most
prominent examples of the state are
certain animal and vegetable sub-
stances, particularly gelatine, albu-
men, starch, the gums, caramel, tan-
nin, and some others. Among sub-
stances not of organic origin, the most
notable instances are hydrated silicic
acid and hydrated alumina, with other
metallic peroxides of the aluminous
class.

Now it is found, that while colloidal
substances are easily penetrated by
water, and by the solutions of crys-
talloid substances, they are very little
penetrable by one another : which
enabled Professor Graham to intro-
duce a highly effective process (termed
dialysis) for separating the crystalloid
substances contained in any liquid

Examples o^ the explanation of laws. 313

mixture, by passing them through a
thin septum of colloidal matter, which
does not sufifer anything colloidal to
pass, or suffers it only in very minute
quantity. This property of colloids
enabled Mr. Graham to account for a
number of special results of observa-
tion not previously explained.

For instance, "while soluble crys-
talloids are always highly sapid,
soluble colloids are singularly in-
sipid," as might be expected ; for, as
the sentient extremities of the nerves
of the palate "are probably protected
by a colloidal membrane," imperme-
able to other colloids, a colloid, when
tasted, probably never reaches those
nerves. Again, " it has been observed
that vegetable gum is not digested in
the stomach ; the coats of that organ
dialyse the soluble food, absorbing
crystalloids, and rejecting all col-
loids." One of the mysterious pro-
cesses accompanying digestion, the
secretion of free muriatic acid by
the coats of the stomach, obtains a
probable hypothetical explanation
through the same law. Finally,
much light is thrown upon the ob-
served phenomena of osmose (the
passage of fluids outward and inward
through animal membranes) by the
fact that the membranes are colloidal.
In consequence, the water and saline
solutions contained in the animal
body pass easily and rapidly through
the membranes, while the substances
directly applicable to nutrition, which
are mostly colloidal, are detained by
them. *

The property which salt possesses
of preserving animal substances from
putrefaction is resolved by Liebig into
two more general laws — the strong
attraction of salt for water, and the
necessity of the presence of water as
a condition of putrefaction. The in-
termediate phenomenon which is in-
terpolated between the remote cause

* Vide Memoir by Tliomas Graham,
F.R.S., Master of the Mint, "On Liquid
Diffusion Applied to Analysis ; " in the
Philosophical Transactions for 1862, re-
printed in the Journal of the Chemical
•Society, and also separntely as a pamphlei.

anct the effect, can here be not merely
inferred but seen ; for it is a familiar
fact, that flesh upon which salt has
been thrown is speedily found swim-
ming in brine.

The second of the two factors (as
they may be termed) into which the
preceding law has been resolved, the
necessity of water to putrefaction,
itself affords an additional example
of the Resolution of Laws. The law
itself is proved by the Method of Dif-
ference, since flesh completely dried
and kept in a dry atmosphere does
not putrefy ; as we see in the case of
dried provisions, and human bodies
in very dry climates. A deductive
explanation of this same law re-
sults from Liebig's speculations. The
putrefaction of animal and other azo-
tised bodies is a chemical process, by
which they are gradually dissipated
in a gaseous form, chiefly in that of
carbonic acid and ammonia ; now to
convert the carbon of the animal sub-
stance into carbonic acid rec^uires oxy-
gen, and to convert the azote into
ammonia requires hydrogen, which
are the elements of water. The ex-
treme rapidity of the putrefaction of
azotised substances, compared with
the gradual decay of non-azotised
bodies (such as wood and the like)
by the action of oxygen alone, he
explains from the general law that
substances are much more easily de-
composed by the action of two dif-
ferent afl&nities upon two of their ele-
ments than by the action of only one.

§ 3. Among the many important
properties of the nervous system which
have either been first discovered or
strikingly illustrated by Dr. Brown-
Sequard, I select the reflex influence
of the nervous system on nutrition
and secretion. By reflex nervoias
action is meant action which one part
of the nervous system exerts over
another part, without any interme-
diate action on the brain, and con-
sequently without consciousness ; or
which, if it does pass through the
brain, at least produces its effects in-

3»4

INDUCTION.

dependently of the will. There are
many experiments which prove that
irritation of a nerve in one part of
the body may in this manner excite
powerful action in another part ; for
example, food injected into the sto-
mach through a divided oesophagus
nevertheless produces secretion of
saliva ; warm water injected into the
bowels, and various other irritations
of the lower intestines, have been
found to excite secretion of the gastric
juice, and so forth. The reality of
the power being thus proved, its
agency explains a great variety of
apparently anomalous phenomena, of
which I select the following from Dr.
Brown-S^quard's Lectures on the Ner-
vous System : —

The production of tears by irrita-
tation of the eye, or of the mucous
membrane of the nose.

The secretions of the eye and nose
increased by exposure of other parts
of the body to cold.

Inflammation of the eye, especially
when of traumatic origin, very fre-
quently excites a similar affection in
the other eye, which may be cured
by section of the intervening nerve.

Loss of sight sometimes produced
by neuralgia ; and has been known
to be at once cured by the extirpation,
for instance, of a carious tooth.

Even cataract has been produced
in a healthy eye by cataract in the
other eye, or by neuralgia, or by a
wound of the frontal nerve.

The well-known phenomenon of a
sudden stoppage of the heart's ac-
tion, and consequent death, produced
by irritation of some of the nervous
extremities, e.g., by drinking very
cold water, or by a blow on the ab-
domen, or other sudden excitation
of the abdominal sympathetic nerve,
though this nerve may be irritated
to any extent without stopping the
heart's action if a section be made of
the communicating nerves.

The extraordinary effects produced
on the internal organs by an extensive
burn on the surface of the body, con-
sisting of violent inflammation of the

tissues of the abdomen, chest, of
head, which, when death ensues from
this kind of injury, is one of the most
frequent causes of it.

Paralysis and anaesthesia of one
part of the body from neuralgia in
another part ; and muscular atrophy
from neuralgia, even when there is
no paralysis.

Tetanus produced by the lesion of
a nerve ; Dr. Brown- Sequard thinks
it highly probable that hydrophobia
is a phenomenon of a similar nature.

Morbid changes in the nutrition of
the brain and spinal cord, manifest-
ing themselves by epilepsy, chorea,
hysteria, and other diseases, occa-
sioned by lesion of some of the ner-
vous extremities in remote places, as
by worms, calculi, tumours, carious
bones, and in some cases even by very
slight irritations of the skin.

§ 4- From the foregoing and similar
instances we may see the importance,
when a law of nature previously un-
known has been brought to light, or
when new light has been thrown upon
a known law by experiment, of ex-
amining all cases which present the
conditions necessary for bringing that
law into action ; a process fertile in
demonstrations of special laws pre-
viously unsuspected, and explanations
of others already empirically known.

For instance, Faraday discovered
by experiment that voltaic electricity
could be evolved from a natural mag-
net, provided a conducting body were
set in motion at right angles to the
direction of the magnet ; and this he
found to hold not only of small mag-
nets, but of that great magnet, the
earth. The law being thus estab-
lished experimentally that electricity
is evolved by a magnet and a con-
ductor moving at right angles to the
direction of its poles, we may now
look out for fresh instances in which
these conditions meet. Wherever a
conductor moves or revolves at right
angles to the direction of the earth's
magnetic poles, there we may expect
an evolution of electricity. In the

EXAMPLES OF THE EXPLANATION OE LAWS.

315

borthem regions, where the polar
direction is nearly perpendicular to
the horizon, all horizontal motions of
conductors will produce electricity ;
horizontal wheels, for example, made
of metal ; likewise all running streams
will evolve a current of electricity,
which will circulate round them ; and
the air thus charged with electricity
may be one of the causes of the
aurora borealis. In the equatorial
regions, on the contrary, upright
wheels placed parallel to the equator
will originate a voltaic circuit, and
waterfalls will naturally become elec-
tric.

For a second example ; it has been
proved, chiefly by the researches of
Professor Graham, that gases have a
strong tendency to permeate animal
membranes, and diffuse themselves
through the spaces which such mem-
branes enclose, notwithstanding the
presence of other gases in those spaces.
Proceeding from this general law, and
reviewing a variety of cases in which
gases lie contiguous to membranes,
we are enabled to demonstrate or to
explain the following more special
laws : I St. The human or animal
body, when surrounded with any gas
not already contained within the
body, absorbs it rapidly ; such, for
instance, as the gases of putrefying
matters : which helps to explain
malaria. 2d. The carbonic acid gas
of effervescing drinks, evolved in the
stomach, permeates its membranes,
and rapidly spreads through the sys-
tem. 3d. Alcohol taken into the
stomach passes into vapour and
spreads through the system with great
rapidity, (which, combined with the
high combustibility of alcohol, or, in
other words, its ready combination
with oxygen, may perhaps help to ex-
plain the bodily warmth immediately
consequent on drinking spirituous
liquors). 4th. In any state of the
body in which peculiar gasea are
formed within it, these will rapidly
exhale through all parts of the body ;
and hence the rapidity with which,
in certain states of disease, the sur-

rounding atmosphere becomes tainted.
5th. The putrefaction of the interior
parts of a carcase will proceed as
rapidly as that of the exterior, from
the ready passage outwards of the
gaseous products. 6th. The exchange
of oxygen and carbonic acid in the
lungs is not prevented, but rather
promoted, by the intervention of the
membrane of the lungs and the coats
of the blood-vessels between the blood
and the air. It is necessary, however,
that there should be a substance in
the blood with which the oxygen of
the air may immediately combine ;
otherwise, instead of passing into the
blood, it would permeate the whole
organism : and it is necessary that the
carbonic acid, as formed in the capil-
laries, should also find a substance in
the blood with which it can combine ;
otherwise it would leave the body at
all points, instead of being discharged
through the lungs.

§ 5. The following is a deduction
which confirms, by explaining, the
empirical generalisation that soda
powders weaken the human system.
These powders, consisting of a mix-
ture of tartaric acid with bicarbonate
of soda, from which the carbonic acid
is set free, must pass into the stomach
as tartrate of soda. Now, neutral
tartrates, citrates, and acetates of the
alkalis are found, in their passage
through the system, to be changed
into carbonates ; and to convert a
tartrate into a carbonate requires an
additional quantit}' of oxygen, the
abstraction of which must lessen the
oxygen destined for assimilation with
the blood, on the quantity of which
the vigorous action of the human
system partly depends.

The instances of new theories agree-
ing with and explaining old empiri-
cisms are innumerable. All the just
remarks made by experienced persons
on human character and conduct are
so many special laws which the gene-
ral laws of the human mind explain
and resolve. The empirical generali-
sations on which the operations of the

316

INDtJCTION.

arts have usually been founded, are
continually justified and confirmed on
the one hand, or corrected and im-
proved on the other, by the discovery
of the simpler scientific laws on which
the efficacy of those operations de-
pends. The effects of the rotation of
crops, of the various manures, and
other processes of improved agricul-
ture, have been for the first time re-
solved in our own day into known
laws of chemical and organic action
by Davy, Liebig, and others. The
processes of the medical art are even
now mostly empirical : their efficacy
is concluded, in each instance, from a
special and most precarious experi-
mental generalisation : but as science
advances in discovering the simple
laws of chemistry and physiology,
progress is made in ascertaining the
intermediate links in the series of
phenomena, and the more general laws
on which they depend ; and thus,
while the old processes are either ex-
ploded, or their efficacy, in so far
as real, explained, better processes,
founded on the knowledge of proxi-
mate causes, are continually suggested
and brought into use.* Many even
f the truths of geometry were gene-
ralisations from experience before
they were deduced from first prin-
ciples. The quadrature of the cycloid
is said to have been first effected by
measurement, or rather by weighing
a cycloidal card, and comparing its
weight with that of a piece of similar
card of known dimensions.

§ 6. To the foregoing examples from
physical science let us add another
from mental. The following is one
of the simple laws of mind : Ideas of
a pleasurable or painful character

* It was an old generalisation in surgery
that tight bandaging had a tendency to pre-
vent or dissipate local inflammation. This
sequence being, in the progress of physio-
logical knowledge, resolved into more gene-
ral laws, led to the important surgical in-
vention made by Dr. Arnott, the treatment
of local inflammation and tumours by
means of an equable pressure, produced by
a bladder partially filled with air. The
pressure, by keeping back the blood from

form associations tnore easily and
strongly than other ideas, that is,
they become associated after fewer
repetitions, and the association is
more durable. This is an experi-
mental law, grounded on the Method
of Difference. By deduction from
this law, many of the more special laws
which experience shows to exist among
particular mental phenomena may be
demonstrated and explained : — the
ease and rapidity, for instance, with
which thoughts connected with our
passions, or our more cherished in-
terests are excited, and the firm hold
which the facts relating to them have
on our memory ; the vivid recollec-
tion we retain of minute circumstances
which accompanied any object or event
that deeply interested us, and of the
times and places in which we have
been very happy or very miserable ;
the horror with which we view the
accidental instrument of any occur-
rence which shocked us, or the locality
where it took place, and the pleasure
we derive from any memorial of past
enjoyment ; all these effects being
proportional to the sensibility of the
individual mind, and to the consequent
intensity of the pain or pleasure from
which the association originated. It
has been suggested by the able writer
of a biographical sketch of Dr. Priest-
ley in a monthly periodical,* that the
same elementary law of our mental
constitution, suitably followed out,
would explain a variety of mental
phenomena previously inexplicable,
and in particular some of the funda-
mental diversities of human character
and genius. Associations being of
two sorts, either between synchronous,
or between successive impressions ;
and the influence of the law which

the part, prevents the inflammation, or the
tumour, from being nourished : in the case
of inflammation, it removes the stimulus,
whicii the organ is unfit to receive ; in the
case of tumours, by keeping back the
nutritive fluid, it causes the absorption of
matter to exceed the supply, and the
diseased mass is gradually absorbed and
disappears.

* Since acknowledged and reprinted in
Mr. Martineau's MUceUanies.

EXAMPLES OF THE EXPLANATION OF LAWS.

317

renders associations stronger in pro-
portion to the pleasurable or painful
character of the impressions, being felt
with peculiar force in the synchronous
class of associations ; it is remarked
by the writer referred to, that in
minds of strong organic sensibility
synchronous associations will be likely
to predominate, producing a tendency
to conceive things in pictures and in
the concrete, richly clothed in attri-
butes and circumstances, a mental
habit which is commonly called Ima-
gination, and is one of the peculiari-
ties of the painter and the poet ; while
persons of more moderate susceptibi-
lity to pleasure and pain will have a
tendency to associate facts chiefly in
the order of their succession, and such
persons, if they possess mental supe-
riority, will addict themselves to his-
tory or science rather than to creative
art. This interesting speculation the
author of the present work has en-
deavoured, on another occasion, to
pursue farther, and to examine how
far it will avail towards explaining
the peculiarities of the poetical tem-
perament. * It is at least an example
which may serve, instead of many
others, to show the extensive scope
which exists for deductive investiga-
tion in the important and hitherto so
imperfect Science of Mind.

§ 7. The copiousness with which
the discovery and explanation of
special laws of phenomena by deduc-
tion from simpler and more general
ones has here been exemplified, was
prompted by a desire to characterise
clearly, and place in its due position
of importance, the Deductive Method ;
which, in the present state of know-
ledge, is destined henceforth irrevo-
cably to predominate in the course of
scientific investigation. A revolution
is peaceably and progressively effect-
ing itself in philosophy, the reverse of
that to which Bacon has attached his
name. That great man changed the
method of the sciences from deductive

* IHuertations and Discmnont, toI. i.,
fourth paper.

to experimental, and it is now rapidly
reverting from experimental to deduc-
tive. But the deductions which Bacon
abolished were from premises hastily
snatched up or arbitrarily assumed.
The principles were neither established
by legitimate canons ot experimental
inquiry, nor the results tested by that
indispensable element of a rational
Deductive Method, verification by
specific experience. Between the
primitive method of Deduction and
that which I have attempted to
characterise, there is all the difference
which exists between the Aristotelian
physics and the Newtonian theory of
the heavens.

It would, however, be a mistake to
expect that those great generalisations,
from which the subordinate truths of
the more backward sciences will pro-
bably at some future period be de-
duced by reasoning, (as the truths of
astronomy are deduced from the gene-
ralities of the Newtonian theory,) will
be found, in all, or even in most cases,
among truths now known and ad-
mitted. We may rest assured, that
many of the most general laws of
nature are as yet entirely unthought
of ; and that many others, destined
hereafter to assume the same charac-
ter, are known, if at all, only as laws
or properties of some limited class of
phenomena ; just as electricity, now
recognised as one of the most univer-
sal of natural agencies, was once
known only as a curious property
which certain substances acquired by
friction, of first attracting and then
repelling light bodies. If the theories
of heat, cohesion, crystallisation, and
chemical action are destined, as there
can be little doubt that they are, to
become deductive, the truths which
will then be regarded as the principia
of those sciences would probably, if
now announced, appear quite as novel*
as the law of gravitation appeared to
the contemporaries of Newton ; pos-

* Written before the rise of the new
views respecting the relation of heat to
mechanicad force ; but confirmed rather
thaTi contradicted by thena.

3x8

INDUCTION.

sibly even more so, since Newton's
law, after all, was but an extension of
the law of weight— that is, of a gene-
ralisation familiar from of old, and
which already comprehended a not
inconsiderable body of natural pheno-
mena. The general laws of a similarly
commanding character, which we still
look forward to the discovery of, may
not always find so much of their foun-
dations already laid.

These general truths will doubtless
make thei? first appearance in the
character or hypotheses ; not proved,
nor even admitting of proof, in the
first instance, but assumed as premises
for the purpose of deducing from them
the known laws of concrete pheno-
mena. But this, though their initial,
cannot be their final state. To entitle
an hypothesis to be received as one of
the truths of nature, and not as a
mere technical help to the human
faculties, it must be capable of being
tested by the canons of legitimate
induction, and must actually have
been submitted to that test. When
this shall have been done, and done
successfully, premises will have been
obtained from which all the other
propositions of the science will thence-
forth be presented as conclusions, and
the science will, by means of a new
and unexpected Induction, be rendered
Deductive.

CHAPTER XIV.

OF THE LIMITS TO THE EXPLANATION
OP LAWS OP NATURE, AND OP HYPO-

§ I. The preceding considerations
have led us to recognise a distinction
between two kinds of laws or observed
uniformities in nature — ultimate laws
and what may be termed derivative
laws. Derivative laws are such as
are deducible from, and may, in any
of the modes which we have pointed
out, be resolved into other and more
general ones. Ultimate laws are those
which cannot. We are not sure that
any of the uniformities with which

we are yet acquainted are ultimate
laws ; but we know that there must
be ultimate laws, and that every
resolution of a derivative law into
more general laws brings us nearer
to them.

Since we are continually discover-
ing that uniformities, not previously
known to be other than ultimate, are
derivative and resolvable into more
general laws — since (in other words)
we are continually discovering the
explanation of sOme sequence which
was previously known only as a fact —
it becomes an interesting question
whether there ,are any necessary
limits to this philosophical operation,
or whether it may proceed until all
the uniform sequences in nature are
resolved into some one universal law.
For this seems at first sight to be
the ultimatum towards which the
progress of induction, by the Deduc-
tive Method resting on a basis o£
observation and experiment, is tend-
ing. Projects of this kind were uni-
versal in the infancy of philosophy,
any speculations which held out a
less brilliant prospect being in those
early times deemed not worth pursu-
ing. And the idea receives so much
apparent countenance from the nature
of the most remarkable achievements
of modern science, that speculators
are even now frequently appearing
who profess either to have solved the
problem or to suggest modes in which
it may one day be solved. Even
where pretensions of this magnitude
are not made, the character of the
solutions which are given or sought
of particular classes of phenomena
often involves such conceptions of
what constitutes explanation as would
render the notion of explaining all
phenomena whatever by means of
some on ecause or law, perfectly ad-
missible.

§ 2. It is therefore useful to remark
that the ultimate Laws of Nature can-
not possibly be less numerous than
the distinguishable sensations or other
feelings of our nature — those, I mean,

HYPOTHESES.

3'^

lehich are distinguishable from one
another in quality, and not merely in
quantity or degree. For example,
since there is a phenomenon sui gene-
ris called colour, which our conscious-
ness testifies to be not a particular
degree of some other phenomenon, as
heat, or odour, or motion, but intrin-
sically unlike all others, it follows
that there are ultimate laws of colour ;
that though the facts of colour may
admit of explanation, they never can
be explained from laws of heat or
odour alone, or of motion alone, but
that, however far the explanation
may be carried, there will always re-
main in it a law of colour. I do not
mean that it might not possibly be
shown that some other phenomenon,
some chemical or mechanical ac-
tion, for example, invariably precedes
and is the cause of every phenome-
non of colour. But though this, if
proved, would be an important ex-
tension of our knowledge of nature,
it would not explain how or why
a motion or a chemical action can
produce a sensation of colour ; and
however diligent might be our scru-
tiny of the phenomena, whatever
number of hidden links we might de-
tect in the chain of causation termi-
nating in the colour, the last link
would still be a law of colour, not a
law of motion, nor of any other phe-
nomenon whatever. Nor does this
observation apply only to colour, as
compared with any other of the great
classes of sensations ; it applies to
every particular colour, as compared
with others. White colour can in no
manner be explained exclusively by
the laws of the production of red
colour. In any attempt to explain
it, we cannot but introduce, as one
element of the explanation, the pro-
position that some antecedent or other
produces the sensation of white.

The ideal limit, therefore, of the
explanation of natural phenomena
(towards which, as towards other ideal
limits, we are constantly tending,
without the prospect of ever com-
pletely attaining it) would be to show

that each distinguishable variety of
our sensations, or other states of con-
sciousness, has only one sort of cause :
that, for example, whenever we per-
ceive a white colour, there is som©
one condition or set of conditions
which is. always present, and the
presence of which always produces in
us that sensation. As long as there
are several known modes of produc-
tion of a phenomenon, (several dif-
ferent substances, for instance, which
have the property of whiteness, and
between which we cannot trace any
other resemblance,) so long it is not
impossible that one of these modes
of production may be resolved into
another, or that all of them may be
resolved into some more general mode
of production not hitherto recognised.
But when the modes of production
are reduced to one, we cannot, in
point of simplification, go any further.
This one may not, after all, be the
ultimate mode ; there may be other
links to be discovered between the
supposed cause and the effect ; but
we can only further resolve the known
law, by introducing some other law
hitherto unknown ; which will not
diminish the number of ultimate
laws.

In what cases, accordingly, has
science been most successful in ex-
plaining phenomena, by resolving
their complex laws into laws of greater
simplicity and generality ? Hitherto
chiefly in cases of the propagation of
various phenomena through space :
and, first and principally, the most
extensive and important of all facts of
that description, mechanical motion.
Now this is exactly what might be
expected from the principles here laid
down. Not only is motion one of
the most universal of all phenomena,
it is also (as might be expected from
that circumstance) one of those which,
apparently at least, are produced in
the greatest number of ways ; but the
phenomenon itself is always, to our
sensations, the same in every respect
but degree. Differences of duration
or of velocity are evidently differ-

520

INDUCTION.

ences in degree only ; and differences
of direction in space, which alone has
any semblance of being a distinction
in kind, entirely disappear (so far as
our sensations are concerned) by a
change in our own position ; indeed
the very same motion appears to us,
according to our position, to take
place in every variety of direction,
and motions in every different direc-
tion to take place in the same. And
again, motion in a straight line and
in a curve are no otherwise distinct
than that the one is motion continu-
ing in the same direction, the other
is motion which at each instant
changes its direction. There is, there-
fore, according to the principles I
have stated, no absurdity in suppos-
ing that all motion may be produced
in one and the same way, by the
same kind of cause. Accordingly,
the greatest achievements in physical
science have consisted in resolving
one observed law of the production
of motion into the laws of other known
modes of production, or the laws of
several such modes into one more
general mode ; as when the fall of
bodies to the earth, and the motions
of the planets, were brought under
the one law of the mutual attraction
of all particles of matter ; when the
motions said to be produced by mag-
netism were shown to be produced
by electricity ; when the motions of
fluids in a lateral direction, or even
contrary to the direction of gravity,
were shown to be produced by gravity;
and the like. There is an abundance
of distinct causes of motion still un-
resolved into one another — gravita-
tion, heat, electricity, chemical action,
nervous action, and so forth ; but
whether the efforts of the present
generation of savans to resolve all
these different modes of production
into one, are ultimately successful or
not, the attempt so to resolve them
is perfectly legitimate. For though
these various causes produce, in other
respects, sensations intrinsically dif-
ferent, and are not, therefore, capable
of beingf resolved into one another,

yet in so far as they all produce
motion, it is quite possible that the
immediate antecedent of the motion
may in all these different cases be
the same ; nor is it impossible that
these various agencies themselves
may, as the new doctrines assert, all
of them have for their own immediate
antecedent modes of molecular motion.
We need not extend our illustration
to other cases, as, for instance, to the
propagation of light, sound, heat, elec-
tricity, &c., through space, or any of
the other phenomena which have been
found susceptible of explanation by
the resolution of their observed laws
into more general laws. Enough has
been said to display the difference be-
tween the kind of explanation and
resolution of laws which is chimeri-
cal, and that of which the accomplish-
ment is the great aim of science ; and
to show into what sort of elements
the resolution must be effected, if at
all.*

* As is well remarked by Professor Bain,
in the very valuable chapter of his Logic
which treats of this subject (ii. 121), " scien-
tific explanation and inductive generalisa-
tion being the same thing, the limits of
Explanation are the limits of Induction,"
and "the limits to inductive generalisation
are the limits to the agreement or com-
munity of facts. Induction supposes simi-
larity among phenomena; and when such
stmilarity is discovered, it reduces the
phenomena under a common statement.
The similarity of terrestrial gravity to
celestial attraction enables the two to be
expressed as one phenomenon. The simi-
larity between capillary attraction, solu-
tion, the operation of cements, &c., leads
to their being regarded not as a plurality,
but as a unity, a single causative link, the
operation of a single agency. ... If it be
asked whether we can merge gravity itself
in some still higher law, the answer must
depend upon the facts. Are there any
other forces, at present held distinct from
gravity, that we may hope to make frater-
nise with it, so as to join in constituting a
higher unity? Gravity is an attractive
force ; and another great attractive force is
cohesion, or the force that binds together
the atoms of solid matter. Might we then
join these two in a still higher unity, ex-
pressed under a more comprehensive law ?
Certainly we might, but not to any advan-
tage. The two kinds of force agree in the
one point, attraction, but they agree in no
other : indeed, in the manner of the attrac-

HYPOTHESES.

321

§ 3. As, however, there is scarcely
any one of the principles of a true
method of philosophising which does
not require to be guarded against
errors on both sides, I must enter a
caveat against another misapprehen-
sion, of a kind directly contrary to
the preceding. M. Comte, among
other occasions on which he has con-
demned, with some asperity, any at-
tempt to explain phenomena which
are "evidently primordial," (mean-
ing, apparently, no more than that
every peculiar phenomenon must
have at least one peculiar and there-
fore inexplicable law,) has spoken of
the attempt to furnish any explana-
tion of the colour belonging to each
substance, " la couleur el^mentaire
propre k chaque substance," as essen-
tially illusory. "No one," says he,
" in our time attempts to explain the
particular specific gravity of each sub-
stance or of each structure. Why

tion, they differ widely ; so widely that we
should hiive to state totally distinct laws
for each. Gravity is common to all matter,
uud equal in amount in equal masses of
matter, whatever be the kind ; it follows
the law of the diffusion of space from a
point, (the inverse square of the distance ;)
It extends to distances unlimited ; it is
indestructible and invariable. Cohesion is
special for each separate substance ; it de-
creases according to distance much more
rapidly than the inverse square, vanishing
entirely at very small distances. Two such
forces have not suflBcient kindred to be
generalised into one force ; the generalisa-
tion is only illusory ; the itatement of the
difference would still make two forces ;
while the consideration of one would not
in any way simplify the phenomena of the
other, as happened in the generalisation of
gravity itself."

To the impassable limit of the explana-
tion of laws of nature, set forth in the text,
must therefore be added a further limita-
tion. Although, when the phenomena to
be explained are not, in their own nature,
generically distinct, the attempt to refer
them to the same cause is scientifically
legitimate ; yet to the success of the
attempt it is indispensable that the cause
should be shown to be capable of pro-
ducing them according to the same law.
Otherwise tlie unity of cause is a mere
guess, and the generalisation only a nomi-
nal one, which, even if admitted, would
not diminish the number of ultimate laws
ul nature,

should it be otherwise as to the
specific colour, the notion of which
is undoubtedly no less primordial?" *

Now, although, as he elsewhere ob-
serves, a colour must always remain
a different thing from a weight or a
sound, varieties of colour might never-
theless follow, or correspond to, given
varieties of weight, or sound, or some
other phenomenon as different as
these are from colour itself. It is
one question what a thing is, and
another what it depends on ; and
though to ascertain the conditions of
an elementary phenomenon is not
to obtain any new insight into the
nature of the phenomenon itself, that
is no reason against attempting to
discover the conditions. The inter-
dict against endeavouring to reduce
distinctions of colour to any common
principle would have held equally
good against a like attempt on the
subject of distinctions of sound,
which, nevertheless, have been found
to be immediatelypreceded and caused
by distinguishable varieties in the
vibrations of elastic bodies, though a
sound, no doubt, is quite as different
as a colour is from any motion of
particles, vibratory or otherwise. We
might add, that, in the case of colours,
there are strong positive indications
that they are not ultimate properties
of the different kinds of substances,
but depend on conditions capable of
being superinduced upon all sub-
stances ; since there is no substance
which cannot, according to the kind
of light thro\vn upon it, be made to
assume almost any colour ; and since
almost every change in the mode of
aggregation of the particles of the
same substance is attended with
alterations in its colour, and in its opti-
cal properties generally.

The really weak point in the at-
tempts which have been made to
account for colours by the vibrations
of a fluid, is not that the attempt itself
is unphilosophical, but that the exist-
ence of the fluid, and the fact of its

* Court de JPkilosophie Potitive, ii. 656.

322

INDUCTION.

vibratory motion, are not proved, but
are assumed, on no other ground than
the facility they are supposed to
afford of explaining the phenomena.
And this consideration leads to the
important question of the proper use
of scientific hypotheses ; the connec-
tion of which with the subject of the
explanation of the phenomena of
nature, and of the necessary limits
to that explanation, needs not be
pointed out.

§ 4. An hypothesis is any supposi-
tion which we make (either without
actual evidence, or on evidence avow-
edly insufficient) in order to endeavour
to deduce from it conclusions in ac-
cordance with facts which are known
to be real ; under the idea that if the
conclusions to which the hypothesis
leads are known truths, the hypo-
thesis itself either must be, or at least
is likely to be, true. If the hypo-
thesis relates to the cause or mode pf
production of a phenomenon, it will
serve, if admitted, to explain such
facts as are found capable of being
deduced from it. And this explana-
tion is the purpose of many, if not
most, hypotheses. Since explaining,
in the scientific sense, means resolving
an uniformity which is not a law of
causation into the laws of causation
from which it results, or a complex
law of causation into simpler and
more general ones from which it is
capable of being deductively inferred;
if there do not exist any known laws
which fulfil this requirement, we may
feign or imagine some which would
fulfil it ; and this is making an hjrpo-
thesis.

An hjrpothesis being a mere sup-
position, there are no other limits to
hypotheses than those of the human
imagination ; we may, if we please,
imagine, by way of accounting for an
effect, some cause of a kind utterly
unknown, and acting according to a
law altogether fictitious. But as hypo-
theses of this sort would not have any
of the plausibility belonging to those
>vhich all^ themselves by analogy

with known laws of nature, and
besides would not supply the want
which arbitrary hypotheses are gene-
rally invented to satisfy, by enabling
the imagination to represent to itself
an obscure phenomenon in a familiar
light, there is probably no hypothesis
in the history of science in which both
the agent itself and the law of its
operation were fictitious. Either the
phenomenon assigned as the cause is
real, but the law according to which
it acts merely supposed, or the cause
is fictitious, but is supposed to pro-
duce its effects according to laws
similar to those of some known class
of phenomena. An instance of the
first kind is afforded by the different
suppositions made respecting the law
of the planetary central force an-
terior to the discovery of the true law,
that the force varies as the inverse
square of the distance ; which also
suggested itself to Newton, in the first
instance, as an hypothesis, and was
verified by proving that it led de-
ductively to Kepler's laws. Hypo-
theses of the second kind are such as
the vortices of Descartes, which were
fictitious, but were supposed to obey
the known laws of rotatory motion ;
or the two rival hypotheses respecting
the nature of light, the one ascribing
the phenomena to a fluid emitted from
all luminous bodies, the other (now
generally received) attributing them
to vibratory motions among the par-
ticles of an ether pervading all space.
Of the existence of either fluid there
is no evidence, save the explanation
they are calculated to afford of some
of the phenomena ; but they are sup-
posed to produce their effects accord-
ing to known laws ; the ordinary laws
of continued locomotion in the one
case, and in the other, those of the
propagation of undulatory movements
among the particles of an elastic fluid.
According to the foregoing remarks,
hypotheses are invented to enable the
Deductive Method to be earlier ap-
plied to phenomena. But* in order
to discover the cause of any pheno»
* y|d« lupra, book |ii. oh. xi,

HYPOTHESES.

323

meuou by the Deductive Method, the
process must consist of three parts —
induction, ratiocination, and verifica-
tion. Induction, (the place of which,
however, may be supplied by a prior
deduction,) to ascertain the laws of
the causes ; ratiocination, to compute
from those laws how the causes will
operate in the particular combination
known to exist in the case in hand ;
verification, by comparing this calcu-
lated effect with the actual phenome-
non. No one of these three parts of
the process can be dispensed with. In
the deduction which proves the iden-
tity of gravity with the central force
of the solar system, all the three are
found. First, it is proved from the
moon's motions that the earth attracts
her with a force varying as the in-
verse square of the distance. This
(though partly dependent on prior
deductions) corresponds to the first
or purely inductive step, the ascer-
tainment of the law of the cause.
Secondly, from this law, and from
the knowledge previously obtained of
the moon's mean distance from the
earth, and of the actual amount of
her deflection from the tangent, it is
ascertained with what rapidity the
earth's attraction would cause the
moon to fall, if she were no farther
off and no more acted upon by ex-
traneous forces than terrestrial bodies
are ; that is the second step, the
ratiocination. Finally, this calculated
velocity being compared with the ob-
served velocity with which all heavy
bodies fall, by mere gravity, towards
the surface of the earth (sixteen feet
in the first second, forty-eight in the
second, and so forth, in the ratio of
the odd numbers, i, 3, 5, &c,), the
two quantities are found to agree.
The order in which the steps are here
presented was not that of their dis-
covery ; but it is their correct logical
order, as portions of the proof that
the same attraction of the earth which
causes the moon's motion causes also
the fall of heavy bodies to the earth,
a proof which is thus complct* in all
its parts.

Now, the Hypothetical Method sup-
presses the first of the three steps,
the induction to ascertain the law,
and contents itself with the other two
operations, ratiocination and verifica-
tion, the law which is reasoned from
being assumed instead of proved.

This process may evidently be legi-
timate on one supposition, namely, tf
the nature of the case be such that
the final step, the verification, shall
amount to and fulfil the conditions of
a complete induction. We want to
be assured that the law we have hypo-
thetically assumed is a true one ; and
its leading deductively to true results
will afford this assurance, provided
the case be such that a false* law can-
not lead to a true result — provided
no law except the very one which we
have assumed can lead deductively to
the same conclusions which that leads
to. And this proviso is often realised.
For example, in the very complete
specimen of deduction which we just
cited, the original major premise of
the ratiocination, the law of the at-
tractive force, was ascertained in this
mode, by this legitimate employment
of the Hypothetical Method. New-
ton began by an assumption that the
force which at each instant deflects a
planet from its rectilineal course, and
makes it describe a curve round the
sun, is a force tending directly to-
wards the sun. He then proved that
if this be so the planet will describe,
as we know by Kepler's first law that
it does describe, equal areas in equal
times ; and, lastly, he proved that if
the force acted in any other direction
whatever, the planet would not de-
scribe equal areas in equa^ times. It
being thus shown that no other hypo-
thesis would accord with the facts,
the assumption was proved ; the hypo-
thesis became an inductive truth.
Not only did Newton ascertain by
this hypothetical process the direc-
tion of the deflecting force, he pro-
ceeded in exactly the same manner
to ascertain the law of variation of
the quantity of that force. Ho as-
sumed that the force varied inversely

324

INDUCTION.

as the square of the distance, showed
that from this assumption the remain-
ing two of Kepler's laws might be
deduced, and, finally, that any other
law of variation would give results
inconsistent with those laws, and in-
consistent, therefore, with the real
motions of the planets, of which Kep-
ler's laws were known to be a correct
expression.

I have said that in this case the
verification fulfils the conditions of
an induction ; but an induction of
what sort ? On examination we find
that it conforms to the canon of the
Method of Difference. It affords the
two instances, A B C, a 6 c, and B C,
be. A represents central force ;
ABC, the planets plus a central
force ; B C, the planets apart from a
central force. The planets with a
central force give a, areas proportional
to the times ; the planets without a
central force give 6 c (a set of motions)
without a, or with something else in-
stead of a. This is the Method of
Difference in all its strictness. It is
true, the two instances which the
method requires are obtained in this
case, not by experiment, but by a
prior deduction. But that is of no
consequence. It is immaterial what
is the nature of the evidence from
which we derive the assurance that
ABC will produce a h c, and B C
only be; it is enough that we have
that assurance. In the present case, a
process of reasoning furnished New-
ton with the very instances which,
if the nature of the case had admitted
of it, he would have sought by experi-
ment.

It is thus perfectly possible, and
indeed is a very common occurrence,
that what was an hypothesis at the
beginning of the inquiry, becomes a
proved law of nature before its close.
But in order that this should happen,
we must be able, either by deduction
or experiment, to obtain both the in-
stances which the Method of Differ-
ence requires. That we are able from
the hypothesis to deduce the known
f^cts, gives only tJ?e afl&rmative in-

stance, A B C, a t c. It is equally
necessary that we should be able to
obtain, as Newton did, the negative
instance B C, 6 c, by showing that
no antecedent, except the one assumed
in the hypothesis, would in conjunc-
tion with B C produce a.

Now it appears to me that this as-
surance cannot be obtained when the
cause assumed in the hypothesis is an
vmknown cause, imagined solely to
account for a. When we are only
seeking to determine the precise law
of a cause already ascertained, or to
distinguish the particular agent which
is in fact the cause, among several
agents of the same kind, one or other
of which it is already known to be,
we may then obtain the negative in-
stance. An inquiry which of the
bodies of the solar system causes by
its attraction some particular irregu-
larity in the orbit or periodic time of
some satellite or comet, would be a
case of the second description. New-
ton's was a case of the first. If
it had not been previously known
that the planets were hindered from
moving in straight lines by some
force tending towards the interior of
their orbit, though the exact direc-
tion was doubtful ; or if it had not
been known that the force increased
in some proportion or other as the
distance diminished, and diminished
as it increased, Newton's argument
would not have proved his conclusion.
These facts, however, being already
certain, the range of admissible sup-
positions was limited to the various
possible directions of a line, and the
various possible numerical relations
between the variations of the distance,
and the variations of the attractive
force : now among these it was easily
shown that different suppositions
could not lead to identical conse-
quences.

Accordingly, Newton could* not
have performed his second great
scientific operation, that of identify-
ing terrestrial gravity with the cen-
tral force of the solar system, by the
same hypothetical method. When

HYPOTHESES.

325

the law of the moon's attraction had
been proved from the data of the
moon itself, then on finding the same
law to accord with the phenomena of
terrestrial gravity, he was warranted
in adopting it as the law of those
phenomena likewise ; but it would
not have been allowable for him,
without any lunar data, to assume
that the moon was attracted towards
the earth with a force as the inverse
square of the distance, merely because
that ratio would enable him to ac-
count for terrestrial gravity : for it
would have been impossible for him
to prove that the observed law of the
fall of heavy bodies to the earth could
not result from any force, save one
extending to the moon, and propor-
tional to the inverse square.

It appears, then, to be a condition
of the most genuinely scientific hypo-
thesis, that it be not destined always
to remain an hypothesis, but be of
such a nature as to be either proved
or disproved by comparison with ob-
served facts. This condition is ful-
filled when the effect is already known
to depend on the very cause supposed,
and the hypothesis relates only to the
precise mode of dependence ; the law
of the variation of the effect accord-
ing to the variations in the quantity
or in the relations of the cause. With
these may be classed the hypotheses
which do not make any supposition
with regard to causation, but only with
regard to the law of correspondence
between facts which accompany each
other in their variations, though there
may be no relation of cause and effect
between them. Such were the dif-
ferent false hypotheses which Kepler
made respecting the law of the refrac-
tion of light. It was known that the
direction of the line of refraction
varied with every variation in the
direction of the line of incidence, but
it was not known how ; that is, what
changes of the one corresponded to
the different changes of the other.
In this case any law, different from
the true one, must have led to false
results. And, lastly, we must add to

these all hypothetical modes of merely
representing, or describing, pheno-
mena ; such as the hypothesis of the
ancient astronomers that the heavenly
bodies moved in circles ; the various
hypotheses of excentrics, deferents,
and epicycles, which were added to
that original hypothesis ; the nine-
teen false hypotheses which Kepler
made and abandoned respecting the
form of the planetary orbits ; and
even the doctrine in which he finally
rested, that those orbits are ellipses,
which was but an hypothesis like the
rest until verified by facts.

In all these cases, verification is
proof ; if the supposition accords with
the phenomena, there needs no other
evidence of it. But in order that this
may be the case, I conceive it to be
necessary, when the hjrpothesis relates
to causation, that the supposed cause
should not only be a real phenomenon,
something actually existing in nature,
but should be already known to ex-
ercise, or at least to be capable of ex-
ercising, an influence of some sort
over the effect. In any other case,
it is no sufficient evidence of the
truth of the hypothesis that we are
able to deduce the real phenomena
from it.

Is it, then, never allowable, in a
scientific hypothesis, to assume a
cause ; but only to ascribe an as-
sumed law to a known cause ? I do
not assert this. I only say, that in
the latter case alone can the hypo-
thesis be received as true merely
because it explains the phenomena.
In the former case it may be very
useful by suggesting a line of in-
vestigation which may possibly ter-
minate in obtaining real proof. But,
for this purpose, as is justly remarked
by M. Comte, it is indispensable that
the cause suggested by the hypothesis
should be in its own nature suscep-
tible of being proved by other evi-
dence. This seems to be the philoso-
phical import of Newton's maxim, (so
often cited with approbation by sub-
sequent writers,) that the cause as-
signed for any phenomenon must not

326

INDUCTION,

only be such as, if admitted, would
explain the phenomenon, but must
also be a vera cau^a. What he meant
by a vera causa Newton did not in-
deed very explicitly define ; and Dr.
Whewell, who dissents from the pro-
priety of any such restriction upon
the latitude of framing hj'potheses,
has had little difficulty in showing *
that his conception of it was neither
precise nor consistent with itself : ac-
cordingly his optical theory was a
signal instance of the violation of his
own rule. It is certainly not neces-
sary that the cause assigned should
be a cause already known ; otherwise
we should sacrifice our best oppor-
tunities of becoming acquainted with
new causes. But what is true in the
maxim is, that the cause, though not
known previously, should be capable
of being known thereafter ; that its
existence should be capable of being
detected, and its connection with the
eflfect ascribed to it should be suscep-
tible of being proved, by independent
evidence. The hypothesis, by sug-
gesting observations and experiments,
puts us on the road to that inde-
pendent evidence if it be really at-
tainable ; and till it be attained, the
hypothesis ought only to count for a
more or less plausible conjecture.

§ 5. This function, however, of
hypotheses, is one which must be
reckoned absolutely indispensable in
science. When Newton said, " Hypo-
theses non fingo," he did not mean
that he deprived himself of the facili-
ties of investigation afforded by as-
suming in the first instance what he
hoped ultimately to be able to prove.
Without such assumptions, science
could never have attained its present
state : they are necessary steps in the
progress to something more certain ;
and nearly everything which is now
theory was once hypothesis. Even
in purely experimental science, some
inducement is necessary for trying
one experiment rather than another ;

* Philoiojphy of Discover}/, pp, 185 et seq. .

and though it is abstractly possible
that all the experiments which have
been tried might have been produced
by the mere desire to ascertain what
would happen in certain circumstances,
without any previous conjecture as to
the result ; yet, in point of fact, those
unobvious, delicate, and often cum-
brous and tedious processes of ex-
periment, which have thrown most
light upon the general constitution of
nature, would hardly ever have been
undertaken by the persons or at the
time they were, unless it had seemed
to depend on them whether some
general doctrine or theory which had
been suggested, but not yet proved,
should be admitted or not. If this
be true even of merely experimental
inquiry, the conversion of experi-
mental into deductive truths could
still less have been effected without
large temporary assistance from hypo-
theses. The process of tracing regu-
larity in any complicated, and at first
sight confused set of appearances, is
necessarily tentative : we begin by
making any supposition, even a false
one, to see what consequences will
follow from it ; and by observing how
these differ from the real phenomena,
we learn what corrections to make
in our assumption. The simplest
supposition which accords with the
more obvious facts is the best to
begin with, because its consequences
are the most easily traced. This
rude hypothesis is then rudely cor-
rected, and the operation repeated ;
and the comparison of the conse-
quences deducible from the corrected
hypothesis with the observed facts
suggests still further correction, until
the deductive results are at last made
to tally with the phenomena. " Some
fact is as yet little understood, or
some law is unknown ; we frame on
the subject an hypothesis as accordant
as possible with the whole of the data
already possessed ; and the science,
being thus enabled to move forward
freely, always ends by leading to new
consequences capable of observation,
which either confirm or refute, un-

HYPOTHESES.

327

equivocally, the first aupposition."
Neither induction nor deduction would
»»nable us to understand even the
simplest phenomena, "if we did not
often commence by anticipating on
the results ; by making a provisional
uipposition, at first essentially con-
jectural, as to some of the very
notions which constitute the final
object of the inquiry."* Let any
one watch the manner in which he
kimself unravels a complicated mass
cf evidence ; let him observe how, for
instance, he elicits the true history
of any occurrence from the involved
itatements of one or of many wit-
nesses : he will find that he does not
take all the items of evidence into
his mind at once, and attempt to
weave them together : ho extem-
porises, from a few of the particulars,
a first rude theory of the mode in
which the facts took place, and then
looks at the other statements one by
one, to try whether they can be recon-
ciled with that provisional theory,
or what alterations or additions it
requires to make it square with them.
In this way, which has been justly
compared to the Methods of Approxi-
mation of mathematicians, we arrive,
by means of hypotheses, at conclu-
sions not hypothetical.t

* Comte, Philosophie Positive, ii. 434-437.

t As an example of legitimate hypothesis
according to the test here laid down, has
been justly cited that of Broussaia, who,
proceeding on the very rational principle
that every disease must originate in some
definite part or other of the organism,
boldly assumed that certain fevers, which
not being known to be local were called
constitutional, had their origin in the
mucous membrane of the aliment-iry canal.
The supposition was indeed, as is now
generally admitted, erroneous ; but he was
justified in making it, since by deducing
the consequences of the supposition, and
comparing them with the facts of those
maladies, he might be certain of disprovint,'
his hypothesis if it was ill-founded, and
might expect that the comparison would
materially aid him in framing anoth^
more conformable to the phenomena.

The doctrine now universally received
that the earth is a natural magnet, was
originsQly an hypothesis of the celebrated
Gilbert.

Another hypothesis, to the legitimacy of

§ 6. It is perfectly consistent with
the spirit of the method, to assuni**
in this provisional manner not only
an hypothesis respecting the law of
what we already know to be the
cause, but an hypothesis respecting
the cause itself. It is allowable, use-
ful, and often even necessary, to begin
by asking ourselves what cause mai/
have produced the effect, in order
that we may know in what direction
to look out for evidence to determine
whether it actually did. The vortices
of Descartes would have been a per-
fectly legitimate hypothesis, if it had
been pcissible, by any mode of explo-
ration which we could entertain the
hope of ever possessing, to bring the
reality of the vortices, as a fact in
nature, conclusively to the test of
observation. The vice of the h3rpo-
thesis was that it could not lead to
any course of investigation capable of
converting it from an hypothesis into
a proved fact. It might chance to
be disproved, either by some want of
correspondence with the phenomena
it purported to explain, or (as actu-
ally happened) by some extraneous
fact. "The free passage of comets
through the spaces in which these
vortices should have been, convinced
men that these vortices did not

which no objection can He, and which ie
well calculated to light tlie path of scien-
tific inquiry, is that suggested by several
recent writers, that the brain is a voltaic
pile, and that each of its pulsations is a
discharge of electricity through the system.
It has been remarked that the sensation
felt by the hand from the beating of a
brain bears a strong resemblance to a
voltaic shock. And the hypothesis, if fol-
lowed to its consequences, might afford a
plausible explanation of many physiologi-
cal facts, while there is nothing to dis-
courage the hope that we may in time
suflSciently understand the conditions of
voltaic phenomena to render the truth of
the hypothesis amenable to observation
and experiment.

The attempt to localise, in different
regions of the brain, the physical organs
of our different mental faculties and pro-
pensities, was, on the part of its original
author, a legitimate example of a scientific
hyjothesis; and we ought not, therefore,
to blame him for the extremely slight
grounds on which he often proceeded in

32S

INDUCTION.

exist." * But the hypothesis would
have been false, though no such direct
evidence of its falsity had been pro-
curable. Direct evidence of its truth
there could not be.

The prevailing hypothesis of a lu-
miniferous ether, in other respects not
without analogy to that of Descartes,
is not in its own" nature entirely cut
off from the possibility of direct evi-
dence in its favour. It is well known
that the difference between the cal-
culated and the observed times of the
periodical return of Encke's comet,
has led to a conjecture that a medium
capable of opposing resistance to mo-
tion is diffused through space. If
this surmise should be confirmed, in

an operation which could only be tentative,
though we may regret that materials barely
sufficient for a first rvide hypothesis should
have been hastily worked up into the vain
semblance of a science. If there be really
a connection between the scale of mental
endowments and the various degrees of
complication in the cerebral system, the
nature of that connection was in no other
way so likely to be brought to light as by
framing, in the first instance, an hypo-
thesis similar to that of Gall. But the
verification of any such hypothesis is at-
tended, from the peculiar nature of the
J)henomena, with difficulties which phreno-
ogists have not shown themselves even
competent to appreciate, much less to
overcome.

Mr. Darwin's remarkable speculation on
the Origin of Species is another unimpeach-
able example of a legitimate hypothesis.
What he terms "natural selection" is not
only a vera causa, but one proved to be
capable of producing effects of the same
kind with those which the hypothesis
ascribes to it : the question of possibility
is entirely one of degree. It is unreason-
able to accuse Mr. Darwin (as has been
done) of violating the rules of Induction.
The rules of Induction are concerned with
the conditions of Proof. Mr. Darwin has
never pretended that his doctrine was
proved. He was not bound by the rules
of Induction, but by those of Hypothesis.
And these last have seldom been more
completely fulfilled. He has opened a
path of inquiry full of promise, the results
of which none can foresee. And is it not
a wonderful feat of scientific knowledge
and ingenuity to have rendered so bold a
suggestion, which the first impulse of every
one was to reject at once, admissible and
discussable, even as a conjecture?

* Whttwell'a Phil, of Ditcovery, pp. 275,
276.

the course of ages, by the gradual
accumulation of a similar variance in
the case of the other bodies of the
solar system, the luminiferous ether
would have made a considerable ad-
vance towards the character of a vera
can^a, since the existence would have
been ascertained of a great cosmicai
agent, possessing some of the attri-
butes which the hypothesis assumes 1
though there would still remain manj
difficulties, and the identification of
the ether with the resisting medium
would even, I imagine, give rise to
new ones. At present, however, this
supposition cannot be looked upon as
more than a conjecture ; the exist-
ence of the ether still rests on the
possibility of deducing from its as-
sumed laws a considerable number of
actual phenomena ; and this evidence
I cannot regard as conclusive, be-
cause we cannot have, in the case
of such an hypothesis, the assurance
that if the hypothesis be false it must
lead to results at variance with the
true facts.

Accordingly, most thinkers of any
degree of sobriety allow, that an
hypothesis of this kind is not to be
received as probably true because it
accounts for all the known pheno-
mena, since this is a condition some-
times fulfilled tolerably well by two
conflicting hypotheses ; while there
are probably many others which are
equally possible, but which, for want
of anything analogous in our expe-
rience, our minds are unfitted to con-
ceive. But it seems to be thought
that an hypothesis of the sort in ques-
tion is entitled to a more favourable
reception, if, besides accotinting for
all the facts previously known, it has
led to the anticipation and prediction
of others which experience afterwards
verified ; as the undulatory theory of
light led to the prediction, subse-
quently realised by experiment, that
two luminous rays might meet each
other in such a manner as to produce
darkness. Such predictions and their
fulfilment are, indeed, well calculated
to impress the uninformed, whose

HYPOTHESES.

329

faith in science rests solely on similar
coincidences between its prophecies
and what comes to pass. But it is
strange that any considerable stress
should be laid upon such a coinci-
dence by persons of scientific attain-
ments. If the laws of the propagation
of light accord with those of the vibra-
tions of an elastic fluid in as many
respects as is necessary to make the
hypothesis afford a correct expression
of all or most of the phenomena known
at the time, it is nothing strange that
they should accord with each other
in one respect more. Though twenty
such coincidences should occur, they
would not prove the reality of the
undulatory ether ; it would not fol-
low that the phenomena of light were
results of the laws of elastic fluids,
but at most that they are governed
by laws partially identical with these ;
which, we may observe, is already
certain, from the fact that the hypo-
thesis in question could be for a
moment tenable.* Cases may be
cited, even in our imperfect acquain-
tance with nature, where agencies
that we have good reason to consider
as radically distinct produce their
effects, or some of their effects, accord-
ing to laws which are identical. The
law, for example, of the inverse square
of the distance, is the measure of the
intensity not only of gravitation, but
(it is believed) of illumination, and of
heat diffused from a centre. Yet no
one looks upon this identity as proving
similarity in the mechanism by which
the three kinds of phenomena are
produced.

According to Dr. Whewell, the co-

* What has most contributed to accredit
the hypothesis of a physical medium for
the conveyance of light, is the certain fact
that light travels, (which cannot be prored
of gravitation ;) that its communication is
not instantaneous, but requires time ; and
that it is intercepted (which gravitation
is not) by intervening objects. These are
analogies between its phenomena and those
of the mechanical motion of a solid or fluid
substance. But we are not entitled t»
assume that mechanical motion is the only
power in nature capable of exhibiting those
attributes.

incidence of results predicted from an
hypothesis with facts afterwards ob-
served amounts to a conclusive proof
of the truth of the theory. "If I
copy a long series of letters, of which
the last half-dozen are concealed, and
if I guess these aright, as is found to
be the case when they are afterwards
uncovered, this must be because I
have made out the import of the in-
scription. To say, that because I
have copied all that I could see, it is
nothing strange that I should guess
those which I cannot see, would be
absurd, without supposing such a
ground for guessing."* If any one,
from examining the greater part of
a long inscription, can interpret the
characters so that the inscription
gives a rational meaning in a known
language, there is a strong presump-
tion that his interpretation is correct ;
but I do not think the presumption
much increased by his being able to
guess the few remaining letters with-
out seeing them : for we should
naturally expect (when the nature of
the case excludes chance) that even
an erroneous interpretation which
accorded with all the visible parts of
the inscription would accord also with
the small remainder ; as would be the
case, for example, if the inscription
had been designedly so contrived as
to admit of a double sense. I assume
that the uncovered characters afford
an amount of coincidence too great to
be merely casual : otherwise the illus-
tration is not a fair one. No one sup-
poses the agreement of the phenomena
of light with the theory of undulations
to be merely fortuitous. It must arise
from the actual identity of some of
the laws of undulations with some
of those of light ; and if there be that
identity, it is reasonable to suppose
that its consequences would not end
with the phenomena which first sug-
gested the identification, nor be even
confined to such phenomena as were
known at the time. But it does not
follow, because some of the lawa agree

* Phil, of Disc, p. 274.

330

INDUCTION.

with those of undulations, that there
are any actual undulations ; no more
than it followed because some (though
not so many) of the same laws agreed
with those of the projection of- par-
ticles, that there was actual emission
of particles. Even the undulatory
hypothesis does not account for all
the phenomena of light. The natural
colours of objects, the compound na-
ture of the solar ray, the absorption of
light, and its chemical and vital action,
the hypothesis leaves as mysterious
as it found them ; and some of these
facts are, at least apparently, more
reconcilable with the emission theory
than with that of Young and Fresnel.
Who knows but that some third hy-
pothesis, including all these pheno-
mena, may in time leave the undula-
tory theory as far behind as that has
left the theory of Newton and his
successors ?

To the statement that the condi-
tion of accounting for all the known
phenomena is often fulfilled equally
well by two conflicting hypotheses,
Dr. Whewell makes answer that he
knows " of no such case in the history
of science, where the phenomena are
at all numerous and complicated."*
Such an affirmation, by a writer of
Dr. Whewell's minute acquaintance
with the history of science, would
carry great aiithority, if he had not, a
few pages before, taken pains to re-
fute it,+ by maintaining that even the
exploded scientific hypotheses might
always, or almost always, have been
so modified as to make them correct
representations of the phenomena.
The hypothesis of vortices, he tells
us, was, by successive modifications,
brought to coincide in its results with
the Newtonian theory and with the
facts. The vortices did not indeed
explain all the phenomena which the
Newtonian theory was ultimately
found to account for, such as the pre-
cession of the equinoxes ; but this

* P. 371.

t P. 251 and the wiiola of Appendix G.

phenomenon was not, at the time, in
the contemplation of either party, am
one of the facts to be accounted for.
All the facts which they did contem-
plate we may believe on Dr. Whe-
well's authority to have accorded as
accurately with the Cartesian h3^po-
thesis, iix its finally improved state, as
with Newton's.

But it is not, I conceive, a valid
reason for accepting any given hypo-
thesis that we are unable to imagine
any other which will account for the
facts. There is no necessity for sup-
posing that the true explanation must
be one which, with only our present
experience, we could imagine. Among
the natural agents with which we are
acquainted, the vibrations of an elastic
fluid may be the only one whose laws
bear a close resemblance to those of
light ; but we cannot tell that there
does not exist an unknown cause, other
than an elastic ether diffused through
space, yet producing effects identical
in some respects with those which
would result from the undulations of
such an ether. To assume that no
such cause can exist appears to me
an extreme case of assumption with-
out evidence. And at the risk of
being charged with want of modesty,
I cannot help expressing astonish-
ment that a philosopher of Dr. Whe-
well's abilities and attainments should
have written an elaborate treatise on
the philosophy of induction, in which
he recognises absolutely no mode of
induction except that of trying hy-
pothesis after h3rpothesis until one
is found which fits the phenomena ;
which one, when found, is to be as-
sumed as true, with no other reserva-
tion than that if on re-examination it
should appear to assume more than is
needful for explaining the phenomena,
the superfluous part of the assumption
should be cut off. And this without
the slightest distinction between the
cases in which it may be known be-
forehand that two different hypo-
theses cannot lead to the same result,
and those in which, for aught we can
ever know, the range of suppositions,

HYPOTHESES.

33'

all equally colisisteht with the phe-
nomena, may be infinite.*

Nevertheless, I do not agree with M.
Comte in condemning those who em-
ploy themselves in working out into
detail the application of these hypo-
theses to the explanation of ascer-
tained facts, provided they bear in
mind that the utmost they can prove
is, not that the hypothesis is, but that
it may be true. The ether hypothesis
has a very strong claim to be so fol-
lowed out, a claim greatly strength-
ened since it has been shown to afford
a mechanism which would explain
the mode of production not of light
only, but also of heat. Indeed the
speculation has a smaller element of
hypothesis in its application to heat
than in the case for which it was ori-
ginally framed. We have proof by
our senses of the existence of mole-
cular movement among the particles
of all heated bodies, while we have
no similar experience in the case of
light. When, therefore, heat is com-
municated from the sun to the earth,
across apparently empty space, the
chain of causation has molecular mo-
tion both at the beginning and end.
The hypothesis only makes the mo-
tion continuous by extending it to
the middle. Now motion in a body
is known to be capable of being im-
parted to another body contiguous to
it ; and the intervention of a hypo-

* In Dr. Whewell's latest version of this
theory {Philosophy of Discovery, p. 331) he
makes a concession respecting the medium
of the transmission of light, which, taken
in conjunction with the rest of his doctrine
on the subject, is not, I confess, very intel-
ligible to me, but which goes far towards
removing, if it does not actually remove,
the whole of the difference between us.
He is contending, against Sir William
Hamilton, that all matter has weight. Sir
William, in proof of the contrary, cited the
luminiferous ether and the calorific and
electric fluids, "which," he said, "we can
neither denude of their character of sub-
stance nor clothe with the attribute of
weight." " To wliich," continues Dr. Whe-
well, " my reply is, that precisely because
I cannot clothe these agents with the attri-
bute of Weight, I do denude them of the
character of Substance. They are not
substances, but agencies. These Impon-

thetical elastic fluid occupying the
space between the sun and the earth
supplies the contiguity which is the
only condition wanting, and which
can be supplied by no supposition but
that of an intervening medium. The
.supposition, notwithstanding, is at
best a probable conjecture, not a
proved truth ; for there is no proof
that contiguity is absolutely required
for the communication of motion from
one body to another. Contiguity does
not always exist, to our senses at
least, in the cases in which motion
produces motion. The forces which
go under the name of attraction,
especially the greatest of all, gravita-
tion, are examples of motion producing
motion without apparent contiguity.
When a planet moves, its distant
satellites accompany its motion. The
sun carries the whole solar system
along with it in the progress which it
is ascertained to be executing through
space. And even if we were to ac-
cept as conclusive the geometrical
reasonings (strikingly similar to those
by which the Cartesians defended
their vortices) by which it has been
attempted to show that the motions
of the ether may account for gravita-
tion itself, even then it would only
have been proved that the supposed
mode of production may be, but not
that* no other mode can be, the true

derable Agents are not properly called Im-
ponderable Fluids. This I conceive that I
have«proved." Nothing can be more philo-
sophical. But if the luminiferous ether is
not matter, and fluid matter too, what is
the meaning of its undulations? Can an
agency undulare? Can there be alternate
motion forward and backward of the par-
ticles of an agency? And does not the
whole mathematical theory of the undula-
tions imply them to be material ? Is it not
a series of deductions from the known pro-
perties of elastic fluids? This opinion of
Dr. Whewell reduces the undulations to a
figure of speech, and the undulatory theory
to the proposition, which all must admit,
that the transmis-sion of light takes place
according to laws which present a very
striking and remarkable agreement with
those of undulations. If Dr. Whewell if
prepared to stand by this doctrine, I hava
no difference with him on the subject.

332

INDttCTlON.

§ 7. It is necessary, before quitting
the subject of hypotheses, to guard
against the appearance of reflecting
upon the scientific value of several
branches of physical inquiry, which,
though only in their infancy, I hold
to be strictly inductive. There is a
great difference between inventing
agencies to account for classes of phe-
nomena, and endeavouring, in con-
formity with known laws, to conjec-
ture what former collocations of known
agents may have given birth to indi-
vidual facts still in existence. The
latter is the legitimate operation of
inferring from an observed effect the
existence, in time past, of a cause
similar to that by which we know it
to be produced in all cases in which
we have actual experience of its origin.
This, for example, is the scope of the
inquiries of geology ; and they are no
more illogical or visionary than judi-
cial inquiries, which also aim at dis-
covering a past event by inference
from those of its effects which still
subsist. As we can ascertain whether
a man was murdered or died a natural
death from the indications exhibited
by the corpse, the presence or absence
of signs of struggling on the ground
or on the adjacent objects, the marks
of blood, the footsteps of the sup-
posed murderers, and so on, proceed-
ing throughout on uniformities ascer-
tained by a perfect induction without
any mixture of hypothesis, so if we
find, on and beneath the surface of
our planet, masses exactly similar to
deposits from water, or to results of
the cooling of matter melted by fire,
we may justly conclude that such has
been their origin ; and if the effects,
though similar in kind, are on a far
larger scale than any which are now
produced, we may rationally and
without hypothesis conclude, either
that the causes existed formerly with
greater intensity, or that they have
operated during an enormous length
of time. Further than this no geolo-
gist of authority has, since the rise of
the present enlightened school of geolo-
gical speculation, attempted to go.

In many geological inquiries it
doubtless happens that though the
laws to which the phenomena are
ascribed are known laws, and the
agents known agents, those agents
are not known to have been present
in the particular case. In the specu-
lation respecting the igneous origin
of trap or granite, the fact does not
admit of direct proof, that those sub-
stances have been actually subjected
to intense heat. But the same thing
might be said of all judicial inquiries
which proceed on circumstantial evi-
dence. We can conclude that a man
was murdered, though it is not proved
by the testimony of eyewitnesses that
some person who had the intention of
murdering him was present on the
spot. It is enough, for most pur-
poses, if no other known cause could
have generated the effects shown to
have been produced.

The celebrated speculation of La-
place concerning the origin of theearth
and planets participates essentially
in the inductive character of modern
geological theory. The speculation
is, that the atmosphere of the sun
originally extended to the present
limits of the solar system ; from
which, by the process of cooling, it
has contracted to its present dimen-
sions ; and since, by the general
principles of mechanics, the rotation
of the sun and of its accompanying
atmosphere must increase in rapidity
as its volume diminishes, the increased
centrifugal force generated by the
more rapid rotation, overbalancing
the action of gravitation, has caused
the sun to abandon successive rings
of vaporous matter, which are sup-
posed to have condensed by cooling,
and to have become the planets.
There is in this theory no unknown
substance introduced on supposition,
nor any unknown property or law
ascribed to a known substance. The
known laws of matter authorise us to
suppose that a body which is con-
stantly giving out so large an amount
of heat as the sun is miist be pro-
gressively cooling, and that, by the

PROGRESSIVE EFFECTS.

333

process of cooling, it must contract ;
if, therefore, we endeavour, from the
.present state of that luminary, to in-
fer its state in a time long past, we
must necessarily suppose that its
atmosphere extended much farther
than at present, and we are entitled
to suppose that it extended as far as
we can trace effects such as it might
naturally leave behind it on retiring ;
and such the planets are. These sup-
positions being made, it follows from
known laws that successive zones of
the solar atmosphere might be aban-
doned ; that these would continue to
revolve round the sun with the same
velocity as when they formed part of
its substance ; and that they would
cool down, long before the sun itself,
to any given temperature, and conse-
quently to that at which the greater
part of the vaporous matter of which
they consisted would become liquid
or solid. The known law of gravita-
tion would then cause them to ag-
glomerate in masses, which would
assume the shape our planets actually
exhibit ; would acquire, each about
its own axis, a rotatory movement ;
and would in that state revolve, as
the planets actually do, about the
sun, in the same direction with the
sun's rotation, but with less velocity,
because in the same periodic time
which the sun's rotation occupied
when his atmosphere extended to
that point. There is thus, in La-
place's theory, nothing, strictly speak-
ing, hypothetical ; it is an example
of legitimate reasoning from a pre-
sent effect to a possible past cause,
according to the known laws of that
cause. The theory therefore is, as I
have said, of a similar character to
the theories of geologists, but con-
siderably inferior to them in point
of evidence. Even if it were proved
(which it is not) that the conditions
necessary for determining the breaking
off of successive rings would certainly
occur ; there would still be a much
greater chance of error in assuming
that the existing laws of nature are
the same whfcl) existed at the origin

of the solar system, than in merely
presuming (with geologists) that those
laws have lasted through a few revo-
lutions and transformations of a single
one among the bodies of which that
system is composed.

CHAPTER XV.

OF PROGRESSIVE EFFECTS ; AND OF THE
CONTINUED ACTION OF CAUSES.

§ I. In the last four chapters we
have traced the general outlines of
the theory of the generation of deri-
vative laws from ultimate ones. In
the present chapter our attention will
be directed to a particular case of the
derivation of laws from other laws,
but a case so general, and so impor-
tant, as not only to repay, but to re-
quire, a separate examination. This
is the case of a complex phenome-
non, resulting from one simple law, by
the continual addition of an effect to
itself.

There are some phenomena, some
bodily sensations, for example, which
are essentially instantaneous, and
whose existence can only be pro-
longed by the prolongation of the
existence of the cause by which they
are produced. But most phenomena
are in their own nature permanent;
having begun to exist, they would
exist for ever unless some cause in-
tervened having a tendency to alter
or destroy them. Such, for example,
are all the facts or phenomena which
we call bodies. Water, once pro-
duced, will not of itself relapse into
a state of hydrogen and oxygen ; such
a change requires some agent having
the power of decomposing the com-
pound. Such, again, are the positions
in space and the movements of
bodies. No object at rest alters its
position without the intervention of
some conditions extraneous to itself ;
and when once in motion, no object
returns to a state of rest, or alters
either its direction or its velocity,
unless some pew external conditions

334

INDUCTION.

are superinduced. It, therefore, per-
petually happens that a temporary
cause gives rise to a permanent effect.
The contact of iron with moist air for
a few hours produces a rust which
may endure for centuries ; or a pro-
jectile force which launches a cannon-
ball into space produces a motion
which would continue for ever unless
some other force counteracted it.

Between the two examples which
we have here given there is a differ-
ence worth pointing out. In the
former, (in which the phenomenon
produced is a substance, and not a
motion of a substance,) since the rust
remains for ever and unaltered un-
less some new cause supervenes, we
may speak of the contact of air a
hundred years ago as even the proxi-
mate cause of the rust which has
existed from that time until now.
But when the effect is motion, which
is itself a change, we must use a
different language. The permanency
of the effect is now only the per-
manency of a series of changes. The
second foot, or inch, or mile of mo-
tion, is not the mere prolonged dura-
tion of the first foot, or inch, or mile,
but another fact which succeeds, and
which may in some respects be very
unlike the former, since it carries the
body through a different region of
space. Now, the original projectile
force which set the body moving is
the remote cause of all its motion,
however long continued, but the
proximate cause of no motion except
that which took place at the first in-
stant. The motion at any subsequent
instant is proximately caused by the
motion which took place at the in-
stant preceding. It is on that, and
not on the original moving cause, that
the motion at any given moment de-
pends. For suppose that the body
passes through some resisting medium,
which partially counteracts the effect
of the original impulse and retards
the motion, this counteraction (it
need scarcely here be repeated) is as
strict an example of obedience to the
Jaw of th^ impulse as if the body had

gone on moving with its original velo-
city ; but the motion which results is
different, being now a compound of
the effects of tv/o causes acting in
contrary directions, instead of the
single effect of one cause. Now,
what cause does the body obey in
its subsequent motion ? The original
cause of motion, or the actual motion
at the preceding instant? The latter;
for when the object issues from the re-
sisting medium, it continues moving,
not with its original, but with its re-
tarded velocity. The motion having
once been diminished, all that which
follows is diminished. The effect
changes, because the cause which it
really obeys, the proximate cause, the
real cause, in fact, has changed. This
principle is recognised by mathema-
ticians when they enumerate among
the causes by which the motion of a
body is at any instant determined,
the ^orce generated by the previous
motion ; an expression which would
be absurd if taken to imply that this
*' force " was an intermediate link be-
tween the cause and the effect, but
which really means only the previous
motion itself, considered as a cause of
further motion. We must, therefore,
if we would speak with perfect pre-
cision, consider each link in the suc-
cession of motions as the effect of the
link preceding it. But if, for the
convenience of discourse, we speak of
the whole series as one effect, it must
be as an effect produced by the ori-
ginal impelling force ; a permanent
effect produced by an instantaneous
cause, and possessing the property of
self- perpetuation .

Let us now suppose that the origi-
nal agent or cause, instead of being in-
stantaneous, is permanent. Whatever
effect has been produced up to a given
time, would (unless prevented by the
intervention of some new cause) sub-
sist permanently, even if the cause
were to perish. Since, however, the
oause does not perish, but continues
to exist and to operate, it must go
on producing more and more of the
effect J and instejid pf an uniform

PROGRESSIVE EFFECTS.

effect, we have a progressive series
of effects, arising from the accumu-
lated influence of a permanent cause.
Thus, the contact of iron with the
atmosphere causes a portion of it to
rust ; and if the cause ceased, the
effect already produced would be per-
manent, but no further effect would
be added. If, however, the cause,
namely, exposure to moist air, con-
tinues, more and more of the iron
becomes rusted, until all which is e.x-
posed is converted into a red powder,
when one of the conditions of the
production of rust, namely, the pre-
sence of unoxidised iron, has ceased,
and the effect cannot any longer be
produced. Again, the earth causes
bodies to fall towards it, that is, the
existence of the earth at a given in-
stant causes an unsupported body to
move towards it at the succeeding
instant ; and if the earth were anni-
hilated, as much of the effect as is
already produced would continue ;
the object would go on moving in
the same direction, with its acquired
velocity, until intercepted by some
body or deflected by some other force.
The earth, however, not being anni-
hilated, goes on producing in the
second instant an effect similar
and of equal amount with the first,
which two effects being added to-
gether, there results an accelerated
velocity ; and this operation being
repeated at each successive instant,
the mere permanence of the cause,
though without increase, gives rise to
a constant progressive increase of the
effect, so long as all the conditions,
negative and positive, of the produc-
tion of that effect continue to be
realised.

It is obvious that this state of
things is merely a case of the Com-
position of Causes. A cause which
continues in action must on a strict
analysis be considered as a number of
causes exactly similar successively
introduced, and producing by their
combination the sum of the effects
which they would ■everally produce
if they^ actad singly. The progressive

rusting of the iron is in strictness the
sum of the effects of many particles
of air acting in succession upon cor-
responding particles of iron. The
continued action of the earth upon a
falling body is equivalent to a series
of forces, applied in successive in-
stants, each tending to produce a cer-
tain constant quantity of motion ;
and the motion at each instant is the
sum of the effects of the new force
applied at the preceding instant, and
the motion already acquired. In each
instant, a fresh effect, of which gravity
is the proximate cause, is added to
the effect of which it was the remote
cause ; or (to express the same thing
in another manner) the effect pro-
duced by the earth's influence at the
instant last elapsed is added to the
sum of the effects of which the remote
causes were the influences exerted by
the earth at all the previous instants
since the motion began. The case,
therefore, comes under the principle
of a concurrence of causes producing
an effect equal to the sum of their
separate effects. But as the causes
come into play not all at once, but
successively, and as the effect at each
instant is the sum of the effects of
those causes only which have come
into action up to that instant, the
result assumes the form of an ascend-
ing series ; a succession of sums, each
greater than that which preceded it :
and we have thus a progressive effect
from the continued action of a cause.
Since the continuance of the cause
influences the effect only by adding
to its quantity, and since the addition
takes place according to a fixed law,
(equal quantities in equal times,) the
result is capable of being computed
on mathematical principles. In fact,
this case, being that of infinitesimal
increments, is precisely the case which
the differential calculus was invented
to meet. The questions, what effect
will result from the continual addition
of a given cause to itself, and what
amount of the cause, being continually
added to itself, will produce a given
amount of the effect, j^re evidently

336

INDUCTION.

mathematical questions, and to be
treated, therefore, deductively. If,
as we have seen, cases of the Com-
position of Causes are seldom adapted
for any other than deductive investi-
gation, this is especially true in the
case now examined, the continual
composition of a cause with its own
previous effects ; since such a case is
peculiarly amenable to the deductive
method, while the undistinguishable
manner in which the effects are blended
with one another and with the causes
must make the treatment of such an
instance experimentally still more chi-
merical than in any other case.

§ 2. We shall next advert to a
rather more intricate operation of the
same principle, namely, when the
cause does not merely continue in
action, but undergoes, during the
same time, a progressive change in
those of its circumstances which con-
tribute to determine the effect. In
this case, as in the former, the total
effect goes on accumulating by the
continual addition of a fresh effect to
that already produced, but it is no
longer by the addition of equal quan-
tities in equal times ; the quantities
added are unequal, and even the
quality may now be different. If the
change in the state of the permanent
cause be progressive, the effect will
go through a double series of changes,
arising partly from the accumulated
action of the cause, and partly from
the changes in its action. The effect
is still a progressive effect, produced,
however, not by the mere continuance
of a cause, but by its continuance and
its progressiveness combined.

A familiar example is afforded by
the increase of the temperature as
summer advances, that is, as the sun
draws nearer to a vertical position,
and remains a greater number of
hours above the horizon. This in-
stance exemplifies in a very interest-
ing manner the twofold operation on
the effect, arising from the continu-
ance of the cause, and from its pro-
^rressive change. When once the sun

has come near enough to the zenith,
and remains above the horizon long
enough to give more warmth during
one diurnal rotation than the counter-
acting cause, the earth's radiation,
can carry off, the mere continuance
of the cause would progressively in-
crease the effect, even if the sun
came no nearer and the days grew
no longer ; but in addition to this,
a change takes place in the accidents
of the cause (its series of diurnal
positions) tending to increase the
quantity of the effect. When the
summer solstice has passed, the pro-
gressive change in the cause begins
to take place the reverse way ; but,
for some time, the accumulating effect
of the mere continuance of the cause
exceeds the effect of the changes in
it, and the temperature continues to
increase.

Again, the motion of a planet is a
progressive effect, prodiiced by causes
at once permanent and progressive.
The orbit of a planet is determined
( omitting perturbations ) by two causes :
first, the action of the central body,
a permanent cause, which alternately
increases and diminishes as the planet
draws nearer to or goes farther from
its perihelion, and which acts at every
point in a different direction ; and,
secondly, the tendency of the planet
to continue moving in the direction
and with the velocity which it has
already acquired. This force also
grows greater as the planet draws
nearer to its perihelion, because as it
does so its velocity increases ; and
less, as it recedes from its perihelion :
and this force as well as the other
acts at each point in a different direc-
tion, because at every point the action
of the central force, by deflecting the
planet from its previous direction,
alters the line in which it tends to
continue moving. The motion at
each instant is determined by the
amount and direction of the motion,
and the amount and direction of the
sun's action, at the previous instant :
and if we speak of the entire revolu-
tion of the planet as one phenomenon,

PROGRESSIVE EFFECTS.

337

(which, as it is periodical and similar
to itself, we often find it convenient
to do,) that phenomenon is the pro-
gressive effect of two permanent and
progressive causes, the central force
and the acquired motion. Those
causes happening to be progressive
in the particular way which is called
periodical, the effect necessarily is so
too ; because the quantities to be
added together returning in a regular
order, the same sums must also regu-
larly return.

This example is worthy of con-
sideration also in another respect.
Though the causes themselves are
permanent, and independent of all
conditions known to us, the changes
which take place in the quantities
and relations of the causes are actu-
ally caused by the periodical changes
in the effects. The causes, as they
exist at any moment, having produced
a certain motion, that motion, be-
coming itself a cause, reacts upon
the causes, and produces a change
in them. By altering the distance
and direction of the central body
relatively to the planet, and the
direction and quantity of the force
in the direction of the tangent, it
alters the elements which determine
the motion at the next succeeding
instant. This change renders the
next motion somewhat different ; and
this difference, by a fresh reaction
upon the causes, renders the next
motion again different, and so on.
The original state of the causes might
have been such, that this series of
actions modified by reactions would
not have been periodical. The sun's
action and the original impelling
force might have been in such a
ratio to one another that the reaction
of the effect would have been such as
to alter the causes more and more,
without ever bringing them back to
what they were at any former time.
The planet would then have moved
in a parabola or an hyperbola, curves
not returning into themselves. The
quantities of the two forces were,
however, originally such, that the suc-

cessive reactions of the effect bring
back the causes, after a certain time,
to what they were before ; and from
that time all the variations continue
to recur again and again in the same
periodical order, and must so con-
tinue while the causes subsist and are
not counteracted.

§ 3. In all cases of progressive
effects, whether arising from the
accumulation of unchanging or of
changing elements, there is an uni-
formity of succession not merely be-
tween the cause and the effect, but
between the first stages of the effect
and its subsequent stages. That a
body in vacuo falls sixteen feet in the
first second, forty -eight in the second,
and so on in the ratio of the odd
numbers, is as much an uniform se-
quence as that when the supports are
removed the body falls. The sequence
of spring and summer is as regular
and invariable as that of the approach
of the sun and spring, but we do not
consider spring to be the cause of
summer ; it is evident that both are
successive effects of the heat received
from the sun, and that, considered
merely in itself, spring might con-
tinue for ever, without having the
slightest tendency to produce summer.
As we have so often remarked, not
the conditional but the unconditional
invariable antecedent is termed the
cause. That which would not be
followed by the effect unless some-
thing else had preceded, and which
if that something else had preceded
would not have been required, is
not the cause, however invariable the
sequence may in fact be.

It is in this way that most of those
uniformities of succession are gene-
rated which are not cases of causa-
tion. When a phenomenon goes on
increasing, or periodically increases
and diminishes, or goes through any
continued and unceasing process of
variation reducible to an uniform
rule or law of succession, we do not
on this account presume that any
two successive terms of the series are

338

INDUCTION.

cause and effect. We presume the
contrary j we expect to find that the
whole series originates either from
the continued action of fixed causes,
or from causes which go through a
corresponding process of continuous
change. A tree grows from half an
inch high to a hundred feet, and some
trees will generally grow to that
height unless prevented by some coun-
teracting cause. But we do not call
the seedling the cause of the full-
grown tree ; the invariable antece-
dent it certainly is, and we know
very imperfectly on what other ante-
cedents the sequence is contingent,
but we are convinced that it is con-
tingent on something, because the
homogeneousness of the antecedent
with the consequent, the close re-
semblance of the seedling to the tree
in all respects except magnitude, and
the graduality of the growth, so ex-
actly resembling the progressively
accumulating effect produced by the
long action of some one cause, leave
no possibility of doubting that the
seedling and the tree are two terms
in a series of that description, the
first term of which is yet to seek.
The conclusion is further confirmed
by this, that we are able to prove by
strict induction the dependence of
the growth of the tree, and even of
the continuance of its existence, upon
the continued repetition of certain
processes of nutrition, the rise of the
sap, the absorptions and exhalations
by the leaves, &c. ; and the same ex-
periments would probably prove to
us that the growth of the tree is the
accumulated sum of the effects of
these continued processes, were we not,
for want of sufficiently microscopic
eyes, unable to observe correctly and
in detail what those effects are.

This supposition by no means re-
quires that the effect should not,
during its progress, undergo many
modifications besides those of quan-
tity, or that it should not sometimes
appear to undergo a very marked
change of character. This may be
•ither because the unknown cause

consists of several component ele-
ments or agents, whose effects, accu-
mulating according to different laws,
are compounded in different propor-
tions at different periods in the ex-
istence of the organised being ; or
because, at certain points in its pro-
gress, fresh causes or agencies come
in, or are evolved, which intermix
their laws with those of the orime
agent.

CHAPTER XVI.

OP EMPIRICAL LAWS.

§ I. Scientific inquirers give the
name of Empirical Laws to those uni-
formities which observation or experi-
ment has shown to exist, but on which
they hesitate to rely in cases varying
much from those which have been
actually observed, for want of seeing
any reason wAy such a law should exist.
It is implied, therefore, in the notion
of an empirical law, that it is not an
ultimate law ; that if true at all, its
truth is capable of being, and requires
to be accounted for. It is a derivative
law, the derivation of which is not yet
known. To state the explanation, the
ichyy of the empirical law, would be to
state the laws from which it is de-
rived ; the ultimate causes on which
it is contingent. And if we knew
these, we should also know what are
its limits — under what conditions it
would cease to be fulfilled.

The periodical return of eclipses,
as originally ascertained by the per-
severing observation of the early
Eastern astronomers, was an empiri-
cal law until the general laws of the
celestial motions had accounted for it.
The following are empirical laws still
waiting to be resolved into the simpler
laws from which they are derived.
The local laws of the flux and reflux
of the tides in different places : the
succession of certain kinds of weather
to certain appearances of sky : the
apparent exceptions to the almost uni-
versal truth that bodies expand by
increase of temperature ; the law that

EMPIRICAL LAWS.

339

breeds, both animal and vegetable,
are improved by crossing : that gases
have a strong tendency to permeate
animal membranes : that substances
containing a very high proportion of
nitrogen (such as hydrocyanic acid
and morphia) are powerful poisons :
that when different metals are fused
together, the alloy is harder than the
various elements : that the number of
atoms of acid required to neutralise
one atom of any base is equal to the
number of atoms of oxygen in the
base : that the solubility of substances
in one another depends * (at least in
some degree) on the similarity of their
elements.

An empirical law, then, is an ob-
served uniformity, presumed to be
resolvable into simpler laws, but not
yet resolved into them. The ascertain-
ment of the empirical laws of pheno-
mena often precedes by a long interval
the explanation of those laws by the
Deductive Method ; and the verifica-
tion of a deduction usually consists in
the comparison of its results with
empirical laws previously ascertained.

§ 2. From a limited number of ulti-
mate laws of causation, there are
necessarily generated a vast number
of derivative uniformities, both of
succession and of co-existence. Some
are laws of succession or of co-exist-
ence between different effects of the
same cause : of these we had examples
in the last chapter. Some are laws

' * Thus, water, of which eight-ninths in
weight are oxygen, dissolves most bodies
"whicli contain a high proportion of oxygen,
such as all the nitrates (which have more
oxygen than any others of the common
salts,) most of the sulphates, many of ihe
carbonates, <fec. Again, bodies largely com-
posed of combustible elementa, like hydro-
gen and carbon, are soluble in bodies of
similar composition ; rosin, for instance,
will dissolve in alcohol, tar in oil of tur-
pentine. This empirical genenilisation is
far from being universally true ; no doubt
because it is a remote, and therefore easily
defeated, result of general laws too deep
for us at present to penetrate ; but it will
probably in time suggest processes of in-
quiry, leading to the discovery of those
laws.

of succession between effects and their
remote causes, resolvable into the
laws which connect each with the in-
termediate link. Thirdly, when causes
act together and compound their
effects, the laws of those causes gene-
rate the fundamental law of the effect,
namely, that it depends on the co-
existence of those causes. And, finally,
the order of succession or of co-exist-
ence which obtains among effects
necessarily depends on their causes.
If they are effects of the same cause,
it depends on the laws of that cause ;
if on different causes, it depends on
the laws of those causes severally, and
on the circumstances which determine
their co-existence. If we inquire fur-
ther when and how the causes will
co-exist, that, again, depends on their
causes ; and we may thus trace back
the phenomena higher and higher,
until the different series of effects
meet in a point, and the whole is
showTi to have depended ultimately
on some common cause ; or until,
instead of converging to one point,
they terminate in different points,
and the order of the effects is proved
to have arisen from the collocation
of some of the primeval causes or
natural agents. For example, the
order of succession and of co-existence
among the heavenly motions, which
is expressed by Kepler's laws, is de-
rived from the co-existence of two
primeval causes, the sun and the
original impulse or projectile force
belonging to each planet. * Kepler's
laws are resolved into the laws of
these causes and the fact of their co-
existence.

Derivative laws, therefore, do not
depend solely on the ultimate laws
into which they are resolvable : they
mostly depend on those ultimate laws
and an ultimate fact, namely, the
mode of co-existence of some of the
component elements of the universe.
The ultimate laws of causation might
be the same as at present, and yet
the derivative laws completely dif-

* Or (according to Laplace's theory) tha
sun and the sun'g rotation.

340

INDUCTION.

ferent, if the causes co-existed in
different proportions, or with any
difference in those of their relations
by which the effects are influenced.
If, for example, the sun's attraction
and the original projectile force had
existed in some other ratio to one
another than they did, (and we know
of no reason why this should not have
been the case,) the derivative laws of
the heavenly motions might have been
quite different from what they are.
The proportions which exist happen
to be such as to produce regular
elliptical motions ; any other propor-
tions would have produced different
ellipses, or circular, or parabolic, or
hyperbolic motions, but still regular
ones ; because the effects of each of
the agents accumulate according to
an uniform law ; and two regular
series of quantities, when their cor-
responding terms are added, must
produce a regular series of some sort,
whatever the quantities themselves

§ 3. Now this last-mentioned ele-
ment in the resolution of a derivative
law, the element which is not a law
of causation, but a collocation of
causes, cannot itself be reduced to
any law. There is (as formerly re-
marked*) no uniformity, no norma,
principle, or rule, perceivable in the
distribution of the primeval natural
agents through the universe. The
different substances composing the
earth, the powers that pervade the
universe, stand in no constant relation
to one another. One substance is
more abundant than others, one power
acts through a larger extent of space
than others, without any pervading
analogy that we can discover. We
not only do not know of any reason
why the sun's attraction and the
force in the direction of the tangent
co-exist in the exact proportion they
do, but we can trace no coincidence
between it and the proportions in
which any other elementary powers

* Supra, book iii. ch. v. { 7.

in the universe are intermingled. The
utmost disorder is apparent in the
combination of the causes ; which is
consistent with the most regular order
in their effects ; for when each agent
carries on its own operations accord-
ing to an uniform law, even the most
capricious combination of agencies
will generate a regularity of some sort ;
as we see in the kaleidoscope, where
any casual arrangement of coloured
bits of glass produces by the laws of
reflection a beautiful regularity in the
effect.

§ 4. In the above considerations
lies the justification of the limited
degree of reliance which scientific
inquirers are accustomed to place in
empirical laws.

A derivative law which results
wholly from the operation of some
one cause will be as universally true
as the laws of the cause itself : that
is, it will always be true except where
some one of those effects of the cause,
on which the derivative law depends,
is defeated by a counteracting cause.
But when the derivative law results
not from different effects of one cause,
but from effects of several causes, we
cannot be certain that it will be true
under any variation in the mode of
co-existence of those causes, or of the
primitive natural agents on which
the causes ultimately depend. The
proposition that coal-beds rest on
certain descriptions of strata exclu-
sively, though true on the earth so
far as our observation has reached,
cannot be extended to the moon or
the other planets, supposing coal to
exist there ; because we cannot be
assured that the original constitution
of any other planet was such as to
produce the different depositions in
the same order as in our globe. The
derivative law in this case depends
not solely on laws, but on a colloca-
tion ; and collocations cannot be re-
duced to any law.

Now it is the very nature of a
derivative law which has not yet
been resolved into its elements, in

EMPIRICAL LAWS.

541

other words, an empirical law, that
we do not know whether it results
from the different effects of one cause
or from effects of different causes.
We cannot tell whether it depends
wholly on laws, or partly on laws and
partly on a collocation. If it depends
on a collocation, it will be true in all
the cases in which that particular
collocation exists. But since we are
entirely ignorant, in case of its de-
pending on a collocation, what the
collocation is, we are not safe in
extending the law beyond the limits
of time and place in which we have
actual experience of its truth. Since
within those limits the law has always
been found true, we have evidence
that the collocations, whatever they
are, on which it depends, do really
exist within those limits. But, know-
ing of no rule or principle to which
the collocations themselves conform,
we cannot conclude that because a
collocation is proved to exist within
certain limits of place or time, it will
exist beyond those limits. Empirical
laws, therefore, can only be received
as true within the limits of time and
place in which they have been found
true by observation ; and not merely
the limits of time and place, but of
time, place, and circumstance ; for
since it is the very meaning of an
empirical law that we do not know
the ultimate laws of causation on
which it is dependent, we cannot
foresee, without actual trial, in what
manner or to what extent the intro-
duction of any new circumstance may
affect it.

§ 5. But how are we to know that
an uniformity ascertained by experi-
ence is only an empirical law ? Since,
by the supposition, we have not been
able to resolve it into any other laws,
how do we know that it is not an
ultimate law of causation ?

I answer, that no generalisation
amounts to more than an empirical
law when the only proof on which it
rests is that of the Method of Agree-
ment. For it has been seen that by

that method alone we never can ar-
rive at causes. The utmost that the
Method of Agreement can do is, to
ascertain the whole of the circum-
stances common to all cases in which
a phenomenon is produced ; and this
aggregate includes not only the cause
of the phenomenon, but all pheno-
mena with which it is connected by
any derivative uniformity, whether as
being collateral effects of the same
cause, or effects of any other cause
which, in all the instances we have
been able to observe, co-existed with
it. The method affords no means of
determining which of these uniformi-
ties are laws of causation, and which
are merely derivative laws, resulting
from those laws of causation and
from the collocation of the causes.
None of them, therefore, can be re-
ceived in any other character than
that of derivative laws, the derivation
of which has not been traced ; in
other words, empirical laws : in which
light, all results obtained by the
Method of Agreement (and therefore
almost all truths obtained by simple
observation without experiment) must
be considered, until either confirmed
by the Method of Difference or ex-
plained deductively, in other words,
accounted for a priori.

These empirical laws may be of
greater or less authority according as
there is reason to presume that they
are resolvable into laws only, or into
laws and collocations together. The
sequences which we observe in the
production and subsequent life of an
animal or a vegetable, resting on the
Method of Agreement only, are mere
empirical laws ; but though the ante-
cedents in those sequences may not
be the causes of the consequents, both
the one and the other are doubtless,
in the main, successive stages of a
progressive effect originating in a
common cause, and therefore inde-
pendent of collocations. The uni-
formities, on the other hand, in the
order of superposition of strata on the
earth, are empirical laws of a much
weaker kind, since they not only are

M^

iNDtrcrrioN.

not laws of causation, but there is no
reason to believe that they depend on
any common cause ; all appearances
are in favour of their depending on
the particular collocation of natural
agents which at some time or other
existed on our globe, and from which
no inference can be drawn as to the
collocation which exists or has existed
in any other portion of the vmi verse.

§ 6. Our definition of an empirical
law including not only those uni-
formities which are not known to
be laws of causation, but also those
which are, provided there be reason
to presume that they are not ultimate
laws, this is the proper place to con-
sider by what signs we may judge
that even if an observed uniformity
be a law of causation, it is not an
ultimate but a derivative law.

The first sign is, if between the
antecedent a and the consequent b
there be evidence of some intermedi-
ate link, some phenomenon of which
we can surmise the existence, though
from the imperfection of our senses
or of our instruments we are unable
to ascertain its precise nature and
laws. If there be such a phenomenon,
(which may be denoted by the letter
X,) it follows that even if a be the
cause of 6, it is but the remote cause,
and that the law, a causes h, is re-
solvable into at least two laws, a
causes x, and x causes h. This is a
very frequent case, since the opera-
tions of nature mostly take place on
so minute a scale, that many of the
successive steps are either impercep-
tible, or very indistinctly perceived.

Take, for e.\ ample, the laws of the
chemical composition of substances,
as that hydrogen and oxygen being
combined, water is produced. All
we see of the process is, that the two
gases being mixed in certain propor-
tions, and heat or electricity being
applied, an explosion takes place, the
gases disappear, and water remain*.
There is no doubt about the law, or
about its being a law of causation.
But between the antecedent (the

gases in a state of mechanical mix-
ture, heated or electrified) and the
consequent (the production of water)
there must be an intermediate pro-
cess which we do not see. For if we
take any portion whatever of the
water and subject it to analysis, we
find that it always contains hydro-
gen and oxygen ; nay, the very same
proportions of them, namely, two-
thirds in volume of hydrogen, and
one-third oxygen. This is true of a
single drop ; it is true of the minutest
portion which our instruments are
capable of appreciating. Since, then,
the smallest perceptible portion of
the water contains both these sub-
stances, portions of hydrogen and
oxygen smaller than the smallest
perceptible must have come together
in every such minute portion of
space ; must have come closer to-
gether than when the gases were in
a state of mechanical mixture, since
(to mention no other reasons) the
water occupies far less space than
the gases. Now, as we cannot see
this contact or close approach of the
minute particles, we cannot observe
with what circumstances it is at-
tended, or according to what laws it
produces its effects. The production
of water, that is, of the sensible
phenomena which characterise the
compound, may be a very remote
effect of those laws. There may be
innumerable intervening links ; and
we are sure that there must be some.
Having full proof that corpuscular
action of some kind takes place pre-
vious to any of the great transforma-
tions in the sensible properties of sub-
stances, we can have no doubt that
the laws of chemical action, as at
present known, are not ultimate but
derivative laws ; however ignorant
we may be, and even though we
should for ever remain ignorant, of
the nature of the laws of corpuscular
action from which they are derived.

In like manner, all the processei
of vegetative life, whether in the
vegetable properly so called or in the
animal body, are corpuscular pro-

ftMPtRICAL LAWS.

345

cefesefi. Nutrition is the addition of
particles to one another, sometimes
merely replacing other particles sepa-
rated and excreted, sometimes oc-
casioning an increase of bulk or
weight so gradual, that only after
a long continuance does it become per-
ceptible. Various organs, by means
of peculiar vessels, secrete from the
blood fluids, the component particles
of which must have been in the blood,
but which differ from it most widely
both in mechanical properties and in
chemical composition. Here, then,
aie abundance of unknown links to
be filled up ; and there can be no
doubt that the laws of the pheno-
mena of vegetative or organic life are
derivative laws, dependent on pro-
perties of the corpuscles, and of those
elementary tissues which are com-
paratively simple combinations of cor-
puscles.

The first sign, then, from which a
law of causation, though hitherto im-
resolved, may be inferred to be a
derivative law, is any indication of
the existence of an intermediate link
or links between the antecedent and
the consequent. The second is, when
the antecedent is an extremely com-
plex phenomenon, and its effects
therefore, probably in part at least,
compounded of the effects of its dif-
ferent elements ; since we know that
the case in which the effect of the
whole is not made up of the effects
of its parts is exceptional, the Com-
position of Causes being by far the
more ordinary case.

We will illustrate this by two ex-
amples, in one of which the antece-
dent is the sum of many homogeneous,
in the other of heterogeneous, parts.
The weight of a body is made up of
the weights of its minute particles —
a truth which astronomers express in
its most general terms when they say
that bodies at equal distances gravi-
tate to one another in proportion to
their quantity of matter. All true
propositions, therefore, which can be
made concerning gravity are deri-
vative laws : the ultimate law into

which they are all resolvable being
that every particle of matter attracts
every other. As our second example,
we may take any of the sequence*
observed in meteorology ; for instance,
a diminution of the pressure of the
atmosphere (indicated by a fall of the
barometer) is followed by rain. The
antecedent is here a complex pheno-
menon, made up of heterogeneous
elements ; the column of the atmos-
phere over any particular place con-
sisting of two parts, a column of air
and a column of aqueous vapour
mixed with it ; and the change in the
two together manifested by a fall of
the barometer, and followed by rain,
must be either a change in one of
these, or in the other, or in both.
We might, then, even in the absence
of any other evidence, form a reason-
able presumption, from the invariable
presence of both these elements in the
antecedent, that the sequence is pro-
bably not an ultimate law, but a re-
sult of the laws of the two different
agents ; a presumption only to be de-
stroyed when we had made ourselves
so well acquainted with the laws of
both as to be able to affirm that those
laws could not by themselves produce
the observed result.

There are but few known cases of
succession from very complex ante-
cedents which have not either been
actually accounted for from simpler
laws, or inferred with great proba-
jility (from the ascertained existence
of intermediate links of causation not
yet understood) to be capable of being
so accounted for. It is, therefore,
highly probable that all sequences
from complex antecedents are thus
resolvable, and that ultimate laws
are in all cases comparatively simple.
If there were not the other reasons
already mentioned for believing that
the lawis of organised nature are re-
solvable into simpler laws, it would
be almost a sufficient reason that the
antecedents in most of the sequence*
are so very complex.

§ 7. In the preceding discussion we

344

iNDtJCTION.

have recognised two kinds of empi-
rical laws : those known to be laws
of causation but presumed to be re-
solvable into simpler laws, and those
not known to be laws of causation at
all. Both these kinds of laws agree
in the demand which they make for
being explained by deduction, and
agree in being the appropriate means
of verifying such deduction, since they
represent the experience with which
the result of the deduction must be
compared. They agree, further, in
this, that, until explained and con-
nected with the ultimate laws from
which they result, they have not at-
tained the highest degree of certainty
of which laws are susceptible. It has
been shown on a former occasion that
laws of causation which are deriva-
tive and compounded of simpler laws
are not only, as the nature of the case
implies, less general, but even less
certain, than the simpler laws from
which they result, not in the same
degree to be relied on as universally
true. The inferiority of evidence,
however, which attaches to this class
of laws is trifling compared with that
which is inherent in uniformities
not known to be laws of causation
at all. So long as these are unre-
solved, we cannot tell on how many
collocations, as well as laws, their
truth may be dependent ; we can
never, therefore, extend them with
any confidence to cases in which we
have not assured ourselves by trial
that the necessary collocation of causes,
whatever it may be, exists. It is to
this class of laws alone that the pro-
perty, which philosophers usually con-
sider as characteristic of empirical
laws, belongs in all its strictness —
the property of being unfit to be re-
lied on beyond the limits of time,
place, and circumstance, in which the
observations have been made. These
are empirical laws in a more emphatic
sense ; and when I employ that term
(except where the context manifestly
indicates the reverse) I shall generally
mean to designate those uniformities
only, whether of succession or of co-

existence» which are Hot known to be
laws of causation.

CHAPTER XVIL

OF CHANCE AND ITS ELIMINATION.

§ I. CoNSiDEKiNG then as empiri-
cal laws only those observed uniformi-
ties respecting which the question
whether they are laws of causation
must remain undecided until they can
be explained deductively, or until
some means are found of applying the
Method of Difference to the case ; it
has been shown in the preceding
chapter, that until an uniformity can,
in one or the other of these modes, be
taken out of the class of empirical
laws, and brought either into that of
laws of causation or of the demon-
strated results of laws of causation, it
cannot with any assurance be pro-
nounced true beyond the local and
other limits within which it has been
found so by actual observation. It
remains to consider how we are to
assure ourselves of its truth even with-
in those limits ; after what quantity
of experience a generalisation which
rests solely on the Method of Agree-
ment can be considered sufficiently
established, even as an empirical law.
In a former chapter, when treating of
the Methods of Direct Induction, we
expressly reserved this question,* and
the time has now come for endeavour-
ing to solve it.

We found that the Method of Ag-
reement has the defect of not prov-
ing causation, and can therefore only
be em^ployed for the ascertainment of
empirical laws. But we also found
that besides this deficiency, it labours
under a characteristic imperfection,
tending to render uncertain even such
conclusions as it is in itself adapted
to prove. This imperfection arises
from Plurality of Causes. Although
two or more cases in which the phe-
nomenon a has been met with may

* Supra, book iii. cli. x. § 2,

CHANCE, AND ITS ELIMINATION.

345

have no common antecedent except
A, this does not prove that there is
any connection between a and A, since
a may have many causes, and may
have been produced, in these different
instances, not by anything which the
instances had in common, but by some
of those elements in them which were
different. We nevertheless observed,
that in proportion to the multipli-
cation of instances pointing to A as
the antecedent the characteristic un-
certainty of the method diminishes,
and the existence of a law of con-
nection between A and a more nearly
approaches to certainty. It is now
to be determined after what amount
of experience this certainty may be
deemed to be practically attained, and
the connection between A and a may
be received as an empirical law.

This question may be otherwise
stated in more familiar terms : — After
how many and what sort of instances
may it be concluded that an observed
coincidence between two phenomena
is not the effect of chance ?

It is of the utmost importance for
understanding the logic of induction
that we should form a distinct con-
ception of what is meant by chance,
and how the phenomena which com-
mon language ascribes to that abstrac-
tion are really produced.

§ 2. Chance is usually spoken of in
direct antithesis to law ; whatever (it
is supposed) cannot be ascribed to any
law is attributed to chance. It is,
however, certain, that whatever hap-
pens is the result of some law ; is an
effect of causes, and could have been
predicted from a knowledge of the
existence of those causes, and from
their laws. If I turn up a particular
card, that is a consequence of its place
in the pack. Its place in the pack
was a consequence of the manner in
which the cards were shuffled, or of
the order in which they were played
in the last game ; which, again, were
effects of prior causes. At every stage,
if we had possessed an accurate know-
ledge of the causes in existence, it

would have been abstractly possible to
foretell the effect.

An event occurring by chance may
be better described as a coincidence
from which we have no ground to
infer an uniformity : the occurrence
of a phenomena, in certain circum-
stances, without our having reason on
that account to infer that it will
happen again in those circumstances.
This, however, when looked closely
into, implies that the enumeration of
the circumstances is not complete.
Whatever the fact be, since it has
occurred once, we may be sure that if
all the same circumstances were re-
peated, it would occur again ; and
not only if all, but there is some
particular portion of those circum-
stances on which the phenomenon is
invariably consequent. With most of
them, however, it is not connected in
any permanent manner : its conjunc-
tion with those is said to be the effect
of chance, to be merely casual. Facts
casually conjoined are separately the
effects of causes, and therefore of laws;
but of different causes, and causes not
connected by any law.

It is incorrect, then, to say that any
phenomenon is produced by chance ;
but we may say that two or more
phenomena are conjoined by chance,
that they co-exist or succeed one an-
other only by chance ; meaning that
they are in no way related through
causation ; that they are neither cause
and effect, nor effects of the same
cause, nor effects of causes between
which there subsists any law of co-
existence, nor even effects of the same
collocation of primeval causes.

If the same casual coincidence
never occurred a second time, we
should have an easy test for distin-
guishing such from the coincidences
which are the results of a law. As
long as the phenomena had been found
together only once, so long, unless we
knew some more general laws from
which the coincidence might have re-
sulted, we could not distinguish it
fn^m a casual one ; but if it occurred
twice, we should know that the phfe-

346

im>tTCTlON.

nomena. so conjoined must be in some
way connected through their causes.

There is, however, no euch test.
A coincidence may occur again and
again, and yet be only casual. Nay,
it would be inconsistent with what
we know of the order of nature to
doubt that every casual coincidence
will sooner or later be repeated, as
long as the phenomena between which
it occurred do not cease to exist, or to
be reproduced. The recurrence, there-
fore, of the same coincidence more
than once, or even its frequent re-
currence, does not prove that it is an
instance of any law ; does not prove
that it is not casual, or, in common
language, the effect of chance.

And yet, when a coincidence can-
not be deduced from known laws, nor
proved by experiment to be itself a
case of causation, the frequency of its
occurrence is the only evidence from
which we can infer that it is the
result of a law. Not, however, its
absolute frequency. The question is
not whether the coincidence occurs
often or seldom, in the ordinary sense
of those terms ; but whether it occurs
more often than chance will account
for ; more often than might rationally
be expected if the coincidence were
casual. We have to decide, therefore,
what degree of frequency in a coinci-
dence chance will account for. And
to this there can be no general answer.
We can only state the principle by
which the answer must be determined:
the answer itself will be different in
every different case.

Suppose that one of the phenomena,
A, exists always, and the other pheno-
menon, B, only occasionally ; it fol-
lows that every instance of B will be
an instance of its coincidence with A,
and yet the coincidence will be merely
casual, and not the result of any con-
nection between them. The fixed
stars have been constantly in exist-
ence since the beginning of human
experience, and all phenomena that
have come under human observation
have, in every single instance, co-
existed with them ; yet this coinci-

dence, though equally invariable with
that which exists between any of
those phenomena and its own cause,
does not prove that the stars are its
cause, nor that they are in any wise
connected with it. As strong a case
of coincidence, therefore, as can pos-
sibly exist, and a much stronger one
in point of mere frequency than most
of those which prove laws, does not
here prove a law. Why? because,
since the stars exist always, they
must co-exist with every other phe-
nomenon, whether connected with
them by causation or not. The uni-
formity, great though it be, is no
greater than would occur on the sup-
position that no such connection exists.
On the other hand, suppose that
we were inquiring whether there be
any connection between rain and any
particular wind. Rain, we know,
occasionally occurs with every wind ;
therefore the connection, if it exists,
cannot be an actual law : but still,
rain may be connected with some
particular wind through causation ;
that is, though they cannot be always
effects of the same cause, (for if so,
they would regularly co-exist,) there
may be some causes common to the
two, so that in so far as either is pro-
duced bj' those common causes, they
will, from the laws of the causes, be
found to co-exist. How, then, shall
we ascertain this ? The obvious
answer is, by observing whether rain
occurs with one wind more frequently
than with any other. That, however,
is not enough ; for perhaps that one
wind blows more frequently than any
other ; so that its blowing more fre-
quently in rainy weather is no more
than would happen, although it had
no connection with the causes of rain,
provided it were not connected with
causes adverse to rain. In England,
westerly winds blow during about
twice as great a portion of the yeai-
as easterly. If, therefore, it rains
only twice as often with a westerly
as with an easterly wind, we have no
reason to infer that any law of nature
is concerned in the coincidence. If

CHANCE, ANB ITS fiLIMINATION.

347

It rains more than twice as often, we
may be sure that some law is con-
cerned ; either there is some cause in
nature which, in this climate, tends
to produce both rain and a westerly
wind, or a westerly wind has itself
some tendency to produce rain. But
if it rains less than twice as often,
we may draw a directly opposite in-
ference : the one, instead of being a
cause, or connected with causes, of
the other, must be connected with
causes adverse to it, or with the
absence of some cause which pro-
duces it ; and though it may still
rain much oftener with a westerly
wind than with an easterly, so far
would this be from proving any con-
nection between the phenomena, that
the connection proved would be be-
tween rain and an easterly wind, to
which, in mere frequency of coinci-
dence, it is less allied.

Here, then, are two examples : in
one, the greatest possible frequency
of coincidence, with no instance what-
ever to the contrary, does not prove
that there is any law ; in the other, a
much less frequency of coincidence,
even when non -coincidence is still
more frequent, does prove that there
is a law. In both cases the principle
is the same. In both we consider the
positive frequency of the phenomena
themselves, and how great frequency
of coincidence that must of itself
bring about, without supposing any
connection between them, provided
there be no repugnance ; provided
neither be connected with any cause
tending to frustrate the other. If
we find a greater frequency of coin-
cidence than this, we conclude that
there is some connection ; if a less
frequency, that there is some repug-
nance. In the former case, we con-
clude that one of the phenomena can
under some circumstances cause the
other, or that there exists something
capable of causing them both ; in the
latter, that one of them, or some cause
which produces one of them, is cap-
able of counteracting the production
of the other. We have thus to deduct

from the observed frequency of coin-
cidence as much as may be the effect
of chance, that is, of the mere fre-
quency of the phenomena themselves ;
and if anything remains, what does
remain is the residual fact which
proves the existence of a law.

The frequency of the phenomena
can only be ascertained within definite
limits of space and time ; depending
as it does on the quantity and distri-
bution of the primeval natural agents,
of which we can know nothing be-
yond the boundaries of human obser-
vation, since no law, no regularity,
can be traced in it, enabling us to
infer the unknown from the known.
But for the present purpose this is no
disadvantage, the question being con-
fined within the same limits as the
data. The coincidences occurred in
certain places and times, and within
those we can estimate the frequency
with which such coincidences would
be produced by chance. If, then, we
find from observation that A exists
in one case out of every two, and B
in one case out of every three ; then,
if there be neither connection nor re-
pugnance between them, or between
any of their causes, the instances in
which A and B will both exist, that
is to say, will co-exist, will be one
case in every six. For A exists in
three cases out of six : and B, exist-
ing in one case out of every three
without regard to the presence or
absence of A, will exist in one case
out of those three. There will there-
fore be, of the whole number of cases,
two in which A exists without B ;
one case of B without A ; two in
which neither B nor A exists, and
one case out of six in which they both
exist. If, then, in point of fact, they
are found to co-exist oftener than in
one case out of six, and, consequently,
A does not exist without B so often
as twice in three times, nor B without
A so often as once in every twice,
there is some cause in existence which
tends to produce a conjunction between
A and B.

Generalising the result, we may say.

34^

INDUOTIOI^.

that if A occurs in a larger proportion
of the cases where B is than of the
cases where B is not, then will B
also occur in a larger proportion of
the cases where A is than of the cases
where A is not, and there is some
connection through causation between
A and B. If we could ascend to the
causes of the two phenomena, we
should find, at some stage, either
proximate or remote, some cause or
causes common to both ; and if we
could ascertain what these are, we
could frame a generalisation which
would be true without restriction of
place or time ; but until we can do
so, the fact of a connection between
the two phenomena remains an em-
pirical law.

§ 3. Having considered in what
manner it may be determined whether
any given conjunction of phenomena
is casual or the result of some law,
to complete the theory of chance it
is necessary that we should now con-
sider those effects which are partly
the result of chance and partly of
law, or, in other words, in which the
effects of casual conjunctions of causes
are habitually blended in one result
with the effects of a constant cause.

This is a case of Composition of
Causes ; and the peculiarity of it is,
that instead of two or more causes
intermixing their effects in a regular
manner with those of one another, we
have now one constant cause, produc-
ing an effect which is successively
modified by a series of variable causes.
Thus, as summer advances, the ap-
proach of the sun to a vertical position
tends to produce a constant increase
of temperature ; but with this effect
of a constant cause there are blended
the effects of many variable causes,
winds, clouds, evaporation, electric
agencies and the like, so that the
temperature of any given day depends
in part on these fleeting causes, and
only in part on the constant cause.
If the effect of the constant cause is
always accompanied and disguised by
effects of variable causes, it is impos-

sible to ascertain the law of the con-
stant cause in the ordinary manner,
by separating it from all other causes
and observing it apart. Hence arises
the necessity of an additional rule of
experimental inquiry.

When the action of a cause A is
liable to be interfered with, not steadily
by the same cause or causes, but by
different causes at different times,
and when these are so frequent, or so
indeterminate, that we cannot pos-
sibly exclude all of them from any
experiment, though we may vary
them, our resource is, to endeavour
to ascertain what is the effect of all
the variable causes taken together.
In order to do this, we make as many
trials as possible, preserving A invari-
able. The result of these different
trials will naturally be different, since
the indeterminate modifying causes
are different in each ; if, then, we do
not find these results to be progressive,
but, on the contrary, to oscillate about
a certain point, one experiment giving
a result a little greater, another a
little less, one a result tending a little
more in one direction, another a little
more in the contrary direction ; while
the average or middle point does not
vary, but different sets of experiments
(taken in as great a variety of cir-
cumstances as possible) yield the same
mean, provided only they be suffi-
ciently numerous ; then that mean or
average result is the part in each
experiment which is due to the cause
A, and is the effect which would have
been obtained if A could have acted
alone : the variable remainder is the
effect of chance, that is, of causes the
co-existence of which with the cause
A was merely casual. The test of
the sufficiency of the induction in this
case is, when any increase of the
number of trials from which the aver-
age is struck does not materially alter
the average.

This kind of elimination, in which
we do not eliminate any one assign-
able cause, but the multitude of float-
ing unassignable ones, may be termed
the Elimination of Chance. We

CHANCE, AND ITS ELIMINATION.

349

aflPord an example of it when we re-
peat an experiment, in order, by tak-
ing the mean of different results, to
get rid of the effects of the unavoid-
able errors of each individual experi-
ment. Whtn there is no permanent
cause such a?, would produce a ten-
dency to error peculiarly in one direc-
tion, we are warranted by experience
in assuming that the errors on one
side will, in a certain number of ex-
periments, about balance the errors
on the contrary side. "We therefore
repeat the experiment, until any
change which is produced in the aver-
age of the whole by further repeti-
tion falls within limits of error con-
sistent with the degree of accuracy
required by the purpose we have in
view.*

§ 4, In the supposition hitherto
made, the effect of the constant cause
A has been assumed to form so great
and conspicuous a part of the general
result, that its existence never could
be a matter of uncertainty, and the
object of the eliminating process was
only to ascertain how much is attri-
butable to that cause ; what is its
exact law. Cases, however, occur in
which the effect of a constant cause is
so small, compared with that of some
of the changeable causes with which
it is liable to be casually conjoined,
that of itself it escapes notice, and the
very existence of any effect arising
from a constant cause is first learnt
by the process which in general serves
only for ascertaining the quantity of
that effect. This case of Induction

"* In the preceding discussion, the mean
is spoken of as if it were exactly the same
thing with the average. But the mean, for
purposes of inductive inquiry, is not the
average or arithmetical mean, though in a
familiar illustration of the theory the dif-
ference may be disregarded. If the devia-
tions on one side of the average are much
more numerous than those on the other,
(these last being fewer but greater,) the
effect due to the invariable cause, as dis-
tinct from the variable ones, will not coin-
cide with the average, but will be either
below or above the average, the deviation
being toward* the side on which the

may be characterised as follows. A
given effect is known to be chiefly,
and not known not to be wholly, deter-
mined by changeable causes. If it be
wholly so produced, then if the aggre-
gate be taken of a sufficient number
of instances, the effects of these dif-
ferent causes will cancel one another.
If, therefore, we do not find this tt»
be the case, but, on the contrary, after
such a number of trials has been
made that no further increase alters
the average result, we find that aver-
age to be, not zero, but some other
quantity, about which, though small
in comparison with the total effect,
the effect nevertheless oscillates, and
which is the middle point in .its oscil-
lation ; we may conclude this to be
the effect of some constant cause :
which cause, by some of the methods
already treated of, we may hope to
detect. This may be called the dis-
covery of a residual phenomenon by
eliminating the effects of chance.

It is in this manner, for example,
that loaded dice may be discovered.
Of course no dice are so clumsilj
loaded that they must always throw
certain numbers ; otherwise the fraud
would be instantly detected. The
loading, a constant cause, mingles
with the changeable causes which
determine what cast will be thrown
in each individual instance. If the
dice were not loaded, and the throw
were left to depend entirely on the
changeable causes, these in a suffi-
cient number of instances would
balance one another, and there would
be no preponderant number of throws

greatest number of instances are found.
This follows from a truth, ascertained both
inductively and deductively, that small
deviations from the true central point are
greatly more frequent than large ones.
The mathematical law is, " that the most
probable determination of one or more in-
variable elements from observation is that
in which the sum of the squares of the indi-
vidual aberrations," or deviations, "shall
be the least possible." See this principle
stated, and its grounds popularly explained,
by Sir John Herschel, in liis review of
Qu^telet on Probabilities, Essays, pp. 395
et seq.

350

INDUCTION.

of any one kind. If, therefore, after
such a number of trials that no fur-
ther increase of their number has
any material effect upon the average,
we find a preponderance in favour of
a particular throw, we may conclude
with assurance that there is some
constant cause acting in favour of
that throw, or, in other words, that
the dice are not fair ; and the exact
amount of the unfairness. In a
similar manner, what is called the
diurnal variation of the barometer,
which is very small compared with
the variations arising from the irre-
gular changes in the state of the
atmosphere, was discovered by com-
paring the average height of the
barometer at different hours of the
day. When this comparison was
made, it was found that there was
a small difference, which on the
average was constant, however the
absolute quantities might vary, and
which difference, therefore, must be
the effect of a constant cause. This
cause was afterwards ascertained,
deductively, to be the rarefaction of
the air, occasioned by the increase of
temperature as the day advances.

§ 5. After these general remarks
on the nature of chance, we are pre-
pared to consider in what manner
assurance may be obtained that a
conjunction between two phenomena,
which has been observed a certain
number of times, is not casual, but a
result of causation, and to be received
therefore as one of the uniformities
of nature, though (until accounted
for d priori) only as an empirical
2aw.

We will suppose the strongest case,
namely, that the phenomenon B has
never been observed except in con-
junction with A. Even then, the
probability that they are connected
is not measured by the total number
of instances in which they have been
found together, but by the excess of
that number above the number due
to the absolute frequency of A. If,
for example, A exists always, and

therefore co-exists with everything,
no number of instances of its co-
existence with B would prove a con-
nection ; as in our example of the
fixed stars. If A be a fact of such
common occurrence that it may be
presumed to be present in half of all
the cases that occur, and therefore
in half the cases in which B occurs,
it is only the proportional excess
above half that is to be reckoned as
evidence towards proving a connec-
tion between A and B,

In addition to the question, What
is the number of coincidences which,
on an average of a great multitude
of trials, may be expected to arise
from chance alone ? there is also
another question, namely. Of what
extent of deviation from that average
is the occurrence credible, from chance
alone, in some number of instances
smaller than that required for strik-
ing a fair average ? It is not only to
be considered what is the general
result of the chances in the long-run,
but also what are the extreme limits
of variation from the general result
which may occasionally be expected
as the result of some smaller number
of instances.

The consideration of the latter
question, and any consideration of
the former beyond that already given
to it, belong to what mathematicians
term the Doctrine of Chances, or, in
a phrase of greater pretension, the
Theory of Probabilities.

CHAPTER XVIII.

OF THE CALCULATION OP CHANCES.

§ I. "Probability," says Laplace,*
" has reference partly to our ignorance,
partly to our knowledge. We know
that among three or more events, one,
and only one, must happen ; but there
is nothing leading us to believe that
any one of them will happen rather
than the others. In this state of

* Essai Philosophique sur let ProbabiliUs,
fifth Paris edition, p. 7.

OF THE CALCULATION OF CHANCES.

3Sl

Indecision, it is impossible for ua to
pronounce with certainty on their
occurrence. It is, however, probable
that any one of these events, selected
at pleasure, will not take place ; be-
cause we perceive several cases, all
equally possible, which exclude its
occurrence, and only one which fav-
ours it.

** The theory of chances consists in
reducing all events of the same kind
to a certain number of cases equally
possible, that is, such that we are
equally undecided as to their exist-
ence ; and in determining the number
of these cases which are favourable
to the event of which the probability
is sought. The ratio of that number
to the number of all the possible cases
is the measure of the probability ;
which is thus a fraction, having for
its numerator the number of cases
favourable to the event, and for its
denominator the number of all the
cases which are possible."

To a calculation of chances, then,
according to Laplace, two things are
necessary : we must know that of
sevei;3.1 events some one will certainly
happen, and no more than one ; and
we must not know, nor have any
reason to expect, that it will be one
of these events rather than another.
It has been contended that these are
not the only requisites, and that La-
place has overlooked, in the general
theoretical statement, a necessary part
of the foundation of the doctrine of
chances. To be able (it has been
said) to pronounce two events equally
probable, it is not enough that we
should know that one or the other
must happen, and should have no
grounds for conjecturing which. Ex-
perience must have shown that the
two events are of equally frequent
occurrence. Why, in tossing up a
halfpenny, do we reckon it equally
probable that we shall throw cross
or pile? Because we know that in
any great number of throws, cross
and pile are thrown about equally
often ; and that the more throws we
make, the more nearly the equality is

perfect. We may know this if we
please by actual experiment ; or by
the daily experience which life affords
of events of the same general char-
acter ; or deductively, from the effect
of mechanical laws on a symmetrical
body acted upon by forces varying
indefinitely in quantity and direction.
We may know it, in short, either by
specific experience, or on the evidence
of our general knowledge of nature.
But, in one wa}' or the other, we
must know it, to justify us in calling
the two events equally probable ; and
if we knew it not, we should proceed
as much at haphazard in staking
equal sums on the result as in laying
odds.

This view of the subject was taken
in the first edition of the present
work ; but I have since become con-
vinced that the theory of chances, as
conceived by Laplace and by mathe-
maticians generally, has not the funda-
mental fallacy which I had ascribed
to it.

We must remember that the proba-
bility of an event is not a quality of
the event itself, but a mere name for
the degree of ground which we, or
some one else, have for expecting it.
The probability of an event to one
person is a different thing from the
probability of the same event to an-
other, or to the same person after
he has acquired additional evidence.
The probability to me that an indi-
vidual of whom I know nothing but
his name will die within the year, is
totally altered by my being told, the
next minute, that he is in the last
stage of a consumption. Yet this
makes no difference in the event
itself, nor in any of the causes on
which it depends. Every event is
in itself certain, not probable : if we
knew all, we should either know posi-
tively that it will happen, or positively
that it will not. But its probability
to us means the degree of expectation
of its occurrence, which we are war-
ranted in entertaining by our present
evidence.

Bearing this in mind, I think it

352

INDUCTION.

must be admitted, that even when
we have no knowledge whatever to
guide our expectations, except the
knowledge that what happens must
be some one of a certain number of
possibilities, we may still reasonably
judge that one supposition is more
probable to us than another supposi-
tion ; and if we have any interest at
stake, we shall best provide for it by
acting conformably to that judgment.

§ 2. Suppose that we are required
to take a ball from a box, of which
we only know that it contains balls
both black and white, and none of
any other colour. We know that the
ball we select will be either a black
or a white ball ; but we have no
ground for expecting black rather
than white, or white rather than
black. In that case, if we are obliged
to make a choice, and to stake some-
thing on one or the other supposition,
it will, as a question of prudence, be
perfectly indifferent which ; and we
shall act precisely as we should have
acted if we had known beforehand
that the box contained an equal
number of black and white balls.
But though our conduct would be
the same, it would not be founded
on any surmise that the balls were
in fact thus equally divided, for we
might, on the contrary, know, by
authentic information, that the box
contained ninety-nine balls of one
colour, and only one of the other ;
still, if we are not told which colour
has only one, and which has ninety-
nine, the drawing of a white and of a
black ball will be equally probable to
us; we shall have no reason for staking
anything on the one event rather than
on the other ; the option between the
two will be a matter of indifference ;
in other words, it will be an even
chance.

But let it now be supposed that
instead of two there are three colours
— white, black, and red ; and that we
are entirely ignorant of the proportion
in which they are mingled. We should
then have no reason for expecting one

more than another, and if obliged to
bet, should venture our stake on red,
white, or black, with equal indiffer-
ence. But should we be indifferent
whether we betted for or against
some one colour, as, for instance,
white ? Surely not. Erom the very
fact that black and red are each of
them separately equally probable to
us with white, the two together must
be twice as probable. We should in
this case expect not- white rather than
white, and so much rather, that we
would lay two to one upon it. It is
true, there might, for aught we knew,
be more white balls than black and
red together ; and if so, our bet would,
if we knew more, be seen to be a dis-
advantageous one. But so also, for
aught we knew, might there be more
red balls than black and white, or
more black balls than white and red,
and in such case the effect of additional
knowledge would be to prove to us
that our bet was more advantageous
than we had supposed it to be. There
is in the existing state of our know-
ledge a rational probability of two to
one against white ; a probability fit
to be made a basis of conduct. No
reasonable person would lay an even
wager in favour of white against
black and red ; though against black
alone, or red alone, he might do so
without imprudence.

The common theory, therefore, of
the calculation of chances appears to
be tenable. Even when we know no-
thing except the number of the pos-
sible and mutually excluding con-
tingencies, and are entirely ignorant
of their comparative frequency, we
may have grounds, and grounds nu-
merically appreciable, for acting on one
supposition rather than on another ;
and this is the meaning of Proba-
bility.

§ 3. The principle, however, on
which the reasoning proceeds is suf-
ficiently evident. It is the obvious
one, that when the cases which exist
are shared among several kinds, it is
impossible that each of those kinds

OF THE CALCULATION OF CHANCES.

353

should be a majority of the whole :
on the contrary, there must be a
majority against each kind, except
one at most ; and if any kind has
more than its share in proportion to
the total number, the others collec-
tively must have less. Granting this
axiom, and assuming that we have
no ground for selecting any one kind
as more likely than the rest to surpass
the average proportion, it follows that
we cannot rationally presume this of
any ; which we should do if we were
to bet in favour of it, receiving less
odds than in the ratio of the number
of the other kinds. Even, therefore,
in this extreme case of the calculation
of probabilities, which does not rest on
special experience at all, the logical
ground of the process is our knowledge,
such knowledge as we then have, of
the laws governing the frequency of oc-
currence of the different cases ; but in
this case the knowledge is limited to
that which, being universal and axio-
matic, does not require reference to
specific experience, or to any con-
siderations arising out of the special
nature of the problem under dis-
cussion.

Except, however, in such cases as
games of chance, where the very pur-
pose in view requires ignorance instead
of knowledge, I can conceive no case
in which we ought to be satisfied with
such an estimate of chances as this ;
an estimate founded on the absolute
minimum of knowledge respecting the
subject. It is plain that, in the case
of the coloured balls, a very slight
ground of surmise that the white balls
were really more numerous than either
of the other colours would suffice to
vitiate the whole of the calculations
made in our previous state of in-
difference. It would place us in
that position of more advanced know-
ledge, in which the probabilities, to
us, would be different from what they
were before ; and in estimating these
new probabilities we should have to
proceed on a totally different set of
data, furnished no longer by mere
pounting of possible suppositions, but

by specific knowledge of facts. Such
data it should always be our en-
deavour to obtain ; and in all inquiries,
unless on subjects equally beyond the
range of our means of knowledge and
our practical uses, they may be ob-
tained, if not good, at least better
than none at all.*

It is obvious, too, that even when the
probabilities are derived from observa-
tion and experiment, a very slight im-
provement in the data, by better obser-
vations, or by taking into fuller con-
sideration the special circumstances
of the case, is of more use than the
most elaborate application of the cal-
culus to probabilities founded on the
data in their previous state of in-
feriority. The neglect of this obvious
reflection has given rise to misapplica-
tions of the calculus of probabilities
which have made it the real oppro-
brium of mathematics. It is sufficient
to refer to the applications made of
it to the credibility of witnesses, and
to the correctness of the verdicts of
juries. In regard to the first, common
sense would dictate that it is im-
possible to strike a general average of
* It even appears to me that the calcula-
tion of chances, where there are no data
grounded either on special experience or
on special inference, must, in an immense
majority of cases, break down, from sheer
impossibility of assigning any principle by
which to be guided in setting out the list
of possibilities. In the case of the coloured
baUs we have no difficulty in making the
enumeration, because we ourselves deter-
mine what the possibilities shall be. But
suppose a case more analogous to thosa
which occur in nature : instead of three
colours, let there be in the box all possible
colours : we being supposed ignorant of
the comparative frequency with which
different colours occur in nature, or in the
productions of art. How is the list of cases
to be made out? Is every distinct shade to
count as a colour ? If so, is the test to be a
common eye, or an educated eye— a pain-
ter's, for instance? On the answer to
these questions would depend whether
the chances against some particular colour
would be estimated at ten, twenty, or per-
haps five hundred to one. While if we
knew from experience that the particular
colour occurs on an average a certain num-
ber of times in every hundred or thousand,
we should not require to know anything
either of the frequency or of the number of
the other possibilities.

354

INDUCTION.

the veracity, and other qualifications
for true testimony, of mankind, or of
any class of them ; and even if it were
possible, the employment of it for
such a purpose implies a misappre-
hension of the use of averages : which
nerve indeed to protect those whose
interest is at stake against mistaking
the general result of large masses of
instances, but are of extremely small
value as grounds of expectation in any
one individual instance, unless the case
be one of those in which the great
majority of individual instances do
not differ much from the average.
In the case of a witness, persons of
common sense would draw their con-
clusions from the degree of consis-
tency of his statements, his conduct
under cross-examination, and the re-
lation of the case itself to his interests,
his partialities, and his mental capa-
city, instead of applying so rude a
standard (even if it were capable of
being verified) as the ratio between
the number of true and the number of
erroneous statements which he may
be supposed to make in the course of
his life.

Again, on the subject of juries, or
other tribunals, some mathematicians
have set out from the proposition that
the judgment of any one judge or
juryman is, at least in some small
degree, more likely to be right than
wrong, and have concluded that the
chance of a number of persons con-
curring in a wrong verdict is dimi-
nished the more the number is in-
creased ; so that if the judges are only
made suflBciently numerous, the cor-
rectness of the judgment may be
reduced almost to certainty. I say
nothing of the disregard shown to the
effect produced on the moral position
of the judges by multiplying their
numbers ; the virtual destruction of
their individual responsibility, and
weakening of the application of their
minds to the subject. I remark only
the fallacy of reasoning from a wide
average to cases necessarily differing
greatly from any average. It may be
true that, taking all causes one with

another, the opinion of any one of the
judges would be oftener right than
wrong ; but the argument forgets that
in all but the more simple cases, in all
cases in which it is really of mudi
consequence what the tribunal is, the
proposition might probably be re-
versed ; besides which, the cause of
error, whether arising from the intri-
cacy of the case or from some common
prejudice or mental infirmity, if it
acted upon one judge, would be extre-
mely likely to affect all the others in
the same manner, or at least a majo-
rity, and thus render a wrong instead
of a right decision more probable, the
more the number was increased.

These are but samples of the errors
frequently committed by men who,
having made themselves familiar with
the difficult formulae which algebra
affords for the estimation of chances
under suppositions of a complex cha-
racter, like better to employ those
formulae in computing what are the
probabilities to a person half informed
about a case, than to look out for means
of being better informed. Before
applying the doctrine of chances to
any scientific purpose, the foundation
must be laid for an evaluation of the
chances, by possessing ourselves of the
utmost attainable amount of positive
knowledge. The knowledge required
is that of the comparative frequency
with which the different events in fact
occur. For the purposes, therefore,
of the present work, it is allowable
to suppose that conclusions respecting
the probability of a fact of a particular
kind rest on our knowledge of the
proportion between the cases in which
facts of that kind occur and those in
which they do not occur : this know-
ledge being either derived from spe-
cific experiment, or deduced from our
knowledge of the causes in operation
which tend to produce, compared with
those which tend to prevent, the fact
in question.

Such calculation of chances is
grounded on an induction ; and to
render the calculation legitimate, the
induction inust be 3, valid one, It

OF THE CALCULATION OF CHANCES.

355

is not less an induction, though it
does not prove that the event occiirs
in all cases of a given description,
but only that out of a given number
of such cases it occurs in about so
many. The fraction which mathe-
maticians use to designate the pro-
bability of an event is the ratio of
these two numbers ; the ascertained
proportion between the number of
cases in which the event occurs and
the sum of all the cases, those in
which it occurs and in which it does
not occur taken together. In plajdng
at cross and pile, the description of
eases concerned are throws, and the
probability of cross is one-half, be-
cause if we throw often enough, cross
is thrown about once in every two
throws. In the cast of a die, the
probability of ace is one-sixth ; not
.simply because thei-e are six possible
throws, of which ace is one, and be-
cause we do not know any reason
why one should turn up rather than
another, though I have admitted the
validity of this ground in default of
a better, but because we do actu-
ally know, either by reasoning or by
experience, that in a hundred or a
million of throws, ace is thrown in
about one-sixth of that number, or
<mce in six times,

§ 4. I say, "either by reasoning or
by experience ; " meaning specific ex-
perience. But in estimating pro-
babilities, it is not a matter of in-
difference from which of these two
sources we derive our assurance. The
probability of events as calculated
from their mere frequency in past
experience affords a less secure basis
for practical guidance than their pro-
bability as deduced from an equally
accurate knowledge of the frequency
of occurrence of their causes.
' The generalisation that an event
occurs in ten out of every hundred
cases of a given description is as real
an induction as if the generalisation
were that it occurs in all cases. But
when we arrive at the conclusion by
loerelj' coupting instances in victual

experience, and comparing the num-
ber of cases in which A has been
present with the number in which
it has been absent, the evidence is
only that of the Method of Agree-
ment, and the conclusion amounts
only to an empirical law. We can
make a step beyond this when we
can ascend to the causes on which the
occurrence of A or its non -occurrence
will depend, and form an estimate
of the comparative frequency of the
causes favourable and of those un-
favourable to the occurrence. These
are data of a higher order, by which
the empirical law derived from a
mere numerical comparison of affirm,
ative and negative instances will b(^
either corrected or confirmed, and in
either case we shall obtain a more
correct measure of probability than
is given by that numerical compari-
son. It has been well remarked that
in the kind of examples by which
the doctrine of chances is usually
illustrated, that of balls in a box,
the estimate of probabilities is sup-
ported by reasons of causation stronger
than specific experience. "What is
the reason that in a box where there
are nine black balls and one white,
we expect to draw a black ball nine
times as much (in other words, nine
times as often, frequency being the
gauge of intensity in expectation) as
a white? Obviously because the local
conditions are nine times as favour-
able, because the hand may alight in
nine places and get a black ball, while
it can only alight in one place and
find a white ball ; just for the same
reason that we do not expect to suc-
ceed in finding a friend in a crowd,
the conditions in order that we and
he should come together being many
and difficult. This of course would
not hold to the same extent were the
white balls of smaller size than the
black, neither would the probability
remain the same : the larger ball
would be much more likely to meet
the hand." *

It i», in fact, evident, that when
* Prosptctive Review for February 185Q,

356

INDUCTION.

once causation is admitted as an uni-
versal law, our expectation of events
can only be rationally grounded on
that law. To a person who recog-
nises that every event depends on
causes, a thing's having happened
once is a reason for expecting it to
happen again, only because proving
that there exists, or is liable to exist,
a cause adequate to produce it.* The
frequency of the particular event,
apart from all surmise respecting
its cause, can give rise to no other
induction than that^je?* enumerationem
simplicem ; and the precarious infer-
ences derived from this are super-
seded and disappear from the field,
as soon as the principle of causation
makes its appearance there.

Notwithstanding, however, the ab-

* " If this be not so, why do we feel so
much more probability added by the first
instance than by any single subsequent
instance? Why, except that the first in-
stance gives us its possibility, (a cause
adequate to it,) while every other only gives
us the frequency of its conditions ? If no
reference to a cause be supposed, possi-
bility would have no meaning ; yet it is
clear that, antecedent to its happening,
we might have supposed the event impos-
sible, i.e., have believed that there was no
physical energy really existing in the world
equal to producing it. . . . After the first
time of happening, which is, then, more
important to the whole probability than
any other single instance, (because proving
the possibility,) the number of times be-
comes important as an index to the inten-
sity or extent of the cause, and its inde-
pendence of any particular time. If we
took the case of a tremendous leap, for
instance, und wished to form an estimate
of the probability of its succeeding a certain
number of times; the first instance, by
showing its possibility, (before doubtful,) is
of the most importance ; but every suc-
ceeding leap shows the power to be more
perfectly under control, greater and more
invariable, and so increases the probability ;
and no one would think of reasoning in
this case straight from one instance to the
next, without referring to the physical
energy which each leap indicated. Is it
not then clear that we do not ever " (let us
rather say, that we do not in an advanced
state of our knowledge) "conclude directly
from the happening of an event to the pro-
bability of its happening again ; but that
we refer to the cause, regarding the past
cases as an index to the cause, and the
cause as our guide to the future?"— Pro-
apective Review for February 1850.

stract superiority of an estimate of
probability grounded on causes, it is
a fact that in almost all cases in which
chances admit of estimation suflB-
ciently precise to render their nume-
rical appreciation of any practical
value, the numerical data are not
drawn from knowledge of the causes,
but from experience of the events
themselves. The probabilities of life
at different ages or in different cli-
mates ; the probabilities of recovery
from a particular disease ; the chances
of the birth of male or female off-
spring ; the chances of the destruc-
tion of houses or other property by
fire ; the chances of the loss of a ship
in a particular voyage — are deduced
from bills of mortality, returns from
hospitals, registers of births, of ship-
wrecks, (fee, that is, from the observed
frequency not of the causes, but of
the effects. The reason is, that in all
these classes of facts, the causes are
either not amenable to direct obser-
vation at all, or not with the requisite
precision, and we have no means of
judging of their frequency except
from the empirical law afforded by
the frequency of the effects. The in-
ference does not the less depend on
causation alone. We reason from an
effect to a similar effect by passing
through the cause. If the actuary
of an insurance office infers from
his tables that among a hundred
persons now living, of a particular
age, five on the average will attain
the age of seventy, his inference is
legitimate, not for the simple reason
that this is the proportion who have
lived till seventy in times past, but
because the fact of their having so
lived shows that this is the proportion
existing, at that place and time, be-
tween the causes which prolong life
to the age of sevent}', and those tend-
ing to bring it to an earlier close.*

* The writer last quoted says that the
valuation of chances by comparing the
number of cases in which the event occuis
with the number in which it does not occur
"would generally be wholly erroneous,"
and " is not the true theory of probability."
It is a^ least that which fornis the fovmd^-

01^ THE CALCULATION OF CHANCES.

357

§ 5. From the preceding principles
it is easy to deduce the demonstration
of that theorem of the doctrine of pro-
babilities which is the foundation of
its application to inquiries for ascer-
taining the occurrence of a given
event or the reality of an individual
fact. The signs or evidences by which
a fact is usually proved are some of
its consequences : and the inquiry
hinges upon determining what cause
is most likely to have produced a
given effect. The theorem applicable
to such investigations is the Sixth
Principle in Laplace's Bssai Philoso-
phique sur les Probabilites, which is
described by him as the "fundamental
principle of that branch of the Analy-
sis of Chances which consists in as-
cending from events to their causes." *

Given an effect to be accounted for,
and there being several causes which
might have produced it, but of the
presence of which in the particular
case nothing is known ; the proba-
bility that the effect was produced
by any one of these causes is as the
antecedent probability of the cause,
viuUiplied by the probability that the

tion of insurance, and of all those calcula-
tions of chances in the business of life
which experience so abtmdantly verifies.
The reason which the reviewer gives for
rejecting the theory, is that it " would re-
gard an event as certain which had hitherto
never failed ; which is exceedingly f;ir from
the truth, even for a very large number of
constant successes." This is not a defect
in a particular theory, but in any theory
of chances. No principle of evaluation can
provide for such a case as that which the
reviewer supposes. If an event has never
once failed, in a number of trials suflBcient
to eliminate chance, it really has all the
certainty which can be given by an em-
pirical law : it is certain during the con-
tinuance of the same collocation of causes
which existed during the observations. If
it ever fails, it is in consequence of some
change in that collocation. Now, no theory
of chances will enable us to infer the future
probability of an event from the past, if
the causes in operation capable of influen-
cing the event have internaediately under-
gone a change,

* Pp. 18, 19. The theorem is not stated by
Laplace in the exact terms in which I have
Slated it ; but the identity of import of the
two modes of expression is easily demon-
strable.

Cause, if it existed, would have pro-
duced the given effect.

Let M be the effect, and A, B, two
causes, by either of which it might
have been prodiiced. To find the
probability that it was produced by
the one and not by the other, ascer-
tain which of the two is most likely
to have existed, and which of them,
if it did exist, was most likely to pro-
duce the effect M : the probability
sought is a compound of these two
probabilities.

Cask I. Let the causes be both
alike in the second respect ; either A
or B, when it exists, being supposed
equally likely (or equally certain) to
produce M ; but let A be in itself
twice as likely as B to exist, that is,
twice as frequent a phenomenon.
Then it is twice as likely to have
existed in this case, and to have been
the cause which produced M.

For, since A exists in nature twice
as often as B, in any 300 cases in
which one or other existed, A has
existed 200 times and B 100. But
either A or B must have existed
wherever M is produced : therefore
in 300 times that M is produced, A
was the producing cause 200 times,
B only 100, that is, in the ratio of 2
to I. Thus, then, if the causes are
alike in their capacity of producing
the effect, the probability as to which
actually produced it is in the ratio
of their antecedent probabilities.

Case IL Reversing the last hypo-
thesis, let us suppose that the causes
are equally frequent, equally likely to
have existed, but not equally likely,
if they did exist, to produce Si : that
in three times in which A occurs, it
produces that effect twice, while B,
in three times, produces it only once.
Since the two causes are equally fre-
quent in their occurrence ; in every
six times that either one or the other
exists, A exists three times and B
three times. A, of its three times,
produces M in two ; B, of its three
times, produces M in one. Thiis, in
the whole six times, M is only pro-
duced thrice ; but of that thrice it is

35^

INDUCTION.

produced twice by A, once only by
B. Consequently, when the ante-
dent probabilities of the causes are
equal, the chances that the effect
was produced by them are in the
ratio of the probabilities that if they
did exist they would produce the
effect.

Case III. The third case, that in
which the causes are unlike in both
respects, is solved by what has pre-
ceded. For when a quantity depends
on two other quantities, in such a
manner that while either of them
remains constant it is proportional to
the other, it must necessarily be pro-
portional to the product of the two
quantities, the product being the only
function of the two which obeys that
law of variation. Therefore the pro-
bability that M was produced by
either cause is as the antecedent pro-
bability of the cause, multiplied by
the probability that if it existed it
would produce M. Which was to be.
demonstrated.

Or we may prove the third case as
we proved the first and second. Let
A be twice as frequent as B ; and let
them also be unequally likely, when
they exist, to produce M ; let A pro-
duce it twice in four times, B thrice in
four times. The antecedent probabi-
lity of A is to that of B as 2 to i ; the
probabilities of their producing M are
as 2 to 3 ; the product of these ratios
is the ratio of 4 to 3 ; and this will
be the ratio of the probabilities that
A or B was the producing cause in
the given instance. For, since A is
twice as frequent as B, out of twelve
cases in which one or other exists, A
exists in 8 and B in 4. But of its
eight cases. A, by the supposition,
produces M in only 4, while B of its
four cases produces M in 3. M,
therefore, is only produced at all in
seven of the twelve cases ; but in
four of these it is produced by A, in
three by B ; hence the probabilities
of its being produced by A and by
B are as 4 to 3, and are expressed by
the fractions ^ and f . Which was to
be demonstrated.

§ 6. It remains to examine the
bearing of the doctrine of chances on
the peculiar problem which occupied
us in the preceding chapter, namely,
how to distinguish coincidences which
are casual from those which are the
result of law — ^from those in which
the facts which accompany or follow
one another are somehow connected
through causation.

The doctrine of chances affords
means by which, if we knew the
average number of coincidences to be
looked for between two phenomena
connected only casually, we could
determine how often any given devia-
tion from that average will occur by
chance. If the probability of any
casual coincidence, considered in it-
self, be -, the probability that the
same coincidence will be repeated n
times in succession is -—. For ex-
ample, in one throw of a die the pro-
bability of ace being -^, the probabi-
lity of throwing ace twice in succession
will be I divided by the square of 6, or

-. For ace is thrown at the first
36

throw once in six, or six in thirty-
six times, and of those six, the die
being cast again, ace will be thrown
but once ; being altogether once in
thirty-six times. The chance of the
same cast three times successively is,

by a similar reasoning, ^ or — - ; that

is, the event will happen, on a large
average, only once in two hundred
and sixteen throws.

We have thus a rule by whicn to
estimate the probability that any
given series of coincidences arises
from chance, provided we can mea-
sure correctly the probability of a
single coincidence. If we can obtain
an equally precise expression for the
probability that the same series of
coincidences arises from causation,
we should only have to compare the
numbers. This, however, can rarely
be done. Let us see what degree

OF THE CALCULATION OF CHANCES.

3S9

of approximation can practically be
made to the necessary precision.

The question falls within Laplace's
Sixth Principle, just demonstrated.
The given fact, that is to say, the
series of coincidences, may have origi-
nated either in a casual conjunction
of causes or in a law of nature. The
probabilities, therefore, that the fact
originated in these two modes are, as
their antecedent probabilities, multi-
plied by the probabilities that if they
existed they would produce the effect.
But the particular combination of
chances, if it occurred, or the law of
nature if real, would certainly pro-
duce the series of coincidences. The
probabilities, therefore, that the co-
incidences are produced by the two
causes in question are as the ante-
cedent probabilities of the causes.
One of these, the antecedent probabi-
lity of the combination of mere chances
which would produce the given result,
is an appreciable quantity. The an-
tecedent probability of the other sup-
position may be susceptible of a more
or less exact estimation, according to
the nature of the case.

In some cases the coincidence, sup-
posing it to be the result of causation
at all, must be the result of a known
cause, as the succession of aces, if not
accidental, must arise from the load-
ing of the die. In such cases we
may be able to form a conjecture as
to the antecedent probability of such
a circumstance from the characters of
the parties concerned, or other such
evidence ; but it would be impossible
to estimate that probability with any-
thing like numerical precision. The
counter-probability, however, that of
the accidental origin of the coinci-
dence, dwindling so rapidly as it does
at each new trial ; the stage is soon
reached at which the chance of un-
fairness in the die, however small in
itself, must be greater than that of
a casual coincidence ; and on this
ground a practical decision can gene-
rally be come to without much hesita-
tion, if there be the power of repeating
the experiment.

When, however, the coincidence is
one which cannot be accounted for
by any known cause, and the con-
nection between the two phenomena,,
if produced by causation, must be the
result of some law of nature hitherto
unknown, which is the case we had
in view in the last chapter ; then,
though the probability of a casual
coincidence may be capable of ap-
preciation, that of the counter-sup-
position, the existence of an undis-
covered law of nature, is clearl}' un-
susceptible of even an approximate
valuation. In order to have the data
which such a case would require, it
would be necessary to know what
proportion of all the individual se-
quences or co-existences occurring
in nature are the result of law, and
what proportion are mere casual coin-
cidences. It being evident that we
cannot form any plausible conjecture
as to this proportion, much less ap-
preciate it numerically, we cannot
attempt any precise estimation of the
comparative probabilities. But of this
we are sure, that the detection of
an unknown law of nature — of some
previously unrecognised constancy of
conjunction among phenomena — is no
uncommon event. If, therefore, the
number of instances in which a coin-
cidence is observed, over and above
that which would arise on the average
from the mere concurrence of chances,
be such that so great an amount of co-
incidences from accident alone would
be an extremely uncommon event ;
we have reason to conclude that the
coincidence is the effect of causation,
and may be received (subject to cor-
rection from further experience) as an
empirical law. Further than this, in
point of precision, we cannot go ; nor,
in most cases, is greater precision re-
quired for the solution of any practi-
cal doubt.*

* For a fuller treatment of the many
interesting questions raised by the theory
of probabilities, I may now refer to a recent
work by Mr. Venn, Fellow of Caius College,
Cambridge, "The Logic of Chance," one
of the most thoughtful and philosophical
treatises on any subject connected with

36o

fNDtrCTIOK

CHAPTER XIX.

OF THE EXTENSION OP DERIVATIVE
LAWS TO ADJACENT CASES.

§ I. We have had frequent occa-
sion to notice the inferior generality
of derivative laws compared with the
ultimate laws from which they are de-
rived. This inferiority, which affects
not only the extent of the propositions
themselves, but their degree of cer-
tainty within that extent, is most con-
spicuous in the uniformities of co-exist-
ence and sequence obtaining between
effects which depend ultimately on
different primeval causes. Such uni-
formities will only obtain where there
exists the same collocation of those
primeval causes. If the collocation
varies, though the laws themselves
remain the same, a totally different
set of derivative uniformities may,
and generally will, be the result.

Even where the derivative uni-
formity is between different effects of
the same cause, it will by no means
obtain as universally as the law of the
cause itself. If a and h accompany
or succeed one another as effects of
the cause A, it by no means follows
that A is the only cause which can
produce them, or that if there be
another cause, as B, capable of pro-
ducing a, it must produce h like-
wise. The conjunction therefore of a
and h perhaps does not hold univer-
sally, but only in the instances in
which a arises from A. When it is
produced by a cause other than A, a
and h may be dissevered. Day (for
example) is always in our experience
followed by night : but day is not the
cause of night ; both are successive
effects of a common cause, the periodi-
cal passage of the spectator into and

Logic and Evidence which have been pro-
duced, to my knowledge, for many years.
Some criticisms contained in it have been
very useful to me in revising the corre-
sponding chapters of the present work. In
■eyeral of Mr. Venn's opinions, however, I
do not agree. What these are will be
obvious to any reader of Mr. Venn's work j
who is also a reader of thia.

out of the earth's shadow, consequent
on the earth's rotation, and on the
illuminating property of the sun. If,
therefore, day is ever produced by a
different cause or set of causes from this,
day will not, or at least may not, be fol-
lowed by night. On the sun's own sur-
face, for instance, this may be the case.
Finally, even when the derivative
uniformity is itself a law of causation,
(resulting from the combination of
several causes,) it is not altogether
independent of collocations. If a cause
supervenes capable of wholly or par-
tially counteracting the effect of any
one of the conjoined causes, the effect
will no longer conform to the deriva-
tive law. While, therefore, each ulti-
mate law is only liable to frustration
from one set of counteracting causes,
the derivative law is liable to it from
several. Now, the possibility of the
occurrence of counteracting causes
which do not arise from any of the
conditions involved in the law itself
depends on the original collocations.

It is true that (as we formerly re-
marked) laws of causation, whether
ultimate or derivative, are, in most
cases, fulfilled even when counter-
acted : the cause produces its effect,
though that effect is destroyed by
something else. That the effect may
be frustrated, is, therefore, no objec-
tion to the universality of laws of
causation. But it is fatal to the uni-
versality of the sequences or co-exist-
ences of effects which compose the
greater part of the derivative laws
flowing from laws of causation. When
from the law of a certain combination
of causes there results a certain order
in the effects, as from the combina-
tion of a single sun with the rotation
of an opaque body round its axis,
there results, on the whole surface of
that opaque body, an alternation of
day and night ; then if we suppose
one of the combined causes counter-
acted, the rotation stopped, the sun
extinguished, or a second sun super-
added, the truth of that particular law
of causation is in no way affected ; it
is still true that one sun shining on an

EXTENSION OF LAWS TO ADJACENT CASES.

3^t

opaque revolving body will alternately
produce day and night ; but since the
sun no longer does shine on such
a body, the derivative uniformity,
the succession of day and night on
the given planet, is no longer true.
Those derivative uniformities, there-
fore, which are not laws of causation,
are (except in the rare case of their
depending on one cause alone, not on
a combination of causes) always more
or less contingent on collocations ;
and are hence subject to the charac-
teristic infirmity of empirical laws,
that of being admissible only where
the collocations are known by expe-
rience to be such as are requisite for
the truth of the law, that is, only
within the conditions of time and place
confirmed by actual observation.

§ 2. This principle, when stated in
general terms, seems clear and indis-
putable ; yet many of the ordinary
judgments of mankind, the propriety
of which is not questioned, have at
least the semblance of being incon-
sistent with it. On what grotmds, it
may be asked, do we expect that the
sun will rise to-morrow ? To-morrow
IS beyond the limits of time compre-
hended in our observations. They
have extended over some thousands
of years past, but they do not in-
clude the future. Yet we infer with
confidence that the sun will rise to-
morrow ; and nobody doubts that we
are entitled to do so. Let us con-
sider what is the warrant for this con-
fidence.

In the example m question, we
know the causes on which the deri-
vative uniformity depends. They are,
the sun giving out light, the earth in
a state of rotation and intercepting
light. The induction which shows
these to be the real causes, and not
merely prior effects of a common
cause, being complete, the only cir-
cumstances which could defeat the
derivative law are such as would
destroy or counteract one or other
of the combined causes. While the
causes exist, and are not counter-

acted, the effect will continue. If
they exist and are not counteracted
to-morrow, the sun will rise to-
morrow.

Since the causes, namely, the sun
and the earth, the one in the state of
giving out light, the other in a state
of rotation, will exist until sojnething
destroys them, all depends on the
probabilities of their destruction, or
of their counteraction. We know by
observation (omitting the inferential
proofs of an existence for thousands
of ages anterior) that these pheno-
mena have continued for (say) five
thousand years. Within that time
there has existed no cause sufficient
to diminish them appreciably, nor
which has counteracted their effect in
any appreciable degree. The chance,
therefore, that the sun may not rise
to-morrow amounts to the chance
that some cause, which has not mani-
fested itself in the smallest degree
during five thousand years, will exist
to-morrow in such intensity as to
destroy the sun or the earth, the
sun's light or the earth's rotation, or
to produce an immense disturbance
in the effect resulting from those
causes.

Now, if such a cause will exist to-
morrow, or at any future time, some
cause, proximate or remote, of that
cause must exist now, and must have
existed during the whole of the five
thousand years. If, therefore, the
sun do not rise to-morrow, it will be
because some cause has existed, the
effects of which, though during five
thousand years they have not amounted
to a perceptible quantity, will in one
day become overwhelming. Since
this cause has not been recognised
during such an interval of time by
observers stationed on our earth, it
must, if it be a single agent, be either
one whose effects develop themselves
gradually and very slowly, or one
which existed in regions beyond our
observation, and is now on the point
of arriving in our part of the universe.
Now all causes which we have expe-
rience of act according to laws in-

362

INDUCTION.

compatible with the supposition that
their effects, after accumulating so
slowly as to be imperceptible for five
thousand years, should start into im-
mensity in a single day. No mathe-
matical law of proportion between an
effect and the quantity or relations of
its cause could produce such contra-
dictory results. The sudden develop-
ment of an effect of which there was
no previous trace always arises from
the coming together of several distinct
causes not previously conjoined ; but
if such sudden conjunction is destined
to take place, the causes, or their
causes, must have existed during the
entire five thousand years ; and their
not having once come together during
that period shows how rare that par-
ticular combination is. We have,
therefore, the warrant of a rigid in-
duction for considering it probable,
in a degree un distinguishable from
certainty that the known conditions
requisite for the sun's rising will exist
to-morrow.

§ 3. But this extension of deriva-
tive laws, not causative, beyond the
limits of observation, can only be to
adjacent cases. If instead of to-mor-
row, we had said this day twenty
thousand years, the inductions would
have been anything but conclusive.
That a cause which, in opposition to
very powerful causes, produced no
perceptible effect during five thousand
years, should produce a very con-
siderable one by the end of twenty
thousand, has nothing in it which is
not in conformity with our experience
of causes. We know many agents,
the effect of which in a short period
does not amount to a perceptible
quantity, but by accumulating for a
much longer period becomes con-
siderable. Besides, looking at the im-
mense multitude of the heavenly
bodies, their vast distances, and the
rapidity of the motion of such of them
as are known to move, it is a supposi-
tion not at all contradictory to ex-
perience that some body may be in
motion towards us, or we towards it,

within the limits of whose influence
we have not come during five thousand
years, but which in twenty thousand
more may be producing effects upon
us of the most extraordinary kind.
Or the fact which is capable of pre-
venting sunrise may be, not the cumu-
lative effect of one cause, but some
new combination of causes ; and the
chances favourable to that combina-
tion, though they have not produced
it once in five thousand years, may
produce it once in twenty thousand. So
that the inductions which authorise us
to expect future events grow weaker
and weaker the farther we look into
the future, and at length become in-
appreciable.

We have considered the probabili-
ties of the sun's rising to-morrow,
as derived from the real laws, that is,
from the laws of the causes on which
that uniformity is dependent. Let us
now consider how the matter would
have stood if the uniformity had been
known only as an empirical law ; if
we had not been aware that the sun's
light and the earth's rotation (or the
sun's motion) were the causes on
which the periodical occurrence of
daylight depends. We could have-
extended this empirical law to cases
adjacent in time, though not so great
a distance of time as we can now.
Having evidence that the effects had
remained unaltered, and been punc-
tually conjoined for five thousand
years, we could infer that the un-
known causes on which the conjunc-
tion is dependent had existed undi-
minished and uncounteracted during
the same period. The same conclu-
sions, therefore, would follow as in the
preceding case ; except that we should
only know that during five thousand
years nothing had occurred to defeat
perceptibly this particular effect ;
while, when we know the causes, we
have the additional assurance that
during that interval no such change
has been noticeable in the causes
themselves as by any degree of mul-
tiplication or length of continuance
could defeat the effect.

EXTENSION OF LAWS TO ADJACENT CASES.

3^5

To this must be added, that when
we know the causes, we may be able
to judge whether there exists any
known cause capable of counteracting
them ; while as long as they are un-
known, we cannot be sure but that if
we did know them, we could predict
their destruction from causes actually
in existence. A bedridden savage,
who had never seen the cataract of
Niagara, but who lived within hearing
of it, might imagine that the sound
he heard would endure for ever ; but
if he knew it to be the effect of a rush
of waters over a barrier of rock which
is progressively wearing away, he
would know that within a number of
ages which may be calculated it will
be heard no more. In proportion,
therefore, to our ignorance of the
causes on which the empirical law
depends, we can be less assured that
it will continue to hold good ; and
the farther we look into futurity, the
less improbable is it that some one of
the causes whose co-existence gives
rise to the derivative uniformity may
be destroyed or counteracted. With
every prolongation of time the chances
multiply of such an event, that is to
say, its non -occurrence hitherto be-
comes a less guarantee of its not
occurring within the given time. If,
then, it is only to cases which in point
of time are adjacent (or nearly adja-
cent) to those which we have actually
observed that any derivative law, not
of causation, can be extended with
an assurance equivalent to certainty,
much more is this true of a merely
empirical law. Happily, for the pur-
poses of life it is to such cases alone
that we can almost ever have occasion
to extend them.

In respect of place, it might seem
that a merely empirical law could not
be extended even to adjacent cases ;
that we could have no assurance of
its being true in any place where it
has not been specially observed. The
past duration of a cause is a guarantee
for its future existence, unless some-
thing occurs to destroy it ; but the
existence of a cause in one or any

number of places, is no guarantee for
its existence in any other place, since
there is no uniformity in the collo-
cations of primeval causes. When,
therefore, an empirical law is ex-
tended beyond the local limits within
which it has been found true^by ob-
servation, the cases to which it is thus
extended must be such as are presum-
ably within the influence of the same
individual agents. If we discover a
new planet within the known bounds
of the solar system, (or even beyond
those bounds, but indicating its con-
nection with the system by revolving
round the sun,) we may conclude,
with great probability, that it revolves
on its axis. For all the known planets
do so ; and this uniformity points to
some common cause antecedent to
the first records of astronomical ob-
servation : and though the nature of
this cause can only be matter of con-
jecture, yet if it be, as is not unlikely,
and as Laplace's theory supposes, not
merely the same kind of cause, but
the same individual cause, (such as an
impulse given to all the bodies at
once,) that cause, acting at the ex-
treme points of the space occupied by
the sun and planets, is likely, unless
defeated by some counteracting cause,
to have acted at every intermediate
point, and probably somewhat beyond;
and therefore acted, in all probability,
upon the supposed newly-discovered
planet.

When, therefore, effects which arti
always found conjoined can be traced
with any probability to an identical
(and not merely a similar) origin, we
may with the same probability extend
the empirical law of their conjunction
to all places within the extreme local
boundaries within which the fact has
been observed ; subject to the possi-
bility of counteracting causes in some
portion of the field. Still more con-
fidently may we do so when the law
is not merely empirical ; when the
phenomena which we find conjoined
are effects of ascertained causes, from
the laws of which the conjunction of
their effects is deducible. In that

364

INDUCTION.

case, we may both extend the deriva-
tive uniformity over a larger space,
and vi^ith less abatement for the chance
of counteracting causes. The first, be-
cause, instead of the local boundai'ies
of our observation of the fact itself,
we may include the extreme boun-
daries of the ascertained influence of
its causes. Thus the succession of
day and night, we know, holds true
of all the bodies of the solar system
except the sun itself ; but we know
this only because we are acquainted
with the causes : if we were not, we
could not extend the proposition be-
yond the orbits of the earth and
moon, at both extremities of which
we have the evidence of observation
for its truth. With respect to the
probability of counteracting causes,
it has been seen that this calls for a
greater abatement of confidence, in
proportion to our ignorance of the
causes on which the phenomena de-
pend. On both accounts, therefore,
a derivative law which we know how
to resolve is susceptible of a greater
extension to cases adjacent in place
than a merely empirical law.

CHAPTER XX.

OF ANALOGY.

§ I. Thk word Analogy, as the
name of a mode of reasoning, is gene-
rally taken for some kind of argu-
ment supposed to be of an inductive
nature, but not amounting to a com-
plete induction. There is no word,
however, which is used more loosely,
or in a greater variety of senses, than
Analogy. It sometimes stands for
arguments which may be examples of
the most rigorous Induction. Arch-
bishop Whately, for instance, fol-
lowing Ferguson and other writers,
defines Analogy conformably to
its primitive acceptation, that which
was given to it by mathematicians,
Resemblance of Relations. In this
sense, when a country which has
sent out colonies ia termed the mother

country, the expression is analogi-
cal, signifying that the colonies of a
country stand in the same relation to
her in which children stand to their
parents. And if any inference be
drawn from this resemblance of rela-
tions, as, for instance, that obedience
or affection is due from colonies to
the mother country, this is called
reasoning by analogy. Or if it be
argued that a nation is most bene-
ficially governed by an assembly
elected by the people, from the ad-
mitted fact that other associations
for a common purpose, such as joint-
stock companies, are best managed
by a committee chosen by the parties
interested ; this, too, is an argument
from analogy in the preceding sense,
because its foundation is, not that
a nation is like a joint-stock company,
or Parliament like a board of direc-
tors, but that Parliament stands in
the same relation to the nation in
which a board of directors stands to
a joint-stock company. Now, in an
argument of this nature, there is no
inherent inferiority of conclusiveness.
Like other arguments from resem-
blance, it may amount to nothing, or
it may be a perfect and conclusive
induction. The circumstance in which
the two cases resemble may be cap-
able of being shown to be the material
circumstance ; to be that on which
all the consequences necessary to be
taken into account in the particular
discussion depend. In the example
last given, the resemblance is one of
relation ; the fundamentum relationis
being the management by a few
persons of affairs in which a much
greater number are interested along
with them. Now, some may contend
that this circumstance, which is com-
mon to the two cases, and the various
consequences which follow from it,
have the chief share in determining
all the effects which make up what
we term good or bad administration.
If they can establish this, their argu-
ment has the force of a rigorous in-
duction ; if they cannot, they are
said to have failed in proving the

ANALOGY. 365

analogy between the two cases ; a
mode of speech which implies that
when the analogy can be proved, the
argfument founded on it cannot be
resisted.

§ 2. It is on the whole more usual,
however, to extend the name of ana-
logical evidence to arguments from
any sort of resemblance, provided
they do not amount to a complete
induction : without peculiarly dis-
tinguishing resemblance of relations.
Analogical reasoning, in this sense,
may be reduced to the following for-
mula : — Two things resemble each
other in one or more respects ; a
certain proposition is true of the one,
therefore it is true of the other. But
we have nothing here by which to
discriminate analogy from induction,
since this type will serve for all
reasoning from experience. In the
strictest induction, equally with the
faintest analogy, we conclude because
A resembles B in one or more pro-
perties, that it does so in a certain
other property. The difference is,
that in the case of a complete induc-
tion it has been previously shown,
by due comparison of instances, that
there is an invariable conjunction
between the former property or pro-
perties and the latter property ; but
in what is called analogical reasoning,
no such conjunction has been made
out. There have been no oppor-
tunities of putting in practice the
Method of Difference, or even the
Method of Agreement ; but we con-
clude (and that is all which the argu-
ment of analogy amounts to) that a
fact m, known to be true of A, is
more likely to be true of B if B
agrees with A in some of its proper-
ties, (even though no connection is
known to exist between m and those
properties,) than if no resemblance at
all could be traced between B and
any other thing known to possess the
attribute m.

To this argument it is of course
requisite that the properties common
Xq a with B shall be merely pot

known to be connected with m ; they
must not be properties known to be
unconnected with it. If, either by
processes of elimination, or by deduc-
tion from previoiis knowledge of the
laws of the properties in question, it
can be concluded that they have no-
thing to do with m, the argument of
analogy is put out of court. The
supposition must be that in is an
effect really dependent on some pro-
perty of A, but we know not on
which. We cannot point out any of
the properties of A which is the
cause of ?», or united with it by
any law. After rejecting all which
we know to have nothing to do with
it, there remain several between
which we are unable to decide : of
which remaining properties B pos-
sesses one or more. This accordingly
we consider as affording grounds, of
more or less strength, for concluding
by analogy that B possesses the attri-
bute m.

There can be no doubt that every
such resemblance which can be
pointed out between B and A aflfords
some degree of probability, beyond
what would otherwise exist, in favour
of the conclusion drawn from it. If
B resembled A in all its ultimate
properties, its possessing the attribute
m would be a certainty, not a proba-
bility ; and every resemblance which
can be shown to exist between them
places it by so much the nearer to
that point. If the resemblance be in
an ultimate property, there will be
resemblance in all the derivative pro-
perties dependent on that ultimate
property, and of these m maj'^ be one.
If the resemblance be in a derivative
property, there is reason to expect
resemblance in the ultimate property
on which it depends, and in the other
derivative properties dependent on
the same ultimate property. Every
resemblance which can be shown to
exist affords ground for expecting an
indefinite number of other resem-
blances : the particular resemblance
sought will, therefore, be oftener
found among things thus known to

366

INDUCTION.

resemble, than among things between
which we know of no resemblance.

For example, I might infer that
there are probably inhabitants in the
moon, because there are inhabitants
on the earth, in the sea, and in the
air ; and this is the evidence of ana-
logy. The circumstance of having
inhabitants is here assumed not to
be an ultimate property, but (as is
reasonable to suppose) a consequence
of other properties ; and depending,
therefore, in the case of the earth, on
some of its properties as a portion of
the universe, but on which of those
properties we know not. Now the
moon resembles the earth in being a
solid, opaque, nearly spherical sub-
stance, appearing to contain, or to
have contained, active volcanoes ; re-
ceiving heat and light from the sun
in about the same quantity as our
earth ; revolving on its axis ; com-
posed of materi-als which gravitate,
and obeying all the various laws re-
sulting from that property. And I
think no one will deny that if this
were all that was known of the moon,
the existence of inhabitants in that
luminary would derive from these
various resemblances to the earth a
greater degree of probability than it
would otherwise have : though the
amount of the augmentation it would
be useless to attempt to estimate.

If, however, every resemblance
proved between B and A, in any
point not known to be immaterial
with respect to m, forms some addi-
tional reason for presuming that B
has the attribute m, it is clear, t
contra, that every dissimilarity which
can be proved between them fur-
nishes a counter-probability of the
same nature on the other side. It is
not indeed unusual that different
ultimate properties should, in some
particular instances, produce the same
derivative property ; but on the whole
it is certain that things which differ
in their ultimate properties will
differ at least as much in the aggre-
gate of their derivative properties,
aii(} that the differences which are

unknown will on the average of
cases bear some proportion to those
which are known. There will, there-
fore, be a competition between the
known points of agreement and the
known points of difference in A and
B ; and according as the one or the
other may be deemed to preponde-
rate, the probability derived from
analogy wull be for or against B's
having the property m. The moon,
for instance, agrees with the earth in
the circumstances already mentioned ;
but differs in being smaller, in having
its surface more unequal, and ap-
parently volcanic throughout, in hav-
ing, at least on the side next the
earth, no atmosphere sufficient to re-
fract light, no clouds, and (it is there-
fore concluded) no water. These
differences, considered merely as
such, might perhaps balance the re-
semblances, so that analogy would
afford no presumption either way.
But considering that some of the
circumstances which are wanting on
the moon are among those which, on
the earth, are found to be indispens-
able conditions of animal life, we may
conclude that if that phenomenon
does exist in the moon, (or at all
events on the nearer side,) it must be
as an effect of causes totally different
from those on which it depends here;
as a consequence, therefore, of the
moon's differences from the earth, not
of the points of agreement. Viewed
in this light, all the resemblances
which exist become presumptions
against, not in favour of, the moon's
being inhabited. Since life cannot
exist there in the manner in which it
exists here, the greater the resem-
blance of the lunar world to the
terrestrial in other respects, the less
reason we have to believe that it can
contain life.

There are, however, other bodies in
our system, between which and the
earth there is a much closer resem-
blance, which possess an atmosphere,
clouds, consequently water, (or some
fluid analogous to it,) and even give
strong indications of snow in their

ANALOGY.

367

polar regions ; while the cold or heat,
though differing greatly on the aver-
age from ours, is, in some parts at
least of those planets, possibly not
more extreme than in some regions
of our own which are habitable. To
balance these agreements, the ascer-
tained differences are chiefly in the
average light and heat, velocity of
rotation, density of material, inten-
sity of gravity, and similar circum-
stances of a secondary kind. With
regard to these planets, therefore, the
argument of analogy gives a decided
preponderance in favour of their re-
sembling the earth in any of its de-
rivative properties, such as that of
having inhabitants ; though, when we
consider how immeasurably multitu-
dinous are those of their properties
which we are entirely ignorant of,
compared with the few which we
know, we can attach but trifling
weight to any considerations of re-
semblance in which the known ele-
ments bear so inconsiderable a pro-
portion to the unknown.

Besides the competition between
analogy and diversity, there may be
a competition of conflicting analogies.
The new case may be similar in some
of its circumstances to cases in which
the fact m exists, but in others to
cases in which it is known not to
exist. Amber has some properties in
common with vegetable, others with
mineral products. A painting of un-
known origin may resemble, in certain
of its characters, known works of a
particular master, but in others it
may as strikingly resemble those of
some other painter. A vase may
bear some analogy to works of Gre-
cian, and some to those of Etruscan
or Egyptian art. We are of course
supposing that it does not possess
any quality which has been ascer-
tained, by a sufficient induction, to
be a conclusive mark either of the
one or of the other.

§ 3. Since the value of an ana-
logical argument inferring one re-
semblance from other resemblances

without any antecedent evidence of
a connection between them, depends
on the extent of ascertained re-
semblance, compared first with the
amount of ascertained difference, and
next with the extent of the unex-
plored region of unascertained pro-
perties ; it follows that where the
resemblance is very great, the ascer-
tained difference very small, and our
knowledge of the subject-matter toler-
ably extensive, the argument from
analogy may approach in strength
very near to a valid induction. If,
after much observation of B, we find
that it agrees with A in nine out of
ten of its known properties, we may
conclude with a probability of nine
to one, that it will possess any given
derivative property of A. If we dis-
cover, for example, an unknown ani-
mal or plant, resembling closely some
known one in the greater number of
the properties we observe in it, but
differing in some few, we may reason-
ably expect to find in the unobserved
remainder of its properties a gene-
ral agreement with those of the for-
mer, but also a difference correspond-
ing proportionately to the amount of
observed diversity.

It thus appears that the conclusions
derived from analogy are only of any
considerable value when the case to
which we reason is an adjacent case ;
adjacent, not as before, in place or
time, but in circumstances. In the
case of effects of which the causes are
imperfectly or not at all knowTi, when
consequently the observed order of
their occurrence amounts only to an
empirical law, it often happens that
the conditions which have co-existed
whenever the effect was observed
have been very numerous. Now if a
new case presents itself, in which all
these conditions do not exist, but the
far greater part of them do, some one
or a few only being wanting, the in-
ference that the effect will occur, not-
withstanding this deficiency of com-
plete resemblance to the cases in
which it hai been observed, may,
though of the nature of analogy, poa^

368

INDUCTION.

sesB a high degree of pi-obability. It
is hardly necessary to add, that how-
ever considerable this probability may
be, no competent inquirer into nature
will rest satisfied with it when a com-
plete induction is attainable ; but will
consider the analogy as a mere guide-
post, pointing out the direction in
which more rigorous investigations
should be prosecuted.

It is in this last respect that con-
siderations of analogy have the highest
scientific value. The cases in which
analogical evidence affords in itself
any very high degree of probability,
are, as we have observed, only those
in which the resemblance is very close
and extensive ; but there is no ana-
logy, however faint, which may not be
of the utmost value in suggesting ex-
periments or observations that may
lead to more positive conclusions.
When the agents and their effects are
out of the reach of further observa-
tion and experiment, as in the specu-
lations already alluded to respecting
the moon and planets, such slight pro-
babilities are no more than an inter-
esting theme for the pleasant exercise
of imagination ; but any suspicion,
however slight, that sets an ingenious
person at work to contrive an experi-
ment, or affords a reason for trying
one experiment rather than another,
may be of the greatest benefit to
science.

On this ground, though I cannot
accept as positive truths any of those
scientific hypotheses which are unsus-
ceptible of being ultimately brought
to the test of actual induction, such,
for instance, as the two theories of
light, the emission theory of the last
century, and the undulatory theory
which predominates in the present, I
am yet unable to agree with those
who consider such hypotheses to be
worthy of entire disregard. As is
well said by Hartley (and concurred
in by a thinker in general so diame-
trically opposed to Hartley's opinions
as Dugald Stewart), " any hypothesis
which has so much plausibility as to
explain a considerable number of facts,

helps us to digest these facts in proper
order, to bring new ones to light, and
make experimenta crucis for the sake
of future inquirers." * If an hypo-
thesis both explains known facts and
has led to the prediction of others
previously unknown, and since veri-
fied by experience, the laws of the
phenomenon which is the subject of
inquiry must bear at least a great
similarity to those of the class of phe-
nomena to which the hypothesis as-
similates it ; and since the analogy
which extends so far may probably
extend farther, nothing is more likely
to suggest experiments tending to
throw light upon the real properties
of the phenomenon than the follow-
ing out such an hypothesis. But to
this end it is by no means necessary
that the hypothesis be mistaken for a
scientific truth. On the contrary, that
illusion is in this respect, as in every
other, an impediment to the progress
of real knowledge, by leading inquirers
to restrict themselves arbitrarily to
the particular hypothesis which is
most accredited at the time, instead of
looking out for every class of pheno-
mena between the laws of which and
those of the given phenomena any
analogy exists, and trying all such
experiments as may tend to the dis-
covery of ulterior analogies pointing
in the same direction.

CHAPTER XXL

OF THE EVIDENCE OF THE LAW OP
UNIVERSAL CAUSATION.

§ I. We have now completed our
review of the logical processes by
which the laws, or uniformities, of
the sequence of phenomena, and those
uniformities in their co-existence
which depend on the laws of their
sequence, are ascertained or tested.
As we recognised in the commence-
ment, and have been enabled to see

* Hartley's Observations on Man, vol. i,
p. 1 6. The passage is not in Priestley's
curtailed edition.

EVIDENCE OF UNIVERSAL CAUSATION.

369

more clearly in the progress of the
investigation, the basis of all these
logical operations is the law of causa-
tion. The validity of all the Inductive
Methods depends on the assumption
that every event, or the beginning of
every phenomenon, must have some
cause, some antecedent, on the ex-
istence of which it is invariably and
unconditionally consequent. In the
Method of Agreement this is obvious ;
that method avowedly proceeding on
the supposition that we have found
the true cause as soon as we have
negatived every other. The assertion
is equally true of the Method of
Difiference. That method authorises
us to infer a general law from two
instances ; one, in which A exists
together with a multitude of other
circumstances, and B follows ; an-
other, in which A being removed,
and all other circumstances remaining
the same, B is prevented. What,
however, does this prove ? It proves
that B, in the particular instance,
cannot have had any other cause than
A ; but to conclude from this that A
was the cause, or that A will on other
occasions be followed by B, is only
allowable on the assumption that B
must have some cause ; that among
its antecedents in any single instance
in which it occurs, there must be
one which has the capacity of pro-
ducing it at other times. This being
admitted, it is seen that in the case
in question that antecedent can be
no other than A ; but, that if it be
no other than A it must be A, is not
proved, by these instances at least,
but taken for granted. There is no
need to spend time in proving that
the same thing is true of the other
Inductive Methods. The universality
of the law of causation is assumed in
them all.

But is this assumption warranted ?
Doubtless (it may be said) most pheno-
mena are connected as effects with som e
antecedent or cause, that is, are never
produced imless some assignable fact
has preceded them ; but the very cir-
cumstance that complicated processes

of induction are sometimes necessary,
shows that cases exist in which this
regular order of succession is not ap-
parent to our unaided apprehension.
If, then, the processes which bring
these cases within the same category
with the rest require that we should
assume the universality of the very
law which they do not at first sight
appear to exemplify, is not this a
petitio principii? Can we prove a
proposition by an argument which
takes it for granted? And if not
so proved, on what evidence does it
rest?

For this difficulty, which I have
purposely stated in the strongest terms
it will admit of, the school of meta-
physicians who have long predomi-
nated in this country find a ready
salvo. They affirm that the uni-
versality of causation is a truth which
we cannot help believing ; that the
belief in it is an instinct, one of the
laws of our believing faculty. As the
proof of this, they say, and they have
nothing else to say, that everybody
does believe it ; and they number it
among the propositions, rather nume-
rous in their catalogue, which may be
logically argued against, and perhaps
cannot be logically proved, but which
are of higher authority than logic,
and so essentially inherent in the
human mind, that even he who denies
them in speculation shows by his
habitual practice that his arguments
make no impression upon himself.

Into the merits of this question,
considered as one of psychology, it
would be foreign to my purpose to
enter here ; but I must protest against
adducing, as evidence of the truth of
a fact in external nature, the disposi-
tion, however strong or however gene-
ral, of the human mind to believe it.
Belief is not proof, and does not dis-
pense with the necessity of proof. I
am aware that to ask for evidence of
a proposition which we are supposed
to believe instinctively is to expose
oneself to the charge of rejecting the
authority of the human faculties ;
which of course no one can con-

2 A

370

INDUCTION.

sistently do, since the human facul-
ties are all which any one has to
judge by ; and inasmuch as the mean-
ing of the word evidence is supposed
to be something which, when laid
before the mind, induces it to believe ;
to demand evidence when the belief
is ensured by the mind's own laws is
supposed to be appealing to the in-
tellect against the intellect. But this,
I apprehend, is a misunderstanding
of the nature of evidence. By evi-
dence is not meant anything and
everything which produces belief.
There are many things which gene-
rate belief besides evidence. A mere
strong association of ideas often causes
a belief so intense as to be unshake-
able by experience or argument. Evi-
dence is not that which the mind
does or must yield to, but that which
it ought to yield to, namely, that, by
yielding to which, its belief is kept
conformable to fact. There is no ap-
peal from the human faculties gene-
rally, but there is an appeal from one
human faculty to another ; from the
judging faculty to those which take
cognisance of fact, the faculties of
sense and consciousness. The legiti-
macy of this appeal is admitted when-
ever it is allowed that our judgments
ought to be conformable to fact. To
say that belief suffices for its own
justification is making opinion the
test of opinion ; it is denying the ex-
istence of any outward standard, the
conformity of an opinion to which
constitutes its truth. We call one
mode of forming opinions right and
another wrong, because the one does
and the other does not tend to make
the opinion agree with the fact — to
make people believe what really is,
and expect what really will be. Now
a mere disposition to believe, even if
supposed instinctive, is no guarantee
for the truth of the thing believed.
If, indeed, the belief ever amounted
to an irresistible necessity, there would
then be no use in appealing from it,
because there would be no possibility
of altering it. But even then the
truth of the belief would not foUow ;

it would only follow that mankind
were under a permanent necessity of
believing what might possibly not
be true ; in other words, that a case
might occur in which our senses or
consciousness, if they could be ap-
pealed to, might testify one thing and
our reason believe another. But in
fact there is no such permanent neces-
sity. There is no proposition of which
it can be asserted that every human
mind must eternally and irrevocably
believe it. Many of the propositions
of which this is most confidently
stated great numbers of human beings
have disbelieved. The things which
it has been supposed that nobody
could possibly help believing are in-
numerable ; but no two generations
would make out the same catalogue
of them. One age or nation believes
implicitly what to another seems in-
credible and inconceivable ; one indi-
vidual has not a vestige of a belief
which another deems to be absolutely
inherent in humanity. There is not
one of these supposed instinctive be-
liefs which is really inevitable. It is
in the power of every one to cultivate
habits of thought which make him
independent of them. The habit of
philosophical analysis, (of which it is
the surest effect to enable the mind
to command, instead of being com-
manded by, the laws of the merely
passive part of its own nature,) by
showing to us that things are not
necessarily connected in fact because
their ideas are connected in our minds,
is able to loosen innumerable associa-
tions which reign despotically over
the undisciplined or early-prejudiced
mind. And this habit is not without
power even over those associations
which the school of which I have
been speaking regard as connate and
instinctive. I am convinced that any
one accustomed to abstraction and
analysis, who will fairly exert his
faculties for the purpose, will, when
his imagination has once learnt to
entertain the notion, find no difficulty
in conceiving that in some one, for
instance, of the many firmaments

EVIDE^X^E OF UNIVERSAL CAUSATION.

571

into which sidereal astronomy now
divides the universe, events may suc-
ceed one another at random without
any fixed law ; nor can anything in
our experience, or in our mental
nature, constitute a sufficient, or in-
deed any, reason for believing that
this is nowhere the case.

Were we to suppose (what it is per-
fectly possible to imagine) that the
present order of the universe were
brought to an end, and that a chaos
succeeded in which there was no fixed
succession of events, and the past gave
no assurance of the future ; if a human
being were miraculously kept alive to
witness this change, he surely would
soon cease to believe in any uniformity,
the uniformity itself no longer exist-
ing. If this be admitted, the belief
in uniformity either is not an instinct,
or it is an instinct conquerable, like
all other instincts, by acquired know-
ledge.

But there is no need to speculate
on what might be, when we have
positive and certain knowledge of
what has been. It is not true as a
matter of fact that mankind have
always believed that all the succes-
sions of events were uniform and
according to fixed laws. The Greek
philosophers, not even excepting
Aristotle, recognised Chance and
Spontaneity {tOxv and t6 avroixaTov)
as among the agents in nature ; in
other words, they believed that to
that extent there was no guarantee
that the past had been similar to
itself, or that the future would re-
semble the past. Even now a full
half of the philosophical world, in-
cluding the very same metaphysicians
who contend most for the instinctive
character of the belief in uniformity,
consider one important class of phe-
nomena, volitions, to be an exception
to the uniformity, and not governed
by a fixed law.*

* I am happy to be able to qtiote the fol-
lowing excellent passnge from Mr. Badun
Powell's Essoy on the Inductive Pkiloxopht/,
in confirmation, both in regard to history
and to doctrine, of the statement made in
the text. Speaking of the "conviction of

§ 2. As was observed in a former
place,* the belief we entertain in the
universality, throughout nature, of
the law of cause and effect, is itself
an instance of induction, and by no
means one of the earliest which any
of us, or which mankind in general,

\
the universal and permanent uniformity
of nature," Mr, Powell says (pp. 98-100) —

" We may remark that tliis idea, in its
proper extent, ia by no means one of
popular acceptance or natural growth.
Just so far as the daily experience of
every one goes, so far indeed he coUies to
enibnce a certain persuasion of this kind,
but merely to this limited extent, that
what is going on around him at present,
in his own narrow sphere of observation,
will go on in like manner in future. The
peasant believes that the sun which rose,
to-day will rise again to-morrow ; that the
seed put into the ground will be followed
in due time by the luirvest this year as it
was last year, and the like, but ha.s no no-
tion of such inferences in subjects beyond
his immed late observation. A nd it should
be observed that each class of persons, in
admitting this belief within the limited
range of his own experience, though ha
doubt or deny it in everything beyond, in,
in fact, licariiig unconscious testimony to
its universal truth. Nor, again, is it only
among the most ignoraiit that this limitar
tiou is put upon the truth. There is a
very general propensity to believe that
everything beyond common experience,
or especially ascertained laws of nature, la,
left to the dominion of chance or fate or
arbitrary intervention, and even to object
to any attempted explanation by physical
causes, if conjecturally thrown out for an
appa' ently unaccountable phenomenon.

"The precise doctrine of the generalisa'
tion of this idea of the uniformity of nature,
so far from being obvious, natur.il, or in-
tuitive, is utterly beyond the attainment
of the many. In all the extent of its uni-
versality it is characteristic of the philo-
.^opher. It is clearly the result of philo-
sopliic cultivation and training, and by no
means tlie spontaneous offspring of any
primary principle naturally inherent in
the mind, as some seem to believe. It is
no mere vague persuasion taken up with-
out examination, as a common preposses-
sion to which we are always accustomed ;
on the contrary, all common prejudices
and associations are against it. It is pre-
eminently an acquired idea. It is not at-
tained without deep study and reflection.
The best-mfoiToed philosopher is the man
who most fiimly believes it, even in op-
position to received notions; its acceptance
depends on the extent and profoundness
of his inductive studies."

* Supra, book iii. ch. iii. § j.

372

INDUCTION.

can have made. We arrive at this
universal law by generalisation from
many laws of inferior generality. We
should never have had the notion of
causation (in the philosophical mean-
ing of the term) as a condition of
all phenomena, unless many cases of
causation, or, in other words, many
partial uniformities of sequence, had
previously become familiar. The
more obvious of the particular uni-
formities suggest, and give evidence
of, the general uniformity, and the
general uniformity, once established,
enables us to prove the remainder of
the particular uniformities of which
it is made up. As, however, all
rigorous processes of induction pre-
suppose the general uniformity, our
knowledge of the particular uniformi-
ties from which it was first inferred
was not, of course, derived from
rigorous induction, but from the loose
and uncertain mode of induction per
enumei'ationem simplicem; and the
law of universal causation, being
collected from results so obtained,
cannot itself rest on any better
foundation.

It would seem, therefore, that in-
duction pet' enumerationem simplicem
not only is not necessarily an illicit
logical process, but is in reality the
only kind of induction possible ; since
the more elaborate process depends
for its validity on a law, itself ob-
tained in that inartificial mode. Is
there not then an inconsistency in con-
trasting the looseness of one method
with the rigidity of another, when
that other is indebted to the looser
method for its own foundation ?

The inconsistency, however, is only
apparent. Assuredly, if induction by
simple entimeration were an invalid
process, no process grounded on it
could be valid ; just as no reliance
could be placed on telescopes if we
could not trust our eyes. But though
a valid process, it is a fallible one,
and fallible in very different degrees :
if therefore we can substitute for the
more fallible forms of the process an
operation grounded on the same pro-

cess in a less fallible form, we shall
have effected a very material improve-
ment. And this is what scientific in-
duction does.

A mode of concluding from ex-
perience must be pronounced untrust-
worthy when subsequent experience
refuses to confirm it. According to
this criterion, induction by simple
enumeration — in other words, gene-
ralisation of an observed fact from
the mere absence of any known in-
stance to the contrary — affords in
general a precarious and unsafe ground
of assurance ; for such generalisations
are incessantly discovered, on further
experience, to be false. Still, how-
ever, it affords some assurance, suffi-
cient, in many cases, for the ordinary
guidance of conduct. It would be
absurd to say that the generalisations
arrived at by mankind in the outset
of their experience, such as these.
Food nourishes, Fire burns. Water
drowns, were unworthy of reliance.*
There is a scale of trustworthiness in
the results of the original unscientific
Induction ; and on this diversity (as

* It deserves remark, that these early-
generalisations did not, like scientific in-
ductions, presuppose causation. What they
did presuppose, was uniformity in physical
facts. But the obsei-vers were as ready to
presume uniformity in the co-existences of
facts as in the sequences. On the other
hand, they never thought of assuming that
this uniformity was a pi'inciple pervading
all nature ; their generalisations did not
imply that there was unifoi mity in every-
thing, but only that as much uniformity as
existed within their observation, existed
also beyond it. The induction, Fire burns,
does not require for its validity that all na-
ture should observe uniform laws, but only
that there should be uniformity in one par-
ticular class of natuial phenomena; the
effects of fire on the senses and on com-
bustible substances. And uniformity to
this extent was not assumed, anterior to
the experience, but proved by the ex-
perience. The same observed instances
which proved the narrower truth, proved
as much of the wider one as corresponded
to it. It is from losing sight of this fact,
and con-sidering the law of causation in its
full extent as necessarily presupposed in
the very earliest generalisations, that per-
sons, have been led into the belief that the
law of causation is known d priori, and is
not itsulf a conclusion from experience.

EVIDENCE OF tlNlVERSAL CAUSATION.

375

observed in the fourth chapter of the
present book) depend the rules for
the improvement of the process. The
improvement consists in correcting
one of these inartificial generalisations
by means of another. As has been
already pointed out this is all that
art can do. To test a generalisation,
by showing that it either follows from,
or conflicts with, some stronger induc-
tion, some generalisation resting on a
broader foundation of experience is
the beginning and end of the logic of
Induction.

§ 3. Now the precariousness of the
method of simple enumeration is in
an inverse ratio to the largeness of
the generalisation. The process is
delusive and insufficient, exactly in
proportion as the subject-matter of
the observation is special and limited
in extent. As the sphere widens, this
unscientific method becomes less and
less liable to mislead ; and the most
universal class of truths, the law of
causation for instance, and the princi-
ples of number and of geometry, are
duly and satisfactorily proved by that
method alone, nor are they susceptible
of any other proof.

With respect to the whole class of
generalisations of which we have
recently treated, the uniformities
which depend on causation, the truth
of the remark just made follows by
obvious inference from the principles
laid down in the preceding chapters.
When a fact has been observed a
certain number of times to be true,
and is not in any instance known to
be false ; if we at once affirm that
fact as an universal truth or law of
nature, without either testing it by
any of the four methods of induction,
or deducing it from other known laws,
we shall in general err grossly ; but
we are perfectly justified in affirming
it as an empirical law, true within
certain limits of time, place, and
circumstance, provided the number of
coincidences be greater than can with
any probability be ascribed to chance.
The reason for not extending it be-

yond those limits is, that the fact of
its holding true within them may be
a consequence of collocations, which
cannot be concluded to exist in one
place because they exist in another ;
or may be dependent on the accidental
absence of counteracting agencies,
which any variation of time, or the
smallest change of circumstances, may
possibly bring into play. If we sup-
pose, then, the subject-matter of any
generalisation to be so widely diffused
that there is no time, no place, and no
combination of circumstances, but
must afford an example either of its
truth or of its falsity, and if it be never
found otherwise than true, its truth
cannot be contingent on any colloca-
tions, unless such as exist at all times
and places ; nor can it be frustrated
by any counteracting agencies, unless
by such as never actually occur. It
is, therefore, an empirical law co-ex-
tensive with all human experience, at
which point the distinction between
empirical laws and laws of nature
vanishes, and the proposition takes
its place among the most firmly estab-
lished as well as largest truths ac-
cessible to science.

Now, the most extensive in its
subject-matter of all generalisations
which experience warrants, respecting
the sequences and co-existences of
phenomena, is the law of causation.
It stands at the head of all observed
uniformities in point of universality,
and therefore (if the preceding obser-
vations are correct) in point of cer-
tainty. And if we consider, not what
mankind would have been justified
in believing in the infancy of their
knowledge, but what may rationally
be believed in its present more ad-
vanced state, we shall find ourselves
warranted in considering this funda-
mental law, though itself obtained
by induction from particular laws of
causation, as not less certain, but, on
the contrary, more so, than any of
those from which it was drawn. It
adds to them as much proof as it
receives from them. For there is
probably no one even of the best

374

INDtrcTION.

established laws of causation which
is not sometimes counteracted, and
to which, therefore, apparent excep-
tions do not present themselves, which
would have necessarily and justly
shaken the confidence of mankind in
the universality of those laws, if in-
ductive processes founded on the uni-
versal law had not enabled us to refer
those exceptions to the agency of
counteracting causes, and thereby re-
concile them with the law with which
they apparently conflict. Errors,
moreover, may have slipped into the
statement of any one of the special
laws, through inattention to some
material circumstance ; and instead
of the true proposition, another may
have been enunciated, false as an
universal law, though leading, in all
cases hitherto observed, to the same
result. To the law of causation, on
the contrary, we not only do not know
of any exception, but the exceptions
which limit or apparently invalidate
the special laws, are so far from con-
tradicting the universal one, that
they confirm it ; since in all cases
which are sufficiently open to our
observation, we are able to trace the
difference of result, either to the ab-
sence of a cause which had been
present in ordinary cases, or to the
presence of one which had been
absent.

The law of cause and effect, being
thus certain, is capable of imparting
its certainty to all other inductive
propositions which can be deduced
from it ; and the narrower inductions
may be regarded as receiving their
ultimate sanction from that law, since
there is no one of them which is not
rendered more certain than it was
before, when we are able to connect
it with that larger induction, and to
show that it cannot be denied, con-
sistently with the law that everything
which begins to exist has a caiise.
And hence we are justified in the
Beeming inconsistency of holding in-
duction by simple enumeration to be
good for proving this general truth,
the foundation of scientific induction,

and yet refusing to rely on it for any
of the narrower inductions. I fully
admit that if the law of causation
were unknown, generalisation in the
more obvious cases of uniformity in
phenomena would nevertheless be
possible, and though in all cases more
or less precarious, and in some ex-
tremely so, would suffice to constitute
a certain measure of probability ; but
what the amount of this probability
might be we are dispensed from esti-
mating, since it never could amount
to the degree of assurance which the
proposition acquires, when, by the
application to it of the Four Methods,
the supposition of its falsity is shown
to be inconsistent with the Law of
Causation. We are therefore logi-
cally entitled, and, by the necessities
of scientific induction, required to
disregard the probabilities derived
from the early rude method of gene-
ralising, and to consider no minor
generalisation as proved except so far
as the law of causation confirms it,
nor probable except so far as it may
reasonably be expected to be so con-
firmed.

§ 4. The assertion that our in-
ductive processes assume tie law of
causation, while the law of causation
is itself a case of induction, is a para-
dox, only on the old theory of reason-
ing, which supposes the universal
truth, or major premise, in a ratioci-
nation, to be the real proof of the
particular truths which are ostensibly
inferred from it. According to the
doctrine maintained in the present
treatise,* the major premise is not
the proof of the conclusion, but is
itself proved, along with the conclu-
sion, from the same evidence. "All
men are mortal" is not the proof
that 7ord Palmerston is mortal ; but
our past experience of mortality
authorises us to infer both the general
truth and the particular fact, and the
one with exactly the same degree of
assurance as the other. The mor-

* Book ii. chap. iii.

EVIDENCE OF tJNIVERSAL CAUSATION.

375

tality of Lord Palmerston is not an
inference from the mortality of all
men, but from the experience which
proves the mortality of all men ; and
is a correct inference from experience,
if that general truth is so too. This
relation between our general beliefs
and their particular application holds
equally true in the more compre-
hensive case which we are now dis-
cussing. Any new fact of causation
inferred by induction is rightly in-
ferred, if no other objection can be
made to the inference than can be
made to the general truth that every
event has a cause. The utmost cer-
tainty which can be given to a con-
clusion arrived at in the way of in-
ference stops at this point. When
we have ascertained that the parti-
cular conclusion must stand or fall
with the general uniformity of the
laws of nature — that it is liable to
no doubt except the doubt whether
every event has a cause — we have
done all that can be done for it. The
strongest assurance we can obtiiin of
any theory respecting the cause of a
given phenomenon is that the pheno-
menon has either that cause or none.

The latter supposition might have
been an admissible one in a very
early period of our study of nature.
But we have been able to perceive
that in the stage which mankind
have now reached the generalisation
which gives the Law of Universal
Causation has grown into a stronger
and better induction, one deserving
of greater reliance than any of the
subordinate generalisations. We may
even, I think, go a step farther than
this, and regard the certainty of that
great induction as not merely com-
parative, but, for all practical pur-
poses, complete.

The considerations which, as I ap-
prehend, give, at the present day, to
the proof of the law of uniformity of
succession as true of all phenomena
without exception, this character of
completeness and conclusiveness, are
the following : — First, that we now
know it directly to be true of far the

greatest number of phenomena ; that
there are none of which we know it
not to be true, the utmost that can be
said being, that of some we cannot
positively from direct evidence affirm
its truth ; while phenomenon after
phenomenon, as they become better
known to us, are constantly passing
from the latter class into the former ;
and in all cases in which that transi-
tion has not yet taken place, the
absence of direct proof is accounted
for by the rarity or the obscurity of
the phenomena, our deficient means
of observing them, or the logical diffi-
culties arising from the complication
of the circumstances in which they
occur ; insomuch that, notwithstand-
ing as rigid a dependence on given
conditions as exists in the case of any
other phenomenon, it was not likely
that we should be better acquainted
with those conditions than we are.
Besides this first class of considera-
tions, there is a second, which still
further corroborates the conclusion.
Although there are phenomena the
production and changes of which
elude all our attempts to reduce
them universally to any ascertained
law ; yet in every such case the phe-
nomenon, or the objects concerned
in it, are found in some instances to
obey the known laws of nature. The
wind, for example, is the type of un-
certainty and caprice, yet we find it
in some cases obeying with as much
constancy as any phenomenon in
nature the law of the tendency of
fluids to distribute themselves so as
to equalise the pressure on every side
of each of their particles ; as in the
case of the trade winds and the mon-
soons. Lightning might once have
been supposed to obey no laws ; but
since it has been ascertained to be
identical with electricity, we know
that the very same phenomenon in
some of its manifestations is impli-
citly obedient to the action of fixed
causes. I do not believe that there
is now one object or event in all our
experience of nature, within the
bounds of the solar system at least,

376

INDUCTION.

which has not either been ascertained
by direct observation to follow laws
of its own, or been proved to be
closely similar to objects and events
which, in more familiar manifesta-
tions, or on a more limited scale,
follow strict laws : our inability to
trace the same laws on a larger scale
and in the more recondite instances
being accounted for by the number
and complication of the modifying
causes, or by their inaccessibility to
observation.

The progress of experience, there-
fore, has dissipated the doubt which
must have rested on the universality
of the law of causation while there
were phenomena which seemed to be
sui generis, not subject to the same
laws with any other class of pheno-
mena, and not as yet ascertained to
have peculiar laws of their own. This
great generalisation, however, might
reasonably have been, as it in fact
was, acted on as a probability of the
highest order, before there were suffi-
cient grounds for receiving it as a
certainty. In matters of evidence,
as in all other human things, we
neither require, nor can attain, the
absolute. We must hold even our
strongest convictions with an opening
left in our minds for the reception of
facts which contradict them ; and
only when we have taken this pre-
caution, have we earned the right' to
act upon our convictions with com-
plete confidence when no such con-
tradiction appears. Whatever has
been found true in innumerable in-
stances, and never found to be false
after due examination in any, we are
safe in acting on as universal pro-
visionally, until an undoubted excep-
tion appears ; provided the nature of
the case be such that a real exception
could scarcely have escaped notice.
When every phenomenon that we ever
knew sufficiently well to be able to
answer the question had a cause on
which it was invariably consequent,
it was more rational to suppose that
our inability to assign the causes
of other phenomena arose from our

ignorance, than that there were phe-
nomena which were uncaused, and
which happened to be exactly those
which we had hitherto had no suffi-
cient opportunity of studying.

It must, at the same time, be re-
marked, that the reasons for this re-
liance do not hold in circumstances
unknown to us, and beyond the pos-
sible range of our experience. In
distant parts of the stellar regions,
where the phenomena may be entirely
unlike those with which we are ac-
quainted, it would be folly to affirm
confidently that this general law pre-
vails, any more than those special
ones which we have found to hold
universally on our own planet. The
uniformity in the succession of events,
otherwise called the law of causation,
must be received not as a law of the
universe, but of that portion of it
only which is within the range of our
means of sure observation, with a
reasonable degree of extension to ad-
jacent cases. To extend it further la
to make a supposition without evi-
dence, and to which, in the absence
of any ground from experience for
estimating its degree of probability,
it would be idle to attempt to assign
any.*

* One of the most rising thinkers of the
new generation in France, M. Taine, (who
has given, in the Revue des Deux Mondes,
the most masterly analysis, at least in one
point of view, ever made of the present
work,) though he rejects, on this and simi-
lar points of psychology, the intuition
theory in its ordinary form, nevertheless
assigns to the law of causation, and to
some other of the most universal laws, that
certainty beyond the bounds of human ex-
perience, which I have not been able to
accord to them. He does this on the faith
of our faculty of abstraction, in which he
seems to recognise an independent source
of evidence, not indeed disclosing truths
not contained in our experience, but afford-
ing an assurance which experience cannot
give, of the univers^ality of those which it
does contain. By abstraction M. Taino
seems to think that we are able, not
merely to analyse that part of nature
which we see, and exhibit apart the ele-
ments which pervade it, but to distinguish
such of them as are elements of the system
of nature considered as a whole, not inci-
dents belonging to our limited terrestrial
experience. I am not sure that I fully enter

00-teXtSTENCES mDEPBNDBNT Of CAtTSATlON. 377

CHAPTEB XXII.

OF DNirORMITIES OF CO-EXISTENCE
NOT DEPENDENT ON CAUSATION.

§ I, The order of the occurrence of
phenomena in time is either succes-
sive or simultaneous ; the uniformities,

into M. Taine's meaning ; but I confess I
do not see how any mere abstract concep-
tion, elicited by our minds from our ex-
perience, can be evidence of an objective
fact in universal nature, beyond what the
experience itself bears witness of ; or how,
in the process of interpreting in general
language the testimony of experience, the
limitations of the testimony itself can be
cast off.

• Dr. Ward, in an able article in the Dublin
Revieio for October 1871, contends that the
xmifomiity of nature cannot be proved
from experience, but from "transcen-
dental considerations " only, and that, con-
sequently, all physical science would be
deprived of its basis if such transcendental
proof were impossible.

When physical science is said to depend
on the assumption that the course of nature
is invariable, all that is meant is that the
conclusions of physical science are not
known as absolute ti-uths ; the truth of
them is conditional on the uniformity of
the course of nature ; and all that the most
conclusive observations and experiments
can prove, is that the result arrived at will
be true if, and as long as, the present laws
«)f natuie arc valid. But this is all the
assurance we require for the guidance of
our conduct. Dr. Ward himself does not
think that his transcendental proofs make
it practically greater ; for he believes, as a
Catholic, that the course of nature not only
has been, but frequently, and even daily is,
suspended by supernatural intervention.

But though this conditional conclusive-
ness of the evidence of experience, which
is sufficient for the purposes of life, is all
that I was necessarily concerned to prove,
I have given reasons for thinking that the
uniformity, as itself a part of experience,
is sufficiently proved to justify undoubting
reliance on it. This Dr. Ward contests,
for the following reasons : —

First, (p. 315) supposing it true that there
has hitherto been no well-authenticated
case of a breach in the uniformity of
nature, "the number of natural agents
constantly at work is incalculably large ;
and the observed eases of uniformity in
their action must be immeasurably fewer
than one-thousandth of the whole. Scien-
tific men, we assume for the moment, have
discovered that in a certain proportion of
instances — immeasurably fewer than one-
thousandth of the whole — a certain fact
haa picvaikd, the fact of uniformity ; and

therefore, which obtain in their occur-
rence, are either uniformities of succes-
sion or of co-existence. Uniformities
of succession are all comprehended
under the law of causation and its
consequences. Every phenomenon
has a cause, which it invariably fol-
lows ; and from this are derived other

they have not found a single instance in
which that fact does yiot prevail. Are they
justified, we ask, in infeiring from these
premises that the fact is universal ? Surely
the question answers itself. Let us mako
a very grotesque supposition, in which,
however, the conclusion would really bo
tiled according to the arguments adduced.
In some desert of Africa there is an enor-
mous connected edifice, surrounding somo
vast space, in which dwell certain reason-
able beings, who are unable to leave tho
enclosure. In this edifice are more than
a thousand chambers, which some years
asjo were entirely locked up, and the keys
no one knew where. By constant dili-
gence twenty-five keys have been found out
of the whole number, and the correspond-
ing chambers, situated promiscuously
throughout the edifice, have been opened.
Each chamber, when examined, is found
to be in the precise shape of a dodecahe-
dron. Are the inhabitants justified on that
account in holding with certitude that tho
remaining 975 chambers are built on tho
same plan ? "

Not with perfect certitude, but (if tho
chambers to which the keys have been
found are really " situated promiscu-
ously") with so high a degree of proba-
bility that they wotild be justified iii
acting upon the presumption until an ex-
ception appeared.

Dr. Ward's argument, however, does not
touch mine as it stands in the text. My
argviment is grounded on the fact that tho
uniformity of t h e course of nature as a wh olo
is constituted by the uniform sequences
of special efifects from special natural
agencies ; that the number of these natural
agencies in the part of the Universe known
to us is not incalculable, nor even extremely
gi-eat ; that we have now reason to think
that at least the far greater number of
them, if not separately, at least in some of
the combinations into which they enter,
have been made sufficiently amenable to
observation, to have enabled us actually to
ascertain some of their fixed laws ; and
that this amount of experience justifies
the same degree of as-urance that tho
course of natuie is uniform throughout,
which we previously had of the uniformity
of sequence among the phenomena best
known to us. This view of the subject, if
correct, destroys the force of Dr. Ward's
first argument.

His second argument is, that many or

378

INDFCTION.

invariable sequences among the suc-
cessive stages of the same effect, as
well as between the effects resulting
from causes which invariably succeed
one another.

In the same manner with these
derivative uniformities of succession,
a great variety of uniformities of co-
existence also take their rise. Co-
ordinate effects of the same cause
naturally co-exist with one another.
High water at any point on the earth's
surface, and high water at the point
diametrically opposite to it, are effects
uniformly simultaneous, resulting
from the direction in which the com-
bined attractions of the sun and moon
act upon the waters of the ocean. An
eclipse of the sun to us, and an eclipse
of the earth to a spectator situated in
the moon, are in like manner pheno-
mena invariable co-existent ; and their

most persons, both scientific and unscien-
tific, believe that there are well-authenti-
cated cases of breach in the uniformity of
nature, namely, miracles. Neither does this
consideration touch what I have said in the
text. I admit no other uniformity in tiie
events of nature than the law of Causation ;
and (as I have explained in the chapter of
this volume which treats of the Groimds
of Disbelief) a miracle is no exception to
that law. In every case of alleged miracle,
a new antecedent is affirmed to exist ; a
counteracting cause, namely, the volition of
a supernatural being. To all, therefore, to
whom beings with superhuman power over
nature are a vera causa, a miracle is a case
of the Law of Universal Causation, not a
deviation from it

Dr. Ward's last, and, as he says, strongest
argument, is the familiar one of Reid,
Stewart, and their followers — that what-
ever knowledge experience gives us of the
past and present, it uives us none of the
future. I confess that I see no force what-
ever in this argument. Wherein does a
future fact differ from a present or a past
fact, except in their merely momentary
rela:tioii to the human beings at present in
existence ? The answer made by Priestley,
in his examination of Reid, seems to me
sufficient, viz., that though we have had
no experience of what is future, we have
had abundant experience of wliat ua*
future. The "leap in th« dark" (ag Pro-
les.sor Bain call* it) from the past to the
future is exactly as mucli in the dark, and
no more, as the leap from a past which we
liave personally observed to a past which
we have not. I agi'ee with Mr. Bain in the
©pinion that the resemblance of what we

co-existence can equally be deduced
from the laws of their production.

It is an obvious question, therefore,
whether all the uniformities of co-
existence among phenomena may not
be accounted for in this manner. And
it cannot be doubted that between
phenomena which are themselves
effects, the co-existences must neces-
sarily depend on the causes of those
phenomena. If they are effects im-
mediately or remotely of the same
cause, they cannot co-exist except by
virtue of some laws or properties of
that cause : if they are effects of dif-
ferent causes, they cannot co-exist un-
less it be because their causes co-exist ;
and the uniformity of co-existence,
if such there be, between the effects,
proves that those particular causes,
within the limits of our observation,
have uniformly been co-existent.

have not experienced to what we have, is,
by a law of our nature, presumed thiough
the mere energy of the idea, before ex-
perience has proved it. This psychological
truth, however, is not, as Dr. Ward when
criticising Mr. Bain appears to think, in-
consistent with tlie logical truth that ex-
perience does prove it. The proof comes
after the piesumption, and consists in its
invariable verificatioii by experience when
tile experience arrives. The fact which
while it was future could not be observed,
having as yet no existence, is always, when
it becomes present and can be observed,
found conformable to the past.

Dr. M'Cosh maintains {Examination of
Mr. J. S. Mill's Philosophy, p. 257) that the
uniformity of the course of nature is a
different thing from the law of causation ;
and while he allows that the foi-mer is only
proved by a long continuance of experience,
and that it is not inconceivable nor neces-
sarily incredible that there may be worlds
in which it does not prevail, he considers
the law of causation to be known intui-
tively. There is, however, no other uni-
fomiiry in the events of nature than that
which arises from the law of causation :
so long therefore as there remained any
doubt that the coiirse of nature was u 1 dform
throughout, at least when not modified by
the intervention of a new (supernatural)
cause, a doubt was necessarily implied, not
indeed of the reality of cau-sation, but of it«
universality. If the uniformity of the
course of nature has any exceptions— if
any events succeed one another without
fixed Liws — to that extent the law of causa-
tion faiLs : tiiere are events which do not
depend on causes.

CO-EXISTENCES INDEPENDENT OF CAUSATION.

379

§ 2. But these same considerations
compel us to recognise that there
must be one class of co-existences
which cannot depend on causation ;
the co-existencea between the ulti-
mate properties of things — those pro-
perties which are the causes of all
phenomena, but are not themselves
caused by any phenomenon, and a
cause for which could only be sought
by ascending to the origin of all
things. Yet among these ultimate
properties there are not only co-exist-
ences, but uniformities of co-existence.
General propositions may be, and are,
formed, which assert that whenever
certain properties are found, certain
others are found along with them.
We perceive an object ; say, for in-
stance, water. We recognise it to be
water, of course, by certain of its pro-
perties. Having recognised it, we
are able to iffirm of it innumerable
other properties, which we could not
do unless it were a general truth,
a law or uniformity in nature, that
the set of properties by which we
identify the substance as water al-
ways have those other properties con-
joined with them.

In a fonner place,* it has been ex-
plained in some detail what is meant
by the Kinds of objects ; those classes
which differ from one another not by
a limited and definite, but by an in-
definite and unknown, number of dis-
tinctions. To this we have now to
add, that every proposition by which
anything is asserted of a Kind, affirms
an uniformity of co-existence. Since
we know nothing of Kinds but their
properties, the Kind, to us, is the set of
properties by which it is identified, and
which must of course be sxifficient to
distinguish it from every other kind.t

* Book i. chap. viL

t In some cases, a Kind is sufficiently
identified by 8ome one remarkable pro-
perty ; but most commonly sevenil are re-
quired, each property, considered lingly,
being a joint property of that and of other
Kinds. The colour and brightness of the
diamond are common to it with the p.iste
from which false diamonds are made ; its
eictohedral form is common to it with alum
and magnetic iron ore ; but the colour and

In affirming anything, therefore, of a
Kind, we are affirming something to
be uniformly co-existent with the pro-
perties by which the kind is recog-
nised ; and that is the sole meaning
of the assertion.

Among the uniformities of co-exist-
ence which exist in nature, may hence
be numbered all the properties of
Kinds. The whole of these, however,
are not independent of causation, but
only a portion of them. Some are
ultimate properties, others derivative ;
of some, no cause can be assigned,
but others are manifestly dependent
on causes. Thus, pure oxygen gas is
a Kind, and one of its most un-
equivocal properties is its gaseous
form : this property, however, has for
its cause the presence of a certain
quantity of latent heat ; and if that
heat co\ild be taken away, (as has
been done from so many gases in
Faraday's experiments,) the gaseoue
form would doubtless disappear, to-
gether with numerous other properties
which depend on, or are caused by,
that property.

In regard to all substances which
are chemical compounds, and which
therefore may be regarded as products
of the juxtaposition of substances
different in Kind from themselves,
there is considerable reason to pre-
sume that the specific properties of
the compound are consequent, as
effects, on some of the properties of
the elements, though little progress
has yet been made in tracing any
invariable relation between the latter
and the former. Still more strongly
will a similar presumption exist when
the object itself, as in the case of
organised beings, is no primeval agent,
but an effect, which depends on a
cause or causes for its very existence.
The Kinds therefore which are called

brightness and the form together identify
its KinI, that is, are a mark to ug that it
is combustible ; that when burnt it pro-
duces carbonic acid ; that it cannot be cut
with any known substance ; together with
many other ascertained properties, and
the fact that there exist an indefinite num-
ber still unascertained.

3^

INDUCTION.

in chemistry simple substances, or
elementary natural agents, are the
only ones, any of whose properties
can with certainty be considered
ultimate ; and of these the ultimate
properties are probably much more
numerous than we at present recog-
nise, since every successful instance
of the resolution of the properties of
their compounds into simpler laws,
generally leads to the recognition of
properties in the elements distinct
from any previously known. The
resolution of the laws of the heavenly
motions established the previously
unknown ultimate property of a mu-
tual attraction between all bodies:
the resolution, so far as it has yet
proceeded, of the laws of crystallisa-
tion, of chemical composition, elec-
tricity, magnetism, &c., points to
various polarities, ultimately inherent
in the particles of which bodies are
composed ; the comparative atomic
weights of different kinds of bodies
were ascertained by resolving into
more general laws the uniformities
observed in the proportions in which
substances combine with one another ;
and so forth. Thus although every
resolution of a complex uniformity
into simpler and more elementary
laws has an apparent tendency to
diminish the number of the ultimate
properties, and really does remove
many properties from the list ; yet,
(since the result of this simplifying
process is to trace up an ever greater
variety of different effects to the same
agents,) the farther we advance in
this direction, the greater number of
distinct properties we are forced
to recognise in one and the same
object : the co-existences of which
properties must accordingly be ranked
among the ultimate generalities of
nature.

§ 3. There are, therefore, only two
kinds of propositions which assert
uniformity of co-existence between
properties. Either the properties
depend on causes, or they do not. If
they do, the proposition which affirms

them to be co- existent is a derivative
law of co-existence between effects,
and until resolved into the laws of
causation on which it depends, is an
empirical law, and to be tried by the
principles of induction to which such
laws are amenable. If, on the other
hand, the properties do not depend on
causes, but are ultimate properties ;
then if it be true that they invariably
co-exist, they must all be ultimate
properties of one and the same Kind ;
and it is of these only that the co-
existences can be classed as a peculiar
sort of laws of nature.

When we aflfirm that all crows are
black, or that all negroes have woolly
hair, we assert an uniformity of co-
existence. We assert that the pro-
perty of blackness, or of having woolly
hair, invariably co-exists with the
properties which, in common language,
or in the scientific classification that
we adopt, are taken to constitute the
class crow, or the class negro. Now,
supposing blackness to be an ultimate
property of black objects, or woolly
hair an ultimate property of the ani-
mals which possess it ; supposing that
these properties are not results of
causation, are not connected with
antecedent phenomena by any law ;
then if all crows are black, and all
negroes have woolly hair, these must
be ultimate properties of the Kind
croio or negro, or of some Kind which
includes them. If, on the contrary,
blackness or woolly hair be an effect
depending on causes, these general
propositions are manifestly empirical
laws ; and all that has already been
said respecting that class of generali-
sations may be applied without modi-
fication to these.

Now, we have seen that in the case
of all compounds — of all things, in
short, except the elementary sub-
stances and primary powers of nature
— the presumption is, that the pro-
perties do really depend upon causes ;
and it is impossible in any case what-
ever to be certain that they do not
We therefore should not be safe in
claiming for any generalisation re-

CO-EXISTENCES INDEPENDENT OF CAUSATION. 381

specting the co-existence of properties,
a degree of certainty to which, if the
properties should happen to be the
result of causes, it would have no
claim. A generalisation respecting
co-existence, or, in other words, re-
specting the properties of Kinds, may
be an ultimate truth, but it may, also,
be merely a derivative one ; and
since, if so, it is one of those deriva-
tive laws which are neither laws of
causation nor have been resolved into
the laws of causation on which they
depend, it can possess no higher de-
gree of evidence than belongs to an
empirical law.

§ 4. This conclusion will be con-
firmed by the consideration of one
great deficiency, which precludes the
application to the ultimate uniformi-
ties of co-existence of a system of
rigorous scientific induction, such as
the uniformities in the succession of
phenomena have been found to ad-
mit of. The basis of such a system
is wanting ; there is no general axiom,
standing in the same relation to the
uniformities of co-existence as the law
of causation does to those of succes-
sion. The Methods of Induction ap-
plicable to the ascertainment of causes
and effects are grounded on the prin-
ciple that everything which has a
beginning must have some cause or
other ; that among the circumstances
which actually existed at the time of
its commencement, there is certainly
some one combination on which the
effect in question is unconditionally
consequent, and on the repetition of
which it would certainly again recur.
But in an inquiry whether some Kind
(as crow) universally possesses a cer-
tain property (as blackness), there is
no room for any assumption analogous
to this. We have no previous cer-
tainty that the property must have
something which constantly co-exists
with it — must have an invariable co-
existent in the same manner as an
event must have an invariable ante-
cedent. When we feel pain, we must
be in some circumstances under which,

if exactly repeated, we should always
feel pain. But when we are conscious
of blackness, it does not follow that
there is something else present of
which blackness is a constant accom-
paniment. There is, therefore, no
room for elimination ; no Method of
Agreement or Difference, or of Con-
comitant Variations (which is but a
modification either of the Method of
Agreement or of the Method of Dif-
ference). We cannot conclude that
the blackness we see in crows must
be an invariable property of crows,
merely because there is nothing else
present of which it can be an in-
variable property. We therefore in-
quire into the truth of a proposition
like " All crows are black," under the
same disadvantage as if, in our in-
quiries into causation, we were com-
pelled to let in, as one of the possi-
bilities, that the effect may in that
particular instance have arisen with-
out any cause at all.

To overlook this grand distinction
was, as it seems to me, the capital
error in Bacon's view of inductive
philosophy. The principle of elimi-
nation, that great logical instrument
which he had the immense merit of
first bringing into general use, he
deemed applicable in the same sense,
and in as unqualified a manner, to
the investigation of the co-existences
as to that of the successions of pheno-
mena. He seems to have thought
that as every event has a cause or
invariable antecedent, so every pro-
perty of an object has an invariable
co-existent, which he called its Form ;
and the examples he chiefly selected
for the application and illustration of
his method were inquiries into such
Forms — attempts to determine in
what else all those objects resembled
which agreed in some one general
property, as hardness or softness,
dryness or moistness, heat or cold-
ness. Such inquiries could lead to
no result. The objects seldom have
any such circumstances in common.
They usually agree in the one point
inquired into, and in nothing else.

3S2

INDUCTION.

A great proportion of the properties
which, so far as we can conjecture,
are the likeliest to be really ultimate
would seem to be inherently pro-
perties of many different Kinds of
things, not allied in any other respect.
And as for the properties which, be-
ing efiFects of causes, we are able to
give some account of, they have gene-
rally nothing to do with the ultimate
resemblances or diversities in the ob-
jects themselves, but depend on some
outward circumstances, under the in-
fluence of which any objects what-
ever are capable of manifesting those
properties, as is emphatically the case
with those favourite subjects of Bacon's
scientific inquiries, hotness and cold-
ness, as well as with hardness and
softness, solidity and fluidity, and
many other conspicuous qualities.

In the absence, then, of any uni-
versal law of co-existence, similar to
the universal law of causation which
regulates sequence, we are thrown
back upon the unscientific induction
of the ancients, per enumerationem
simplicein ubi non reperitur instantia
coiitradictoria. The reason we have
for believmg that all crows are black
is simply that we have seen and heard
of many black crows, and never one
of any other colour. It remains to
be considered how far this evidence
can reach, and how we are to measure
its strength in any given case.

§ 5. It sometimes happens that a
mere change in the mode of verbally
enunciating a question, though nothing
is really added to the meaning ex-
pressed, is of itself a considerable step
towards its solution. This, I think,
happens in the present instance. The
degree of certainty of any generalisa-
tion which rests on no other evidence
than the agreement, so far as it goes,
of all past observation, is but another
phrase for the degree of improbability
that an exception, if any existed, could
have hitherto remained unobserved.
The reason for believing that all crows
are black is measured by the impro-
\)ability that crows of any other colour

should have existed to the present
time without our being aware of it.
Let us state the question in this last
mode, and consider what is implied
in the supposition that there may ba
crows which are not black, and under
what conditions we can be justified iu
regarding this as incredible.

If there really exist crows which
are not black, one of two things must
be the fact. Either the circumstance
of blackness, in all crows hitherto
observed, must be, as it were, an
accident, not connected with any
distinction of Kind ; or if it be a
property of Kind, the crows which
are not black must be a new Kind,
a Kind hitherto overlooked, though
coming under the same general de-
scription by which crows have hither-
to been characterised. The first sup-
position would be proved true if we
were to discover casually a white
crow among black ones, or if it were
found that black crows sometimes
turn white. The second would be
shown to be the fact if in Australia
or Central Africa a species or a race
of white or grey crows were found to
exist.

§ 6. The former of these supposi-
tions necessarily implies that the
colour is an effect of causation. If
blackness, in the crows in which it
has been observed, be not a property
of Kind, but can be present or absent
without any difference generally in
the properties of the object, then it
is not an ultimate fact in the indi-
viduals themselves, but is certainly
dependent on a cause. There are, no
doubt, many properties which vary
from individual to individual of the
same Kind, even the same infima
species, or lowest Kind. Some flowers
may be either white or red, without
differing in any other respect. But
these properties are not ultimate ;
they depend on causes. So far as
the properties of a thing belong to
its own nature, and do not arise from
some cause extrinsic to it, they are
ahvavs the same in the same Kind.

COEXISTENCES INDEPENDENT OF CAUSATION. 383

Take, for instance, all simple sub-
stances and elementary powers ; the
only things of which we are certain
that some at least of their properties
are really ultimate. Colour is gene-
rally esteemed the most rariable of
all properties ; yet we do not find
that sulphur is sometimes yellow and
sometimes white, or that it varies in
colour at all, except so far as colour
is the effect of some extrinsic cause,
as of the sort of light thrown upon it,
the mechanical arrangement of the
particles, (as after fusion,) &c. We
do not find that iron is sometim.es
fluid and sometimes solid at the same
temperature ; gold sometimes malle-
able and sometimes brittle ; that
hydrogen will sometimes combine
with oxygen and sometimes not ; or
the like. If from simple substances
we pass to any of their definite com-
pounds, as water, lime, or sulphuric
acid, there is the same constancy in
their properties. When properties
vary from individual to individual, it
is either in the case of miscellaneous
aggregations, such as atmospheric air
or rock, composed of heterogeneous
substances, and not constituting or
belonging to any real Kind,* or it is
in the case of organic beings. In
them, indeed, there is variability in
a high degree. Animals of the same
species and race, human beings of the
same age, sex, and country, will be
most different, for example, in face
and figure. But organised beings
(from the extreme complication of
the laws by which they are regulated)
being more eminently modifiable, that
is, liable to be influenced by a greater
number and variety of causes than
any other phenomena whatever, hav-
ing also themselves had a beginning,
and therefore a cause, there is reason
to believe that none of their properties
are ultimate, but all of them deriva-

* This doctrine of course asstimes that
the allotropic forms of what is chenucally
the same substance are so many different
Kinds ; and such, in the sense in which
the word Kind is used in tiu« treatise,
they really «re,

tive, and produced by causation. And
the presumption is confirmed by the
fact that the properties which vary
from one individual to another also
generally vary more or less at different
times in the same individual ; which
variation, like any other event, sup-
poses a cause, and implies, conse-
quently, that the properties are not
independent of causation.

If, therefore, blackness be merely
accidental in crows, and capable of
varying while the Kind remains the
same, its presence or absence is doubt-
less no ultimate fact, but the effect of
some unknown cause ; and in that
case the universality of the experience
that all crows are black is sufficient
proof of a common cause, and estab-
lishes the generalisation as an empiri-
cal law. Since there are innumerable
instances in the affirmative, and
hitherto none at all in the negative,
the causes on which the property
depends must exist everywhere in the
limits of the observations which have
been made ; and the proposition may
be received as universal within those
limits, and with the allowable degree
of extension to adjacent cases.

§ 7. If, in the second place, the
property, in the instances in which it
has been observed, is not an effect of
causation, it is a property of Kind ;
and in that case the generalisation
can only be set aside by the discovery
of a new Kind of crow. That, how-
ever, a peculiar Kind, not hitherto
discovered, should exist in nature, is
a supposition so often realised, that it
cannot be considered at all improbable.
We have nothing to authorise us in
attempting to limit the Kinds of
things which exist in nature. The
only unlikelihood would be that a
new Kind should be discovered in
localities which there was previously
reason to believe had been thoroughly
explored ; and even this improbability
depends on the degree of conspicuous-
ness of the difference between the
newly-discovered Kind and all others,
since new Kinds of minerals, plants,

384

INDUCTION.

and even animals, previously over-
looked or confounded with known
species, are still continually detected
in the most frequented situations.
On this second ground, therefore, as
well as on the first, the observed
uniformity of co-existence can only
hold good as an empirical law, within
the limits not only of actual observa-
tion, but of an observation as accu-
rate as the nature of the case re-
quired. And hence it is that (as re-
marked in an early chapter of the
present Book) we so often give up
generalisations of this class at the
first summons. If any credible wit-
ness stated that he had seen a white
crow, under circumstances which made
it not incredible that it should have
escaped notice previously, we should
give full credence to the statement.

It appears, then, that the unifor-
mities which obtain in the co-existence
of phenomena — those which we have
reason to consider as ultimate, no less
than those which arise from the laws
of causes yet undetected — are entitled
to reception only as empirical laws ;
are not to be presumed true except
within the limits of time, place, and
circumstance, in which the observa-
tions were made, or except in cases
strictly adjacent.

§ 8. We have seen in the last chap-
ter that there is a point of generality
at which empirical laws become as
certain as laws of nature, or rather,
at which there is no longer any dis-
tinction between empirical laws and
laws of nature. As empirical laws
approach this point, in other words, as
they rise in their degree of generality,
they become more certain ; their uni-
versality may be more strongly relied
on. For, in the first place, if they are
results of causation, (which, even in
the class of uniformities treated of in
the present chapter, we never can be
certain that they are not,) the more
general they are, the greater is proved
to be the space over which the neces-
sary collocations prevail, and within
which no causes exist capable of

counteracting the unknown causes on
which the empirical law depends. To
say that anything is an invariable
property of some very limited class of
objects, is to say that it invariably
accompanies some very numerous and
complex group of distinguishing pro-
perties ; which, if causation be at all
concerned in the matter, argues a com-
bination of many causes, and there-
fore a great liability to counterac-
tion ; while the comparatively narrow
range of the observations renders it
impossible to predict to what extent
unknown counteracting causes may be
distributed throughout nature. But
when a generalisation has been found
to hold good of a very large propor-
tion of all things whatever, it is al-
ready proved that nearly all the
causes which exist in nature have no
power over it ; that very few changes
in the combination of causes can
effect it, since the greater number of
possible combinations must have al-
ready existed in some one or other of
the instances in which it has been
found true. If, therefore, any em-
pirical law is a result of causation, the
more general it is, the more it may be
depended on. And even if it be no
result of causation, but an ultimate
co-existence, the more general it is,
the greater amount of experience it is
derived from, and the greater there-
fore is the probability that if excep-
tions had existed, some would already
have presented themselves.

For these reasons, it requires much
more evidence to establish an ex-
ception to one of the more general
empirical laws than to the more
special ones. We should not have
any difficulty in believing that there
might be a new Kind of crow, or a
new kind of bird resembling a crow
in the properties hitherto considered
distinctive of that Kind. But it
would require stronger proof to con-
vince us of the existence of a Kind of
crow having properties at variance
with any generally recognised univer-
sal property of birds ; and a still
higher degree if the properties con-

CO-EXISTENCES INDEPENDENT OF CAUSATION.

flict with any recognised universal
property of animals. And this is
conformable to the mode of judgment
recommended by the common sense
and general practice of mankind, who
are more incredulous as to any novel-
ties in nature, according to the degree
of generality of the experience which
these novelties seem to contradict.

§ 9. It is conceivable that the al-
leged properties might conflict with
some recognised universal property of
all matter. In that case their impro-
bability would be at the highest, but
would not even then amount to in-
credibility. There are only two known
properties common to all matter ; in
other words, there is but one known
uniformity of co-existence of proper-
ties, co-extensive with all physical
nature, namely, that whatever op-
poses resistance to movement, gravi-
tates ; or, as Professor Bain expresses
it, Inertia and Gravity are co-existent
through all matter, and proportionate
in their amount. These properties,
as he truly says, are not mutually im-
plicated ; from neither of them could
we, on grounds of causation, presume
the other. But, for this very reason,
we are never certain that a Kind may
not be discovered possessing one of the
properties without the other. The
hypothetical ether, if it exists, may
be such a Kind. Our senses cannot
recognise in it either resistance or
gravity ; but if the reality of a resist-
ing medium should eventually be
proved, (by alteration, for example, in
the times of revolution of periodic
comets, combined with the evidences
afforded by the phenomena of light
and heat,) it would be rash to con-
clude from this alone, without other
proofs, that it must gravitate.

For even the greater generalisa-
tions which embrace comprehensive
Kinds containing under them a great
number and variety of injimce species,
are only empirical laws, resting on
induction by simple enumeration
merely, and not on any process of
elimination, a process wholly inappli-

cable to this sort of case. Such gene-
ralisations, therefore, ought to be
grounded on an examination of all
the injimce species comprehended in
them, and not of a portion only. We
cannot conclude (where causation is
not concerned) because a proposition
is true of a number of things resem-
bling one another only in being ani-
mals, that it is therefore true of all
animals. If, indeed, anything be
true of species which differ more from
one another than either differs from
a third, (especially if that third spe-
cies occupies in most of its known
properties a position between the two
former,) there is some probability that
the same thing will also be true of
that intermediate species ; for it is
often, though by no means universally
found, that there is a sort of paral-
lelism in the properties of different
Kinds, and that their degree of unlike-
ness in one respect bears some propor-
tion to their unlikeness in others. We
see this parallelism in the properties of
the different metals ; in those of sul-
phur, phosphorus, and carbon ; of chlo-
rine, iodine, and bromine , in the natu-
ral orders of plants and animals, &c.
But there are innumerable anomalies
and exceptions to this sort of confor-
mity ; if indeed the conformity itself
be anything but an anomaly and an
exception in nature.

Universal propositions, therefore,
respecting the properties of superior
Kinds, unless grounded on proved or
presumed connection by causation,
ought not to be hazarded except after
separately examining every known
sub-kind included in the larger Kind.
And even then such generalisations
must be held in readiness to be given
up on the occurrence of some new
anomaly, which, when the uniformity
is not derived from causation, can
never, even in the case of the most
general of these empirical laws, be
considered very improbable. Thus
all the universal propositions which
it has been attempted to lay down
respecting simple substances, or con-
cerning any of the classes which have
2 B

386 INDUCTION.

been formed among simple substances,
(and the attempt has been often
made,) have, with the progress of
experience, either faded into inanity,
or been proved to be erroneous ; and
each Kind of simple substance re-
mains with its own collection of pro-
perties apart from the rest, saving a
certain parallelism with a few other
Kinds, the most similar to itself. In
organised beings, indeed, there are
abundance of propositions ascertained
to be universally true of superior
genera, to many of which the discovery
hereafter of any exceptions must be
regarded as extremely improbable.
But these, as already observed, are,
we have every reason to believe, pro-
perties dependent on causation.*

* Professor Bain {Logic, ii. 13) mentions
two empirical laws, which he considers to
be, with the exception of the law connect-
ing Gravity with Resistance to motion,
''the two most widely operating laws as
yet discovered whe>-eby two distinct pro-
perties are conjoined throughout sub-
stances generally." The first is "a law
connecting Atomic Weight and Specific
Heat by an inverse proportion. For equal
weights of the simple bodies, the atomic
weight multiplied by a number expressing
the specific heat gives a nearly uniform
product. The products, for all the ele-
ments, are near the constant number 6."
The other is a law which obtains "between
the specific gravity of substances In the
gaseous state and the atomic weights.
The relationship of the two numbers is
in some instances equality ; in other in-
stances the one is a multiple of the other."

Neither of these generalisations has the
smallest appearance of being an ultimate
law. They point unmistakably to higher
laws. Since the heat necessary to raise to a
given temperature the same weight of diffe-
rent substances (called their specific heat)
is inversely as their atomic weight, that is,
directly as the number of atoms in a given
weight of the substance, it follows that a
s ngle atom of every substance requires
the same amount of heat to raise it to a
given temperature : a most interesting and
important law, but a law of causation.
The other law mentioned by Mr. Bain
points to the conclusion that in the
gaseous state all substances contain, in
the same space, the same number of
atoms ; which, as the gaseous state sns-
]>end3 all cohesive force, might naturally
be expected, though it could not have
been positively assumed. This law may
a' an be a result of the mode of action of
c luses, namely, of molecular motions. Thp

Uniformities of co-existence, then,
not only when they are consequences
of laws of succession, but also when
they are ultimate truths, must be
ranked, for the purposes of logic,
among empirical laws, and are amen-
able in every respect to the same
rules with those unresolved unifor-
mities which are known to be depen-
dent on caiisatioiu

CHAPTER XXIII.

OF APPROXIMATE GENERALISATIONS,
AND PROBABLE EVIDENCE.

§ I. In our inquiries into the na-
ture of the inductive process, we must

cases in which one of the numbers is not
identical with the other, but a multiple of
it, may be explained on the nowise un-
likely supposition that, in our present
estimate of the atomic weights of some
substances, we mistake two or three atoms
for one, or one for several.

* Dr. M'Cosh (p. 324 of his book) con-
siders the laws of the chemical compo-
sition of bodies as not coming under the
principle of Causation, and thinks it an
omission in this work not to have provided
special canons for their investigation and
proof. But every case of chemical compo-
sition is, as I have explained, a case of
causation. When it is said that water is
composed of hydrogen and oxygen, the
affirmation is that hydrogen and oxygen,
by the action on one another which they
exert under certain conditions, generate
the properties of water. The Canons of
Induction, therefore, as laid down in this
treatise, ai-e applicable to the case. Such
special adaptations as the Inductive me-
tliods may re«[uire in their application
to chemistry, or any other science, are a
proper subject for any one who treats of
the logic of the special sciences, as Pro-
fessor Bain has done in the latter part of
his woik; but they do not appertain to
General Logic.

Dr. M'Cosh also complains (p. 325) that I
have given no canons for those sciences in
which "the end sought is not the dis-
covery of Causes or of Composition, but of
Classes, that is, Natural Classes." Such
canons could be no other than the
principles and rules of Natural Classifi-
cation, which I certainly thought that I
had expounded at considerable length.
But this is far from the only instance
in which Dr. M'Cosh does not appear to bo
aware of tha contents of the books he i^
criticising.

APPROXIMATE GENERALISATIONS.

387

not confine our notice to such genera-
lisations from experience as profess to
be universally true. There is a class
of inductive truths avowedly not uni-
versal, in which it is not pretended
that the predicate is always true of
the subject, but the value of which,
as generalisations, is nevertheless ex-
tremely great. An important portion
of the field of inductive knowledge
does not consist of universal truths,
but of approximations to such truths ;
and when a conclusion is said to rest
on probable evidence, the premises it
is drawn from are usually generalisa-
tions of this sort.

As every certain inference respect-
ing a particular case implies that
there is ground for a general proposi-
tion, of the form, Every A is B ; so
does every probable inference suppose
that there is ground for a proposition
of the form, Most A are B ; and the
degree of probability of the inference
in an average case will depend on the
proportion between the number of
instances existing in nature which
accord with the generalisation, and
the number of those which conflict
with it.

§ 2. Propositions in the form, Most
A are B, are of a very difiFerent degree
of importance in science, and in the
practice of life. To the scientific
inquirer they are valuable chiefly as
materials for, and steps towards, uni-
versal truths. The discovery of these
is the proper end of science : its work
is not done if it stops at the proposi-
tion that a majority of A are B, with-
out circumscribing that majority by
some common character, fitted to dis-
tinguish them from the minority.
Independently of the inferior pre-
cision of such imperfect generaUsa-
tions, and the inferior assurance with
which they can be applied to indivi-
dual cases, it is plain that, compared
with exact generalisations, they are
almost useless as means of discovering
ulterior truths by way of deduction.
We may, it is true, by combining the
proposition Most A are B, with an

universal proposition, Every B is C,
arrive at the conclusion that Most A
are C. But when a second proposi-
tion of the approximate kind is intro-
duced,— or even when there is but
one, if that one be the major premise,
— nothing can in general be positively
concluded. When the major is Most
B are D, then, even if the minor be
Every A is B, we cannot infer that
most A are D, or with any certainty
that even some A are D. Though
the majority of the class B have the
attribute signified by D, the whole of
the sub-class A may belong to the
minority.*

Though so little use can be made,
in science, of approximate generalisa-
tions, except as a stage on the road to
something better, for practical guid-
ance they are often all we have to
rely on. Even when science has
really determined the universal laws
of any phenomenon, not only are
those laws generally too much en-
cumbered with conditions to be
adapted for everyday use, but the
cases which present themselves in life
are too complicated, and our decisions
require to be taken too rapidly, to
admit of waiting till the existence of
a phenomenon can be proved by what
have been scientifically ascertained to
be universal marks of it. To be in-
decisive and reluctant to act, because
we have not evidence of a perfectly
conclusive character to act on, is a
defect sometimes incident to scientific
minds, but which, wherever it exists,
renders them unfit for practical emer-
gencies. If we would succeed in ac-
tion, we must judge by indications
which, though they do not generally
mislead us, sometimes do ; and must
make up, as far as possible, for the

* Mr. De Morgan, in his Formal Logic,
makes the just remark, that from two
such premises as Most A are B, and Most
A are C, we may infer with certainty that
some B are C. But this is the utmost
limit of the conchisions which can be
drawn from two approximate generalisa-
tions, when tlie precise degree of their
approximation to universality is unknQWi»
or undefined.

388 INDUCTION.

incomplete conclusiveness of any one
indication, by obtaining others to
corroborate it. The principles of
induction applicable to approximate
generalisation are therefore a not less
important subject of inquiry than
the rules for the investigation of uni-
versal truths, and might reasonably
be expected to detain us almost as
long, were it not that these principles
are mere corollaries from those which
have been already treated of.

§ 3. There are two sorts of cases in
which we are forced to guide our-
selves by generalisations of the im-
perfect form. Most A are B. The
first is, when we have no others ;
when we have not been able to carry
our investigation of the laws of the
phenomena any farther ; as in the
following propositions : Most dark-
eyed persons have dark hair ; Most
springs contain mineral substances ;
Most stratified formations contain
fossils. The importance of this class
of generalisations is not very great ;
for though it frequently happens that
we see no reason why that which is
true of most individuals of a class is
not true of the remainder, nor are
able to bring the former under any
general description which can dis-
tinguish them from the latter, yet if
we are willing to be satisfied with
propositions of a less degree of gene-
rality, and to break down the class
A into sub-classes, we may generally
obtain a collection of propositions
exactly true. We do not know why
most wood is lighter than water, nor
can we point out any general pro-
perty which discriminates wood that
is lighter than water from that which
is heavier. But we know exactly
what species are the one and what
the other. And if we meet with a
specimen not conformable to any
known species, (the only case in which
our previous knowledge affords no
other guidance than the approximate
generalisation,) we can generally make
a specific experiment, which is $1 surer
^resource,

It often happens, however, that th«
proposition, Most A are B, is not th«
ultimatum of our scientific attain-
ments, though the knowledge we pos-
sess beyond it cannot conveniently b«
brought to bear upon the particular
instance. We may know well enough
what circumstances distinguish the
portion of A which has the attribute
B from the portion which has it not,
but may have no means, or may not
have time to examine whether those
characteristic circumstances exist or
not in the individual case. This is
the situation we are generally in when
the inquiry is of the.kind called moral,
that is, of the kind which has in view
to predict human actions. To enable
us to affirm anj^hing universally con-
cerning the actions of classes of hu-
man beings, the classification must
be grounded on the circumstances of
their mental culture and habits, which
in an individual case are seldom ex-
actly known ; and classes grounded
on these distinctions would never
precisely accord with those into which
mankind are divided for social pur-
poses. All propositions which can
be framed respecting the actions of
human beings as ordinarily classified,
or as classified according to any kind
of outward indications, are merely
approximate. We can only say. Most
persons of a particular age, profes-
sion, country, or rank in society have
such and such qualities ; or. Most
persons when placed in certain cir-
cumstances act in such and such a
way. Not that we do not often know
well enough on what causes the quali-
ties depend, or what sort of persons
they are who act in that particular
way ; but we have seldom the means
of knowing whether any individual
person has been under the influence
of those causes, or is a person of that
particular sort. We could replace
the approximate generalisations by
propositions universally true ; but
these would hardly ever be capable
of being applied to practice. We
should be sure of our majors, but we
should not be able to get minora to

APPROXIMATE GENERALISATIONS.

389

fit : We are forced, therefore, to draw
our conclusions from coarser and more
fallible indications.

§ 4. Proceeding now to consider
what is to be regarded as sufficient
evidence of an approximate generalisa-
tion, we can have no difficulty in at
once recognising that when admissible
at all, it is admissible only as an em-
pirical law. Propositions of the form,
Every A is B, are not necessarily
laws of causation, or ultimate uni-
formities of co-existence ; propositions
like Most A are B, cannot be so.
Propositions hitherto found true in
every observed instance may yet be
no necessary consequence of laws of
causation or of ultimate imiformities,
and unless they are so, may, for aught
we know, be false beyond the limits
of actual observation : still more evi-
dently nmst this be the case w^ith pro-
positions which are only true in a mere
majority of the observed instances.

There is some difference, however,
in the degree of certainty of the pro-
position, Most A are B, according as
that approximate generalisation com-
prises the whole of our knowledge of
the subject or not. Suppose, first,
that the former is the case. We
know only that most A are B, not
why they are so, nor in what respect
those which are, differ from those
which are not. How then did we
learn that most A are B ? Precisely
in the manner in which we should
have learnt, had such happened to be
the fact, that all A are B. We col-
lected a number of instances sufficient
to eliminate chance, and having done
so, compared the number of instances
in the affirmative with the number in
the negative. The result, like other
unresolved derivative laws, can be
relied on solely within the limits not
only of place and time, but also of
circumstance, under which its truth
has been actually observed ; for as
we are supposed to be ignorant of
the causes which make the proposi-
tion true, we cannot tell in what
manner any new circumstance might

perhaps affect it. The proposition,
Most judges are inaccessible to bribes,
would probably be found true of
Englishmen, Frenchmen, Germans,
North Americans, and so forth ; but
if on this evidence alone we extended
the assertion to Orientals, we should
step beyond the limits, not only of
place but of circumstance, within
which the fact had been observed,
and should let in possibilities of the
absence of the determining causes, or
the presence of counteracting ones,
which might be fatal to the approxi-
mate generalisation.

In the case where the approximate
proposition is not the ultimatum of
our scientific knowledge, but only the
most available form of it for practical
guidance ; where we know, not only
that most A have the attribute B,
but also the causes of B, or some
properties by which the portion of A
which has that attribute is distin-
guished from the portion wnich has
it not ; we are rather more favourably
situated than in the preceding case.
For we have now a double mode of
ascertaining whether it be true that
most A are B ; the direct mode, as
before, and an indirect one, that of
examining whether the proposition
admits of being deduced from the
known cause, or from any known
criterion, of B. Let the question, for
example, be whether most Scotchmen
can read? We may not have ob-
served or received the testimony of
others respecting a sufficient number
a!id variety of Scotchmen to ascertain
this fact ; but when we consider that
the cause of being able to read is the
having been taught it, another mode
of determining the question presents
itself, namely, by inquiring whether
most Scotchmen have been sent to
schools where reading is effectually
taught. Of these two modes, some-
times one and sometimes the other is
the more available. In some cases, the
frequency of the effect is the more
accessible to that extensive and varied
observation which is indispensable
to the establishment of an empirical

390

iNDtrCTlON

law ; at other times, the frequency of
the causes, or of some collateral in-
dications. It commonly happens that
neither is susceptible of so satisfactory
an induction as could be desired, and
that the grounds on which the con-
clusion is received ai-e compounded of
both. Thus a person may believe
that most Scotchmen can read, i)e-
cause, so far as his information ex-
tends, most Scotchmen have been
sent to school, and most Scotch
schools teach reading effectually ; and
also because most of the Scotchmen
whom he has known or heard of
could read ; though neither of these
two sets of observations may by
itself fulfil the necessary conditions
of extent and variety.

Although the approximate gene-
ralisation may in most cases be indis-
pensable for our guidance, even when
we know the cause, or some certain
mark, of the attribute predicated ;
it needs hardly be observed that we
may always replace the uncertain in-
dication by a certain one, in any case
in which we can actually recognise
the existence of the cause or mark.
For example, an assertion is made by
a witness, and the question is whether
to believe it. If we do not look to
any of the individual circumstances
of the case, we have nothing to direct
us but the approximate generalisa-
tion that truth is more common than
falsehood, or, in other words, that
most persons, on most occasions, speak
truth. But if we consider in what
circumstances the cases where truth
is spoken differ from those in which
it is not, we find, for instance, the
following : the witness's being an
honest person or not ; his being an
accurate observer or not ; his having
an interest to serve in the matter or
not. Now, not only may we be able
to obtain other approximate gene-
ralisations respecting the degree of
frequency of these various possibili-
ties, but we may know which of them
is positively realised in the individual
case. That the witness has or has
not an interest to serve, we perhaps

know directly, and the other two
points indirectly, by means of marks ;
as, for example, from his conduct on
some former occasion, or from his re-
putation, which, though a very un-
certain mark, affords an approximate
generalisation, (as, for instance. Most
persons who are believed to be honest
by those with whom they have had
frequent dealings are really so,) which
approaches nearer to an universal
truth than the approximate general
proposition with which we set out,
viz., Most persons on most occasions
speak truth.

As it seems unnecessary to dwell
further on the question of the evi-
dence of approximate generalisations,
we shall proceed to a not less im-
portant topic, that df the cautions to
be observed in arguing from these
incompletely universal propositions to
particular cases.

§ 5. So far as regards the direct
application of an approximate gene-
ralisation to an individual instance,
this question presents no difficulty.
If the proposition. Most A are B, has
been established, by a sufficient induc-
tion, as an empirical law, we may
conclude that any particular A is B
with a probability proportioned to
the preponderance of the number of
affirmative instances over the number
of exceptions. If it has been found
practicable to attain numerical pre-
cision in the data, a corresponding
degree of precision may be given to
the evaluation of the chances of error
in the conclusion. If it can be estab-
lished as an empirical law that nine
out of every ten A are B, there will be
one chance in ten of error in assuming
that any A not individually known
to us is a B ; but this, of course,
holds only within the limits of time,
place, and circumstance embraced in
the observations, and therefore can-
not be counted on for any sub-class
or variety of A (or for A in any set
of external circumstances) which were
not included in the average. It must
be added that we can guide ourselves

APPROXIMATE GENERALISATIONS.

391

by the proposition, Nine out of every
ten A are B, only in cases of which
we know nothing except that they
fall within the class A. For if we
know of any particular instance r,
not only that it falls under A, but to
what species or variety of A it be-
longs, we shall generally err in apply-
ing to i the average struck for the
whole genus, from which the average
corresponding to that species alone
would, in all probability, materially
differ. And so if t, instead of being
a particular sort of instance, is an
instance known to be under the in-
fluence of a particular set of circum-
stances, the presumption drawn from
the numerical proportions in the whole
genus would probably, in such a case,
only mislead. A general average
should only be applied to cases which
are neither known nor can be pre-
sumed to be other than average cases.
Such averages, therefore, are com-
monly of little use for the practical
guidance of any affairs but those
which concern large numbers. Tables
of the chances of life are useful to in-
surance offices, but they go a very
little way towards informing any one
of the chances of his own life, or any
other life in which he is interested,
since almost every life is either better
or worse than the average. Such
averages can only be considered as
supplying the first term in a series of
approximations, the subsequent terms
proceeding on an appreciation of the
circumstances belonging to the parti-
cular case.

§ 6. From the application of a single
approximate generalisation to indi-
vidual cases, we proceed to the appli-
cation of two or more of them together
to the same case.

When a judgment applied to an
individual instance is grounded on
two approximate generalisations taken
in conjunction, the propositions may
co-operate towards the result in two
different ways. In the one, each pro-
position is separately applicable to
the case in hand, and our object in

combining them is to give to the con-
clusion in that particular case the
double probability arising from the
two propositions separately. This
may be called joining two probabili-
ties by way of Addition ; and the
result is a probability greater than
either. The other mode is, when only
one of the propositions is directly ap-
plicable to the case, the second being
only applicable to it by virtue of the
application of the first. This is join-
ing two probabilities by way of Ratio-
cination or Deduction ; the result of
which is a less probability than either.
The type of the first argument is,
Most A are B ; most C are B ; this
thing is both an A and a C ; there-
fore it is probably a B. The type of
the second is, Most A are B ; most
C are A ; this is a C ; therefore it is
probably an A, therefore it is pro-
bably a B. The first is exemplified
when we prove a fact by the testi-
mony of two unconnected witnesses ;
the second, when we adduce only the
testimony of one witness that he has
heard the thing asserted by another.
Or again, in the first mode it may be
argued that the accused committed
the crime because he concealed him-
self, and because his clothes were
stained with blood ; in the second,
that he committed it because he
washed or destroyed his clothes,
which is supposed to render it pro-
bable that they were stained with
blood. Instead of only two links, as
in these instances, we may suppose
chains of any length. A chain of the
former kind was termed by Bentham *
a self -corroborative chain of evidence ;
the second, a self-infirmative chain.

When approximate generalisations
are joined by way of addition, we
may deduce from the theory of pro-
babilities laid down in a former chap-
ter, in what manner each of them
adds to the probability of a conclusion
which has the warrant of them all.

If, on an average, two of every
three As are Bs, and three of every

* Rationale of Judicial Evidence, vol. iii.
p. 224.

392

INDUCTION.

four Cs are Bs, the probablity that
something which is both an A and a
C is a B, will be more than two
in three, or than three in four. Of
every twelve things which are As, all
except four are Bs by the supposition ;
and if the whole twelve, and conse-
sequently those four, have the char-
acters of 0 likewise, three of these
will be Bs on that ground. There-
fore, out of twelve which are both
As and Cs, eleven are Bs. To state
the argument in another way : a thing
which is both an A and a C, but
which is not a B, is found in only one
of three sections of the class A, and
in only one of four sections of the
class C ; but this fourth of C being
spread over the whole of A indis-
criminately, only one-third part of it
(or one-twelfth of the whole number)
belongs to the third section of A ;
therefore a thing which is not a B
occurs only once among twelve things
which are both As and Cs. The ar-
gument would, in the language of
the doctrine of chances, be thus ex-
pressed : the chance that an A is not
a B is ^, the chance that a C is not a
B is J ; hence if the thing be both an
A and a C, the chance is ^ of | = ^V-*

* The evaluation of the chances in this
statement has been objected to by a ma-
thematical friend. The correct mode, in
his opinion, of setting out the possibilities
is as follows. If the thing (let us call it T)
which is both an A and a C, is a B, some-
thing is true which is only true twice in
every thrice, and something else which is
only true thrice in every four times. The
first fact being true eight times in twelve,
and the second being true six times in
every eight, and consequently six times in
those eight ; both facts will be true only
six limes in twelve. On the other hand, if
T, although it is both an A and a C, is not
a IJ, something is true which is only true
once in every thrice, and something else
which is only true once in every four
times. The former being true four times
out of twelve, and the latter once in every
four, and therefore once in those four;
both are only true in one case out of twelve.
So that T is a B six times in twelve, and T
is not a B only once; making the com-
parative probabilities, not eleven to one, as
I had previously made them, but six to
•n«.

In the aeventh edition I accepted this

In this computation it is of course
supposed that the probabilities arising
from A and C are independent of each
other. There must not • be any such
connection between A and C, that
when a thing belongs to the one class

reasoning as conclusive. More attentive
consideration, however, has convinced me
that it contains a fallacy.

The objector argues, that the fact of A's
being a B is true eight times in twelve,
and the fact of Cs being a B six times in
eight, and consequently six times in those
eight; both facts therefore are true only
six times in every twelve. That is, he
concludes that because among As taken
indiscriminarely only eight out of twelve
are Bs and the remaining four are not, it
must equally hold that four out of twelve
are not Bs when the twelve are taken from
the select portion of As which are also Cs.
And by this assumption he arrives at the
strange result, that there are fewer Bs
among things which are both As and Cs
than there are among either As or Cs taken
indiscriminately ; so that a thing which
has both chances of being a B is less likely
to be so than if it had only the one chance
or only the other.

The objector (as has been acutely re-
marked by another correspondent) applies
to the problem under consideration a
mode of calculation only suited to the re-
verse problem. Had the question been —
If two of every three Bs are As and three
out of every four Bs are Cs, how many Bs
will be both As and Cs, his reasoning would
have been correct. For the Bs that are
both As and Cs must be fewer than either
the Bs that are As or the Bs that are Cs,
and to find their number we must abate
either of these numbers in the ratio due to
the other. But when the problem is to
find, not how many Bs are both As and Cs,
but how many things that are both As and
Cs are Bs, it is evident that among these
the proportion of Bs must be not less, but
greater, than among things which are only
A, or among things which are only B.

Tlie true theory of the chaTices is best
found by going back to the scientific
grounds on which the proportions rest.
The degree of frequency of a coincidence
depends on, and is a measure of, tiie fre-
quency, combined with the efl&cacy, of the
causes in operation that are favourable
to it. If out of every twelve As taken in-
discriminately eight are Bs and four are
not it is implied that there are causes
operating on A which tend to make it a B,
and that these causea are sufficiently con-
stant and suflSciently powerful to succeed
in eight out of twelve cases, but fail in the
remaining four. So if of twelve Cs, nine
are Bs and three are not, there must be
causes of the same tendency operating on
C, which succeed in nine cases and fail in

APPROXIMATE GENERALISATIONS.

393

it will therefore belong to the other,
or even have a greater chance of
doing so. Otherwise the not-Bs which
are Cs may be, most or even all of
them, identical with the not-Bs which
are As ; in which last case the proba-
bility arising from A and C together
will be no greater than that arising
from A alone.

When approximate generalisations
are joined together in the other mode,
that of deduction, the degree of pro-
bability of the inference, instead of
increasing, diminishes at each step.
From two such premises as Most A
are B, Most B are C, we cannot with
certainty conclude that even a single
A is C ; for the whole of the portion
of A which in any way falls under B
may perhaps be comprised in the ex-
ceptional part of it. Still, the two
propositions in question aflFord an ap-
preciable probability that any given
A is C, provided the average on which
the second proposition is grounded
was taken fairly with reference to
the first ; provided the proposition,
Most B are C, was arrived at in a
manner leaving no suspicion that the
probability arising from it is other-
wise than fairly distributed over
the section of B which belongs to
A. For though the instances which
are A may be all in the minority,
they may also be all in the majo-
rity ; and the one possibility is to
be set against the other. On the
whole, the probability arising from
the two propositions taken together
will be correctly measured by the
probability arising from the ouq,
abated in the ratio of that arising
three. Now suppose twelve cases which
are both As and Cs. The whole twelve are
uow under the operation of both sets of
causes. One set is sufficient to prevail in
eight of the twelve cases, the other in
nine. The analysis of the cases shows that
tiix of the twelve will be Bs through the
operation of both sets of causes ; two more
in virtue of the causes operating on A ;
and three more through those operating
on C, and that there will be only one case
in which all the causes will be inoperative.
The total number therefore which are Bs
will be eleven in twelve, and the evalua-
tion in the text is correct.

from the other. If nine out of ten
Swedes have light hair, and eight out
of nine inhabitants of Stockholm are
Swedes, the probability arising from
these two propositions, that any given
inhabitant of Stockholm is light-
haired, will amount to eight in ten :
though it is rigorously possible that
the whole Swedish population of
Stockholm might belong to that tenth
section of the people of Sweden who
are an exception to the rest.

If the premises are known to be
true not of a bare majority, but of
nearly the whole, of their respective
subjects, we may go on joining one
such proposition to another for several
steps, before we reach a conclusion
not presumably true even of a ma-
jority. The error of the conclusion
will amount to the aggregate of the
errors of all the premises. Let the
proposition. Most A are B, be true
of nine in ten ; Most B are 0, of
eight in nine ; then not only will one
A in ten not be C, because not B,
but even of the nine-tenths which are
B, only eight-ninths will be C : that
is, the cases of A which are C will be
only f of yV, or four-fifths. Let us
now add, Most C are D, and suppose
this to be true of seven cases out of
eight ; the proportion of A which is
D will be only | of f of ^\, or ^.
Thus the probability proi^ressively
dwindles. The experience, however,
on which our approximate generalisa-
tions are grounded has so rarely been
subjected to, or admits of, accurate
numerical estimation, that we cannot
in general apply any measurement to
the diminution of probability which
takes place at each illation, but must
be content with remembering that it
does diminish at every step, and un-
less the premises approach very nearly
indeed to being universally true, the
conclusion after a very few steps is
worth nothing. A hearsay of a hear-
say, or an argument from presumptive
evidence depending not on immediate
marks but on marks of marks, is
worthless at a very few removes from
the first stage.

394

INDUCTION.

§ 7. There are, however, two cases
in which reasonings depending on
approximate generalisations may be
carried to any length we please with
as much assurance, and are as strictly
scientific, as if they were composed of
universal laws of nature. But these
cases are exceptions of the sort which
are currently said to prove the rule.
The approximate generalisations are
as suitable, in the cases in question,
for purposes of ratiocination, as if
they were complete generalisations,
because they are capable of being
transformed into complete generalisa-
tions exactly equivalent.
- First : If the approximate gene-
ralisation is of the class in which our
reason for stopping at the approxima-
tion is not the impossibility, but only
the inconvenience, of going farther ;
if we are cognisant of the character
which distinguishes the cases that
accord with the generalisation from
those which are exceptions to it, we
may then substitute for the approxi-
mate proposition an universal pro-
position with a proviso. The pro-
position, Most persons who have un-
controlled power employ it ill, is a
generalisation of this class, and may
be transformed into the following : —
All persons who have uncontrolled
power employ it ill, provided they are
not persons of unusual strength of judg-
ment and rectitude of purpose. The
proposition, carrying the hypothesis
or proviso with it, may then be dealt
with no longer as an approximate, but
as an universal proposition ; and to
whatever number of steps the reason-
ing may reach, the hjrpothesis, being
carried forward to the conclusion, will
exactly indicate how far that con-
clusion is from being applicable uni-
versally. If in the course of the argu-
ment other approximate generalisa-
tions are introduced, each of them
being in like manner expressed as an
universal proposition with a condition
annexed, the sum of all the conditions
will appear at the end as the sum of
all the errors which affect the con-
clusion. Thus, to the proposition last

cited let us add the following :— All
absolute monarchs have uncontrolled
power, unless their position is such that
they need the active support of their
subjects (as was the case with Queen
Elizabeth,. Frederick of Prussia, and
others). Combining these two pro-
positions, we can deduce from them
an universal conclusion, which will
be subject to both the hypotheses in
the premises ; All absolute monarchs
employ their power ill, unless their
position makes them need the active
support of their subjects, or unless
they are persons of unusual strength
of judgment and rectitude of purpose.
It is of no consequence how rapidly
the errors in our premises accumulate,
if we are able in this manner to record
each error, and keep an account of
the aggregate as it swells up.

Secondly : There is a case in which
approximate propositions, even with-
out our taking note of the condi-
tions under which they are not true
of individual cases, are yet, for the
purposes of science, universal ones ;
namely, in the inquiries which relate
to the properties not of individuals,
but of multitudes. The principal of
these is the science of politics, or of
human society. This science is princi-
pally concerned with the actions not
of solitary individuals, but of masses ;
with the fortunes not of single per-
sons, but of communities. For the
statesman, therefore, it is generally
enough to know that most persons act
or are acted upon in a particular way,
since his speculations and his practi-
cal arrangements refer almost ex-
clusively to cases in which the whole
community, or some large portion of
it, is acted upon at once, and in which,
therefore, what is done or felt by most
persons determines the result pro-
duced by or upon the body at large.
He can get on well enough with ap-
proximate generalisations on human
nature, since what is true approxi-
mately of all individuals is true ab-
solutely of all masses. And even
when the operations of individual men
have a part to play in his deductions,

hemaining laws oi* nature.

39S'

as when he is reasoning of kings, or
other single rulers, still, as he is pro-
viding for indefinite duration, involv-
ing an indefinite succession of such
individuals, he must in general both
reason and act as if what is true of
most persons were true of all.

The two kinds of consideration
above adduced are a sufficient refu-
tation of the popular error, that
speculations on society and govern-
ment, as resting on merely probable
evidence, must be inferior in cer-
tainty and scientific accuracy to the
conclusions of what are called the
exact sciences, and less to be relied
on in practice. There are reasons
enough why the moral sciences must
remain inferior to at least the more
perfect of the physical : why the laws
of their more complicated phenomena
cannot be so completely deciphered,
nor the phenomena predicted with
the same degree of assurance. But
though we cannot attain to so many
truths, there is no reason that those
we can attain should deserve less re-
liance, or have less of a scientific
character. Of this topic, however, I
shall treat more systematically in the
concluding Book, to which place any
further consideration of it must be
deferred.

CHAPTER XXIV.

OF THE REMAINING LAWS OF NATURE.

§ I. In the First Book we found
that all the assertions which can be
conveyed by language express some
one or more of five different things :
Existence ; Order in Place ; Order in
Time ; Causation ; and Resemblance.*
Of these. Causation, in our view of
the subject, not being fundamentally
different from Order in Time, the five
species of possible assertions are re-
duced to four. The propositions
which affirm Order in Time, in either
of its two modes, Co-existence and
Succession, have formed, thus far, the
subject of the present Book. And
* Supra, book i. chap. v.

we have now concluded the exposi-
tion, so far as it falls within the limits
assigned to this work, of the nature
of the evidence on which these pro-
positions rest, and the processes of
investigation by which they are as-
certained and proved. There remain
three classes of facts : Existence,
Order in Place, and Resemblance ;
in regard to which the same ques-
tions are now to be resolved.

Regarding the first of these, very
little needs be said. Existence in
general is a subject not for our
science, but for metaphysics. To de-
termine what things can be recog-
nised as really existing, independently
of our own sensible or other impres-
sions, and in what meaning the
term is, in that case, predicated of
them, belongs to the consideration
of "Things in themselves," from
which, throughout this work, we
have as much as possible kept aloof.
Existence, so far as Logic is con-
cerned about it, has reference only
to phenomena ; to actual or possible
state.s of external or internal con-
sciousness, in ourselves or others.
Feelings of sensitive beings, or pos-
sibilities of having such feelings, are
the only things the existence of
which can be a subject of logical
induction, because the only things of
which the existence in individual cases
can be a subject of experience.

It is true that a thing is said by us
to exist even when it is absent, and
therefore is not and cannot be per-
ceived. But even then, its existence
is to us only another word for our
conviction that we should perceive it
on a certain supposition, namely, if
we were in the needful circumstances
of time and place, and endowed with
the needful perfection of organs. My
belief that the Emperor of China
exists, is simply my belief that if
I were transported to the imperial
palace or some other locality in Pekin,
I should see him. My belief that
Julius Caesar existed, is my belief
that I should have seen him if I had
been present in the field of Pharsalis^

39^

INDUCTION.

or in the senate-house at Rome. When
I believe that stars exist beyond the
utmost range of my vision, though
assisted by the most powerful tele-
scopes yet invented, my belief, philo-
sophically expressed, is, that with still
better telescopes, if such existed, I
could see them, or that they may be
perceived by beings less remote from
them in space, or whose capacities of
perception are superior to mine.

The existence, therefore, of a pheno-
menon is but another word for its
being perceived, or for the inferred
possibility of perceiving it. When
the phenomenon is within the range
of present observation, by present ob-
servation we assure ourselves of its
existence ; when it is beyond that
range, and is therefore said to be
absent, we infer its existence from
marks or evidences. But what can
these evidences be? Other pheno-
mena, ascertained by induction to be
connected with the given phenome-
non, either in the way of succession
or of co-existence. The simple exist-
ence, therefore, of an individual pheno-
menon, when not directly perceived,
is inferred from some inductive law
of succession or co-existence, and is
consequently not amenable to any
peculiar inductive principles. We
prove the existence of a thing by
proving that it is connected by suc-
cession or co-existence with some
known thing.

With respect to general proposi-
tions of this class, that is, which
affirm the bare fact of existence, they
have a peculiarity which renders the
logical treatment of them a very
easy matter ; they are generalisa-
tions which are sufficiently proved
by a single instance. That ghosts,
or unicorns, or sea-serpents exist,
would be fully established if it could
be ascertained positively that such
things had been even once seen.
Whatever has once happened is cap-
able of happening again ; the only
question relates to the conditions
under which it happens.

So far, therefore, as relates to simple

existence, the Inductive Logic has no
knots to untie. And we may pro-
ceed to the remaining two of the great
classes into which facts have been
divided ; Resemblance, and Order in
Place.

§ 2. Resemblance and its opposite,
except in the case in which they as-
sume the names of Equality and In-
equality, are seldom regarded as sub-
jects of science ; they are supposed
to be perceived by simple apprehen-
sion ; by merely applying our senses
or directing our attention to the two
objects at once, or in immediate suc-
cession. And this simultaneous, or
virtually simultaneous application of
our faculties to the two things which
are to be compared, does necessarily
constitute the ultimate, appeal, wher-
ever such application is practical.
But, in most cases, it is not practi-
cable : the objects cannot be brought
so close together that the feeling of
their resemblance (at least a complet*;
feeling of it) directly arises in the
mind. We can only compare each o:
them with some third object, capabh
of being transported from one to th(
other. And besides, even when tht
objects can be brought into immediate
juxtaposition, their resemblance oi
difference is but imperfectly known
to us, unless we have compared them
minutely, part by part. Until this
has been done, things in reality very
dissimilar often appear undistinguish-
ably alike. Two lines of very unequal
length will appear about equal when
lying in different directions ; but
place them parallel with their farther
extremities even, and if we look at
the nearer extremities, their inequality
becomes a matter of direct perception.

To ascertain whether, and in what,
two phenomena resemble or differ is
not always, therefore, so easy a thing
as it might at first appear. When
the two cannot be brought into juxta-
position, or not so that the observer
is able to compare their several parts
in detail, he must employ the indirect
means of reasoning and general pro-

REMAINING LAWS OF NATURE.

397

positions. When we cannot bring
two straight lines together to deter-
mine whether they are equal, we do
it by the physical aid of a foot-rule
applied first to one and then to the
other, and the logical aid of the gene-
ral proposition or formula, " Things
which are equal to the same thing are
equal to one another." The compari-
son of two things through the inter-
vention of a third thing, when their
direct comparison is impossible, is the
appropriate scientific process for as-
certaining resemblances and dissimi-
larities, and is the sum total of what
Logic has to teach on the subject.

An undue extension of this remark
induced Locke to consider reasoning
itself as nothing but the comparison
of two ideas through the medium of a
third, and knowledge as the percep-
tion of the agreement or disagree-
ment of two ideas : doctrines which
the Condillac school blindly adopted,
without the qualifications and dis-
tinctions with which they were stu-
diously guarded by their illustrious
author. Where, indeed, the agree-
ment or disagreement (otherwise
called resemblance or dissimilarity)
of any two things is the very matter
to be determined, as is the case par-
ticularly in the sciences of quantity
and extension ; there, the process by
which a solution, if not attainable b}'
direct perception, must be indirectly
sought, consists in comparing these
two things through the medium of a
third. But this is far from being
true of all inquiries. The know-
ledge that bodies fall to the ground is
not a perception of agreement or dis-
agreement, but of a series of physi-
cal occurrences, a succession of sensa-
tions. Locke's definitions of know-
ledge and of reasoning required to be
limited to our knowledge of, and
reasoning about resemblances. Nor,
even when thus restricted, are the
propositions strictly correct, since the
comparison is not made, as he repre-
sents, between the ideas of the two
phenomena, but between the pheno-
mena themselves. This mistake has

been pointed out in an earlier part of
our inquiry,* and we traced it to an
imperfect conception of what take*
place in mathematics, where very
often the comparison is really made
between the ideas, without any ap-
peal to the outward senses ; only,
however, because in mathematics a
comparison of the ideas is strictly
equivalent to a comparison of the
phenomena themselves. Where, as
in the case of numbers, lines, and
figures, our idea of an object is a
complete picture of the object so far
as respects the matter in hand, we
can, of course, learn from the picture
whatever could be learnt from the ob-
ject itself by mere contemplation of it
as it exists at the particular instant
when the picture is taken. No mere
contemplation of gunpowder would
ever teach us that a spark would
make it explode, nor, consequently,
would the contemplation of the idea
of gunpowder do so ; but the mere
contemplation of a straight line shows
that it cannot enclose a space : ac-
cordingly the contemplation of the
idea of it will show the same. What
takes place in mathematics is thus
no argument that the comparison is
between the ideas only. It is always,
either indirectly or directly, a com-
parison of the phenomena.

In cases in which we cannot bring
the phenomena to the test of direct
inspection at all, or not in a manner
sufficiently precise, but must judge of
their resemblance by inference from
other resemblances or dissimilarities
more accessible to observation, we of
course require, as in all cases of ratio-
cination, generalisations or formulae
applicable to the subject. We must
reason from laws of nature ; from the
uniformities which are observable in
the fact of likeness or unlikeness.'

§ 3. Of these laws or uniformities,
the most comprehensive are those
supplied by mathematics ; the axiom*
relating to equality, inequality, and

* Supra, book i. ch. v. § 1, and book i;
ch. V. §5.

398

INDUCTION.

proportionality, and the various theo-
rems thereon founded. And these
are the only Laws of Resemblance
which require to be, or which can be,
treated apart. It is true there are
innumerable other theorems which
affirm resemblances among pheno-
mena, as that the angle of the reflexion
of light is equal to its angle of inci-
dence (equality being merely exact
resemblance in magnitude). Again,
that the heavenly bodies describe
equal areas in equal times, and that
their periods of revolution are jtro-
poi'tional (another species of resem-
blance) to the sesquiplicate powers of
their distances from the centre of
force. These and similar propositions
affirm resemblances of the same nature
with those asserted in the theorems
of mathematics ; but the distinction
is, that the propositions of mathema-
tics are true of all phenomena what-
ever, or at least without distinction
of origin, while the truths in question
are affirmed only of special pheno-
mena, which originate in a certain
way ; and the equalities, proportion-
alities, or other resemblances which
exist between such phenomena must
necessarily be either derived from,
or identical with, the law of their
origin — the law of causation on which
they depend. The quality of the
areas described in equal times by the
planets is derived from the laws of
the causes, and, until its derivation
was shown, it was an empirical law.
The equality of the angles of reflexion
and incidence is identical with the law
of the cause ; for the cause is the in-
cidence of a ray of light upon a re-
flecting surface, and the equality in
question is the very law according to
which that cause produces its effects.
This class, therefore, of the uniformi-
ties of resemblance between pheno-
mena are inseparable, in fact and in
thought, from the laws of the pro-
duction of those phenomena, and the
principles of induction applicable to
them are no other than those of which
we have treated in the preceding
chapters of this Book,

It is otherwise with the truths of
mathematics. The laws of equality
and inequality between spaces, or be-
tween numbers, have no connection
with laws of causation. That the
angle of reflexion is equal to the
angle of incidence is a statement of
the mode of action of a particular
cause ; but that when two straight
lines intersect each other the opposite
angles are equal is true of all such
lines and angles, by whatever cause
produced. That the squares of the
periodic times of the planets are pro-
portional to the cubes of their dis-
tances from the sun, is an uniformity
derived from the laws of the causes
(or forces) which produce the plane-
tary motions ; but that the square of
any number is four times the square
of half the number is true, indepen-
dently of any cause. The only laws
of resemblance, therefore, which wa
are called upon to consider indepen-
dently of causation belong to the pro-
vince of mathematics.

§ 4. The same thing is evident witl
respect to the only one remaining o]
our five categories. Order in Place.
The order in place of the effects of a
cause is (like everything else belong-
ing to the effects) a consequence oi
the laws of that cause. The order in
place, or, as we have termed it, the
collocation, of the primeval causes is
(as well as their resemblance) in each
instance an ultimate fact, in which
no laws or uniformities are traceable.
The only remaining general proposi-
tions respecting order in place, and
the only ones which have nothing to
do with causation, are some of the
truths of geometry — laws through
which we are able, from the order in
place of certain points, lines, or spaces,
to infer the order in place of others
which are connected with the former
in some known mode, quite indepen-
dently of the particular nature of
those points, lines, or spaces, in any
other respect than position or magni-
tude, as well as independently of the
physical cause from which, in any

REMAINING LAWS OF NATURE.

599

particular case, they happen to derive
their origin.

It thus appears that mathematics
is the only department of science into
the methods of which it still remains
to inquire ; and there is the less
necessity that this inquiry should
occupy us long, as we have already,
in the Second Book, made consider-
able progress in it. We there re-
marked that the directly inductive
truths of mathematics are few in
number, consisting of the axioms, to-
gether with certain propositions con-
cerning existence, tacitly involved in
most of the so-called definitions. And
we gave what appeared conclusive
reasons for affirming that these ori-
ginal premises, from which the re-
maining truths of the science are
deduced, are, notwithstanding all ap-
pearances to the contrary, results of
observation and experience, founded,
in short, on the evidence of the senses.
That things equal to the same thing
jue equal to one another, and that
two straight lines which have once
intersected one another continue to
diverge, are inductive truths, rest-
ing, indeed, like the law of universal
causation, only on induction per enu-
merationem simpliceni, on the fact that
they have been perpetually perceived
to be true, and never once found to
be false. But, as we have seen in a
recent chapter that this evidence, in
the case of a law so completely uni-
versal as the law of causation, amounts
to the fullest proof, so is this even
more evidently true of the general
propositions to which we are now ad-
verting ; because, as a perception of
their truth, in any individual case
whatever, requires only the simple
act of looking at the objects ia a
proper position, there never could
liave been in their case (what, for a
long period, there were in the case of
the law of causation) instances which
were apparently, though not really,
exceptions to them. Their infallible
truth was recognised from the very
dawn of speculation ; and as their
extreme familiarity made it impos-

sible for the mind to conceive the
objects under any other law, they
were, and still are, generally con-
sidered as truths recognised by theiv
own evidence or by instinct.

§ 5. There is something which
seems to require explanation, in the
fact that the immense multitude of
truths (a multitude still as far from
being exhausted as ever) comprised
in the mathematical sciences, can be
elicited from so small a number of
elementary laws. One sees not, at
first, how it is that there can be room
for such an infinite variety of true
propositions on subjects apparently
so limited.

To begin with the science of num-
ber. The elementary or ultimate
truths of this science are the common
axioms concerning equality, namely,
*' Things which are equal to the same
thing are equal to one another," and
" Equals added to equals make equal
sums," (no otheraxioms are required,*)
together with the definitions of the
various numbers. L'lce other so-called
definitions, these i»i« composed of two
things, the explanation of a name and
the assertion of a fact : of which the
latter alone can form a first principle
or premise of a science. The fact

* The axiom, " Equals subtracted from
equals leave equal differences," may be
demonstrated from the two axioms in the
text. If A = a and B = 6, A-B = a-6.
For if not, let A - B = a - 6 H- c. Then
since B=6, adding equals to equals,
A = a -f- c. But A = a. Therefore a = «
+ c; which is impossible.

This proposition having been demon-
strated, we may, by means of it, demon-
strate the following: " If equals be added
to unequals, the sums are unequal." If
A = o and B not = 6, A -I- B is not =a + b.
For suppose it to be so. Then, since A = o
and A -t- B = a -t- 6, subtracting equals from
equals, B = 6 / which is contrary to the
hypothesis.

So again, it may be proved that two
things, one of which is equal and the other
unequal to a third thing, are unequal to
one another. If A = a and A not = B,
neither is a = B. For suppose it to be
equal. Then since A — a and a = B, and
since things equal to the same thing- are
equal to one another, A = B ; which iti
contrary to the hypothesis.

400

INDUCTION.

asserted in the definition of a num-
ber is a physical fact. Each of the
numbers two, three, four, &c., denotes
physical phenomena, and connotes a
physical property of those phenomena.
Two, for instance, denotes all pairs of
things, and twelve all dozens of things,
connoting what makes them pairs or
dozens ; and that which makes them
so is something physical ; since it
cannot be denied that two apples are
physically distinguishable from three
apples, two horses from one horse, and
so forth : that they are a different
visible and tangible phenomenon. I
am not undertaking to say what the
difference is ; it is enough that there
is a difference of which the senses
can take cognisance. And although
a hundred and two horses are not so
easily distinguished from a hundred
and three, as two horses ai:e from three
— though in most positions the senses
do not perceive any difference — yet
they may be so placed that a differ-
ence will be perceptible, or else we
should never have distinguished them,
and given them different names.
Weight is confessedly a physical pro-
perty of things ; yet small differences
between great weights are as imper-
ceptible to the senses in most situa-
tions, as small differences between
great numbers ; and are only put in
evidence by placing the two objects
in a peculiar position — namely, in the
opposite scales of a delicate balance.

What, then, is that which is con-
noted by a name of number? Of
course, some property belonging to
the agglomeration of things which
we call by the name ; and that pro-
perty is the characteristic manner in
which the agglomeration is made up
of, and may be separated into, parts.
I will endeavour to make this more
intelligible by a few explanations.

When we call a collection of ob-
jects two, three, or four, they are not
two, three, or four in the abstract ;
they are two, three, or four things of
some particular kind ; pebbles, horses,
inches, pounds weight. What the
Hame of number connotes is the man-

ner in which single objects of the
given kind must be put together, in
order to produce that particular aggre
gate. If the aggregate be of pebbles,
and we call it two, the name implies
that, to compose the aggregate, one
pebble must be joined to one pebble.
If we call it three, one and one and
one pebble must be brought together
to produce it, or else one pebble must
be joined to an aggregate of the kind
called two, already existing. The
aggregate which we call four has a
still greater number of characteristic
modes of formation. One and one
and one and one pebble may be
brought together ; or two aggregates
of the kind called tivo may be united;
or one pebble may be added to an
aggregate of the kind called three.
Every succeeding number in the as-
cending series may be formed by the
junction of smaller numbers in a pro-
gressively greater variety of ways.
Even limiting the parts to two, the
number may be formed, and conse-
quently may be divided, in as many
different ways as there are numbers
smaller than itself ; and, if we admit
of threes, fours, &c., in a still greater
variety. Other modes of arriving at
the same aggregate present them-
selves, not by the union of smaller,
but by the dismemberment of larger
aggregates. Thus, three pebbles may
be formed by taking away one pebble
from an aggregate of four ; two pebbles,
by an equal division of a similar aggre-
gate, and so on.

Every arithmetical proposition,
every statement of the result of an
arithmetical operation, is a state-
ment of one of the modes of forma-
tion of a given number. It affirms
that a certain aggregate might have
been formed by putting together cer-
tain other aggregates, or by with-
drawing certain portions of some
aggregate ; and that, by consequence,
we might reproduce those aggregates
from it by reversing the process.

Thus, when we say that the cube
of 12 is 1728, what we affirm is this :
that if, having a sufficient number uf

REMAINING LAWS OF NATURE.

401

pebbles or of any other objects, we
put them together into the particular
sort of parcels or aggregates called
twelves ; and put together these
twelves again into similar collec-
tions ; and, finally, make up twelve
of these largest parcels : the aggre-
gate thus formed will be such a one
as we call 1728 ; namely, that which
(to take the most familiar of its modes
of formation) may be made by joining
the parcel called a thousand pebbles,
the parcel called seven hundred peb-
bles, the parcel called twenty pebbles,
and the parcel called eight pebbles.

The converse proposition, that the
cube root of 1728 is 12, asserts that
this large aggregate may again be de-
composed into the twelve twelves of
twelves of pebbles which it consists of.

The modes of formation of any
number are innumerable ; but when
we know one mode of formation of
each, all the rest may be determined
deductively. If we know that a is
formed from b and c, b from a and e,
c from d and /, and so forth, until we
have included all the numbers of any
scale we choose to select, (taking care
that for each number the mode of
formation be really a distinct one,
not bringing us round again to the
former numbers, but introducing a
new number,) we have a set of pro-
positions from which we may reason
to all the other modes of formation
of those numbers from one another.
Having established a chain of induc-
tive truths connecting together all the
numbers of the scale, we can ascer-
tain the formation of any one of those
numbers from any other by merely
travelling from one to the other along
the chain. Suppose that we know
only the following modes of forma-
tion : 6 = 4 + 2, 4 = 7-3, 7p5 + 2,

5 = 9-4. We could determine how

6 may be formed from 9. For 6 = 4
+ 2 = 7-3 + 2 = 5 + 2-3 + 2 = 9-4-f-
2-3-1-2. It may therefore be formed
by taking away 4 and 3, and adding 2
and 2. If we know besides tliat 2 -l-
2 = 4, we obtain 6 from 9 in a simpler
mode, by merely taking away 3.

It is sufficient, therefore, to select
one of the various modes of formation
of each number, as a means of ascer-
taining all the rest. And since things
which are uniform, and therefore
simple, are most easily received and
retained by the understanding, there
is an obvious advantage in selecting
a mode of formation which shall be
alike for all ; in fixing the connotation
of names of number on one uniform
principle. The mode in which our ex-
isting numerical nomenclature is con-
trived possesses this advantage, with
the additional one that it happily
conveys to the mind two of the modes
of formation of every number. Each
number is considered as formed by
the addition of an unit to the numbet
next below it in magnitude, and this
mode of formation is conveyed by the
place which it occupies in the series.
And each is also considered as formed
by the addition of a number of units
less than ten, and a number of aggre-
gates each equal to one of the succes-
sive powers of ten ; and this mode of
its formation is expressed by its spoken
name and by its numerical character.

What renders arithmetic the type
of a deductive science is the fortunate
applicability to it of a law so com-
prehensive as " The sums of equals are
equals ; " or, (to express the same
principle in less familiar but more
characteristic language,) Whatever is
made up of parts is made up of the
parts of those parts. This truth, obvi-
ous to the senses in all cases which
can be fairly referred to their decision,
and so general as to be co-extensive
with nature itself, being true of all
sorts of phenomena, (for all admit of
being numbered,) must be considered
an inductive truth or law of nature
of the highest order. And every
arithmetical operation is an applica-
tion of this law, or of other laws
capable of being deduced from it.
This is our warrant for all calcula-
tions. We believe that five and two
are equal to seven on the evidence
of this inductive law, combined with
the definitions of those numbers. We
2 C

402

INDUCTION.

ftirive at that conclusion (aa all know
who remember how they first learned
it) by adding a single unit at a time :
5+1=6, therefore 5 + 1 + 1 = 6
+ 1 = 7: and again 2=1 + 1, there-
fore 5 + 2 = 5 + 1 + 1 = 7.

§ 6. Innumerable as are the true
propositions which can be formed con-
cerning particular numbers, no ade-
quate conception could be gained from
these alone of the extent of the truths
composing the science of number.
Such propositions as we have spoken
of are the least general of all numeri-
cal truths. It is true that even these
are co-extensive with all nature : the
properties of the number four are true
of all objects that are divisible into
four equal parts, and all objects are
either actually or ideally so divisible.
But the propositions which compose
the science of algebra are true, not of
a particular number, but of all num-
bers ; not of all things under the con-
dition of being divided in a particular
way, but of all things under the con-
dition of being divided in any way —
of being designated by a number at
all.

Since it is impossible for different
numbers to have any of their modes
of formation completely in common,
it is a kind of paradox to say, that all
propositions which can be made con-
cerning numbers relate to their modes
of formation from other numbers, and
yet that there are propositi^ ns which
are true of all numbers. But this
very paradox leads to the real prin
ciple of generalisation concerning the
properties of numbers. Two different
numbers cannot be formed in the
same manner from the same numbers;
but they may be formed in the same
manner from different numbers ; as
nine is formed from three by multi-
plying it into itself, and sixteen is
formed from four by the same pro-
cess. Thus there arises a classifica-
tion of modes of formation, or, in the
language commonly used by mathe-
maticians, a classification of Func-
tioiu. ^y number, considered as

formed from any other number, is
called a function of it ; and there are
as many kinds of functions as there
are modes of formation. The simple
functions are by no means numerous,
most functions being formed by the
combination of several of the opera-
tions which form simple functions, or
by successive repetitions of some one
of those operations. The simple func-
tions of any number x are all reducible
to the following forms : x -V a, x—a,

a X, - X*, v^ X, log. X (to the base a\

and the same expressions varied by
putting X for a and a for x, wherever
that substitution would alter the
value : to which perhaps ought to be
added sin x, and arc (sin = x). All
other functions of x are formed by put-
ting some one or more of the simple
functions in the place of x or a, and
subjecting them to the same elemen-
tary operations.

In order to carry on general reason-
ings on the subject of Functions, we
require a nomenclature enabling us
to express any two numbers by names
which, without specifying what par-
ticular numbers they are, shall show
what function each is of the other,
or, in other words, shall put in evi-
dence their mode of formation from
one another. The system of general
language called algebraical notation
does this. The expressions a and
a^ + 3a denote, the one any number,
the other the number formed from it
in a particular manner. The expres-
sions a, b, n, and (a + 6)«, denote any
three numbers, and a fourth which is
formed from them in a certain mode.

The following may be stated as the
general problem of the algebraical
calculus : F being a certain function
of a given number, to find what func-
tion F will be of any function of that
number. For example, a binomial
a + b is a function of its two parts a
and 6, and the parts are, in their
turn, functions of a + 6 ; now (a + A)»^
is a certain function of the binomial ;
what function will this be of a and 6,
the two parts? The answer to this

REMAINING LAWS OF NATURE.

403

question is the binomial theorem.
The formula (a + 6)* = a* + * a* " ^6 +

~^a'*~'b'- + &c., shows in what man-
1.3 '

ner the number which is fonned by

multiplying a-tb into itself n times,

might be formed without that process,

directly from 0, b, and n. And of

this nature are all the theorems of

the science of number. They assert

the identity of the result of different

modes of formation. They affirm

that some mode of formation from x,

and some mode of formation from a

certain function of x, produce the

same number.

Besides these general theorems or
formulae, what remains in the alge-
braical calculus is the resolution of
e(juations. But the resolution of an
equation is also a theorem. If the
equation he X' + ax = b, the resolution
of this equation, viz. x = - ^a +
y/ ^ ar + b, IB a, general proposition
which may be regarded as an answer
to the question. If 6 is a certain
function of arand a, (namely, X' + ax,)
what function is x of 6 and a ? The
resolution of equati«)ns is, therefore,
a mere variety of the general pro-
blem as above stated. The problem
is — Given a function, what function
is it of some other function ? And in
the resolution of an equation, the
question is, to find what function of
one of its own functions the number
itself is.

Such as above described is the
aim and end of the calculus. As for
its processes, every one knows that
they are simply deductive. In de-
monstrating an algebraical theorem,
or in resolving an equation, we travel
from the datum to the qucesitum by
pure ratiocination ; in wliich the only
premises introduced, besides the ori-
ginal hypotheses, are the fundamen-
tal axioms already mentioned — that
things equal to the same thing are
equal to one another, and that the
sums of equal things are equal. At
each step in the demonstration or
in the calculation, we apply one or

other of these truths, or truths dedu-
cible from them, as, that the differ-
ences, products, &c., of equal num-
bers are equal.

It would be inconsistent with the
scale of this work, and not necessary
to its design, to carry the analysis of
th*' truths and processes of algebra
any farther ; which is also the less
needful, as the task has been, to a
very great extent, performed by other
writers. Peacock's Algebra and Dr.
Whewell's Doctrine of Limits are full
of instruction on the subject. The
profound treatises of a truly philoso-
phical mathematician. Professor De
Morgan, should be studied by every
one who desires to comprehend the
evidence of mathematical truths, and
the meaning of the obscurer processes
of the calcuius ; and the speculations
of M. Comte, in his Cours de I'hilo-
sophie Positive, on the philosophy of
the higher branches of mathenjatics,
are among the many valuable gifts
for which philosophy is indebted to
that eminent thinker.

§ 7. If the extreme generality, and
remoteness not so nmch from sense as
from the visual and tactual imagina-
tion, of the laws of number, renders
it a somewhat ditticult effort of ab-
straction to conceive those laws as
being in reality physical truths ob-
tained by observation ; the same diffi-
culty does not exist with regard to
the laws of extension. The facts of
which those laws are expressions are
of a kind peculiarly accessible to the
senses, and suggesting eminently dis-
tinct images to the fancy. That geo-
metry is a strictly physical science
would doubtless have been recognised
in all ages, had it not been for the
illusions produced by two circum-
stances. One of these is the charac-
teristic property, already noticed, of
the facts of geometry, that they may
be collected from our ideas or mental
pictures of objects as efifectually as
from the objects themselves. The
other is, the demonstrative character
of f>reometrical truths ; which was at

404

INDUCTION.

one time supposed to constitute a
radical distinction between them and
physical truths, the latter, as resting
on merely probable evidence, being
deemed essentially uncertain and un-
precise. The advance of knowledge
has, however, made it manifest that
physical science, in its better under-
stood branches, is quite as demon-
strative as geometry. The task of
deducing its details from a few com-
paratively simple principles is found
to be anything but the impossibility
it was once supposed to be ; and the
notion of the superior certainty of
geometry is an illusion, arising from
the ancient prejudice, which, in that
science, mistakes the ideal data from
which we reason for a peculiar class
of realities, while the corresponding
ideal data of any deductive physical
science are recognised as what they
really are, hypotheses.

Every theorem in geometry is a law
of external nature, and might have
been ascertained by generalising from
observation and experiment, which in
this case resolve themselves into com-
parison and measurement. But it
was found practicable, and being
practicable, was desirable, to deduce
these truths by ratiocination from a
small number of general laws of na-
ture, the certainty and universality
of which are obvious to the most
careless observer, and which compose
the first principles and ultimate pre-
mises of the science. Among these
general laws must be included the
same two which we have noticed as
ultimate principles of the Science of
Number also, and which are appli-
cable to every description of quantity,
viz. The sums of equals are equal,
and Things which are equal to the
same thing are equal to one another ;
the latter of which may be expressed
in a manner more suggestive of the
inexhaustible multitude of its con-
sequences by the following terms :
Whatever is equal to any one of a
number of equal magnitudes, is equal
to any other of them. To these two
must be added, in geometry, a third

law of equality, namely, that lines,
surfaces, or solid spaces, which can be
so applied to one another as to coin-
cide, are equal. Some writers have
asserted that this law of nature is a
mere verbal definition ; that the ex-
pression "equal magnitudes" mcan^
nothing but magnitudes which can
be so applied to one another as to
coincide. But in this opinion I can-
not agree. The equality of two geo-
metrical magnitudes cannot differ fun-
damentally in its nature from the
equality of two weights, two degrees
of heat, or two portions of duration,
to none of which would this defini-
tion of equality be suitable. None of
these things can be so applied to one
another as to coincide, yet we per-
fectly understand what we mean
when we call them equal. Things
are equal in magnitude, as things are
equal in weight, when they are felt
to be exactly similar in respect of the
attribute in which we compare them ;
and the application of the objects to
each other in the one case, like the
balancing them with a pair of scales
in the other, is but a mode of bring-
ing them into a position in which our
senses can recognise deficiencies of
exact resemblance that would other-
wise escape our notice.

Along with these three general
principles or axioms, the remainder
of the premises of geometry consists
of the so-called definitions : that is
to say, propositions asserting the real
existence of the various objects there-
in designated, together with some
one property of each. In some cases
more than one property is commonly
assumed, but in no case is more than
one necessary. It is assumed that
there are such things in nature as
straight lines, and that any two of
them setting out from the same point,
diverge more and more without limit.
This assumption, (which includes and
goes beyond Euclid's axiom that two
straight lines cannot enclose a space,)
is as indispensable in geometry, and
as evident, resting on as simple,
familiar, and universal observation,

REMAINING LAWS OF NATURE.

40s

as any of the other axioms. It is
also assumed that straight lines di-
verge from one another in different
degrees ; in other words, that there
are such things as angles, and that
they are capable of being equal or un-
equal. It is assumed that there is
such a thing as a circle, and that all
its radii are equal ; such things as
ellipses, and that the sums of the
focal distances are equal for every
point in an ellipse ; such things as
parallel lines, and that those lines are
everywhere equally distant.*

§ 8. It is a matter of more than
curiosity to consider to what peculi-
arity of the physical truths which are
the subject of geometry it is owing
that they can all be deduced from so
small a number of original premises :
why it is that we can set out from
only one characteristic property of
each kind of phenomenon, and with
that and two or three general truths
i-elating to equality can travel from

* Geometers have usually preferred to
define parallel Hues by the property of
being in tiio same plane and never meet-
ing. This, however, has rendered it neces-
sary for them to assume, as an additional
axiom, some other property of parallel
lines ; and the unsatisfactory manner in
which properties for that purpose have
been selected by Euclid and otliera has
always been deemed the opprobrium of
elementary geometry. Even as a verbal
definition, equidistance is a fitter pro})erty
to characterise parallels by, since it is the
attribute i-eally involved in the signifi-
cation of the name. If to bo in the same
plane and never to meet were all that is
meant by being parallel, we should feel
no incongruity in speaking of a curve as
parallel to its asymptote. The meaning of
parallel lines is, lines which pursue exactly
the same direction, and which, therefore,
neither draw nearer nor go farther from
one another ; a conception suggested at
once by the contemplation of nature. That
the lines will never meet is of course in
eluded in the more comprehensive pro-
position that they are everywhere equally
distant. And that any straight lines which
are in the same plane and not equidis-
tant will certainly meet, may be demon-
strated in the most rigorous manner from
the fundamental property of straight lines
assumed m the text, viz. that if they set
out from the same point, they diverge more
and more without limit.

mark to mark until we obtain a vast
body of derivative truths, to all ap-
pearance extremely unlike those ele-
mentary ones.

The explanation of this remarkable
fact seems to lie in the following cir-
cumstances. In the first place, all
questions of position and figure may be
resolved into questions of magnitude.
The position and figure of any object
are determined by determining the
position of a sufficient number of
points in it ; and the position of any
point may be determined by the
magnitude of three rectangular co-
ordinates, that is, of the perpendiculars
drawn from the point to three planes
at right angles to one another, arbitra-
rily selected. By this transformation
of all questions of quality into ques-
tions only of quantity, geometry is
reduced to the single problem of the
measurement of magnitudes, that is,
the ascertainment of the equalities
which exist between them. Now
when we consider that by one of the
general axioms, any equality, when
ascertained, is proof of as many other
equalities as there are other things
equal to either of the two equals ;
and that by another of those axioms,
any ascertained equality is proof of
the equality of as many pairs of
magnitudes as can be formed by the
numerous operations which resolve
themselves into the addition of the
equals to themselves or to other
equals ; we cease to wonder that in
proportion as a science is conversant
about equality, it should afford a
more copious supply of marks of
marks ; and that the sciences of
number and extension, which are con-
versant w-ith little else than equality,
should be the most deductive of all
the sciences.

There are also two or three of the
principal laws of space or extension
which are unusually fitted for rendering
one position or magnitude a mark of
anotlier, and thereby contributing to
render the science largely deductive.
First, the magnitudes of enclosed
spaces, whether superficial or solid,

4o6

INDUCTION.

are completely determined by the
magnitudes of the lines and angles
which bound them. Secondly, the
length of any line, whether straight
or curve, is measured (certain other
things being given) by the angle
which it subtends, and vice versa.
Lastly, the angle which any two
straight lines make with each other
at an inaccessible point, is measured
by the angles they severally make
with any third line we choose to
select. By means of these general
laws, the measurement of all lines,
angles, and spaces whatsoever might
be accomplished by measuring a single
straight line and a sufficient number
of angles ; which is the plan actually
pursued in the trigonometrical survey
of a country ; and fortunate it is that
this is practicable, the exact measure-
ment of long straight lines being al-
ways difficult, and often impossible,
but that of angles very easy. Three
such generalisations as the foregoing
afford such facilities for the indirect
measurement of magnitudes, (by sup-
plying us with known lines or angles
which are marks of the magnitude of
unknown ones, and thereby of the
spaces which they enclose,) that it is
easily intelligible how from a few data
we can go on to ascertain the mag-
nitude of an indefinite multitude of
lines, angles, and spaces, which we
could not easily, or could not at all,
measure by any more direct process.

§ 9. Such are the remarks which it
seems necessary to make in this place
respecting the laws of nature which
are the peculiar subject of the sciences
of number and extension. The im
mense part which those laws take in
giving a deductive character to the
other departments of physical science
is well known, and is not surprising
when we consider that all causes
operate according to mathematical
laws. The effect is alv\ays depen-
dent on or is a function of the quantity
of the agent, and generally of its
position also. We cannot, therefore,
reason respecting causation without

introducing considerations of quantity
and extension at every step ; and if
the nature of the phenomena admits
of our obtaining numerical data of
sufficient accuracy, the laws of quan-
tity become the grand instrument for
calculating forward to an effect or
backward to a cause. That in all
other sciences, as well as in geometry,
questions of quality are scarcely ever
independent of questions of quantity,
may be seen from the most familiar
phenomena. Even when several col-
ours are mixed on a painter's palette,
the comparative quantity of each en-
tirely determines the colour of the mix-
ture.

With this mere suggestion of the
general causes which render mathe-
matical principles and processes so pre-
dominant in those deductive sciences
which afford precise numerical data,
I must, on the present occasion, con-
tent myself : referring the reader who
desires a more thorough acquaintance
with the subject to the first two
volumes of M. Comte's systematic
work.

In the same work, and more parti-
cularly in the third volume, are also
fully discussed the limits of the ap-
plicability of matriematical principles
to the improvement of other sciences.
Such principles are manifestly inap-
plicable, where the causes on which
any class of phenomena depend are
so imperfectly accessible to our obser-
vation, that we cannot ascertain, by
a proper induction, their numerical
laws ; or where the causes are so
numerous, and intermixed in so com-
plex a manner with one another, that
even supposing their laws known, the
computation of the aggregate effect
transcends the powers of the calculus
as it is, or is likely to be ; or, lastly,
where the causes themselves are in a
state of perpetual fluctuation ; as in
physiology, and still more, if possible,
in the social science. The mathe-
matical solutions of physical ques-
tions become progressively more diffi-
cult and imperfect in proportion as
the questions divest themselves of

GROUNDS OF DISBELIEF.

407

their abstract and hypothetical char-
acter, and approach nearer to the de-
^ee of complication actually exist-
ing in nature ; insomuch that beyond
the limits of astronomical phenomena,
and of those most nearly analogous
to them, mathematical accuracy is
generally obtained "at the expense
of the reality of the inquiry ; " while
even in astronomical questions, " not-
withstanding the admirable simplicity
of their mathematical elements, our
feeble intelligence becomes incapable
of following out eflfectually the logical
combinations of the laws on which
the phenomena are dependent, as
soon as we attempt to take into
simultaneous consideration more than
two or three essential influences." *
Of this, the problem of the Three
Bodies has already been cited, more
than once, as a remarkable instance ;
the complete solution of so compara-
tively simple a question having vainly
tried the skill of the most profound
mathematicians. We may conceive,
then, how chimerical would be the
hope that mathematical principles
could be advantageously applied to
phenomena dependent on the mutual
action of the innumerable minute par-
ticles of bodies, as those of chemistry,
and still more of physiology ; and
for similar reasons those principles
remain inapplicable to the still more
complex inquiries, the subjects of
which are phenomena of society and
government.

The value of mathematical instruc-
tion as a preparation for those more
difficult investigations consists in the
applicability not of its doctrines, but
of its method. Mathematics will
ever remain the most perfect type
of the Deductive Method in general ;
and the applications of mathematics
to the deductive branches of physics,
furnish the only school in which phi-
losophers can effectually learn the
most difficult and important portion
of their art, the employment of the
laws of simpler phenomena for ex-
plaining and predicting those of the
* PhUotcphie Positive yiii. 4x4-416. I

more complex. These grounds ax«
quite sufficient for deeming mathe-
matical training an indispensable
basis of real scientific education, and
regarding (according to the dictum
which an old but unauthentic tradi-
tion ascribes to Plato) one who is
dyeojfidTprjTOi, as wanting in one of
the most essential qualifications for
the successful cultivation of the higher
branches of philosophy.

CHAPTER XXV.

OF THE GROUNDS OF DISBELIEF.

§ I. The method of arriving at
general truths, or general propositions
fit to be believed, and the nature
of the evidence on which they are
grounded, have been di.scussed, as far
as space and the writer's faculties
permitted, in the twenty-four preced-
ing chapters. But the result of the
examination of evidence is not always
belief, nor even suspension of judg-
ment ; it is sometimes disbelief. The
philosophy, therefore, of induction
and experimental inquiry is incom-
plete, unless the grounds not only of
belief, but of disbelief, are treated of ;
and to this topic we shall devote one,
and the final, chapter.

By disbelief is not here to be under-
stood the mere absence of belief The
ground for abstaining from belief is
simply the absence or insufficiency of
proof ; and in considering what i«
sufficient evidence to support any
given conclusion, we have already, by
implication, considered what evidence
is not sufficient for the same purpose.
By disbelief is here meant, not the
state of mind in which we form no
opinion concerning a subject, but that
in which we are fully persuaded that
!-ome opinion is not true ; insomuch
that if evidence, even of great appa-
rent strength, (whether grounded on
the testimony of others or on our own
supposed perceptions,) were produced
in favour of the opinion, we should
believe that the witne.^ses spoke falsely,

4Q%

INDUCTION.

or that they, or we ourselves, if we
were the direct percipients, w»re mis-
taken.

That there are such cases, no one
is likely to dispute. Assertions for
which there is abundant positive evi-
dence are often disbelieved, on account
of what is called their improbability,
or impossibility. And the question
for consideration is what, in the pre-
sent case, these words mean, and how
far and in what circumstances the
properties which they express are suffi-
cient grounds for disbelief.

§ 2. It is to be remarked in the
first place, that the positive evidence
produced in support of an assertion
which is nevertheless rejected on the
score of impossibility or improbability,
is never such as amounts to full proof.
It is always grounded on some ap-
proximate generalisation. The fact
may have been asserted by a hundred
witnesses ; but there are many ex-
ceptions to the universality of the
generalisation that what a hundred
witnesses affirm is true. We may
seem to ourselves to have actually
seen the fact ; but, that we really see
what we think we see, is by no means
an universal truth ; our organs may
have been in a morbid state, or we
may have inferred something, and
imagined that we perceived it. The
evidence, then, in the affirmative
being never more than an approxi-
mate generalisation, all will depend
on what the evidence in the negative
is. If that also rests on an approxi-
mate generalisation, it is a case for
comparison of probabilities. If the
approximate generalisations leading
to the affirmative are, when added
together, less strong, or in other
words, farther from being universal,
than the approximate generalisations
which support the negative side of
the question, the proposition is said
to be improbable, and is to be disbe-
lieved provisionally. If, however, an
alleged fact be in contradiction, not
to any number of approximate gene-
ralisations, but to a completed gene-

ralisation grounded on a rigorous in-
duction, it is said to be impossible,
and is to be disbelieved totally.

This last principle, simple and evi-
dent as it appears, is the doctrine
which, on the occasion of an attempt
to apply it to the question of the
credibility of miracles, excited so vio-
lent a controversy. Hume's celebrated
doctrine, that nothing is credible
which is contradictory to experience
or at variance with laws of nature, is
merely this very plain and harmless
proposition, that whatever is contra-
dictory to a complete induction is in-
credible. That such a maxim as this
should either be accounted a danger-
ous' heresy, or mistaken for a great
and recondite truth, speaks ill for the
state of philosophical speculation on
such subjects.

But does not (it may be asked) the
very statement of the proposition
imply a contradiction? An alleged
fact, according to this theory, is not
to be believed if it contradict a com-
plete induction. But it is essential
to the completeness of an induction
that it shall not contradict any known
fact. It is not then a petitio principii
to say, that the fact ought to be dis-
believed because the induction op-
posed to it is complete ? How can
we have a right to declare the induc-
tion complete, while facts, supported
by credible evidence, present them-
selves in opposition to it ?

I answer, we have that right when-
ever the scientific canons of induction
give it to us ; that is, whenever the
induction can be complete. We have
it, for example, in a case of causation
in which there has been an experi-
mentum crucis. If an antecedent A,
superadded to a set of antecedents in
all other respects unaltered, is fol-
lowed by an effect B which did not
exist before, A is, in that instance at
least, the cause of B, or an indispen-
sable part of its cause ; and if A be
tried again with many totally different
sets of antecedents and B still follows,
then it is the whole cause. If these
observations or experiments have been

GROUNDS OF DISBELIEF.

469

repeated so often, and by so many
persons, as to exclude all supposition
of error in the observer, a law of
nature is established ; and so long as
this law is received as such, the as-
sertion that on any particular occa-
sion A took place, and yet B did not
follow, without any counteracting cause,
must be disbelieved. Such an asser-
tion is not to be credited on any less
evidence than what would suffice to
overturn the law. The general truths,
that whatever has a beginning has a
cause, and that when none but the
same causes exist, the same effects
frtllow, rest on the strongest inductive
evidence possible ; the proposition
that things affirmed by even a crowd
of respectable witnesses are true, is
but an approximate generalisation ;
and — even if we fancy we actually
saw or felt the fact which is in con-
tradiction to the law — what a human
being can see is no more than a set
of appearances ; from which the real
nature of the phenomenon is merely
an inference, and in this inference ap-
proximate generalisations usually have
a large share. If, therefore, we make
our election to hold by the law, no
quantity of evidence whatever ought
to persuade us that there has occurred
anything in contradiction to it. If,
indeed, the evidence produced is such
that it is more likely that the set of
observations and experiments on which
the law rests should have been inac-
curately performed or incorrectly in-
terpreted, than that the evidence in
question should be false, we may be-
lieve the evidence ; but then we must
abandon the law. And since the law
was received on what seemed a com-
plete induction, it can only be rejec-
ted on evidence equivalent ; namely,
as being inconsistent not with any
number of approximate generalisa-
tions, but with some other and better
established law of nature. This ex-
treme case of a conflict between two
supposed laws of nature has probably
never actually occurred where, in the
process of investigating both the laws,
the true canons of scientific induction

had been kept in view ; but if it did
occur, it must terminate in the total
rejection of one of the supposed laws.
It would prove that there. must be a
flaw in the logical process by which
either one or the other was estab-
lished ; and if there be so, that sup-
posed general truth is no truth at all.
We cannot admit a proposition as a
law of nature, and yet believe a fact
in real contradiction to it. We must
disbelieve the alleged fact, or believe
that we were mistaken in admitting
the supposed law.

But in order that any alleged fact
should be contradictory to a law of
causation, the allegation must be, not
simply that the cause existed without
being followed by the effect, for that
would be no uncommon occurrence ;
but that this happened in the absence
of any adequate counteracting cause.
Now in the case of an alleged miracle,
the assertion is the exact opposite of
this. It is, that the effect was de-
feated, not in the absence, but in
consequence of a counteracting cause,
namely, a direct interposition of an
act of the will of some being who has
power over nature ; and in particular
of a Being whose will being assumed
to have endowed all the causes with
the powers by which they produce
their effects, may well be supposed
able to counteract them. A miracle
(as was justly remarked by Brown*)
is no contradiction to the law of cause
and effect ; it is a new effect, sup-
posed to be produced by the introduc-
tion of a new cause. Of the adequacy
of that cause, if present, there can be
no doubt ; and the only antecedent
improbability which can be ascribed
to the miracle is the improbability
that any such cause existed.

All, therefore, which Hume has made
out, and this he must be considered to
have made out, is, that (at least in the
imperfect state of our knowledge of
natural agencies, which leaves it al-
ways possible that some of the physi-

'* See the two remarkable notes (A) and
(F). appended to his Inquiry into the Rela-
tion of Cause and Effect.

410

INDUCTION.

cal antecedents may have been hidden
from us) no evidence can prove a
miracle to any one who did not pre-
viously believe the existence of a Being
or beings with supernatural power,
or who believes himself to have full
proof that the character of the Being
whom he recognises is inconsistent
with his having seen fit to interfere
on the occasion in question.

If we do not already believe in
supernatural agencies, no miracle can
prove to us their existence. The mir-
acle itself, considered merely as an
extraordinary fact, may be satisfac-
torily certified by our senses or by
testimony ; but nothing can ever prove
that it is a piiracle : there is still
another possible hypothesis, that of its
being the result of some unknown
natural cause ; and this possibility
cannot be so completely shut out as
to leave no alternative but that of
admitting the existence and interven-
tion of a Being superior to nature.
Those, however, who already believe
in such a Being, have two hypotheses
to choose from, a supernatural and an
unknown natural agency ; and they
have to judge which of the two is the
most probable in the particular case.
In forming this judgment, an impor-
tant element of the question will be
the conformity of the result to the
laws of the supposed agent, that is,
to the character of the Deity as they
conceive it. But, with the knowledge
which we now possess of the general
uniformity of the course of nature,
religion, following in the wake of
science, has been compelled to ac-
knowledge the government of the
universe as being on the whole carried
on by general laws, and not by special
interpositions. To whoever holds this
belief, there is a general presumption
against any supposition of divine
agency not operating through general
laws, or, in other words, there is an
antecedent improbability in every
miracle, which, in order to outweigh
it. requires an extraordinary strength
of antecedent probability derived from
the special circimistances of the case.

§ 3. It appeari from what lias been
said, that the assertion that a cause
has been defeated of an effect which
is connected with it by a completely
ascertained law of causation, is to be
disbelieved or not, according to the
probability or improbability that there
existed in the particular instance an
adequate counteracting cause. To
form an estimate of this is not more
difficult than of other probabilities.
With regard to all hnoion causes cap-
able of counteracting the given causes,
we have generally some previous know-
ledge of the frequency or rarity of
their occurrence, from which we may
draw an inference as to the ante-
cedent improbability of their having
been present in any particular case.
And neither in respect to known nor
unknown causes are we required to
pronounce on the probability of their
existing in nature, but only of their
having existed at the time and place
at which the transaction is alleged
to have happened. We are seldom,
therefore, without the means (when
the circumstances of the case are at
all known to us) of judging how far
it is likely that such a cause should
have existed at that time and place
without manifesting its presence by
some other marks, and (in the case of
an unknown cause) without having
hitherto manifested its existence in
any other instance. Accordinij as
this circumstance, or the falsity of
the testimony, appears more impro-
bable, that is, conflicts with an approxi-
mate generalisation of a higher order,
we believe the testimony, or disbelieve
it, with a stronger or a weaker degree
of conviction according to the prepon-
derance, at least until we have sifted
the matter farther.

So much, then, for the case in which
the alleged fact conflicts, or appears
to conflict, with a real law of causa-
tion. But a more common case, per-
haps, is that of its conflicting with
uniformities of mere co-existence, not
proved to be dependent on causation :
in other words, with the properties of
Kinds, It is with these uniformities

GROUNDS OF DISBELIEF.

411

principally that the marvellous stories
related by travellers are apt to be at
variance, as of men with tails or with
wings, and (until confirmed by experi-
ence) of flying fish ; or of ice, in the
celebrated anecdote of the Dutch tra-
vellers and the king of Siam. Facts
of this description, facts previously
unheard of, but which could not from
any known law of causation be pro-
nounced impossible, are what Hume
characterises as not contrary to ex-
perience, but merely imconformable
to it ; and Bentham, in his treatise
on Evidence, denominates them facts
disconforniable m specie, as distin-
guished from such as are disconform-
able in toto or in degree.

In a case of this description, the
fact asserted is the existence of a new
Kind, which in itself is not in the
slightest degree incredible, and only
to be rejected if the improbability
that any variety of object existing at
the particular place and time should
not have been discovered s<x)ner, be
greater than that of error or men-
dacity in the witnesses. Accordingly,
such assertions, when made by cre-
dible persons, and of unexplored places,
are not disbelieved, but at most re-
garded as requiring confirmation from
subsequent observers ; unless the al-
leged properties of the supposed new
Kind are at variance with known pro-
perties of some larger kind which in-
cludes it ; or, in other words, unless,
in the new Kind which is asserted to
exist, some properties are said to have
been found disjoined from others which
have always been known to accom-
pany them ; as in the case of t*liny's
men, or any other kind of animal of
a structure different from that which
has always been found to co-exist
with animal life. On the mode of
dealing with any such case, little
needs be added to what has been
said on the same topic in the twenty-
second chapter. * When the uni-
formities of co-existence which the
alleged fact would violate are such
as to raise a strong presumption of
» Supra, pp. 383» 384-

their being the result of cauBation,
the fact which conflicts with them
is to be disbelieved, at least pro-
visionally, and subject to further in-
vestigation. When the presumption
amounts to a virtual certainty, as in
the case of the general structure of
organised beings, the only question
requiring consideration is whether,
in phenomena so little understood,
there may not be liabilities to coun-
teraction from causes hitherto un-
known ; or whether the phenomena
may not be capable of originating in
some other way, which would pro-
duce a different set of derivative uni-
formities. Where (as in the case of
the flying-fish, or the omithorhyn-
chus) the generalisation to which the
alleged fact would be an exception
is very special and of limited range,
neither of the above suppositions can
be deemed very improbable ; and it is
generally, in the case of such alleged
anomalies, wise to suspend our judg-
ment, pending the subsequent in-
quiries, which will not fail to confirm
the assertion if it be true. But when
the generalisation is very comprehen-
sive, embracing a vast number and
variety of observations, and covering
a considerable province of the domain
of nature, then, for reasons which
have been fully explained, such an
empirical law comes near to the cer-
tainty of an ascertained law of causa-
tion, and any alleged exception to it
cannot be admitted, unless on the evi-
dence of some law of causation proved
by a still more complete induction.

Such uniformities in the course of
nature as do not bear marks of being
the results of causation, are, as we
have already seen, admissible as uni-
versal truths with a degree of cre-
dence proportioned to their generality.
Those which are true of all things
whatever, or at least which are totally
independent of the varieties of Kinds,
namely, the laws of number and ex-
tension, to which we may add the law
cf causation itself, are probably the
only ones, an exception to which is
absolutely and permanently incre-

4t2

INDUCTION.

dible. Accordingly, it is to assertions
supposed to be contradictory to these
laws, or to some others coming near
to them in generality, that the word
impossibility (at least total impossi-
bility) seems to be generally confined.
Violations of other laws, of special
laws of causation for instance, are
said, by persons studious of accuracy
in expression, to be impossible in the
circumstances of the case, or impos-
sible unless some cause had existed
which did not exist in the particular^
case.* Of no assertion, not in con-
tradiction to some of these vezy general
laws, will more than improbability be
asserted by any cautious person ; and
improbability not of the highest de-
gree, unless the time and place in
which the fact is said to have oc-
curred, render it almost certain that
the anomaly, if real, could not have
been overlooked by other observers.
Suspension of judgment is in all other
cases the resource of the judicious
inquirer, provided the testimony in
favour of the anomaly presents, when
well sifted, no suspicious circum-
stances.

But the testimony is scarcely ever
found to stand that test in cases in
which the anomaly is not real. In
the instances on record in which a
great number of witnesses, of good
reputation and scientific acquirements,
have testified to the truth of some-
thing which has turned out untrue,
there have almost always been cir-
cumstances which, to a keen observer
who had taken due pains to sift the
matter, would have rendered the testi-
mony untrustworthy. There have
generally been means of accounting

* A writer to whom I have several times
referred gives as the definition of an im-
possibility, that which there exists in the
world no canse adequate to produce. This
definition does not take in such impossi-
■bilities as these — that two and two should
make five ; tint two straight lines eh uld
enclose a space ; or that anything should
be-iu to exist without a cause. I can
think of no definition of impossibility
comprehensive enough to inchide all its
Tarieties, except the one which I have
given, viz. An impossibility is that, the
truth of which would conflict with a com-

for the impression on the senses or
minds of the alleged percipients by
fallacious appearances ; or some epi-
demic delusion, propagated by the
contagious influence of popular feel-
ing, has been concerned in the case ;
or some strong interest has been im-
plicated— religious zeal, party feeling,
vanity, or at least the passion for the
marvellous, in persons strongly sus-
ceptible of it. When none of these
or similar circumstances exist to ac-
count for the apparent strength of
the testimony ; and where the asser-
tion is not in contradiction either to
those universal laws which know no
counteraction or anomaly, or to the
generalisations next in comprehen-
siveness to them, but would only
amount, if admitted, to the exist-
ence of an unknown cause or an
anomalous Kind, in circumstances
not so thoroughly explored but that
it is credible that things hitherto
unknown may still come to light ; a
cautious person will neither admit
nor reject the testimony, but will
wait for confirmation at other times
and from other unconnected sources.
Such ought to have been the conduct
of the King of Siam when the Dutch
travellers aflBrmed to him the exist-
ence of ice. But an ignorant person
is as obstinate in his contemptuous in-
credulity as he is unreasonably credu-
lous. Anything unlike his own narrow
experience he disbelieves if it flatters
no propensity ; any nursery tale is
swallowed implicitly by him if it does.

§ 4.. I shall now advert to a very
serious misapprehension of the prin-
ciples of the subject, which has been
plete induction, that is, with the most
conclusive evidence which we possess of
universal truth.

As to the reputed impossibilities which
rest on no other grounds than our ignor-
ance of any catise capable of producing the
supposed effects, very few of tliem are
certainly impossible, or permanently in-
credible. The facts of travelling seventy
miles an hour, painless surgical operations,
and conversing by instantaneous signals
between London and New York, held a
high place, not many years ago, among
such impossibilities.

GROUNDS OF DISBELIEF.

413

committed by some of the writers
against Hume's Essay on Miracles,
and by Bishop Butler before them,
in their anxiety to destroy what ap-
peared to them a formidable weapon
of assault against the Christian reli-
gion, and the effect of which is en-
tirely to confound the doctrine of the
Grounds of Disbelief. The mistake
consists in overlooking the distinction
between (what may be called) impro-
bability before the fact and improba-
bility after it ; or (since, as Mr. Venn
remarks, the distinction of past and
future is not the material circum-
stance) between the improbability of a
mere guess being right and the impro-
bability of an alleged fact being true.
Many events are altogether im-
probable to us before they have hap-
pened, or before we are informed of
their happening, which are not in the
least incredible when we are informed
of them, because not contrary to any,
even approximate, induction. In the
cast of a perfectly fair die, the chances
are five to one against throwing ace,
that is, ace will be thrown on an
average only once in six throws. But
this is no reason against believing
that ace was thrown on a given oc-
casion, if any credible witness asserts
it, since, though ace is only thrown
once in six times, some number which
is only thrown once in six times must
have been thrown if the die was
thrown at all. The improbability,
then, or, in other words, the unusual-
ness, of any fact is no reason for dis-
believing it, if the nature of the case
renders it certain that either that or
something equally improbable, that
is, equally unusual, did happen. Nor
is this all ; for even if the other five
sides of the die were all twos or all
threes, yet as ace would still on the
average come up once in every six
throws, its coming up in a given
throw would be not in any way con-
tradictory to experience If we dis-
believed all facts which had the
chances against them beforehand, we
should believe hardly anything. We
are told that A. B. died yesterday :

the moment before we were so told,
the chances against his having died
on that day may have been ten thou-
sand to one ; but since he was certain
to die at some time or other, and when
he died must necessarily die on some
particular day, while the preponder-
ance of chances is very great against
every day in particular, experience
affords no ground for discrediting
any testimony which may be pro-
duced to the event's having taken
place on a given day.

Yet it has been considered, by Dr.
Campbell and others, as a complete
answer to Hume's doctrine (that
things are incredible which are con-
trmy to the uniform course of ex-
perience) that we do not disbelieve,
merely because the chances were
against them, things in strict con-
formity to the uniform course of ex-
perience ; that we do not disbelieve
an alleged fact merely because the
combination of causes on which it
depends occurs only once in a certain
number of times. It is evident that
whatever is shown by observation, or
can be proved from laws of nature, to
occur in a certain proportion (how-
ever small) of the whole number of
possible cases, is not contrary to ex-
perience, though we are right in dis-
believing it if some other supposition
respecting the matter in question in-
volves on the whole a less departure
from the ordinary course of events.
Yet, on such grounds as this have
able writers been led to the extraor-
dinary conclusion that nothing sup-
ported by credible testimony ought
ever to be disbelieved.

§ 5. We have considered two species
of events, commonly said to be im-
probable ; one kind which are in no
way extraordinary, but which, having
an immense preponderance of chances
against them, are improbable until
they are affirmed, but no longer ;
another kind which, being contrary
to some recognised law of nature, are
incredible on any amount of testi-
mony except such as would be suffi-

414

INDUCTION.

cient to shake our belief in the law
itself. But between these two classes
of events there is an itjtennediate
class, consisting of what are commonly
termed Coincidences : in other words,
those combinations of chances which
present some peculiar and unexpected
regularity, assimilating them, in so
far, to the results of law. As if, for
example, in a lottery of a thousand
tickets, the numbers should be drawn
in the exact order of what are called
the natural numbers, i, 2, 3, &c.
We have still to consider the prin-
ciples of evidence applicable to this
case : whether there is any difference
between coincidences and ordinary
events in the amount of testimony
or other evidence necessary to render
them credible.

It is certain that, on every rational
principle of expectation, a combina-
tion of this peculiar sort may be
expected quite as often as any other
given series of a thousand numbers ;
that with perfectly fair dice, sixes
will be thrown twice, thrice, or any
number of times in succession, quite
as often in a thousand or a million
throws, as any other succession of
numbers fixed upon beforehand ; and
that no judicious player would give
greater odds against the one series
than against the other. Notwith-
standing this, there is a general dis-
position to regard the one as much
more improbable than the other, and
as requiring much stronger evidence
to make it credible. Such is the
force of this impression, that it has
led some thinkers to the conclusion,
that natxire has greater difficulty in
producing regular combinations than
irregular ones ; or, in other words,
that there is some general tendency
of things, some law, which prevents
regular combinations from occurring,
or at least from occurring so often as
others. Among these thinkers may
be numbered D'Alembert, who, in
an Essay on Probabilities to be found
in the fifth volume of his Melanf/es,
contends that regular combinations,
though equally probable according to

the mathematical theory with any
others, are physically less probable.
He appeals to connuon sense, or, in
other words, to common impressions ;
saying, if dice thrown repeatedly in
our presence gave sixes every time,
should we not, before the number of
throws had reached ten, (not to speak
of thousands of millions,) be ready to
affirm, with the most positive convic-
tion, that the dice were false ?

The common and natural impres-
sion is in favour of D'Alembert : the
regular series would be thought much
more unlikely than an irregular. But
this common impression is, I appre-
hend, merely grounded on the fact,
that scarcely anybody remembers to
have ever seen one of these peculiar
coincidences : the reason of which is
simply that no one's experience ex-
tends to anything like the number
of trials within which that or any
other given combination of events can
be expected to happen. The chance
of sixes on a single throw of two dice
being -^^ the chance of sixes ten
times in succession is i di\ided by
the tenth power of 36 ; in other words,
such a concurrence is only likely to
happen once in 3,656,158,440,062,976
trials, a number which no dice-player's
experience comes up to a millionth
part of. But if, instead of sixes ten
times, any other given succession of
t n throws had been fixed upon, it
would have been exactly as unlikely
that in any individual's experience
that particular succession had ever
occurred ; although this does not seem
equally improbable, because no one
would be likely to have remembered
whether it had occurred or not,
and because the comparison is tacitly
made, not between sixes ten times and
any one particular series of throws,
but between all regular and all irregu-
lar successions taken together.

That (as D'Alembert says) if the
succession of sixes was actually
thrown before our eyes, we should
ascribe it not to chance, but to un-
fairness in the dice, is unquestionably
true. But this arises from a totally

GROUNDS OF DISBELIEF

41S

flifferent principle. We should then
be considering, not the probability of
the fact in itself, but the comparative
probability with which, when it is
known to have happened, it may be re-
ferred to one or to another cause. The
regular series is not at all less likely
than the irregular one to be brought
about by chance, but it is much more
likely than the irregular one to be
produced by design, or by some gene-
ral cause operating through the struc-
ture of the dice. It is the nature of
casual combinations to produce a
repetition of the same event, as often
and no oftener than any other series
of events. But it is the nature of
general causes to reproduce, in the
same circumstances, always the same
event. Common sense and science
alike dictate that, all other things
being the same, we should rather
attribute the effect to a cause which,
if real, would be very likely to pro-
duce it, than to a cause which would
be very unlikely to produce it. Ac-
cording to Laplace's sixth theorem,
which we demonstrated in a former
chapter, the difference of probability
arising from the superior efficacy of
the constant cause, unfairness in the
dice, would after a very few throws
far outweigh any antecedent proba-
bility which there could be against its
existence.

D'Alembert should have put the
question in another manner. He
should have supposed that we had
ourselves previously tried the dice,
and knew by ample experience that
they were fair. Another person then
tries them in our absence, and assures
us that he threw sixes ten times in
succession. Is the assertion credible
or not? Here the effect to be ac-
counted for is not the occurrence
itself, but the fact of the witness's as-
serting it. This may arise either
from its having really happened, or
from some other cause. What we
have to estimate is the comparative
probability of these two suppositions.

If the witness affirmed that he had
thrown any other ieries of numbers,

supposing him to he a person of
veracity and tolerable accuracy, and
to profess that he took particular
notice, we should believe him. But
the ten sixes are exactly as likely to
have been really thrown as the other
series. If, therefore, this assertion
is less credible than the other, the
reason must be, not that it is less
likely than the other to be made
truly, but that it is more likely than
the other to be made falsely.

One reason obviously presents itself
why what is called a coincidence
should be oftener asserted falsely
than an ordinary combination. It
excites wonder. It gratifies the love
of the marvellous. The motives,
therefore, to falsehood, one of the
most frequent of which is the desire
to astonish, operate more strongly in
favour of this kind of assertion than
of the other kind. Thus far there is
evidently more reason for discrediting
an alleged coincidence, than a state-
ment in itself not more probable, but
which if made would not be thought
remarkable. There are cases, how-
ever, in which the presumption on
this ground would be the other way.
There arc some witnesses who, the
more extraordinary an occurrence
might appear, would be the more
anxious to verify it by the utmost
carefulness of observation before they
would venture to believe it, and still
more before they would assert it to
others.

§ 6. Independently, however, of
any peculiar chances of mendacity
arising from the nature of the asser-
tion, Laplace contends, that merely
on the general ground of the falli-
bility of testimony, a coincidence is
not credible on the same amount of
testimony on which we should be
warranted in believing an ordinary
combination of events. In order to
do justice to his argument, it is neces-
sary to illustrate it by the example
chosen by himself.

If, says Laplace, there were one
thousand tickets in a box, and one

4i6

INDUCTION.

only has been drawn out, then if an
eye-witness affirms that the number
drawn vas 79, this, though the
chances were 999 in 1000 against it,
is not on that account the less
credible ; its credibility is equal to
the antecedent probability of the wit-
ness's veracity. But if there were in
the box 999 black balls and only one
white, and the witness affirms that
the white ball was drawn, the case
according to Laplace is very different :
the credibility of his assertion is but
a small fraction of what it was in the
former case ; the reason of the differ-
ence being as follows : —

The witnesses of whom we are
speaking must, from the nature of
the case, be of a kind whose credi-
bility falls materially short of cer-
tainty : let us suppose, then, the
credibility of the witness in the case
in question to be ^'^ J that is, let us
suppose that in every ten statements
which the witness makes, nine on an
average are correct and one incorrect.
Let us now suppose that there have
taken place a sufficient number of
drawings to exhaust all the possible
combinations, the witness deposing in
every one. In one case out of every
ten in all these drawings he will
actually have made a false announce-
ment. But in the case of the thou-
sand tickets these false announcements
will have been distributed impartially
over all the numbers, and of the 999
cases in which No. 79 was not drawn,
there will have been only one case in
which it was announced. On the
contrary, in the case of the thousand
balls, (the announcement being always
either "black" or "white,") if white
was not drawn, and there was a false
announcement, that false announce-
ment must have been white ; and
since by the supposition there was a
false announcement once in every ten
times, white will have been announced
falsely in one -tenth part of all the cases
in which it was not drawn, that is, in
one-tenth part of 999 cases out 'of every
thousand. White, then, is drawn, on
an average, exactly as often as No. 79,

but it is announced, without having
been really drawn, 999 times as often
as No. 79 ; the announcement there-
fore requires a much greater amount
of testimony to render it credible.*

To make this argument valid it
must of course be supposed that the
announcements made by the witness
are average specimens of hia general
veracity and accuracy, or at least
that they are neither more nor less so
in the case of the black and white
balls than in the case of the thousand
tickets. This assumption, however,
is not warranted- A person is far
less likely to mistake who has only
one form of error to guard against,
than if he had 999 different errors to
avoid. For instance, in the example
chosen, a messenger who might make
a mistake once in ten times in report-
ing the number drawn in a lottery,
might not err once in a thousand
times if sent simply to observe
whether a ball was black or white.
Laplace's argument, therefore, is
faulty even as applied to his own
case. Still less can that case be re-
ceived as completely representing all
cases of coincidence. Laplace has so
contrived his example, that thougli
black answers to 999 distinct possi-
bilities, and white only to one, the
witness has nevertheless no bias which
can make him prefer black to white.
The witness did not know that there
were 999 black balls in the box and
only one white ; or if he did, Laplace
has taken care to make all the 999
cases so undistinguishably alike, that
there is hardly a possibility of any

* Not, however, as might at first sight
appear, 990 times as much. A complete
analysis of the cases shows that (always
assuming the veracity of the witness to
he -^r) in 10,000 drawings, the drawing of
No. 79 will occur nine times, and be an-
nounced incoiTectly once ; the credibility,
therefore, of the announcement of No. 79
is -fo ; while the drawing of a white ball
will occur nine times and be announced
incrrectly 999 times. The credibility,
therefore, of the announcement of white
is yjj'ny, and the ratio of the two 1008 : 10 ;
the one announcement being thus only
about a hundred times more credible than
the other, ius'ead of 999 times.

GROUNDS OF DISBELIEF.

417

cause of falsehood or error operating
in favour of any of them, which would
not operate in the same manner if
there were only one. Alter thi8 sup-
position, and the whole argument
falls to the ground. Let the balls,
for instance, be numbered, and let
the white ball be No. 79. Considered
in respect of their colour, there are
but two things which the witness can
be interested in asserting, or can have
dreanit or hallucinated, or has to
choose from if he answers at random,
viz. black and white ; but considered
in respect of the numbers attached to
them, there are a thousand ; and if
his interest or error happens to be
connected with the numbers, though
the only assertion he makes is about
the colour, the case becomes precisely
assimilated to that of the thousand
tickets. Or instead of the balls sup-
pose a lottery, with looo tickets and
but one prize, and that I hold No. 79,
and being interested only in that, ask
the witness not what was the number
drawn, but whether it was 79 or some
other. There are now only two ca.se8,
as in Laplace's example ; yet he surely
would not say that if the witness an-
swered 79, the assertion would be in
an enormous proportion less credible
than if he made the same answer to
the same question asked in the other
way. If, for instance, (to put a case
supposed by Laplace himself,) he has
staked a large sum on one of the
chances, and thinks that by announc-
ing its occurrence he shall increase
his credit ; he is equally likely to
have betted on any one of the 999
numbers which are attached to black
balls, and, so far as the chances of
mendacity from this cause are con-
cerned, there will be 999 times as
many chances of his announcing black
falsely as white.

Or suppose a regiment of lOOO men,
999 Englishmen and one Frenchman,
and that of these one man has been
killed, and it is not known which. I
ask the question, and the witness an-
swers, the Frenchman. This was not
pol^ as improbable d friori, but i»

in itself as singular a circumstance,
as remarkable a coincidence, as tho
drawing of the white ball ; yet w»
should believe the statement as readily
as if the answer had been John
Thompson. Because, though the 999
Englishmen were all alike in the
point in which they diflfeied from the
Frenchman, they were not, like the
999 black balls, undistinguishable in
every other respect ; but being all
different, they admitted as many
chances of interest or error as if each
man had been of a different nation ;
and if a lie was told or a mistake
made, the misstatement was as likely
to fall on any Jones or Thompson of
the set as on the Frenchman.

The example of a coincidence se-
lected by D'Alembert, that of sixes
thrown on a pair of dice ten times ia
succession, belongs to this sort of case*
rather than to such as Laplace's. The
coincidence is here far more remark-
able, because of far rarer occurrence,
than the drawing of the white ball.
But though the improbability of its
really occurring is greater, the supe-
rior probability of its being an-
nounced falsely cannot be es ablished
with the same evidence. The an-
nouncement "black" represented 999
cases, but the witness may not have
known this, and if he did, the 999
cases are so exactly alike, that there
is really only one set of possible causes
of mendacity corresponding to the
whole. The announcement, "sixes
not drawn ten times," represents, and
is known by the witness to represent,
a great multitude of contingencies,
every one of which being unlike every
other, there may be a different and &
fresh set of causes of mendacity cor-
responding to each.

It appears to me, therefore, that
Laplace's doctrine is not strictly true
of any coincidences, and is wholly
inapplicable to most ; and that to
know whether a coincidence does or
does not require more evidence to
render it credible than an ordinary
event, we must refer, in every in-
stance, to first principles, and esti-

20

4i8

INDUCTION.

mate afresh what is the probability j discussion of the Grounds of Disbe-

that the given testimony would have
been delivered in that instance, sup-
posing the fact which it asserts not
to be true.

With these remarks we close the

lief, and along with it such exposi-
tion as space admits, and as the writer
has it in his power to furnish, of the
Logic of Induction.

BOOK IV.

OF OPERATIONS SUBSIDIAEF TO
INDUCTION.

" Clear and distinct ideas are terms which, though familiar and frequent in men's
mouths, I have reason to think every one who uses does not perfectly understand. And
lX)S8ibly it is but here and there one who gives himself the trouble to consider them
so far as to know wliat he himself or others precisely mean by them ; I have, therefore,
in most places, chose to put determinate or determined, instead of clear and distinct,
as more likely to direct men's thoughts to my meaning in this matter."— Locke's Eaatj
OH the llamun Understanding ; Epistle to the Reader.

" II ne pent y avoir qu'une methode parfaite, qui est la mithode naturelU: on nomme
ainsi uu arrangement dans lequel les etres du mSme genre seraient plus voisins eutro
eux que ceux de tous les autres genres ; les genres du mome ordrc, plus que ceux de tons
les autres ordres ; et ainsi de suite. Cette methode est I'ideal auquel I'histoire naturelle
doit tendre ; car il est Evident que si Ton y parvenait, Ton aurait I'expressiou cxacte ct
complete de la nature entiferc."— Cvvier, Jiegtit Animal, Introduction.

"Deux gi-andes notions philosophiques dominent la thdorie fondamentale de la
Tuethode naturelle proprement ditc, savoir la formation des groupes naturels, et ensuite
leur succession hierarchique."— Comte, Cours de Philosophie Positive, 42me leQon.

CHAPTER I.

OP OBSERVATION AND DESCRIPTION.

§ I. The inquiry which occupied
T19 in the two preceding books has
conducted us to what appears a satis-
factory solution of the principal pro-
blem of Logic, according to the con-
ception I have formed of the science.
We have found that the mental pro-
cess with which Logic is conversant,
the operation of ascertaining truths
by means of evidence, is always, even
when appearances point to a different
theory of it, a process of induction.
And we have particularised the vari-
ous modes of induction, and obtained
a clear view of the principles to which
it must conform, in order to lead to
results which can be relied oo-

The consideration of Induction,
however, does not end with the direct
rules for its performance. Something
must be said of those other operations
of the mind, which are either neces-
sarily presupposed in all induction,
or are instrumental to the more diffi-
cult and complicated inductive pro-
cesses. The present book will be de-
voted to the consideration of these
subsidiary operations, among which
our attention must first be given to
those which are indispensable pre-
liminaries to all induction whatso-
ever.

Induction being merely the exten-
sion to a class of cases of something
which has been observed to be true in
certain individual instances of the
class, the first place among the opej-j^-

420

OPERATIONS SUBSIDIARY TO INDUCTION.

tions subsidiary to induction is claimed
by Observation. This is not, however,
the place to lay down rules for mak-
ing good observers ; nor is it within
the competence of Logic to do so, but
of the art of intellectual Education.
Our business with observation is only
in its connection with the appropriate
problem of Logic, the estimation of
evidence. We have to consider, not
how or what to observe, but under
what conditions observation is to be
relied on ; what is needful, in order
that the fact, supposed to be observed,
may safely be received as true.

§ 2. The answer to this question is
very simple, at least in its first aspect.
The sole condition is, that what is
supposed to have been observed shall
really have been observed ; that it be
an observation, not an inference. For
in almost every act of our perceiving
faculties, observation and inference
are intimately blended. What we are
said to observe is usually a compound
result, of which one-tenth may be ob-
servation, and the remaining nine-
tenths inference.

I affirm, for example, that I hear a
man's voice. This would pass, in com-
mon language, for a direct perception.
All, however, which is really percep-
tion, is that I hear a sound. That
the sound is a voice, and that voice
the voice of a man, are not percep-
tions but inferences. I affirm, again,
that I saw my brother at a certain
hour this morning. If any proposi-
tion concerning a matter of fact would
commonly be said to be known by the
direct testimony of the senses, this
surely would be so. The truth, how-
ever, is far otherwise. I only saw a
certain coloured surface ; or rather I
had the kind of visual sensations
which are usually produced by a
coloured surface ; and from these as
marks, known to be such by pre-
vious experience, I concluded that I
saw my brother. I might have had
sensations precisely similar when my
brother was not there. I might have
(Been eome other person so nearly re-

sembling him in appearance as, at
the distance, and with the degree of
attention which I b«stowed, to be
mistaken for him. I might have
been asleep, and have dreamed that
I saw him ; or in a nervous state of
disorder, which brought his image be-
fore me in a waking hallucination.
In all these modes, many have been
led to believe that they saw persons
well known to them, who were dead
or far distant. If any of these sup-
positions had been true, the affirma-
tion that I saw my brother would
have been erroneous ; but whatever
was matter of direct perception,
namely, the visual sensations, would
have been real. The inference only
would have been ill grounded ; I
should have ascribed those sensations
to a wrong cause.

Innumerable instances might be
given, and analysed in the same man-
ner, of what are vulgarly called errors
of sense. There are none of them
properly errors of sense ; they are erro-
neous inferences from sense. When
I look at a candle through a multi-
plying glass, I see what seems a dozen
candles instead of one : and if the real
circumstances of the case were skil-
fully disguised, I might suppose that
there were really that number ; there
would be what is called an optical
deception. In the kaleidoscope there
really is that deception : when I look
through the instrument, instead of
what is actually there, namely, a casual
arrangement of coloured fragments,
the appearance presented is that of
the same combination several times
repeated in symmetrical arrangement
round a point. The delusion is of
course effected by giving me the same
sensations which I should have had
if such a symmetrical combination
had really been presented to me. If
I cross two of my fingers, and bring
any small object, a marble, for in-
stance, into contact with both, at
points not usually touched simulta-
neously by one object, I can hardly,
if my eyes are shut, help believing
that there 9,vo two mfti'bles instead of

OBSERVATION AND DESCRIPTION.

m

one. But it is not my touch in this
case, nor my sight in the other, which
is deceived ; the deception, whether
durable or only momentary, is in my
judgment. From my senses I have
only the sensations, and those are
genuine. Being accustomed to have
those or similar sensations when, and
only when, a certain arrangement of
outward objects is present to my
organs, I have the habit of instantly,
when I experience the sensations,
inferring the existence of that state
of outward things. This habit has
become so powerful, that the infer-
ence, performed with the speed and
certainty of an instinct, is confounded
with intuitive perceptions. When it
is correct, I am unconscious that it
ever needed proof ; even when I know
it to be incorrect, I cannot, without
considerable effort, abstain from
making it. In order to be aware
that it is not made by instinct but
by an acquired habit, I am obliged
to reflect on the slow process through
which I learnt to judge by the eye
of many things which I now appear
to perceive directly by sight ; and on
the reverse operation performed by
persons learning to draw, who with
difficulty and labour divest them-
selves of their acquired perceptions,
and learn afresh to see things as they
appear to the eye.

It would be easy to prolong these
illustrations, were there any need to
expatiate on a topic so copiously ex-
emplified in various popular works.
From the examples already given, it
is seen sufficiently that the individual
facts from which we collect our in-
ductive generalisations are scarcely
ever obtained by observation alone.
Observation extends only to the sen-
sations by which we recognise objects;
but the propositions which we make
use of, either in science or in common
life, relate mostly to the objects them-
selves. In every act of what is called
observation, there is at least one
inference — from the sensations to
the presence of the object ; from
the marks or diagnostics to the en-

tire phenomenon. And hence, among
other consequences, follows the seem-
ing paradox that a general proposi-
tion collected from particulars is often
more certainly true than any one of
the particular propositions from which,
by an act of induction, it was inferred.
For each of those particular (or rather
singular) propositions involved an in-
ference from the impression on the
senses to the fact which caused that
impression ; and this inference may
have been erroneous in any one of the
instances, but cannot well have been
erroneous in all of them, provided
their number was sufficient to elimi-
nate chance. The conclusion, there-
fore, that is, the general proposition,
may deserve more complete reliance
than it would be safe to repose in any
one of the inductive premises.

The logic of observation, then, con-
sists solely in a correct discrimination
between that, in a result of observa-
tion, which has really been perceived,
and that which is an inference from
the perception. Whatever portion is
inference, is amenable to the rules of
induction already treated of, and re-
quires no further notice here : th©
question for us in this place is, when
all which is inference is taken away,
what remains. There remains, in the
first place, the mind's own feelings
or states of consciousness, namely, its
outward feelings or sensations, and
its inward feelings — its thoughts,
emotions, and volitions. Whether
anything else remains, or all else is
inference from this ; whether the
mind is capable of directly perceiv-
ing or apprehending anything except
states of its own consciousness — is a
problem of metaphysics not to be dis-
cussed in this place. But after ex-
cluding all questions on which meta-
physicians differ, it remains true, that
for most purposes the discrimination
we are called upon practically to ex-
ercise is that between sensations or
other feelings, of our own or of other
people, and inferences drawn from
them. And on the theory of Observa-
tion this is all which seems necessary

4222

OPERATIONS SUBSIDIARY TO INDUCTION.

to be said for the purposes of the
present work.

§ 3. If, in the simplest observation,
or in what passes for such, there is a
large part which is not observation
but something else, so in the simplest
description of an observation, there
is, and must always be, much more
asserted than is contained in the per-
ception itself. We cannot describe a
fact without implying more than the
- fact. The perception is only of one
individual thing ; but to describe it
is to affirm a connection between it
and every other thing which is either
denoted or connoted by any of the
^tenns used. To begin with an ex-
""ample, than which none can be con-
ceived more elementary : I have a
sensation of sight, and I endeavour
^to describe it by saying that I see
p something white. In saying this, I
T do not solely affirm my sensation ; I
^^ also class it. I assert a resemblance
between the thing I see, and all
things which I and others are accus-
tomed to call white. I assert that it
resembles them in the circumstance
in which they all resemble one an-
other, in that which is the ground of
-their being called by the name. This
^/ is not merely one way of describing
C an observation, but the only way.
If I would either register my obser-
vation for my own future use, or make
it known for the benefit of others, I
must assert a resemblance between
the fact which I have observed and
something else. It is inherent in a
description, to be the statement of a
resemblance, or resemblances.

We thus see that it is impossible
to express in words any result of ob-
servation without performing an act
possessing what Dr. Whewell considers
to be characteristic of Induction.
There is always something introduced
which was not included in the obser-
vation itself ; some conception com-
mon to the phenomenon with other
phenomena to which it is compared.
An observation cannot be spoken of
' in language at all without declaring

more than that one observation ; with-
out assimilating it to other phenomena
already observed and classified. But^
this identification of an object — this/
recognition of it as possessing certain '
known characteristics — hasneverbeen
confounded with Induction. It is an
operation which precedes all induc-
tion, and supplies it with its materials.
It is a perception of resemblances, ob-
tained by comparison.

These resemblances are not always
apprehended directly, by merely com-
paring the object observed with some
other present object, or with our re-
collection of an object which is absent.
They are often ascertained through
intei-mediate marks, that is, deduc-
tively. In describing some new kind
of animal, suppose me to say that it
measures ten feet in length, from the
forehead to the extremity of the tail.
I did not ascertain this by the unas-
sisted eye. I had a two-foot rule
which I applied to the object, and,
as we commonly say, measured it ;
an operation which was not wholly *
manual, but partly also mathematical,
involving the two propositions, Five
times two is ten, and Things whicl?
are equal to the same thing are equal
to one another. Hence, the fact that
the animal is ten feet long is not an
immediate perception, but a conclu-
sion from re?'ming; the minor pre-
mises alone b^ (\g furnished by obser-
vation of the object. Nevertheless,
this is called an observation, or a
description of the animal, not an in-
duction respecting it.

To pass at once from a very simple
to a very complex example ; I affirm
that the earth is globular. The as-
sertion is not grounded on direct per-
ception ; for the figure of the earth
cannot, by us, be directly perceived,
though the assertion would not be
true unless circumstances could be
supposed under which its truth could
be so percei ved. That th e form of the
earth is globular is inferred from cer-
tain marks, as, for instance, from this,
that its shadow thrown upon the moon
is circular j or this, that on the sea, or

fl

OBSERVATION AND DESCRIPTION.

423

any extensive plain, our horizon is
always a circle ; either of which
marks is incompatible with any other
than a globular form. I assert fur-
ther, that the earth is that particular
kind of globe which is termed an
oblate spheroid, because it is found
by measurement in the direction of
the meridian that the length on the
surface of the earth which subtends a
given angle at its centre diminishes
as we recede from the equator and
approach the poles. But these pro-
positions, that the earth is globular,
and that it is an oblate spheroid,
assert, each of them, an individual
fact, in its own nature capable of
being perceived by the senses when
the requisite organs and the necessary
position are supposed, and only not
actually perceived because those or-
gans and that position are wanting.
This identification of the earth, first
as a globe, and next as an oblate
ppheroid, which, if the fact could have
been seen, would have been called a
description of the figure of the earth,
may without impropriety be so called
when, instead of being seen, it is in-
ferred. But we could not without
impropriety call either of these asser-
tions an induction from facts respect-
ing the earth. They are not general
propositions collected from particular
facts, but particular facts deduced
from general propositions. They are
conclusions obtained deductively from
premises originating in induction ; but
of these premises some were not ob-
tained by observation of the earth,
nor had any peculiar reference to it.

If, then, the truth respecting the
figure of the earth is not an induction,
why should the truth respecting the
figure of the earth's orbit be so ? The
two cases only differ in this, that the
form of the orbit was not, like the
form of the earth itself, deduced by
ratiocination from facts which were
marks of ellipticitv, but was got at by
boldly guessing that the path was an
ellipse, and finding afterwards, on
examination, that the observations
were in harmony with the hypothesis.

According to Dr. Whewell, however,
this process of guessing and verifying
our guesses is not only induction, but
the whole of induction ; no other ex-
position can be given of that logical
operation. That he is wrong in the
latter assertion, the whole of the pre-
ceding Book has, I hope, suflBciently
proved ; and that the process by
which the ellipticity of the planetary
orbits was ascertained is not induc-
tion at all was attempted to be shown
in the second chapter of the same
Book.* We are now, however, pre-
pared to go more into the heart of
the matter than at that earlier period
of our inquiry, and to show, not
merely what the operation in question
is not, but what it is.

§ 4. We observed, in the second
chapter, that the proposition "the
earth moves in an ellipse," so far as it
only serves for the colligation or con-
necting together of actual observa-
tions, (that is, as it only affirms that
the observed positions of the earth
may be correctly represented by as
many points in the circumference of
an imaginary ellipse,) is not an induc-
tion, but a description ; it is an in-
duction only when it affirms that the
intermediate positions, of which there
has been no direct observation, would
be found to correspond to the re-
maining points of the same elliptic
circumference. Now, though this
real induction is one thing and the
description another, we are in a very
different condition for making the in-
duction before we have obtained the
description, and after it. For inas-
much as the description, like all other
descriptions, contains the assertion of
a resemblance between the phenome-
non described and something else ;
in pointing out something which the
series of observed places of a planet
resembles, it points out something in
which the several places themselves
agree. If the series of places corre-
spond to as many points of an ellipse,

* Supra, book iii. cb. ii. J 3, 4, 5.

424

OPERATIONS SUBSIDIARY TO INDUCTION.

the places themselves agree in being
situated in that ellipse. We have,
therefore, by the same process which
gave us the description, obtained the
requisites for an induction by the
Method of Agreement. The succes-
sive observed places of the earth
being considered as effects, and its
motion as the cause vv^hich produces
them, we find that those effects, that
is, those places, agree in the circum-
stance of being in an ellipse. We
conclude that the remaining effects,
the places which have not been ob-
served, agree in the same circum-
stance, and that the law of the motion
of the earth is motion in an ellipse.

The Colligation of Facts, therefore,
by means of hypothesis, or, as Dr.
Whewell prefers to say, by means of
Conceptions, instead of being, as he
supposes, Induction itself, takes its
proper place among operations sub-
sidiary to Induction. All Induction
supposes that we have previously
compared the requisite number of
individual instances, and ascertained
in what circumstances they agree.
The Colligation of Facts is no other
than this preliminary operation. When
Kepler, after vainly endeavouring to
connect the observed places of a planet
by various hypotheses of circular mo-
tion, at last tried the hypothesis of
an ellipse and found it answer to
the phenomena ; what he really at-
tempted, first unsuccessfully, and at
last successfully, was to discover the
circumstance in which all the ob-
served positions of the planet agreed.
And when he in like manner con-
nected another set of observed facts,
the periodic times of the different
planets, by the proposition that the
squares of the times are proportional
to the cubes of the distances, what
he did was simply to ascertain the
property in which the periodic times
of all the different planets agreed.

Since, therefore, all that is true and
to the purpose in Dr. Whe well's doc-
trine of Conceptions might be fully
expressed by the more familiar term
Hypothesis ; and since his Colliga-

tion of Facts by means of appropriate
Conceptions is but the ordinary pro-
cess of finding by a comparison of
phenomena in what consists their
agreement or resemblance ; I would
willingly have confined myself to those
better understood expressions, and
persevered to the end in the same
abstinence which I have hitherto ob-
served from ideological discussions ;
considering the mechanism of our
thoughts to be a topic distinct from
and irrelevant to the principles and
rules by which the trustworthiness of
the results of thinking is to be esti-
mated. Since, however, a work of such
high pretensions, and, it must also be
said, of so much real merit, has rested
the whole theory of Induction upon
such ideological considerations, it
seems necessary for others who fol-
low to claim for themselves and
their doctrines whatever position may
properly belong to them on the same
metaphysical ground. And this is the
object of the succeeding chapter.

CHAPTER IL

OF ABSTRACTION, OR THE FORMATION
OF CONCEPTIONS.

§ I. The metaphysical inquiry into
the nature and composition of what
have been called Abstract Ideas, or,
in other words, of the notions which
answer in the mind to classes and to
general names, belongs not to Logic,
but to a different science, and our
purpose does not require that we
should enter upon it here. We are
only concerned with the universally
acknowledged fact that such notions
or conceptions do exist. The mind
can conceive a multitude of individual
-things as one assemblage or class ; and
general names do really suggest to us
certain ideas or mental representa-
tions, otherwise we coixld not use the
names with consciousness of a mean-
ing. Whether the idea called up by
a general name is composed of the
various circumstances in which all

ABSTRACTION.

425

the individuals denoted by the name
agree, and of no others, (which is the
doctrine of Locke, Brown, and the
C5onceptualist8 ;) or whether it be the
idea of some one of those individuals,
clothed in its individualising pecu-
liarities, but with the accompanying
knowledge that those peculiarities are
not properties of the class, (which is
the doctrine of Berkeley, Mr. Bailey,*
and the modern Nominalists ;) or
whether (as held by Mi\ James Mill)
the idea of the class is that of a mis-
cellaneous assemblage of individuals
belonging to the class ; or whether,
finally, it be any one or any other of
all these, according to the accidental
circumstances of the case ; certain it
is, that some idea or mental concep-
tion is suggested by a general name,
whenever we either hear it or employ
it with consciousness of a meaning.
And this, which we may call if we
please a general idea, represents in our
minds the whole class of things to
which the name is applied. When-
ever we think or reason concerning
the class, we do so by means of this
idea. And the voluntary power which
the mind has of attending to one
part of what is present to it at any
moment, and neglecting another part,
enables us to keep our reasonings
and conclusions ref<pecting the class
unaffected by anything in the idea
or mental image which is not really,
or at least which we do not really

"* Mr. Bailey has given the best statement
of this theory. "The general name," ho
says, " raises up the image sometimes of
one individual of the class formerly seen,
sometimes of another, not unfrequently of
many individuals in succession ; and it
sometimes suggests an image made up of
elements from several different objects, by
a latent process of which I am not con-
scious " (Letters on the Philosophy of the
Human Mind, ist Series, Letter 22). But
Mr. Bailey must allow that we carry on
inductions and ratiocinatioTis respecting
the class by means of this idea or concep-
tion of some one individual in it. This is
all I require. The name of a class calls up
some idea through which we can, to all
intents and purposes, think of the class as
such, and not solely of an individual mem-
ber of it.

believe to be, common to the whole
class.*

There are, then, such things as
general conceptions, or conceptions
by means of which we can think
generally ; and when we form a set
of phenomena into a class, that is,
when we compare them with one
another to ascertain in what they
agree, some general conception is im-
plied in this ment.al operation. And
inasmuch as such a comparison is a
necessary preliminary to Induction,
it is most true that Induction could
not go on without general concep-
tions.

§ 2. But it does not therefore fol-
low that these general conceptions
must have existed in the mind pre-
viously to the comparison. It is not
a law of our intellect, that, in com-
paring things with each other and
taking note of their agreement, we
merely recognise as realised in the
outward world something that we
already had in our minds. , The con-
ception originally found its way to us
as the result of such a compari-son.
It was obtained (in metaphysical
phrase) by abstraction from individual
things. These things may be things
which we perceived or thought of on
former occasions, but they may also
be the things which we are perceiving
or thinking of on the very occasion.
When Kepler compared the observed
places of the planet Mars, and found
that they agreed in being points of an
elliptic circumference, he applied a
general conception which was already
in his mind, having been derived
from his former experience. But this
is by no means universally the case.
When we compare several objects
and find them to agree in being
white, or when we compare the
various species of ruminating animals

* I bare entered rather fully into this
question in chap, xvii, of An Exoniinu-
tion of Sir William Hamilton's Philosophi/,
headed " The Doctrine of Concepts or
General Notions, " which contains my last
views on the subject.

4.26

Ol?ERA'riONS SUBSIDTARY TO II^DUCtlON.

and find them to agree in being cloven-
footed, we have just as much a gene-
ral conception in our minds as Kepler
had in his ; we have the conception
of a "white thing," or the conception
of a "cloven-footed animal" But
no one supposes that we necessarily
bring these conceptions with us, and
superinduce them (to adopt Dr. Whe-
well's expression) upon the facts ; be-
cause in these simple cases every-
body sees that the very act of com-
parison which ends in our connecting
the facts by means of the conception
may be the source from which we
derive the conception itself. If we
had never seen any white object or
had neVer seen any cloven-footed
animal before, we should at the same
time and by the same mental act ac-
quire the idea and employ it for the
colligation of the observed phenomena.
Kepler, on the contrary, really had to
bring the idea with him and superin-
duce it upon the facts ; he could not
evolve it out of them : if he had not
already had the idea he would not
have been able to acquire it by a com-
parison of the planet's positions. But
this inability was a mere accident ;
the idea of an ellipse could have been
acquired from the paths of the planets
as effectually as from anything else, if
the paths had not happened to be in-
visible. If the planet had left a
visible track, and we had been so
placed that we could see it at the
proper angle, we might have ab-
stracted our original idea of an ellipse
from the planetary orbit. Indeed,
every conception which can be made
the instrument for connecting a set
of facts might have been originally
evolved from those very facts. The
conception is a conception of some-
thing ; and that which it is a concep-
tion of is really in the facts, and
might, under some supposable circum-
stances, or by some supposable exten-
sion of the faculties which we actually
possess, have been detected in them.
And not only is this always in itself
possible, but it actually happens in
uluiost all cases in which the obtainin"^

of the right conception is a matter of
any considerable difficulty. For if
there be no new conception required,
if one of those already familiar to
mankind will serve the purpose, the
accident of being the first to whom
the right one occurs may happen to
almost anybody, at least in the case
of a set of phenomena which the
whole scientific world are engaged in
attempting to connect. The honour,
in Kepler's case, was that of the ac-
curate, patient, and toilsome calcula-
tions by which he compared the re-
sults that followed from his diffe-
rent guesses, with the observations of
Tycho Brahe ; but the merit was
very small of guessing an ellipse ; the
only wonder is that men had not
guessed it before, nor could they have
failed to do so if there had not existed
an obstinate d priori prejudice that
the heavenly bodies must move, if not
in a circle, in some combination of
circles.

The really difficult cases are those
in which the conception destined to
create light and order out of darkness
and confusion has to be sought for
among the very phenomena which it
afterwards serves to arrange. Why,
according to Dr. Whewell himself,
did the ancients fail in discovering
the laws of mechanics, that is, of
equilibrium and of the communica-
tion of motion? Because they had
not, or at least had not clearly, the
ideas or conceptions of pressure and
resistance, momentum, and uniform
and accelerating force. And whence
could they have obtained these ideas
except from the very facts of equi-
librium and motion ? The tardy de-
velopment of several of the physical
sciences, for example, of optics, elec-
tricity, magnetism, and the higher
generalisations of chemistry, he as-
cribes to the fact that mankind had
not yet possessed themselves of the
Idea of Polarity, that is, the idea of
opposite properties in opposite direc- ^
tions. But what was there to suggest
such an idea, until, by a separate ex-
amination of several of these diffe-

ABSTRACTION.

427

tent branches of knowledge, it was
shown that the facts of each of them
did present, in some instances at
least, the curious phenomenon of
opposite properties in opposite direc-
tions? The thing was superficially
manifest only in two cases, those of
the magnet and of electrified bodies ;
and there the conception was encum-
bered with the circumstance of mate-
rial poles, or fixed points in the body
itself, in which points this opposition
of properties seemed to be inherent.
The first comparison and abstraction
had led only to this conception of
poles ; and if anything corresponding
to that conception had existed in the
phenomena of chemistry or optics, the
difficulty now justly considered so
great would have been extremely
small. The obscurity arose from the
fact that the polarities in chemistry
and optics were distinct species,
though of the same genus, with the
polarities in electricity and magne-
tism ; and that in order to assimilate
the phenomena to one another it was
necessary to compare a polarity with-
out poles, such, for instance, as is
exemplified in the polarisation of
light, and the polarity with (apparent)
poles, which we see in the magnet ;
and to recognise that these polarities,
while different in many other respects,
agree in the one character which is
expressed by the phrase, opposite pro-
perties in opposite directions. From
the result of such a comparison it
was that the minds of scientific men
formed this new general conception,
between which, and the first confused
feeling of an analogy between some
of the phenomena of light and those
of electricity and magnetism there is
a long interval, filled up by the labours
and more or less sagacious suggestions
of many superior minds.

The conceptions, then, which we
employ for the colligation and methodi-
sation of facts, do not develop them-
selves from within, but are impressed
upon the mind from without ; they
are never obtained otherwise than by
way of comparison and abstraction.

and, in the most important and the
most numerous cases, are evolved by
abstraction from the very phenomena
which it is their oflfice to colligate.
I am far, however, from wishing to
imply that it is not often a very diffi-
cult thing to perform this process of
abstraction well, or that the success
of an inductive operation does not, in
many cases, principally depend on the
skill with which we perform it. Bacon
was quite justified in designating a.s
one of the principal obstacles to good
induction, general conceptions wrongly
formed, "notiones temer^ k rebus
abstractae ; " to which Dr. Whewell
adds, that not only does bad abstrac-
tion make bad induction, but that
in order to perform induction well,
we must have abstracted well ; our
general conceptions must be "clear"
and "appropriate" to the matter in
hand.

§ 3. In attempting to .show what
the difficulty in this matter really is,
and how it is surmounted, I must
beg the reader, once for all, to bear
this in mind ; that although, in dis-
cussing the opinions of a different
school of philosophy, I am willing to
adopt their language, and to speak,
therefore, of connecting facts through
the instrumentality of a conception,
this technical phraseology means
neit"her more nor less than what is
commonly called comparing the facts
with one another and determining in
what they agree. Nor has the techni-
cal expression even the advantage of
being metaphysically correct. The
facts are not connected, except in a
merely metaphorical acceptation of
the term. The ideas of the facts may
become connected, that is, we may
be lead to think of them together ;
but this consequence is no more than
what may be produced by any casual
association. What really takes place
is, I conceive, more philosophically
expressed by the common word Com-
parison, than by the phrases "to con-
nect" or "to superinduce." For as the
general conception is itself obtained

4aS

OPERATIONS SUBSIDIARY TO INDUCTION.

by a comparison of particular pheno-
mena,, so, when obtained, the mode
in which we apply it to other pheno-
mena is again by comparison. We
compare phenomena with each other
to get the conception, and we then
compare those and other phenomena
with the conception. We get the
conception of an animal (for instance)
by comparing different animals, and
when we afterwards see a creature
resembling an animal, we compare
it with our general conception of an
animal ; and if it agrees with that
general conception, we include it in
the class. The conception becomes
the type of comparison.

And we need only consider what
comparison is, to see that where the
objects are more than two, and still
more when they are an indefinite
number, a type of some sort is an
indispensable condition of the com-
parison. When we have to arrange
and classify a great number of objects
according to their agreements and
differences, we do not make a con-
fused attempt to compare all with all.
We know that two things are as
much as the mind can easily attend
to at a time, and we therefore fix
upon one of the objects, either at
hazard or because it offers in a peculi-
arly striking manner some important
character, and, taking this as our
standard, compare it with one object
after another. If we find a second
object which presents a remarkable
agreement with the first, inducing us
to class them together, the question
instantly arises, in what particular
circumstances do they agree ? and to
take notice of these circumstances is
already a first stage of abstraction,
giving rise to a general conception.
Having advanced thus far, when we
now take in hand a third object, we
naturally ask ourselves the question,
not merely whether this third object
agrees with the first, but whether it
agrees with it in the same circum-
stances in which the second did? in
other words, whether it agrees with
the general conception which has been

obtained by abstraction from the first
and second? Thus we see the ten-
dency of general conceptions, as soon
as formed, to substitute themselves
as types for whatever individual ob-
jects previously answered that pur-
pose in our comparisons. We may,
perhaps, find that no considerable
number of other objects agree with
this first general conception, and
that we must drop the conception,
and beginning again with a different
individual case, proceed by fresh com-
parisons to a different general con-
ception. Sometimes, again, we find
that the same conception will serve,
by merely leaving out some of its
circumstances ; and by this higher
effort of abstraction we obtain a still
more general conception ; as in the
case formerly referred to, the scientific
world rose from the conception of
poles to the general conception of
opposite properties in opposite direc-
tions ; or as those South-Sea islanders,
whose conception of a quadruped had
been abstracted from hogs, (the only
animals of that description which they
had seen,) when they afterwards com-
pared that conception with other
quadrupeds, dropped some of the cir-
cumstances, and arrived at the more
general conception which Europeans
associate with the term.

These brief remarks contain, I be-
lieve, all that is well-grounded in the
doctrine that the conception by which
the mind arranges and gives unity to
phenomena m.ust be furnished by the
mind itself, and that we find the right
conception by a tentative process, try-
ing first one and then another until
we hit the mark. The conception is
not furnished by the mind until it has
been furnished to the mind ; and the
facts which supply it are sometimes
extraneous facts, but more often the
very facts which we are attempting
to arrange by it. It is quite true,
however, that in endeavouring to
arrange the facts, at whatever point
we begin, we never advance three
steps without forming a general con-
ception, more or less distinct and

ABSTRACTION.

429

precise ; and that this general con-
ception becomes the chie which we
instantly endeavour to trace through
the rest of the facts, or rather, be-
comes the standard with which we
thenceforth compare them. If we
are not satisfied with the agreements
which we discover among the pheno-
mena by comparing them with this
type, or with some still more gene-
ral conception which by an additional
stage of abstraction we can form from
the type ; we change our path and
look out for other agreements : we
recommence the comparison from a
different starting-point, and so gene-
rate a different set of general concep-
tions. This is the tentative process
which Dr. Whewell speaks of, and
which has not unnaturally suggested
the theory that the conception is sup-
plied by the mind itself, since the
different conceptions which the mind
successively tries, it either already
possessed from its previous experi-
ence, or they were supplied to it in
the first stage of the corresponding
act of comparison ; so that, in the
subsequent part of the process, the
conception manifested itself as some-
thing compared with the phenomena
not evolved from them.

§ 4. If this be a correct account of
the instrumentality of general con-
ceptions in the comparison which
necessarily precedes Induction, we
are now able to translate into our
own language what Dr. Whewell
means by saying that conceptions, to
be subservient to Induction, must be
"clear" and "appropriate."

If the conception corresponds to a
real agreement among the pheno-
mena ; if the comparison which we
have made of a set of objects has led
us to class them according to real
resemblances and differences ; the
conception which does this cannot
fail to be appropriate, for some pur-
pose or other. The question of appro-
priateness is relative to the particular
object we have in view. As soon as,
by ovu- comparison, we have ascer*

tained some agreement, something
which can be predicated in common
of a number of objects, we have ob-
tained a basis on which an inductive
process is capable of being founded.
But the agreements, or the ulterior
consequences to which those agree-
ments lead, may be of very different
degrees of importance. If, for in-
stance, we only compare animals ac-
cording to their colour, and class those
together which are coloured alike, we
form the general conceptions of a
white animal, a black animal, &c.,
which are conceptions legitimately
formed ; and if an induction were to
be attempted concerning the causes
of the colours of animals, this com-
parison would be the proper and
necessary preparation for such an
induction, but would not help us
towards a knowledge of the laws of
any other of the properties of animals ;
while if, with Cuvier, we compare and
class them according to the structure
of the skeleton, or, with Blainville,
according to the nature of their out-
ward integuments, the agreements
and differences which are observable
in these respects are not only of much
greater importance in themselves, but
are marks of agreements and differ-
ences in many other important parti-
culars of the structure and mode of
life of the animals. If, therefore, the
study of their structure and habits be
our object, the conceptions generated
by these last comparisons are far more
" appropriate " than those generated
by the former. Nothing, other than
this, can be meant by the appropriate-
ness of a conception.

When Dr. Whewell says that the
ancients, or the schoolmen, or any
modern inquirers, missed discovering
the real law of a phenomenon because
they applied it to an inappropriate
instead of an appropriate conception,
he can only mean that in comparing
various instances of the phenomenon,
to ascertain in what those instances
agreed, they missed the important
points of agreement, and fastened
upon such as were either ima^nary,

430

OPERATIONS SUBSIDIARY TO INDUCTION.

and not agreements at all, or, if
real agreements, were comparatively
trifling, and had no connection with
the phenomenon the law of which was
sought.

Aristotle, philosophising on the
subject of motion, remarked that cer-
tain motions apparently take place
spontaneously ; bodies fall to the
ground, flame ascends, bubbles of air
lise in water, &c. : and these he called
natural motions ; while others not
only never take place without inter-
nal incitement, but even when such
incitement is applied tend spontane-
ously to cease ; which, to distinguish
them from the former, he called vio-
lent motions. Now, in comparing
the so-called natural motions with
one another, it appeared to Aristotle
that they agreed in one circumstance,
namely, that the body which moved
(or seemed to move) spontaneously
was moving towards its ovm place;
meaning thereby the place from
whence it originally came, or the
place where a great quantity of matter
similar to itself was assembled. In
the other class of motions, as when
bodies are thrown up in the air, they
are, on the contrary, moving froin
their ovm place. Now, this concep-
tion of a body moving towards its
own place may justly be considered
inappropriate ; because, though it ex-
presses a circumstance really found
in some of the most familiar instances
of motion apparently spontaneous, yet,
first, there are many other cases of
such motion, in which that circum-
stance is absent : the motion, for
instance, of the earth and planets.
Secondly, even when it is present, the
motion, on closer examination, would
often be seen not to be spontaneous :
as, when air rises in water, it does
not rise by its own nature, but is
pushed up by the superior weight of
the water which presses upon it.
Finally, there are many cases in
which the spontaneous motion takes
place in the contrary direction to
what the theory considei-s as the
body's own place ; for iustanc*, when

a fog rises from a lake, or when water
dries up. The agreement, therefore,
which Aristotle selected as his prin-
ciple of classification did not extend
to all cases of the phenomenon he
wanted to study, spontaneous motion ;
while it did include cases of the ab-
sence of the phenomenon, cases of
motion not spontaneous. The con-
ception was hence "inappropriate."
We may add that, in the case in
question, no conception would be
appropriate ; there is no agreement
which runs through all the cases of
spontaneous or apparently sponta-
neous motion and no others : they
cannot be brought under one law : it
is a case of Plurality of Causes.*

§ 5. So much for the first of Dr.
Whewell'a conditiona, that concep
tions most be appropriate. The bo-
cond is, that they shall be "clear ;"
and let ns consider what this implies.
Unless the conception corresponds to
a real agreement, it has a worse defect

* Other examples of inappropriate Con-
ceptions are given by Dr. Whcwell (Phil.
Ind. Sc, ii. 185) as follows :—" Aristotlo
and his followers endeavoured in vain to
account for the mechanical relation of
forces in the lever, by applying the inap-
propriate geometrical conceptions of tho
properties of the circle : they failed in
explaining the form of the luminous spot
made by the sun shining through a hole,
because they appUed the inappropriate
conception of a circular quality in the
sun's light ; they speculated to no purpose
about the elementary composition of bodies,
because they assumed the inappropriate
conception of likeness between the elements
and the compound, instead of the genuine
notion of elements merely determining th»
qualities of the compound." But in these
cases there is more than an inappropriate
conception ; there is a false conception ;
one which has no prototype in nature,
nothing corresponding to it in facrs. This
is evident in the last two examples, and ia
equally true in the first; the "properties
of the circle, " which were referred to, being
purely fantastical. There is, therefore, aa
error beyond the wrong choice of a prin-
ciple of generalisjition ; there is a false
assumption of matters of fact The attempt
is made to resolve certain laws of nature
into a more general law, that law not being
one which, though real, la inuppropriate,
but oa« wholly ima^arj^.

ABSTRACTION.

43'

than that of not being clear : it is not
applicable to the case at all. Among
the phenomena, therefore, which we
are attempting to connect by means
of the conception, we must suppose
that there really is an agreement,
and that the conception is a concep-
tion of that agreement. In order,
then, that it may be clear, the only
requisite is, that we shall know ex-
actly in what the agreement con-
sists ; that it shall have been care-
fully observed and accurately remem-
bered. "We are said not to have a
clear conception of the resemblance
among a set of objects when we have
only a general feeling that they
resemble, without having analysed
their resemblance, or perceived in
what points it consists, and fixed in
our memory an exact recollection of
those points. This want of clearness,
or, as it may be otherwise called,
this vagueness, in the general con-
ception, may be owing either to our
having no accurate knowledge of the
objects themselves, or merely to our
not having carefully compared them.
Thus a person may have no clear
idea of a ship because he. has never
seen one, or because he remembers
but little, and that faintly, of what
he has seen. Or he may have a per-
fect knowledge and remembrance of
many ships of various kinds, frigates
among the rest, but he may have no
clear, but only a confused idea of a
frigate, because he has never been
told, and has not compared them
sufficiently to have remarked and re-
jnembered in what particular points
a frigate differs from some other kind
of ship.

It is not, however, necessary, in
order to have clear ideas, that we
should know all the common proper-
ties of the things which we class to-
gether. That would be to have our
conception of the class complete as
well as clear. It is sufficient if we
never class things together without
knowing exactly why we do so, — with-
out having ascertained exactly what
agreements we ar« about to include

in our conception ; and if, after hav-
ing th\is fixed our conception, we
never vary from it, never include in
the class anything which has not
those common properties, nor exclude
from it anything which has. A clear
conception means a determinate con-
ception ; one which does not fluctuate,
which is not one thing to day and
another to-morrow, but remains fixed
and invariable, except when, from the
progress of our knowledge or the cor-
rection of some error, we consciously
add to it or alter it. A person of clear
ideas is a person who always knows
in virtue of what properties his clas.ses
are constituted, what attributes are
connoted by his general names.

The principal requisites, therefore,
of clear conceptions aro habits of
attentive observation and extensive
experience, and a memory which re-
ceives and retains an exact image of
what is observed. And in proportion
as any one has the habit of observing
minutely and comparing carefully a
particular class of phenomena, and an
accurate memory for the results of the
observation and comparison, so will
his conceptions of that class of phe-
nomena be clear ; provided he has
the indispensable habit, (naturally,
however, resulting from those other
endowments,) of never using general
names without a precise connota-
tion.

As the clearness of our conceptions
chiefly depends on the carefulness and
accuracy of our observing and com-
paring faculties, so their appropriate-
ness, or rather the chance we have of
hitting upon the appropriate concep-
tion in any case, mainly depends on
the activity of the same faculties. He
who by habit, grounded on sufficient
natural aptitude, has acquired a readi-
ness in accurately observing and com-
paring phenomena, will perceive so
many more agreements and will per-
ceive them so much more rapidly than
other people, that the chances are
much greater of his perceiving, in any
instance, the agreement on which the
important consequenoes depend

432

OPERATIONS SlTBSIDIARY TO INDUCTION.

§ 6. It is of so much importance
that the part of the process of investi-
gating truth, discussed in this chapter,
should be rightly understood, that I
think it is desirable to restate the re-
sults we have arrived at, in a some-
what different mode of expression.

We cannot ascertain general truths,
that is, truths applicable to classes,
unless we have formed the classes in
such a manner that general truths can
be affirmed of them. In the formation
of any class, there is involved a con-
ception of it as a class, that is, a con-
ception of certain circumstances as
being those which characterise the
class, and distinguish the objects
composing it from all other things.
When we know exactly what these
circumstances are, we have a clear
idea (or conception) of the class, and
of the meaning of the general name
which designates it. The primary
condition implied in having this clear
idea is that the class be really a
class ; that it correspond to a real
distinction ; that the things it in-
cludes really do agree with one another
in certain particulars, and differ, in
those same particulars, from all other
things. A person without clear ideas
is one who habitually classes together,
under the same general names, things
which have no common properties, or
none which are not possessed also by
other things ; or who, if the usage
of other people prevents him from
actually misclassing things, is unable
to state to himself the common pro-
perties in virtue of which he classes
them rightly.

But it is not the sole requisite of
classification that the classes should
be real classes, framed by a legitimate
mental process. Some modes of class-
ing things are more valuable than
others for human uses, whether of
speculation or of practice ; and our
classifications are not well made un-
less the things which they bring to-
gether not only agree with each other
in something which distinguishes
them from all other things, but agree
with each other and differ from other

things in the very circumstances which
are of primary importance for the pur-
pose (theoretical or practical) which
we hav« in view, and which consti-
tutes the problem before us. In other
words, our conceptions, though they
may be clear, are not appropriate for
our purpose, unless the properties we
comprise in them are those which
will help us towards what we wish to
understand — i.e., either those which
go deepest into the nature of the
things, if our object be to understand
that, or those which are most closely
connected with the particular property
which we are endeavouring to investi-
gate.

We cannot, therefore, frame good
general conceptions beforehand. That
the conception we have obtained is
the one we want, can only be known
when we have done the work for the
sake of which we wanted it ; when
we completely understand the general
character of the phenomena, or the
conditions of the particular property
with which we concern ourselves.
General conceptions formed without
this thorough knowledge are Bacon's
"notiones temer^ a rebus abstractae."
Yet such premature conceptions we
must be continually making up in
our progress to something better.
They are an impediment to the pro-
gress of knowledge only when they
are permanently acquiesced in. When
it has become our habit to group
things in wrong classes — in groups
which either are not really classes,
having no distinctive points of agree-
ment (absence of clear ideas), or which
are not classes of which anything im-
portant to our purpose can be predi-
cated (absence of appropriate ideas) ;
and when, in the belief that these
badly mad eclasses are those sanctioned
by Nature, we refuse to exchange
them for others, and cannot or will
not make up our general conceptions
from any other elements ; in that case
all the evils which Baccm ascribes to
his "notiones temerd abstracts " really
occur. This was what the ancients did
in physics, and what the world in gene-

NAMING.

433

ral Joes in morals and politics to the
present day.

It would thus, in my view of the
matter, be an inaccurate mode of ex-
pression to say, that obtaining appro-
priate conceptions is a condition pre-
cedent to generalisation. Throughout
the whole process of comparing pheno-
mena with one another for the purpose
of generalisation, the mind is trying
to make up a conception ; but the
conception which it is trying to make
up is that of the really important
point of agreement in the phenomena.
As we obtain more knowledge of the
phenomena themselves, and of the
c(mditions on which their important
properties depend, our views on this
subject naturally alter ; and thus we
advance from a less to a more " appro-
priate " general conception, in the pro-
gress of our investigations.

We ought not, at the same time,
to forget that . the really important
agreement cannot always be dis-
covered by mere comparison of the
\ery phenomena in question, without
the aid of a conception acquired else-
where ; as in the case, so often re-
ferred to, of the planetary orbits.

The search for the agreement of a
set of phenomena is in truth very
similar to the search for a lost or
liidden object. At first we place our-
selves in a sufficiently commanding
position, and cast our eyes around us,
and if we can see the object, it is
well ; if not, we ask ourselves men-
tally what are the places in which it
may be hid, in order that we may
there search for it : and so on, until
we imagine the place where it really
is. And here too we require to have
had a previous conception or know-
ledge of those different places. As
in this familiar process so in the
philosophical operation which it illus-
trates, we first endeavour to find the
lost object or recognise the common
attribute, without conjecturally in-
voking the aid of any previously ac-
quired conception, or, in other M'ords,
of any hypothesis. Having failed in
this, we call upon our imagination

for some hypothesis of a possible
place, or a possible point of resem-
blance, and then look to see whether
the facts agree with the conjecture.

For such cases something more in
required than a mind accustomed to
accurate observation and comparison.
It must be a mind stoi-ed with gene-
ral conceptions, previously acquired,
of the sorts which bear affinity to
the subject of the particular inquiry.
And much will also depend on the
natural strength and acquired culture
of what has been termed the scien-
tific imagination ; on the faculty pos-
sessed of mentally arranging known
elements into new combinations, such
as have not yet been observed in
nature, though not contradictory to
any known laws.

But the variety of intellectual ha-
bits, the purposes which they serve,
and the modes in which they may be
fostered and cultivated, are considera-
tions belonging to the Art of Educa-
tion : a subject far wider than Logic,
and which this treatise does not pro-
fess to discuss. Here, therefore, the
present chapter may properly close.

CHAPTER III.

OK NAMING, AS SUBSIDIARY TO
INDUCTION.

§ I. It does not belong to the pre-
sent undertaking to dwell on the im-
portance of language as a medium of
human intercourse, whether for pur-
jx)ses of sympathy or of information.
Nor does out design admit of more
than a passing allusion to that great
property of names on which their
functions as an intellectual instru-
ment are, in reality, ultimately de-
pendent— their potency as a means of
forming and of riveting associations
among our other ideas : a subject on
which an able thinker* has thus
written : —

"Names are impressions of sense,

* Profesaor Bain.

434

OPERATIONS SUBSIDIARY TO INDUCTION.

II

and as such take the strongest hold
on the mind, and of all other impres-
sions can be most easily recalled and
retained in view. They therefore
serve to give a point of attachment to
all the more volatile objects of thought
and feeling. Impressions that when
passed might be dissipated for ever
are, by their connection with lan-
guage, always within reach. Thoughts,
of themselves, are perpetually slipping
out of the field of immediate mental
vision ; but the name abides with us,
and the utterance of it restores them
in a m,oment. Words are the cus-
todiers of every product of mind less
impressive than themselves. All ex-
tensions of human knowledge, all new
generalisations, are fixed and spread,
even unintentionally, by the use of
words. The child growing up learns,
along with the vocables of his mother
tongue, that things which he would
have believed to be different are, in
important points, the same. Without
any formal instruction, the language
in which we grow up teaches us all
the common philosophy of the age. It
directs us to observe and know things
which we should have overlooked ; it
supplies us with classifications ready
made, by which things are arranged
(as far as the light of bygone genera-
tions admits) with the objects to
which they bear the greatest total re-
semblance. The number of general
names in a language, and the degree
of generality of those names, afford a
test of the knowledge of the era and
of the intellectual insight which is the
birthright of any one born into it."

It is not, however, of the functions
of Names, considered generally, that
we have here to treat, but only of the
manner and degree in which they are
directly instrumental to the investi-
gation of truth ; in other words, to
the process of induction.

§ 2. Observation and Abstraction,
the operations which formed the sub-
ject of the two foregoing chapters,
are conditions indispensable to induc-
tion ; there can be no induction where

they are not. It has been imagined
that Naming is also a condition
equally indispensable. There are
thinkers who have held that lan-
guage is not solely, according to a
phrase generally current, an instru-
ment of thought, but the instrument ;
that names, or something equivalent
to them, some species of artificial
signs, are necessary to reasoning ;
that there could be no inference, and
consequently no induction, without
them. But if the nature of reasoning
was correctly explained in the earlier
part of the present work, this opinion
must be held to be an exaggeration,
though of an important truth. ]f
reasoning be from particulars to par-
ticulars, and if it consist in recognis-
ing one fact as a mark of another, or
a mark of a mark of another, nothing
is required to render reasoning pos-
sible, except senses and association :
senses to perceive that two facts are
conjoined ; association, as the law by
which one of those two facts raises up
the idea of the other.* For these
mental phenomena, as well as for the
belief or expectation which follows,
and by which we recognise as having
taken place, or as about to take
place, that of which we have per-
ceived a mark, there is evidently no
need of language. And this inference
of one particular fact from another is
a case of induction. It is of this sort
of induction that brutes .nre capable ;
it is in this shape that \;:)cnltivated

* Tliis sentence having been cv.Ancously
understood as if I had meant to assert tliat
belief is nothing but an irresistiijle associa-
tion, I think it necessary to observe that I
express no theory respecting tlie nllimnte
analysis either of reasoning or of 1 .li. •',
two of the most obscure points in .-naly-
tical psychology. I am speaking )l•^t of
the powers themselves, but of the j rovi-
ous conditions necessary to enable those
powers to exert themselves ; of which
conditions I am contending that langu.age
is not one, senses and association being
sufficient without it. The irresistible-
nssociation theory of belief, and the diflTi-
culties connected with the subject, have
been discussed at length in the notes to
the new edition of Mr. James Mill's
Analysis of the phenomena of the Human
Mind,

NAMING.

435

minda make almost all their Induc-
tions, and that we all do so in the
cases in which familiar experience
forces our conclusions upon us with-
out any active process of inquiry on
our part, and in which the belief or
expectation follows the suggestion of
the evidence with the promptitude
and certainty of an instinct.*

§ 3. But though inference of an in-
ductive character is possible without
the use of signs, it could never, with-
out them, be carried much beyond the
very simple cases which we have just
described, and which form, in all pro-
bability, the limit of the reasonings
of those animals to whom conventional
language is unknown. Without lan-
guage, or something equivalent to it,
there could only be as much reasoning
from experience as can take place
without the aid of general proposi-
tions. Now, though in strictness we
may reason from past experience to a
fresh individual case without the in-
termediate stage of a general propo-
sition, yet without general proposi-
tions we should seldom remember
what past experience we have had,
and scarcely ever what conclusions
that experience will warrant. The
division of the inductive process into
two parts, the first ascertaining what
is a m.ark of the given fact, the second
whether in the new case that mark
exists, is natural, and scientifically
indispensable. It is, indeed, in a
majority of cases, rendered necessary
by mere distance of time. The ex-
perience by which we are to guide our
judgments may be other people's ex-
perience, little of which can be com-
municated to us otherwise than by

* Mr. Bailey agrees with me in thinking
that whenever " from something actually
present to my senses, conjoined with past
experience, 1 feel satisfied that something
has happened, or will happen, or is hap-
pening beyi aid the sphere of my personal
observation," I may with strirt propriety
be said to reason, and of course to reason
inductively, for demonstrative reasoning
is excluded by the circumstances of the
case. {The Theory of Reasoning, 2nd ed.,
p. 27.)

language : when It Is our own, it Is
generally experience long past ; unless,
therefore, it were recorded by means
of artificial signs, little of it (except in
cases involving our intenser sensations
or emotions, or the subjects of our daily
and hourly contemplation) would be
retained in the memory. It is hardly
necessary to add, that when the induc-
tive inference is of any but the most
direct and obvious nature — when it re-
quires several observations or experi-
ments in varymg circumstances, and
the comparison of one of these with
another — it is impossible to proceed
a step without the artificial memory
which words bestow. Without words,
we should, if we had often seen A
and B in immediate and obvious con-
junction, expect B whenever we saw
A ; but to discover their conjunction
when not obvious, or to determine
whether it is really constant or only
casual, and whether there is reason to
expect it under any given change of
circumstances, is a process far too
complex to be performed without some
contrivance to make our remembrance
of our own mental operations accu-
rate. Now, language is such a con-
trivance. When that instrument is
called to our aid, the difficulty is re-
duced to that of making our remem-
brance of the meaning of words accu-
rate. This being secured, whatever
passes through our minds may be
remembered accurately by putting it
carefully into words, and committing
the words either to writing or to me-
mory.

The function of Naming, and par-
ticularly of General Names, in Induc-
tion may be recapitulated as follows.
Every inductive inference which is
good at all is good for a whole class
of cases ; and, that the inference may
have any better warrant of its correct-
ness than the mere clinging together
of two ideas, a process of experimen-
tation and comparison is necessary,
in which the whole class of cases must
be brought to view, and some uni-
formity in the course of nature evolved
and ascertained, since the existence

43^

OPERATIONS SUBSIDIARY TO INDUCTION.

of such an uniformity is required as
a justification for drawing the infer-
ence in even a single case. This uni-
formity, therefore, may be ascertained
once for all ; and if, being ascertained,
it can be remembered, it will serve as
a formula for making, in particular
cases, all such inferences as the pre-
vious experience will warrant. But
we can only secure its being remem-
bered, or give ourselves even a chance
of carrying in our memory any con-
siderable number of such uniformi-
ties, by registering them through the
medium of permanent signs, which
(being, from the nature of the case,
signs not of an individual fact, but of
an vmiformity, that is, of an indefinite
number of facts similar to one an-
other) are general signs, universals,
general names, and general proposi-
tions.

§ 4. And here I cannot omit to
notice an oversight committed by
some eminent thinkers, who have
said that the cause of our using general
names is the infinite multitude of in-
dividual objects, which, making it
impossible to have a name for each,
compels us to make one name serve
for many. This is a very limited view
of the function of general names.
Even if there were a name for every
individual object, we should require
general names as much as we now do.
Without them we could not express
the result of a single comparison, nor
record any one of the uniformities
existing in nature ; and should be
hardly better off in respect to Induc-
tion than if we had no names at all.
With none but names of individuals,
(or, in other words, proper names,)
we might, by pronouncing the name,
suggest the idea of the object, but
we could not assert any proposition,
except the unmeaning ones formed by
predicating two proper names one
of another. It is only by means of
general names that we can convey
any information, predicate any attri-
bute, even of an individual, much
more of a class. Rigorously speaking,

J

ther

we could get on without any otner
general names than the abstract names
of attributes ; all our propositions
might be of the form "such an indi-
vidual object possesses such an attri-
bute," or " such an attribute is always
(or never) conjoined with such another
attribute." In fact, however, man-
kind have always given general names
to objects as well as attributes, and
indeed before attributes; but the
general names given to objects imply
attributes, derive their whole meaning
from attributes, and are chiefly use-
ful as the language by means of which
we predicate the attributes which they
connote.

It remains to be considered what
principles are to be adhered to in
giving general names, so that thessi
names, and the general propositions
in which they fill a place, may con-
duce most to the purposes of Induc-
tion.

CHAPTER IV.

OF THE REQUISITES OP A PHILCSO-
PHICAL LANGUAGE, AND THE PRIN-
CIPLES OF DEFINITION.

§ I . In order that we may possess
a language perfectly suitable for the
investigation and expression of gene-
ral truths, there are two principal and
several minor requisites. The first
is, that every general name should
have a meaning, steadily fixed and
precisely determined. When, by the
fulfilment of this condition, such
names as we possess are fitted for the
due performance of their functions,
the next requisite, and the second in
order of importance, is that we should
possess a name wherever one isneeded ;
wherever there is anything to be de-
signated by it, which it is of import-
ance to express.

The former of these requisites is
that to which our attention will be
exclusively directed in the present
chapter.

§ 2. Every general name, then, must

I

REQUISITES OE LANGUAGE.

437

^

lijvvc a certain and knowable mean-
ing. Now the meaning (as has so
often been explained) of a general
connotative name resides in the con-
notation ; in the attribnte on account
of which, and to express which, the
name is given. Thus, the name ani-
mal being given to all things which
j)ossess the attributes of sensation
and voluntary motion, the word con-
notes those attributes exclusively, and
tiiey constitute the whole of its mean-
ing. If the name be abstract, its
denotation is the same with the con-
notation of the corresiK)nding con-
crete ; it designates directly the attri-
bute which the concrete term implies.
To give a precise meaning to general
names is, then, to fix with steadiness
the attribute or attributes connoted
by each concrete general name, and
denoted by the corresponding ab-
stract. Since abstract names, in the
t)rder of their creation, do not pre-
cede but follow concrete ones, a.s is
proved by the etymological fact that
they are almost always derived from
them, we may consider their meaning
;is determined by and dependent on
the meaning of their concrete ; and
thus the problem of giving a distinct
meaning to general language is all
included in that of giving a precise
connotation to all concrete general
names.

This is not difficult in the case of
new names — of the technical terms
created by scientific inquirers for the
piu-poses of science or art. But when
a name is in common use, the dii^-
culty is greater ; the problem in this
case not being that of choosing a con-
venient connotation for the name,
but of ascertaining and fixing the
connotation with which it is already
used. That this can ever be a matter
of doubt is a sort of paradox. But
the vulgar (including in that term
all who have not accurate habits of
thought) seldom know exactly what
assertion they intend to make, what
common property they mean to ex-
press, when they apply the same name
to a number of dilfereut thin-rs. All

which the name expresses with them,
when they predicate it of an object,
is a confused feeling of resemblance
b(;tween that object and some of the H
other things which they have been
accustomed to denote by the name.
They have applied the name Stone to
various objects previously seen ; they
see a new object, which appears to
them somewhat like the former, and
they call it a stone, without asking
themselves in what respect it is like,
or what nuxle or degree of resemblance
the best authorities, or even they them-
selves, require as a warrant for using
the name. This rough general im-
pression of resemblance is, however,
made up of particular circumstances
of resemblance ; and into these it is
the business of the logician to analyse
it — to ascertain what points of re-
semblance among the different things
commonly called by the name have
pnxluced in the common mind this
vague feeling of likeness — have given
to the things the similarity of aspect
which has made them a class, and has
caused the same name to be bestowed
upon them.

But though general names are im-
posed by the vulgar without any more
definite connotation than that of a
vague resemblance, general proposi-
tions come in time to be made, in
which predicates are applied to those
names, that is, general assertions are
made concerning the whole of the
things which are denoted by the
name. And since by each of these
propositions some attribute, more or
less precisely conceived, is of course
predicated, the ideas of these various
attributes thus become associated with
the name, and in a sort of uncertain
way it comes to connote them ; there
is a hesitation to apply the name in
any new case in which any of the
attributes familiarly predicated of the
class do not exist. And thus, to com-
mon minds, the propositions which
tliey are in the habit of liearing or
uttering concerning a class make up
in a loose way a sort of connotation
for the class-name. Let us take, for

438

OPERATIONS SUBSIDIARY TO INDUCTION,

instance, the word Civilised. How
few could be found, even among the
most educated persons, who would
undertake to say exactly what the
term Civilised connotes. Yet there
is a feeling in the minds of all who
use it that they are using it with a
meaning ; and this meaning is made
up, in a confused manner, of every-
thing which they have heard or read
that civilised men or civilised com-
munities are or may be expected to
be.

It is at this stage, probably, in the
progress of a concrete name, that the
corresponding abstract name gener-
ally comes into use. Under the no-
tion that the concrete name must of
course convey a meaning, or, in other
words, that there is some property
common to all things which it denotes,
people give a name to this common
property ; from the concrete Civilised,
they form the abstract Civilisation.
But since most people have never
compared the different things which
are called by the concrete name, in
such a manner as to ascertain what
properties these things have in com-
mon, or whether they have any ; each
is thrown back upon the marks by
which he himself has been accustomed
to be guided in his application of the
term ; and these, being merely vague
hearsays and current phrases, are not
the same in any two persons, nor in
the same person at different times.
Hence the word (as Civilisation, for
example) which professes to be the
designation of the unknown common
property, conve3's scarcely to any two
minds the same idea. No two per-
sons agree in the things they predi-
cate of it ; and when it is itself predi-
cated of anything, no other person
knows, nor does the speaker himself
know with precision, what he means
to assert. Many other words which
could be named, as the word honour,
or the word gentleman, exemplify this
uncertainty still more strikingly.

It needs scarcely be observed that
general propositions, of which no one
can tell exactly what they assert,

■

isfnt

cannot possibly have been brougl
to the test of a correct induction.
Whether a name is to be used as
an instrument of thinking, or as a
means of communicating the result
of thought, it is imperative to deter-
mine exactly the attribute or attri-
butes which it is to express : to give
it, in short, a fixed and ascertained
connotation.

§ 3. It would, however, be a com-
plete misunderstanding of the proper
office of a logician in dealing with
terms already in use, if we were to
think that because a name has not at
present an ascertained connotation, it
is competent to any one to give it
such a connotation at his own choice.
The meaning of a term actually in
use is not an arbitrary quantity to be
fixed, but an unknown quantity to be
sought.

In the first place, it is obviously
desirable to avail ourselves, as far as
possible, of the associations already
connected with the name ; not en-
joining the employment of it in a.
manner which conflicts with all pre-
vious habits, and especially not so as
to require the rupture of those strong-
est of all associations between names,
which are created by familiarity with
propositions in which they are predi-
cated of one another. A philosopher
would have little chance of having
his example followed if he were t»>
give such a meaning to his terms as
should require us to call the North
American Indians a civilised people,
or the higher classes in Europe sa-
vages ; or to say that civilised people
live by hunting, and savages by agri-
culture. Were there no other reason,
the extreme difficulty of effecting so
complete a revolution in speech would
be more than a sufficient one. The
endeavour should be that all generally
received propositions into which the
term enters should be at least as true
after its meaning is fixed as they
were before ; and that the concrete
name, therefore, should not receive
such a connotation as shall prevent it

I

REQUISITES OE LANGUAGE

from denoting things which, in com-
mon language, it is currently affirmed
of. The fixed and precise connota-
tion which it receives should not be
in deviation frcnn, but in agreement
(as far as it goes) with the vague and
fluctuating connotation which the
term already had.

To fix the connotatiitn of a con-
ci-ete name,' or the denotation of the
corresponding abstract, is to define
the name. When this can be done
without rendering any received asser-
tions inadmissible, the name can be
defined in accordance with its received
use, which is vulgarly called defining
not the name but the thing. What
is meant by the improper expression
of defining a thing, (or rather a class
of things — for nobody talks of defin-
ing an individual,) is to define the
name, subject to the condition that it
shall denote those things. This, of
course, supposes a comparison of the
things, feature by feature and pro-
perty by property, to ascertain what
attributes they agree in ; and not
unfrequently an operation strictly in-
ductive, for the purpose of ascertain-
ing some unobvious agreement, which
is the cause of the obvious agreement.

For, in order to give a connotation
to a name consistently with its de-
noting certain objects, we have to
make our selection from among the
various attributes in which those ob-
jects agree. To ascertain in what
they do agree is, therefore, the first
logical operation requisite. When
this has been done as far as is ne-
cessary or practicable, the question
arises, which of these common attri-
butes shall be selected to be asso-
ciated with the name ? For if the
tdass which the name denotes be a
Kind, the common properties are in-
numerable ; and even if not, they are
(»ften extremely numerous. Our choice
is first limited by the preference to
be given to properties which are well
known and familiarly predicated of
the class ; but even these are often
too numerous to be all included in
the definition, and, besides, the pro-

439

perties most generally known may
not be those which serve best to mark
out the class from all others. We
should therefore select from among
the common properties (if among
them any such are to be found) those
on which it has been ascertained by
experience, or proved by deduction,
that many others depend ; or at least
which are sure marks of them, and
from whence, therefore, many others
will follow by inference. We thus
see that to frame a good definition of
a name already in use is not a matter
of chaice but of discussion, and dis-
cussion not merely respecting the
usage of language, but respecting the
properties of things, and even the
origin of those properties. And hence
every enlargement of our knowledge
of the objects to which the name h
applied is liable to suggest an im-
provement in the definition. It is
impossible to frame a perfect set of
definitions on any subject until the
theory of the subject is perfect ; and
as science makes progress, its defini-
tions are also progressive.

§ 4. The discussion of Definitions,

in so far as it does not turn on the s/
use of words but on the properties of
things, Dr. Whewell calls the Expli
cation of Conceptions. The act of
ascertaining, better than before, in
what particulai's any phenomena
which are classed together agree, he
calls in his technical phraseology, un-
folding the general conception in
virtue of which they are so classed.
Making allowance for what appears
to me the darkening and misleading
tendency of this mode of expression,
several of his remarks are so much to
the purpose, that I shall take the
liberty of transcribing them.

He observes,* that many of the
controversies which have had an im-
portant share in the formation of the
existing body of science have "as-
sumed the form of a battle of Defi-
nitions. For example, the inquiry

* yovum Oi-fjanum Kenovadan, pp. 35-37.

440

OPERATIONS SUBSIDIARY TO INDUCTION.

concerning the laws of falling bodies
led to the question whether the pro-
per definition of a uniform force is
that it generates a velocity propor-
tional to the space from rest, or to the
time. The controversy of the vis viva
•was what was the proper definition
of the measure of force. A principal
(question in the classification of mine-
rals is, what is the definition of a
'mineral species? Physiologists have
endeavoured to throw light on their
subject by defining organisation, or
some similar term." Questions of the
same nature were long open, and are
not yet completely closed, i-especting
the definitions of Specific Heat, La-
tent Heat, Chemical Combination,
and Solution.

"It is very important for us to
observe, that these controversies have
never been questions of insulated and
arbitrary definitions, as men seem
often tempted to imagine them to
have been. In all cases there is a
tacit assumption of some proposition
which is to be expressed by means of
the definition, and which gives it its
importance. The dispute concerning
the definition thus acquires a real
value, and becomes a question con-
cerning true and false. Thus in the
discussion of the question. What is
a uniform force? it was taken for
granted that gravity is a uniform
force. In the debate of the vis viva,
it was assumed that in the mutual
action of bodies the whole effect of
the force is unchanged. In the zoo-
logical definition of species, (that it
consists of individuals which have, or
may have, sprung from the same
parents,) it is presumed that indivi-
duals so related resemble each other
more than those which are excluded
by such a definition ; or, perhaps,
that species so defined have per-
manent and definite differences. A
definition of organisation, or of some
other term, which was not employed
to express some principle, would be
of no value.

"The establishment, therefore, of
a right definition of a term, may

be a useful step in the explication ot
our conceptions ; but this will be the
case then only when we have under
our consideration some proposition in
which the term is employed. Por
then the question really is, how the
conception shall be understood and
defined in order that the proposition
may be true.

"To unfold our conceptions by
means of definitions has never been
serviceable to science, except when it
has been associated with an imme-
diate use of the definitions. The
endeavour to define a Uniform Force
was combined with the assertion that
gravity is a uniform force : the attempt
to define Accelerating Force was
immediately followed by the doctrine
that accelerating forces may be com-
pounded : the process of defining Mo-
mentum was connected with the prin-
ciple that momenta gained and lost
are equal : naturalists would have
given in vain the definition of Species
which we have quoted, if they had
not also given the characters of species
so separated. . . . Definition may be
the best mode of explaining our con-
ception, but that which alone makes
it worth while to explain it in any
mode, is the opportunity of using it
in the expression of truth. When a
definition is propounded to us as a
useful step in knowledge, we art;
always entitled to ask what principle
it serves to enunciate."

In giving, then, an exact connota-
tion to the phrase, "a uniform force,"
the condition was understood that
the phrase should continue to denote
gravity. The discussion, therefore,
respecting the definition resolved
itself into this question. What is there
of an uniform nature in the motions
produced by gravity? By observa-
tions and comparisons it was found,
that what was uniform in those mo-
tions was the ratio of the velocity
acquired to the time elapsed ; equal
velocities being added in equal times.
An uniform force, thei-efore, was
defined, a force wliich adds equal
velocities in equal times. So, again,

UKQUISITES OV LANGtTAGE.

44t

in (lelining momentum. It was al-
ready' a received doctrine, that when
two objects impinge upon one an-
other, the momentum lost by the one
is equal to that gained by the other.
This proposition it was deemed neces-
sary to preserve, not from the motive
(which operates in many other cases)
that it was firmly fi.xed in a popular
belief, for the proposition in question
had never been heard of by any but
the scientifically instructed ; but it
was felt to contain a trutii : even a
superficial observation of the pheno-
mena left no doubt that in the pro-
pagation of motion from one b<xly to
another there was something of which
the one body gained precisely what
the other lost ; and the word momen-
tum had been invented to express
this unknown something. The settle-
ment, therefore, of the definition of
momentum involved the determina-
tion of the question. What is that of
which a body, when it sets another
body in motion, loses exactly as much
as it communicates ? And when ex-
periment had shown that this somc-
th in;/ was the product of the velocity
of the body by its mass, or quantity
of matter, this became the definition
of momentum.

The following remarks,* therefore,
arc perfectly just : " The business of
definition is part of the business of
discovery. ... To define, so that our
definition shall have any scientific
value, requires no small portion of
that sagacity by which truth is de-
tected. . . . When it has been clearly
seen what ought to be our definition,
it must be pi*etty well known what
truth we have to state. The defini-
tion, as well as the discovery, sup-
poses a decided step in our knowledge
to have been made. The writers on
Logic in the Middle Ages made Defi-
nition the last stage in the progress of
knowledge ; and in this arrangement
at least, the history of science, and
the philosophy derived from the his-
tory, confirm their speculative views."
For in order to judge finally how the
* Nov. Onj. Iknov., p. 39-40.

name which denotes a class may best
be defined, we nuist kntnv all the pro-
perties common to the class, and all
the relations of causation or depen-
dence among those properties.

If the properties which are fittest
to be selected as marks of other com-
mon properties are also obvious and
familiar, and especially if they bear a
great part in producing that general
air of resemblance which was the ori-
ginal inducement to the formation of
the class, the definition will then be
most felicitous. But it is often neces-
sary to define the class by some pro-
perty not familiarly known, provided
that property be the best mark of
those which are known. M. de Blain-
ville, for instance, founded his defini-
ti«)n of life on the process of decom-
position and recomposition which in-
cessantly takes place in every living
body, so that the particles composing
it are never for two instants the same.
This is by no means one of the most
obvious properties of living bodies ; it
might escape altogether the notice of
an unscientific observer. Yet great
authorities (independently of M. de
Blainville, who is himself a first-rato
authority) have thought that no other
property so well answers the condi-
tions required for the definition.

§ 5. Having laid down the prin-
ciples which ought for the most part
to be observed in attempting ti) give
a precise connotation to a term in use,
I must now add that it is not always
practicable to adhere to those prin-
ciples, and that even when practicable
it is occasionally not desirable.

Cases in which it is impossible to
comply with all the conditions of a
precise definition of a name in agree-
ment with usage occur very frequently.
There is often no one connotation
capable of being given to a word, so that
it shall still denote everything it is ac-
customed todenote ; or that allthepro-
positions into which it is accustomed to
enter, and which have any foundation
in truth, shall remain true. Indepcn-
dentlv of accidental ambiiruities, in

442

OPERATIONS SUBSIDIARY TO INDUCTION.

which the diffei-ent meanings have no
connection with one another, it conti-
nually happens that a word is used in
two or more senses derived from each
other, but yet radically distinct. So
long as a term is vague, that is, so long
as its connotation is not ascertained
and permanently fixed, it is constantly
liable to be applied by extension from
one thing to another, until it reaches
things which have little, or even no
resemblance to those which were first
designated by it.

Suppose, says Dugald Stewart, in
his Philosophical Essays* " that the
letters A, B, C, D, E, denote a series
of objects ; that A possesses some one
quality in common with B ; B a qua-
lity in common with C ; C a quality
in common with D ; D a quality in
common with E ; while at the same
time no quality can be found which
belongs in common to any three ob-
jects in the series. Is it not conceiv-
able that the aflSnity between A and
B may produce a transference of the
name of the first to the second ; and
that, in consequence of the other
affinities which connect the remain-
ing objects together, the same name
may pass in succession from B to C,
from C to D, and from D to E ? In
this manner a common appellation
will arise between A and E, although
the two objects may, in their nature
and properties, be so widel}' distant
from each other, that no stretch of
imagination can conceive how the
thoughts were led from the former to
the latter. The transitions, never-
theless, may have been all so easy
and gradual, that, were they success-
fully detected by the fortunate inge-
nuity of a theorist, we should instantly
recognise, not only the verisimilitude,
but the truth of the conjecture ; in
the same way as we admit, with the
confidence of intuitive conviction, the
certainty of the well-known etymolo-
gical process which connects the Latin
preposition c or ex with the English
substantive stranger, the moment that

* P. 217, 4to edition.

tlie intermediate links of the chain
are submitted to our examination."*

The applications which a word ac-
quires by this gradual extension of it
from one set of objects to another,
Stewart, adopting an expression from
Mi\ Payne Knight, calls its transitive
applications ; and after briefly illus-
trating such of them as are the re-
sult of local or casual associations, he
proceeds as follows : f —

" But although by far the greater
part of the transitive or derivative
applications of words depend on casual
and unaccountable caprices of the
feelings or the fancy, there are certain
cases in which they open a very in-
teresting field of philosophical specu-
lation. Such are those in which an
analogous transference of the cor-
responding term may be remarked
universally, or very generally, in other

' " E, ex, extra, extrancus, stranger,
stranger."

Another etymological example some-
times cited is the derivation of the English
uncle from the Latin ants. It i.s scarcely
possible for two words to bear fewer out-
ward marks of relationshijj, yet there is but
one step between them — avus, avunculus,
uncle. So pilgrim, from ager : per agrum,
peragrimis, peregrinus, 'pMegrino, pilgrim.

Professor Bain giv^s some apt examples
of these transitions of meaning. "The
word 'damp' primarily signified moist,
humid, wet. But the property is often
accompanied with the feeling of cold or
chillness, and hence the idea of cold is
strongly suggested by the word. This is
not all. Proceeding upon the superadded
meaning, we speak of damping a man's
ardour, a metaphor where the cooling is
the only circumstance concerned ; we go
on still further to designate the iron slide
that shuts off the draft of a stove, 'the
damper,' the primary meaning being now
entirely dropped. ' Dry,' in like manner,
through signifying the absence of moisture,
water, or liquidity, is applied to sulphuric
acid containing water, although not thei-eby
ceasing to be a moist, wet, or liquid sub-
stance." So in tlie phrases dry shen-y or
champagne.

" ' Street,' originally a paved way, with
or without houses, has been extended to
roads lined with houses, whether paved or
unpaved. ' Impertinent ' signified at first
irrelevant, alien to the purpose in hand,
through which it has come to mean med-
dling, intrusive, unmannerly, insolent."
{Loqic, ii. 173, 174).

t P. 226-227.

I

HEQtriSlTES OP LANGUAGE:

languages ; and in which, of course,
the uniformity of the result must be
ascribed to the essential principles
of the human frame. Even in such
cases, however, it will by no means
be always found, on examination, that
the various applications of the same
term have arisen from any common
quality or qualities in the objects to
which they relate. In the greater
luxmber of instances, they may be
traced to some natural and universal
associations of ideas, founded in the
common faculties, common organs,
and common condition of the human
race. . . . According to the different
degrees of intimacy and strength in
the associations on which the traiisi-
tions of languages are founded, very
tiiflferent effects may be expected to
arise. Where the association is slight
and casual, the several meanings will
remain distinct from each other, and
will often, in process of time, assume
the appearance of capricious varieties
in the use of the same arbitrary sign.
Whc7'e the association is so natural and
habitual as to become virtually indis-
soluble, the transitive meanings will
coalesce in one complex conception;
and every neio transition will become a
more comprehensive generalisation of
the term in question.'^

I solicit particular attention to the
law of mind expressed in the last sen-
tence, and which is the source of the
perplexity so often experienced in de-
tecting these transitions of meaning.
Ignorance of that law is the shoal on
which some of the most powerful in-
tellects which have adorned the hu-
man race have been stranded. The
inquiries of Plato into the definitions
of some of the most general terms of
moral speculation are characterised by
Bacon as a far nearer approach to a
true inductive method than is else-
where to be found among the ancients,
and are, indeed, almost perfect ex-
amples of the preparatory process of
comparison and abstraction ; but, from
being unaware of the law just men-
tioned, he often wasted the powers of
this great logical instrument on in-

443

quiries in which it could realise no
result, since the phenomena, whose
common properties he so elaborately
endeavoured to detect, had not really
any common properties. Bacon him-
self fell into the same error in his
speculations on the nature of heat, in
which he evidently confounded under
the name hot, classes of phenomena
which have no property in common.
Stewart certainly overstates the mat-
ter when he speaks of "a prejudice
which has descended to modern times
from the scholastic ages, that when a
word admits of a variety of signifi
cations, these different significations
must all be species of the same genus,
and must consequently include some
essential idea common to every indi-
vidual to which the generic term can
be applied ; " * for both Aristotle and
his followers were well aware that
there are such things as ambiguities
of language, and delighted in distin-
guishing thenj. But they never sus-
pected ambiguity in the cases where
(as Stewart remarks) the association
on which the transition of meaning
was founded is so natural and habi-
tual, that the two meanings blend to-
gether in the mind, and a real transi-
tion becomes an apparent generalisa-
tion. Accordingly they wasted in-
finite pains in endeavouring to find a
definition which would serve for seve-
ral distinct meanings at once ; as in
an instance noticed by Stewart him-
self, that of " causation : the am-
biguity of the word, which, in the
Greek language, corresponds to the
English word cause, having suggested
to them the vain attempt of tracing
the common idea which, in the case of
any effect, belongs to the efficient, to
the matter, to the /orwi, and to the
end. The idle generalities " (he adds)
" we meet with in other philosophers,
about the ideas of the good, the fit,
and the becoming, have taken their
rise from the same undue influence of
popular epithets on the speculations
of the learned." t

* Essays, p. 214. f Ibid., p.' 215.

444

OPllRATlONS SUBSIBlAkV TO iNDtTCTION.

Among the words which have un-
dergone so many successive transi-
tions of meaning that every trace of
a property common to all the things
they are ^applied to, or at least com-
mon and also peculiar to those things,
has been lost, Stewart considers the
vvord Beautiful to be one. And (with-
out attempting to decide a question
which in no respect belongs to Logic)
I cannot but feel, with him, con-
siderable doubt whether the word
Beautiful connotes the same property
when we speak of a beautiful colour,
a beautiful face, a beautiful scene, a
beautiful character, and a beautiful
poem. The word was doubtless ex-
tended from one of these objects to
another on account of a resemblance
between them, or more probably be-
tween the motions they excited ; and,
by this pi'ogressive extension it has
at last reached things very remote
from those objects of sight to which
there is no doubt that it was first
appropriated ; and it is at least
questionable whether there is now
any property common to all the things
which, consistently with Tisage, may
be called beautiful, except the pro-
perty of agreeableness, which the term
certainly does connote, but which can-
not be all that people usually intend
to express by it, since there are many
agreeable things which are never
called beautiful. If such be the case,
it is impossible to give to the word
Beautiful any fixed connotation, such
that it shall denote all the objects
which in common use it now denotes,
but no others. A fixed connotation,
however, it ought to have ; for, so long
as it has not, it is unfit to be used as
a scientific term, and is a perpetual
source of false analogies and erroneous
generalisations.

This, then, constitutes a case in ex-
emplification of our remark, that even
when there is a property common to
all the things denoted by a name, to
erect that property into the definition
and exclusive connotation of the name
is not always desirable. The various
things called beautiful unquestionably

I

resemble one another in being agree*
able ; but to make this the definition
of beauty, and so extend the word
Beautiful to all agreeable things, would
be to drop altogether a portion of
meaning which the word really, though
indistinctly, conveys, and to do what
depends on us towards causing those
qualities of the objects which the word
previously, though vaguely, pointed
at, to be overlooked and forgotten.
It is better, in such a case, to give a
fixed connotation to the terra by re-
stricting, than by extending its use ;
rather excluding from the epithet
Beautiful some things to which it is
commonly considered applicable, than
leaving out of its connotation any of
the qualities by which, though oc-
casionally lost sight of, the general
mind may have been habitually guided
in the commonest and most interest-
ing applications of the term. For
there is no question that when people
call anything beautiful, they think
they are asserting more than that it is
merely agreeable. They think they
are ascribing a peculiar sort of agree-
ableness, analogous to that which they
find in some other of the things to
which they are accustomed to apply
the same name. If, therefore, there
be any particular sort of agreeable-
ness which is common, though not to
all, yet to the principal things which
are called beautiful, it is better to
limit the denotation of the term ti»
those things, than to leave that kind
of quality without a term to connote
it, and thereby divert attention from
its peculiai'ities.

§ 6. The last remark exemplifies
a X'ule of terminology, which is of
great importance, and which has
hardly yet been recognised as a rule,
but by a few thinkers of the present
century. In attempting to rectify
the use of a vague term by giving it
a fixed connotation, we must taks
care not to discard (unless advisedly,
and on the ground of a deeper know-
ledge of the subject) any portion of
the connotation which the word, in

I

REQUISITES OF LANGUAGE.

445

however indistinct a manner, pre-
viously carried with it. For other-
wise language loses one of its inherent
and most valuable properties, that of
being the conservator of ancient ex-
perience ; the keeper-alive of those
thoughts and observations of former
ages which may be alien to the ten-
dencies of the passing time. This
function of language is so often over-
looked or undervalued, that a few
observations on it appear to be ex-
tremely required.

Even when the connotation of a
term has been accurately fixed, and
still more if it has been left in the
state of a vague imanalysed feeling
t)f resemblance, there is a constant
tendency in the word, through familiar
tise, to part with a portion of its con-
notation. It is a well-known law of
the mind, that a word originally as-
sociated with a very complex cluster
of ideas is far from calling up all
those ideas in the mind every time
the word is used : it calls up only
one or two, from which the mind runs
on by fresh associations to another
set of ideas, without waiting for tiie
suggestion of the remainder of the
complex cluster. If this were not the
case, processes of thought could not
take place with anything like the
rapidity which we know they possess.
Very often, indeed, when we are
employing a word in our mental
operations, we are so far from wait-
ing until the complex idea which cor-
responds to the meaning of the word
is consciously brought before us in
all its parts, that we run on to new
trains of ideas by the other associa-
tions which the mere word excites,
without having realised in our ima-
gination any part whatever cvf the
meaning : thus using the word, and
even using it well and accurately,
and carrying on important processes
of reasoning by means of it, in an
almost mechanical manner ; so much
so, that some metaphysicians, general-
ising from an extreme case, have
fancied that all reasoning is but the
mechanical use of a set of terms ac-

cording to a certain form. We may
discuss and settle the most important
interests of towns or nations by the
application .of general theorems or
practical maxims previously laid down,
without having had consciously sug-
gested to us once in the whole pro-
cess the houses and green fields, the
thronged market-places and domestic
hearths, of which not only thos(i
towns and nations consist, but whicli
the words town and nation confessedly
mean.

Since, then, general names come in
this manner to be used (and even to
do a portion of their work well) with-
out suggesting to the mind the whole
of their meaning, and often with the
suggestion of a very small, or no part
.at all of that meaning ; we cannot
wonder that words so used come in
time to be no longer capable of sug-
gesting any other of the ideas appro-
priated to them than those with
which the association is most imme-
diate and strongest, or most kept up
by the incidents of life, the remainder
being lost altogether, unless the mind,
by often consciously dwelling on them,
keeps up the association. Words na-
turally retain much more of their
meaning to persons of active imagi-
nation, who habituall}' represent to
themselves things in the concrete,
with the detail which belongs to them
in the actual world. To minds of a
different description, the only anti-
dote to this corruption of language is
predication. The habit of predicat-
ing of the name all the various pro,
perties which it originally connoted,
keeps up the association between the
name and those properties.

But in order that it may do so, it
is necessary that the predicates should
themselves retain their association
with the properties which they sever-
ally connote. For the propositions
cannot keep the meaning of the words
alive, if the meaning of the proposi-
tions themselves should die. And
nothing is more common than for
propositions to be mechanically re-
peated, mechanically retained in the

446

OPERATIONS SUBSIDIARY TO INDUCTION.

memory, and their truth undoubtingly
assented to and relied on, while yet
they carry no meaning distinctly home
to the mind ; and while the matter
of fact or law of nature which they ori-
ginally expressed is as much lost sight
of, and practically disregarded, as if
it never had been heard of at all. In
those subjects which are at the same
time familiar and complicated,and espe-
cially in those which are so in as great
a degree as moral and social subjects
are, it is a matter of common remark
how many important propositions are
believed and repeated from habit,
while no account could be given, and
no sense is practically manifested, of
the truths which they convey. Hence
it is that the traditional maxima of
old experience, though seldom ques-
tioned, have often so little effect on
the conduct of life, because their
meaning is never, by most persons,
really felt, until personal experience
has brought it home. And thus also
it is that so many doctrines of religion,
ethics, and even politics, so full of
meaning and reality to first converts,
have manifested (after the association
of that meaning with the verbal for-
mulas has ceased to be kept up by the
controversies which accompanied their
first introduction) a tendency to de-
generate rapidly into lifeless dogmas ;
which tendency, all the efforts of an
education expressly and skilfully di-
rected to keeping the meaning alive,
are barely sufficient to counteract.

Considering, then, that the human
mind, in different generations, occu-
pies itself with different things, and
in one age is led by the circumstances
which surround it to fix more of its
attention upon one of the properties
of a thing, in another age upon an-
other ; it is natural and inevitable
that in every age a certain portion
of our recorded and traditional know-
ledge, not being continually suggested
by the pursuits and inquiries with
which mankind are at that time en-
grossed, should fall asleep, as it were,
and fade from the memory. It would
be in danger of being totally lost if

the propositions or formulas, the re-
sults of the previous experience, did
not remain, as forms of words it may
be, but of words that once really
conveyed, and are still supposed to
convey, a meaning ; which meaning,
though suspended, may be historically
traced, and, when suggested, may be
recognised by minds of the necessary
endowments as being still matter of
fact or truth. While the formulas
remain, the meaning may at any time
revive ; and as on the one hand the
formulas progressively lose the mean-
ing they were intended to convey, so,
on the other, when this forgetfulnes.s
has reached its height and begun to
produce obvious consequences, minds
arise which from the contemplation
of the formulas rediscover the truth,
when truth it was, which was con-
tained in them, and announce it agahi
to mankind, not as a discovery, but
as the meaning of that which they
have been taught, and still profess to
believe.

Thus there is a perpetual oscillation
in spiritual truths, and in spiritual
doctrines of any significance, even
when not truths. Their meaning U
almost always in a process either of
being lost or of being recovered.
Whoever has attended to the history
of the more serious convictions of
mankind — of the opinions by which
the general conduct of their lives is,
or as they conceive ought to be, more
especially regulated^-is aware that
even when recognising verbally the
same doctrines, they attach to them
at different periods a greater or less
quantity, and even a different kind,
of meaning. The words in their
original acceptation connoted, and
the propositions expressed, a compli-
cation of outward facts and inward
feelings, to different portions of which
the general mind is more particularly
alive in different generations of man-
kind. To common minds, only that
portion of the meaning is in each
generation suggested, of which that
generation possesses the counterpart
in its own habitual experience. But

I

REQUISITES OF LANGUAGE.

447

the words and propositions lie ready
to suggest to any mind duly prepared
the remainder of the meaning. Such
individual minds are almost always
to be found ; and the lost meaning,
revived by them, again by degrees
works its way into the general mind.
The arrival of this salutary reaction
may, however, be materially retarded
by the shallow conceptions and in-
cautious proceedings of mere logicians.
It sometimes happens that towards
the close of the downward period,
when the words have lost part of their
.significance, and have not yet begun
to recover it, persons arise whose lead-
ing and favourite idea is the impor-
tance of clear conceptions and precise
thought, and the necessity, therefore,
i»f definite language. These persons,
in examining the old formulas, easily
perceive that words are used in them
without a meaning ; and if they are
n«)t the sort of persons who are cap-
able of rediscovering the lost signifi-
cation, they naturally enough dismiss
the formula, and define the name
without reference to it. In so doing
they fasten down the name to what
it connotes in common use at the
time when it conveys the .«;mallest
quantity of meaning ; and introduce
the practice of employing it consis-
tently and imiformly, according to
that connotation. The word in this
way acquires an extent of denotation
far beyond what it had before ; it be-
comes extended to many things to
which it was previously, in appear-
ance capriciously, refused. Of the
propositions in which it was formerly
used, those which were true in virtue
of the forgotten part of its meaning
are now, by the clearer light which
the definition diffuses, seen not to
be true according to the definition ;
which, however, is the recognised and
sufficiently correct expression of all
that is perceived to be in the mind of
any one by whom the term is used at
the present day. The ancient for-
mulas are consequently treated as
prejudices ; and people are no longer
taught as before, though not to under-

stand them, yet to believe that there
is truth in them. They no longer re-
main in the general mind surrounded
by respect, and ready at any time to
suggest their original meaning. What-
ever truths they contain are not only,
in these circumstances, rediscovered
far more slowly, but, when redis-
covered, the prejudice with which
novelties are regarded is now, in some
degree at least, against them, instead
of being on their side.

An example may make these re-
marks more intelligible. In all ages,
except where moral speculation has
been silenced by outward compulsion,
or where the feelings which prompt
to it still continue to be satisfied by
the traditional doctrines of an estab
lished faith, one of the subjects which
have most occupied the minds of
thinking persons is the inquiry, What
is virtue ? or, What is a virtuous char-
acter ? Among the different theories
on the subject which have, at different
times, grown up and obtained partial
currency, every one of which reflected
as in the clearest mirror the express
image of the age which gave it birth,
there was one, according to whicli
virtue consists in a correct calculation
of our own personal interests, either
in this world only, or also in another.
To make this theory plausible, it was
of course necessary that the only bene-
ficial actions which people in gene-
ral were accustomed to see, or were
therefore accustomed to praise, should
be such as were, or at least might
without contradicting obvious facts
b3 supposed to be, the result of a
prudential regard to self-interest ; so
that the words really connoted no
more, in common acceptation, than
was set down in the definition.

Suppose, now, that the pj^rtisans
of this theory had contrived to intro-
duce a consistent and undeviating use
of the term according to this defini-
tion. Suppose that they had seriously
endeavoured, and had succeeded in
the endeavour, to banish the word
disinterestedness from the language ;
had obtained the disuse of all expres-

448

OrERATIONS SUBSIDIARY TO INDUCTION.

sions attaching odium to selfishness
or commendation to self-sacrifice, or
which implied generosity or kindness
to be anything but doing a benefit in
order to receive , a greater personal
advantage in turn. Need we say that
this abrogation of the old formulas
for the sake of preserving clear ideas
and consistency of thought would
have been a great evil ? while the
very inconsistency incurred by the
co-existence of the formulas with
philosophical opinions, which seemed
to condemn them as absurdities, oper-
ated as a stimulus to the re-examina-
tion of the subject ; and thus the very
doctrines originating in the oblivion
into which a part of the truth had
fallen were rendered indirectly, but
powerfully, instrumental to its re-
vival.

The doctrine of the Coleridge school,
that the language of any people among
whom culture is of old date is a sacred
deposit, the property of all ages, and
which no one age should consider it-
self empowered to alter, borders in-
deed, as thus expressed, on an extra-
vagance ; but it is grounded on a
truth, frequently overlooked by that
class of logicians who think more of
having a clear than of having a com-
prehensive meaning, and who per-
ceive that every age is adding to the
truths which it has received from its
predecessors, but fail to see that a
counter-process of losing truths already
possessed is also constantly going on,
and requiring the most sedulous at-
tention to counteract it. Language
is the depository of the accumulated
body of experience to which all former
ages have contributed their part, and
which is the inheritance of all yet to
come. We have no right to prevent
ourselves from transmitting to pos-
terity a larger portion of this inherit-
ance than we may ourselves have
profited by. However much we may
be able to improve on the conclusions
of our forefathers, we ought to be
careful not inadvertently to let a:ny
of their premises slip through our
fingers. It may be good to alter the

1

id tr>«l

meaning of a word, but it is bad to
let any part of the meaning drop.
Whoever seeks to introduce a more
correct use of a term with which
important associations are connected,
should be required to possess an ac-
curate acquaintance with the history
of the particular " word, and of the
opinions which in different stages of
its progress it served to express. To
be qualified to define the name, we
must know all that has ever been
known of the properties of the class
of objects which are, or originally
were, denoted by it. For if we give
it a meaning according to which any
proposition will be false which has
ever been generally held to be true,
it is incumbent on us to be sure that
we know and have considered all
which those who believed the pro-
position understood by it.

CHAPTER V.

ON THE NATURAL HISTORY OP THK !
VARIATIONS IN THE MEANING OK i
TERMS.

§ I. It is not only in the mode
which has now been pointed out,
namely, by gradual inattention to a
portion of the ideas conveyed, that
words in common use are liable to
shift their connotation. The truth is,
that the connotation of such words
is perpetually varying, as might be
expected from the manner in which
words in common use acquire their
connotation. A technical term, in-
vented for purposes of art or science,
has, from the first, the connotation
given to it by its inventor ; but a
name which is in every one's mouth
before any one thinks of defining it,
derives its connotation only from the
circumstances which are habitually
brought to mind when it is pro-
nounced. Among these circumstances
the properties common to the things
denoted by the name have naturally
a principal place, and would have
the sole place if language were regu-

fl

VARIATIONS IN MEANING OF TERMS.

449

lated by convention rather than by
custom and accident. But besides
these common properties, which if
they exist are certainly present when-
ever the name is employed, any other
circumstance may casually be found
along with it so frequently as to
become associated with it in the
same manner, and as strongly as the
common properties themselves. In
proportion as this association forms
itself, people give up using the name
in cases in which those casual cir-
cumstances do not exist. They pre-
fer using some other name, or the
same name with some adjunct, rather
than employ an expression which will
call up an idea they do not want to
excite. The circumstance originally
casual thus becomes regularly a part
of the connotation of the word.

It is this continual incorporation
of circumstances originally accidental
into the permanent signification of
words which is the cause that there
are so few exact synonyms. It is
this also which renders the dictionary
meaning of a word, by universal re-
mark, so imperfect an exponent of its
real meaning. The dictionary mean-
ing is marked out in a broad, blunt
way, and probably includes all that
was originally necessary for the cor-
rect employment of the term ; but in
process of time so many collateral
associations adhere to words, that
whoever should attempt to use them
with no other guide than the dic-
tionary would confound a thousand
nice distinctions and subtle shades
of meaning which dictionaries take
no account of ; as we notice in the
use of a language in conversation or
writing by a foreigner not thoroughly
master of it. The history of a word,
by showing the causes which deter-
mine its use, is in these cases a better
guide to its employment than any defi-
nition ; for definitions can only show
its meaning at the particular time, or
at most the series of its successive
meanings, but its history may show
the law by which the succession was
produced, The word gmtleman, for

instance, to the correct employment
of which a dictionary would be no
guide, originally meant simply a man
born in a certain rank. From this
it came by degrees to connote all
such qualities or adventitious circum-
stances as were usually found to be-
long to persons of that rank. This
consideration at once explains why in
one of its vulgar acceptations it means
any one who lives without labour, in
another without manual labour, and
in its more elevated signification it
has in every age signified the con-
duct, character, habits, and outward
appearance, in whomsoever found,
which, according to the ideas of that
age, belonged or were expected to
belong to persons born and educated
in a high social position.

It continually happens that of two
words, whose dictionary meanings are
either the same or very slightly
different, one will be the proper
word to use in one set of circum-
stances, another in another, without
its being possible to show how the
custom of so employing them origi-
nally grew up. The accident that
one of the words was used and not
the other on a particular occasion
or in a particular social circle, will
be sufiicient to produce so strong an
association between the word and
some speciality of circumstances,
that mankind abandon the use of
it in any other case, and the specia-
lity becomes part of its signification.
The tide of custom first drifts the
word on the shore of a particular
meaning, then retires and leaves it
there.

An instance in point is the remark-
able change which, in the English
language at least, has taken place in
the signification of the word loyalty.
That word originaftg, meant in Eng-
lish, as it still mea^ in the language
from whence it came, fair, open deal-
ing, and fidelity to engagements ; in
that sense the quality it expressed
was part of the ideal chivalrous or
knightly character. By what pro-
cess, in England, the term became re*

2 F

450

OPERATIONS SUBSIDIARY TO INDUCTION.

stricted to the single case of fidelity
to the throne, I am not sufficiently
versed in the history of courtly lan-
guage to be able to pronounce. The
interval between a hyal chevalier and
a loyal subject is certainly great. I
can only suppose that the word was,
at some period, the favourite term at
court to express fidelity to the oath of
allegiance ; until at length those who
wished to speak of any other, and as
it was probably deemed, inferior sort
of fidelity, either did not venture to
use so dignified a term, or found it
convenient to employ some other in
order to avoid being misunderstood.

§ 2. Cases are not unfrequent in
•which a circumstance, at first casu-
ally incorporated into the connotation
of a word which originally had no
reference to it, in time wholly super-
sedes the original meaning, and be-
comes not merely a part of the con-
notation, but the whole of it. This
is exemplified in the word pagan,
paganus — which originally, as its ety-
mology imports, was equivalent to
villager — the inhabitant of a pagus, or
village. At a particular era in the
extension of Christianity over the
Roman empire, the adherents of the
old religion, and the villagers or
country people, were nearly the same
body of individuals, the inhabitants
of the towns having been earliest con-
verted ; as in our own day, and at all
times, the greater activity of social
intercourse renders them the earliest
recipients of new opinions and modes,
while old habits and prejudices linger
longest among the country people ;
not to mention that the towns were
more immediately under the direct in-
fluence of the Government, which at
that time had embraced Christianity.
From this casual coincidence, the
word paganus carried with it, and
began more and more steadily to sug-
gest, the idea of a worshipper of the
ancient divinities ; until at length it
suggested that idea so forcibly, that
people who did not desire to suggest
the idetk avoided using the word,

But when paganus had come to con-
note heathenism, the very unimpor-
tant circumstance, with reference to
that fact, of the place of residence,
was soon disregarded in the employ-
ment of the word. As there was
seldom any occasion for making sepa-
rate assertions respecting heathens
who lived in the country, there was
no need for a separate word to de-
note them ; and pagan came not only
to mean heathen, but to mean that
exclusively.

A case still more familiar to most
readers is that of the word villain
or villein. This term, as everybody
knows, had in the Middle Ages a con-
notation as strictly defined as a word
could have, being the proper legal
designation for those persons who
were the subjects of the less onerous
forms of feudal bondage. The scorn
of the semi -barbarous military aristo-
cracy for these their abject dependants
rendered the act of likening any per-
son to this class of people a mark of
the greatest contumely ; the same
scorn led them to ascribe to the same
people all manner of hateful qualities,
which doubtless also, in the degrading
situation in which they were held,
were often not unjustly imputed to
them. These circumstances combined
to attach to the term villain ideas of
crime and guilt, in so forcible a man-
ner that the application of the epithet
even to those to whom it legally be-
longed became an affront, and was
abstained from whenever no affront
was intended. From that time guilt
was part of the connotation, and soon
became the whole of it, since man-
kind were not prompted by any urgent
motive to continue making a distinc-
tion in their language between bad
men of servile station and bad men
of any other rank in life.

These and similar instances in which
the original signification of a term is
totally lost — another and an entirely
distinct meaning being first engrafted
upon the former, and finally substi-
tuted for it — ^afford examples of the
double jnovement which is always

VARIATIONS IN MEANING OF TERMS.

451

taking place in language ; two counter-
movements, one of Generalisation, by
which words are perpetually losing
portions of their connotation, and be-
coming of less meaning and more
general acceptation ; the other of Spe-
cialisation, by which other, or even
these same words, are continually
taking on fresh connotation ; acquir-
ing additional meaning, by being re-
stricted in their employment to a part
only of the occasions on which they
might properly be used before. This
double movement is of sufficient im-
portance in the natural history of
language, (to which natural history
the artificial modifications ought al-
ways to have some degree of refer-
ence,) to justify our dwelling a little
longer on the nature of the twofold
phenomenon, and the causes to which
it owes its existence.

§ 3. To begin with the movement
of generalisation. It might seem un-
necessary to dwell on the changes in
the meaning of names which take
place merely from their being used
ignorantly, by persons who, not hav-
ing properly mastered the received
connotation of a word, apply it in a
looser and wider sense than belongs
to it. This, however, is a real source
of alterations in the language ; for
when a word, from being often em-
ployed in cases where one of the qua-
lities which it connotes does not exist,
ceases to suggest that quality with
certainty, then even those who are
under no mistake as to the proper
meaning of the word prefer express-
ing that meaning in some other way,
and leave the original word to its fate.
The word 'Squire, as standing for an
owner of a landed estate ; Parson, as
denoting not the rector of the parish,
but clergymen in general ; Artist, to
denote only a painter or sculptor, are
cases in point. Such cases give a clear
insight into the process of the degenera-
tion of languages in periods of history
when literary culture was suspended ;
and we are now in danger of ex-
periencing a similar evil through the

superficial extension of the same cul'
ture. So many persons without any-
thing deserving the name of education
have become writers by profession,
that written language may almost be
said to be principally wielded by per-
sons ignorant of the proper use of the
instrument, and who are spoiling it
more and more for those who under-
stand it. Vulgarisms, which creep in
nobody knows how, are daily depriv-
ing the English language of valuable
modes of expressing thought. To take
a present instance : the verb transpire
formerly conveyed very expressively
its correct meaning, viz. to become
known through unnoticed channels —
to exhale, as it were, into publicity
through invisible pores, like a vapour
of gas disengaging itself. But of late
a practice has commenced of employ-
ing this word, for the sake of finery,
as a mere synonym of to happen :
*' the events which have transpired in
the Crimea," meaning the incidents of
the war. This vile specimen of bad
English is already seen in the de-
spatches of noblemen and viceroys :
and the time is apparently not far
distant when nobody will understand
the word if used in its proper sense.
In other cases it is not the love of
finery, but simple want of education,
which makes writers employ words in
senses unknown to genuine English.
The use of " aggravating " for *' pro-
voking," in my boyhood a vulgarism
of the nursery, has crept into almost
all newspapers, and into many books ;
and when the word is used in its proper
sense, as when writers on criminal law
speak of aggravating and extenuating
circumstances, their meaning, it is
probable, is already misunderstood.
It is a great error to think that these
corruptions of language do no harm.
Those who are struggling with the
difficulty (and who know by experience
how great it already is) of expressing
oneself clearly with precision, find
their resources continually narrowed
by illiterate writers, who seize and
twist from its purpose some form of
speech which once served to convey

452

OPERATIONS SUBSIDIARY TO INDUCTION.

briefly and compactly an unambiguous
meaning. It would hardly be believed
how often a writer is compelled to a
circumlocution by the single vulgar-
ism, introduced during the last few
years, of using the word alone as an
adverb, only not being fine enough for
the rhetoric of ambitious ignorance.
A man will say, "To which I am not
alone bound by honour, but also by
law," unaware that what he has un-
intentionally said is, that he is not
alone bound, some other person being
bound with him. Formerly, if any
one said, " I am not alone responsible
for this," he was understood to mean
(what alone his words mean in correct
English) that he is not the sole per-
son responsible ; but if he now used
such an expression, the reader would
be confused between that and two
other meanings — that he is not only
responsible but something more, or
that he is responsible not only for this
but for something besides. The time
is coming when Tennyson's CEnone
could not say, *' I will not die alone,"
lest she should be supposed to mean
that she would not only die but do
something else.

The blunder of writing predicate
for predict has become so widely dif-
fused that it bids fair to render one
of the most useful terms in the scien-
tific vocabulary of Logic unintelli-
gible. The mathematical and logical
term "to eliminate" is undergoing
a similar destruction. All who are
acquainted either with the proper use
of the word or with its etjnoiology,
know that to eliminate a thing is to
thrust it out ; but those who know
nothing about it, except that it is a
fine-looking phrase, use it in a sense
precisely the reverse, to denote, not
turning anything out, but bringing it
in. They talk of eliminating some
truth, or other useful result, from a
mass of details.* A similar permanent

* Though no such evil consequences as
take place in these instances are likely to
arise from the modern freak of writing
tanatory instead of sanitary, it deserves
notice as a charming specimen of pedantry
engrafted upon ignorance. Those who thus

deterioration in the language is in
danger of being produced by the
blunders of translators. The writers
of telegrams and the foreign corre-
spondents of newspapers have gone
on so long translating demander by
" to demand," without a suspicion that
it means only to ask, that (the context
generally showing that nothing else is
meant) English readers are gradually
associating the English word demand
with simple asking, thus leaving the
language without a term to express a
demand in its proper sense. In like
manner, "transaction," the French
word for a compromise, is translated
into the English word transaction ;
while, curiously enough, the inverse
change is taking place in France,
where the word '* compromis " has
lately begun to be used for expressing
the same idea. If this continues, the
two countries will have exchanged
phrases.

Independently, however, of the gene-
ralisation of names through their igno-
rant misuse, there is a tendency in
the same direction consistently with
a perfect knowledge of their meaning,
arising from the fact that the number
of things known tc us, and of which
we feel a desire to speak, multiply
faster than the names for them. Ex-
cept on subjects for which there has
been constructed a scientific termino-
logy, with which unscientific persons
do not meddle, great difficulty is gene-
rally found in bringing a new name
into use ; and independently of that
difficulty, it is natural to prefer giving
to a new object a name which at least
expresses its resemblance to something
already known, since by predicating
of it a name entirely new we at first
convey no information. In this man-
ner the name of a species often be-
comes the name of a genus ; as salt,
for example, or oil; the former of
which words originally denoted only

undertake to correct the spelling of the
classical English writers are not aware
that the meaning of sanatory, if there were
such a word in the language, would have
reference not to the preservation of health,
but to the cure of disease.

I

VARIATIONS IN MEANING OF TERMS.

453

the muriate of soda, the latter, as its
etymology indicates, only olive oil ;
but which now denote large and diver-
sified classes of substances resembling
these in some of their qualities, and
connote only those common qualities,
instead of the whole of the distinctive
properties of olive oil and sea salt.
The words glass and soap are used by
modem chemists in a similar manner,
to denote genera of which the sub-
stances vulgarly so called are single
species. And it often happens, as in
those instances, that the term keeps
its special signification in addition to
its more general one, and becomes
ambiguous, that is, two names instead
of one.

These changes, by which words in
ordinary use become more and more
generalised, and less and less expres-
sive, take place in a still greater de-
gree with the words which express
the complicated phenomena of mind
and society. Historians, travellers,
and in general those who speak or
write concerning moral and social
phenomena with which they are not
familiarly acquainted, are the great
agents in this modification of langu-
age. The vocabulary of all except
unusually instructed as well as think-
ing persons, is, on such subjects,
eminently scanty. They have a cer-
tain small set of words to which they
are accustomed, and which they em-
ploy to express phenomena the most
heterogeneous, because they have
never sufficiently analysed the facts
to which those words correspond in
their own country, to have attached
perfectly definite ideas to the words.
The first English conquerors of Ben-
gal, for example, carried with them
the phrase landed proprietor into a
country where the rights of indivi-
duals over the soil were extremely
different in degree, and even in na-
ture, from those recognised in Eng-
land. Applying the term with all
its English associations in such a state
of things, to one who had only a
limited right they gave an absolute
right, from another because he had

not an absolute right they took away
all right, drove whole classes of people
to ruin and despair, filled the country
with banditti, created a feeling that
nothing was secure, and produced,
with the best intentions, a disorganisa-
tion of society which had not been
produced in that country by the most
ruthless of its barbarian invaders.
Yet the usage of persons capable of
so gross a misapprehension determines
the meaning of language ; and the
words they thus misuse grow in
generality, until the instructed are
obliged to acquiesce, and to employ
those words (first freeing them from
vagueness by giving them a definite
connotation) as generic terms, sub-
dividing the genera into species.

§ 4. While the more rapid growth
of ideas than of names thus creates a
perpetual necessity for making the
same names serve, even if imperfectly,
on a greater number of occasions,
a counter-operation is going on, by
which names become, on the contrary,
restricted to fewer occasions, by tak-
ing on, as it were, additional connota-
tion, from circumstances not origin-
ally included in the meaning, but
which have become onnected with
it in the mind by some accidental
cause. We have seen above, in the
words pagan and villain, remarkable
examples of the specialisation of the
meaning of words from casual as-
sociations, as well as of the generali-
sation of it in a new direction, which
often follows.

Similar specialisations are of fre-
quent occurrence in the history even
of scientific nomenclature. " It is by
no means uncommon," says Dr. Paris
in his Pharmacologia* " to find a word
which is used to express general char-
acters subsequently become the name
of a specific substance in which such
characters are predominant ; and we
shall find that some important ano
malies in nomenclature may be thus
explained The term ApaeviKOv, from

* Historical Introductiorii vol. 1. p. 66-68.

454

OPEHATIOKS SUBSIDIARY TO iJ^DtTCTlON.

which the word Arsenic is derived,
was an ancient epithet applied to
those natural substances which pos-
sessed strong and acrimonious pro-
perties, and as the poisonous quality
of arsenic was found to be remark-
ably powerful, the term was especi-
ally applied to Orpiment, the form in
which this metal most usually occurred.
So the term Verbena (quasi Herb'na)
originally denoted all those herbs
that were held sacred on account of
their being employed in the rites of
sacrifice, as we learn from the poets ;
but as one herb was usually adopted
upon these occasions, the word Ver-
bena came to denote that particular
herb only, and it is transmitted to us
to this day under the same title, viz.
Verbena or Vervain, and indeed until
lately it enjoyed the medical reputa-
tion which its sacred origin conferred
upon it, for it was worn suspended
around the neck as an amulet. Vit7'iol,
in the original application of the word,
denoted any crystalline body with a
certain degree of transparency {vit-
rum); it is hardly necessary to ob-
serve that the term is now appropri-
ated to a particular species : in the
same manner, Bark, which is a general
term, is applied to express one genus,
and by way of eminence it has the
article The prefixed, as The bark :
the same observation v^dll apply to
the word Opium, which, in its primi-
tive sense, signifies any juice {dirbs,
Succus), while it now only denotes
one species, viz. that of the poppy.
So, again, Elaterium was used by
Hippocrates to signify various internal
applications, especially purgatives, of
a violent and drastic nature (from the
word iXavvu), agito, moveo, stimulo),
but by succeeding authors it was ex-
clusively applied to denote the active
matter which subsides from the juice
of the wild c^vjumber. The word
Fecvla, again, originally meant to
imply any substance which was de-
rived by spontaneous subsidence from
a liquid (from fcex, the grounds or
settlement of any liquor) ; afterwards
it was applied to Starch, which is de-

posited in this manner by agitating
the flour of wheat in water ; and
lastly, it has been applied to a peculiar
vegetable principle, which, like starch,
is insoluble in cold, but completely
soluble in boiling water, with which
it forms a gelatinous solution. This
indefinite meaning of the word fecvla^
has created numerous mistakes in
pharmaceutic chemistry. Elaterium,
for instance, is said to be fecula, and,
in the original sense of the word, it
is properly so called, inasmuch as it
is procured from a vegetable juice by
spontaneous subsidence, but in the
limited and modern acceptation of the
term it conveys an erroneous idea ;
for instead of the active principle of
the juice residing in fecula, it is a
peculiar proximate principle, sui gen-
eHs, to which I have ventured to
bestow the name of Elatin. For the
same reason, much doubt and ob-
scurity involve the meaning of the
word Extract, because it is applied
generally to any substance obtained
by the evaporation of a vegetable
solution, and specifically to a peculiar
proximate principle, possessed of cer-
tain characters, by which it is dis-
tinguished from every other elemen-
tary body."

A generic term is always liable to
become thus limited to a single species,
or even individual, if people have oc-
casion to think and speak of that indi-
vidual or species much oftener than of
anything else which is contained in
the genus. Thus by cattle, a stage-
coachman will understand horses ;
beasts, in the language of agricultu-
rists, stands for oxen ; and birds,
with some sportsmen, for partridges
only. The law of language which
operates in these trivial instances is
the very same in conformity to which
the terms 9e6j, Dens, and God were
adopted from Polytheism by Christi-
anity, to express the single object of
its own adoration. Almost all the
terminology of the Christian Church
is made up of words originally used in
a much more general acceptation :
Ecclesia, Assembly ; Bishop, Episco-

TERMINOLOGY AND NOMENCLATURE

45S

pus, Overseer ; Priest, Presbyter,
Elder ; Deacon, Diaconus, Adminis-
trator ; Sacrament, a vow of allegi-
ance ; Evangelium, good tidings ; and
some words, as Minister, are still used
both in the general and in the limited
sense. It would be interesting to
trace the progress by which Author
came, in its most familiar sense, to
signify a writer, and iroiTjrrjs, or
maker, a poet.

Of the incorporation into the mean-
ing of a term of circumstances acciden-
tally connected with it at some parti-
cular period, as in the case of Pagan,
instances might easily be multiplied.
Physician ((pvalKOi, or naturalist) be-
came, in England, synonymous with
a healer of diseases, because until a
comparatively late period medical
practitioners were the onlj- naturalists.
Clerc, or clericus, a scholar, came to
signify an ecclesiastic, because the
clergy were for many centuries the
only scholars.

Of all ideas, however, the most
liable to cling by association to any-
thing with which they have ever been
connected by proximity are those of
our pleasures and pains, or of the
things which we habitually contem-
plate as sources of our pleasures or
pains. The additional connotation,
therefore, which a word soonest and
most readily takes on is that of agree -
ableness or painfulness, in their vari-
ous kinds and degrees : of being a
good or bad thing ; desirable or to
be avoided ; an object of hatred, of
dread, contempt, admiration, hope, or
love. Accordingly there is hardly a
single name, expressive of any moral
or social fact calculated to call forth
strong affections either of a favourable
or of a hostile nature, which does not
"carry with it decidedly and irresistibly
a connotation of those strong affec-
tions, or, at the least, of approbation
or censure ; insomuch that to employ
those names in conjunction with others
by which the contrary sentiments
were expressed, would produce the
effect of a paradox, or even a contra-
diction in terms. The baneful in-

fluence of a connotation thus acquired
on the prevailing habits of thought,
especially in morals and politics, has
been well pointed out on many oc-
casions by Bentham. It gives rise
to the fallacy of "question-begging
names." The very property which
we are inquiring whether a thing
possesses or not, has become so as-
sociated with the name of the thing
as to be part of its meaning, insomuch
that by merely uttering the name we
assume the point which was to be
made out : one of the most frequent
sources of apparently self-evident pro-
positions.

Without any further multiplication
of examples to illustrate the changes
which usage is continually making in
the signification of terms, I shall add,
as a practical rule, that the logician,
not being able to prevent such trans-
formations, should submit to them
with a good grace when they are irre-
vocably effected, and if a definition is
necessary, define the word according
to its new meaning, retaining the
former as a second signification, if it
is needed, and if there is any chance
of being able to preserve it either
in the language of philosophy or in
common use. Logicians cannot make
the meaning of any but scientific
terms : that of all other words is
made by the collective human race.
But logicians can ascertain clearly
what it is which, working obscurely,
has guided the general mind to a
particular employment of a name ;
and when they have found this, they
can clothe it in such distinct and per-
manent terms, that mankind shall
see the meaning which before they
only felt, and shall not suffer it to
be afterwards forgotten or misappre-
hended.

CHAPTER VI.

THE PRINCIPLES OP A PHILOSOPHICAL
LANGUAGE FURTHER CONSIDERED.

§ I. We have thus far considered
only one of the requisites of a Ian-

45^

OPERATIONS SUBSmiARY TO IICDUCTION.

guage adapted for the investigation
of truth — that its terms shall each
of them convey a determinate and
tinmistakable meaning. There are,
however, as we have already re-
marked, other requisites : some of
them important only in the second
degree, but one which is fundamental,
and barely yields in point of import-
ance, if it yields at all to the quality
which we have already discussed at
so much length. That the language
may be fitted for its purposes, not
only should every word perfectly ex-
press its meaning, but there should
be no important meaning without its
word. Whatever we have occasion
to think of often, and for scientific
purposes, ought to have a name ap-
propriated to it.

This requisite of philosophical lan-
guage may be considered under three
different heads, that number of sepa-
rate conditions being involved in it.

§ 2. First, there ought to be all
such names as are needful for making
such a record of individual observa-
tions that the words of the record
shall exactly show what fact it is
which has been observed. In other
words, there should be an accurate
Descriptive Terminology.

The only things which we can ob-
serve directly being our own sensa-
tions or other feelings, a complete
descriptive language would be one in
which there should be a name for
every variety of elementary sensation
or feeling. Combinations of sensa-
tions or feelings may always be de-
scribed if we have a name for each of
the elementary feelings which com-
pose them ; but brevity of descrip-
tion and clearness (which often de-
pends very much on brevity) are
greatly promoted by giving distinctive
names not to the elements alone, but
also to all combinations which are of
frequent recurrence. On this occa-
sion I cannot do better than quote
from Dr. Whewell * some of the ex-

* History of Scientific Ideas, li. no, in.

cellent remarks which he has made
on this important branch of our sub-
ject.

*' The meaning of [descriptive] tech-
nical terms can be fixed in the first
instance only by convention, and can
be made intelligible only by present-
ing to the senses that which the terms
are to signify. The knowledge of a
colour by its name can only be taught
through the eye. No description can
convey to a hearer what we mean by
apple-green or French-grey. It might,
perhaps, be supposed that, in the first
example, the term apple, referring to
so familiar an object, sufficiently sug-
gests the colour intended. But it
may easily be seen that this is not
true ; for apples are of many different
hues of green, and it is only by a con-
ventional selection that we can appro-
priate the term to one special shade.
When this appropriation is once made,
the term refers to the sensation, and
not to the parts of the term ; for these
enter into the compound merely as a
help to the memory, whether the sug-
gestion be a natural connection as in
'apple-green,' or a casual one as in
* French-grey.' In order to derive
due advantage from technical terms
of the kind, they must be associated
immediately with the perception to
which they belong, and not connected
with it through the vague usages of
common language. The memory must
retain the sensation ; and the tech-
nical word must be understood as
directly as the most familiar word,
and more distinctly. When we find
such terms as tin-white or pinchbeck-
hrown, the metallic colour so denoted
ought to start up in our memory
without delay or search.

" This, which it is most important
to recollect with respect to the simpler
properties of bodies, as colour and
form, is no less true with respect to
more compound notions. In all cases
the term is fixed to a peculiar mean-
ing by convention ; and the student,
in order to use the word, must be
completely familiar with the conven-
tion, so that he has no need to frame

TERMINOLOGY AND NOMENCLATtlRE.

457

conjectures from the word itself. Such
conjectures would always be insecure,
and often erroneous. Thus the term
papilionaceous applied to a flower is
employed to indicate, not only a re-
semblance to a butterfly, but a resem-
blance arising from five petals of a
certain peculiar shape and arrange-
ment ; and even if the resemblance
were much stronger than it is in such
cases, yet, if it were produced in a
different way, as, for example, by one
petal or two only, instead of a * stan-
dard ' two * wings,' and a * keel ' con-
sisting of two parts more or less united
into one, we should be no longer jus-
tified in speaking of it as a * papilio-
naceous ' flower."

When, however, the thing named
is, as in this last case, a combination
of simple sensations, it is not neces-
sary, in order to learn the meaning of
the word, that the student should refer
back to the sensations themselves ; it
may be communicated to him through
the medium of other words ; the
terms, in short, may be defined. But
the names of elementary sensations,
or elementary feelings of any sort,
cannot be defined ; nor is there any
mode of making their signification
known but by making the learner
experience the sensation, or referring
him, through some known mark, to
his remembrance of having experi-
enced it before. Hence it is only the
impressions on the outward senses, or
those inward feelings which are con-
nected in a very obvious and uniform
manner with outward objects, that
are really susceptible of an exact de-
scriptive language. The countless
variety of sensations which arise, for
instance, from disease, or from pecu-
liar physiological states, it would be
in vain to attempt to name ; for as no
one can judge whether the sensation
I have is the same with his, the name
cannot have, to us two, real commu-
nity of meaning. The same may be
said to a considerable extent of purely
mental feelings. But in some of the
sciences which are conversant with
external objects, it is scarcely possible

to surpass the perfection to which this
quality of a philosophical language has
been carried.

"The formation* of an exact and
extensive descriptive language for bo-
tany has been executed with a degree
of skill and felicity, which, before it
was attained, could hardly have been
dreamt of as attainable. Every part
of a plant has been named ; and the
form of every part, even the most
minute, has had a large assemblage
of descriptive terms appropriated to
it, by means of which the botanist can
convey and receive knowledge of form
and structure, as exactly as if each
minute part were presented to him
vastly magnified. This acquisition
was part of the Linnaean reform. . . .
'Toumefort,' says Decandolle, 'ap-
pears to have been the first who really
perceived the utility of fixing the sense
of terms in such a way as always to
employ the same word in the same
sense, and always to express the same
idea by the same words ; but it was
Linnaeus who really created and fixed
this botanical language, and this is
his fairest claim to glory, for by this
fixation of language he has shed clear-
ness and precision over all parts of
the science.'

"It is not necessary here to give
any detailed account of the terms of
botany. The fundamental ones have
been gradually introduced, as the
part of plants were more carefully and
minutely examined. Thus the flower
was necessarily distinguished into the
calyx, the corolla, the stamens, and the
pistils ; the sections of the corolla were
termed petals by Columna ; those of
the calyx were called sepals by Necker.
Sometimes terms of greater generality
were devised ; as perianth, to include
the calyx and corolla, whether one
or both of these were present : peri-
carp, for the part enclosing the grain,
of whatever kind it be, fruit, nut, pod,
&c. And, it may easily be imagined
that descriptive terms may, by defini-
tion and combination, become very

* Hi$t, Sc. Id., ii. 1H-X13.

45S

OPERATIONS SUBSIDIARY TO INDUCTION.

numerous and distinct. Thus leaves
may be called pinnatifid, pinnatipar-
tite, pinnatisect, pinnatilobate, palma-
tifid, palmatipartitef &c., and each of
these words designates different com-
binations of the modes and extent
of the divisions of the leaf with the
divisions of its outline. In some cases,
arbitrary numerical relations are in-
troduced into the definition : thus, a
leaf is called hilobate when it is divided
into two parts by a notch ; but if the
notch go to the middle of its length,
it is bifid ; if it go near the base of the
leaf, it is bipartite ; if to the base, it
is bisect. Thus, too, a pod of a cruci-
ferous plant is a slliqua, if it is four
times as long as it is broad, but if it
be shorter than this it is a silicvla.
Such terms being established, the form
of the very complex leaf or frond of
a fern (Hymenophyllum Wilsoni) is
exactly conveyed by the following
phrase : — 'Fronds rigid pinnate, pinnae
recurved subunilateral pinnatifid, the
segments linear undivided or bifid,
spinulososerrate. '

" Other characters, as well as form,
are conveyed with the like precision :
colour by means of a classified scale
of colours. . . . This was done with
most precision by Werner, and his
scale of colours is still the most usual
standard of naturalists. Werner also
introduced a more exact terminology
with regard to other characters which
are important in mineralogy, as lustre,
hardness. But Mohs improved upon
this step by giving a numerical scale
of hardness, in which talc is i, gyp-
sum 2, calc spar 3, and so on. . . .
Some properties as specific gravity, by
their definition give at once a mimeri-
cal measure ; and others, as crystal-
line form, require a very considerable
array of mathematical calculation and
reasoning to point out their^relations
and gradations."

§ 3. Thus far of Descriptive Ter-
minology, or of the language requisite
for placing on record our observation
of individual instances. But when
we proceed from this to Induction, or

rather to that comparison of observed
instances which is the preparatory
step towards it, we stand in need of
an additional and a different sort of
general names.

Whenever, for purposes of Induc-
tion, we find it necessary to introduce
(in Dr. Whewell's phraseology) some
new general conception — that is,
whenever the comparison of a set of
phenomena leads to the recognition
in them of some common circum-
stance, which, our attention not hav-
ing been directed to it on any former
occasion, is to us a new phenomenon —
it is of importance that this new con-
ception, or this new result of abstrac-
tion, should have a name appropriated
to it ; especially if the circumstance
it involves be one which leads to many
consequences, or which is likely to be
found also in other classes of pheno-
mena. No doubt, in most cases of
the kind, the meaning might be con-
veyed by joining together several
words already in use. But when
a thing has to be often spoken of,
there are more reasons than the
saving of time and space for speaking
of it in the most concise manner pos-
sible. What darkness would be spread
over geometrical demonstrations, if
wherever the word cirde is used, the
definition of a circle were inserted in-
stead of it. In mathematics and its
applications, where the nature of the
processes demands that the attention
should be strongly concentrated, but
does not require that it should be
widely diffused, the importance of
concentration also in' the expressions
has always been duly felt ; and a
mathematician no sooner finds that
he shall often have occasion to speak
of the same two things together, than
he at once creates a term to express
them whenever combined : just as, in
his algebraical operations, he substi-
tutes for (a™ + 6°)|, or forl + ^ + ^-f-
fcc, the single letter P, Q, or S ; not
solely to shorten his sjrmbolical ex-
pressions, but to simplify the purely
intellectual part of his operations, by

TERMINOLOGY AND NOMENCLATURE.

459

enabling the mind to give its exclu-
sive attention to the relation between
the quantity S and the other quanti-
ties which enter into the equation,
without being distracted by thinking
unnecessarily of the parts of which S
is itself composed.

But there is another reason, in ad-
dition to that of promoting perspi-
cuity, for giving a brief and compact
name to each of the more considerable
results of abstraction which are ob-
tained in the course of our intellec-
tual phenomena. By naming them,
we fix our attention upon them ; we
keep them more constantly before the
mind. The names are remembered,
and, being remembered, suggest their
definition ; while if, instead of specific
and characteristic names, the mean-
ing had been expressed by putting
together a number of other names,
that particular combination of words
already in common use for other pur-
poses would have had nothing to
make itself remembered by. If we
want to render a particular combina-
tion of ideas permanent in the mind,
there is nothing which clenches it
like a name specially devoted to ex-
press it. If mathematicians had been
obliged to speak of "that to which a
quantity, in increasing or diminish-
ing, is always approaching nearer, so
that the difference becomes less than
any assignable quantity, but to which
it never becomes exactly equal," in-
stead of expressing all this by the
simple phrase, " the limit of a quan-
tity," we should probably have long
remained without most of the impor-
tant truths which have been dis-
covered by means of the relation
between quantities of various kinds
and their limits. If, instead of speak-
ing of momentum, it had been neces-
sary to say, "the product of the
number of units of velocity in the
velocity by the number of units of
mass in the mass," many of the dyna-
mical truths now apprehended by
means of this complex idea would
probably have escaped notice, for
want of recalling the idea itself with

sufficient readiness and familiarity.
And on subjects less remote from the
topics of popular discussion, whoever
wishes to draw attention to some
new or unfamiliar distinction among
things will find no way so sure as to
invent or select suitable names for
the express purpose of marking it.

A volume devoted to explaining
what the writer means by civilisation
does not raise so vivid a conception
of it as the single expression, that
Civilisation is a different thing from
Cultivation ; the compactness of that
brief designation for the contrasted
quality being an equivalent for a long
discussion. So, if we would impress
forcibly upon the understanding and
memory the distinction between the
two different conceptions of a repre-
sentative government, we cannot more
effectually do so than by saying that
Delegation is not Representation.
Hardly any original thoughts on
mental or social subjects ever make
their way among mankind, ^or assume
their proper importance in the minds
even of their inventors, until aptly-
selected words or phrases have, as it
were, nailed them down and held
them fast.

§ 4. Of the three essential parts of
a philosophical language, we have now
mentioned two : a terminology suited
for describing with precision the in-
dividual facts observed ; and a name
for every common property of any
importance or interest, which we de-
tect by comparing those facts : in-
cluding (as theconcretes corresponding
to those abstract terms) names for the
classes which we artificially construct
in virtue of those properties, or as
many of them, at least, as we have
frequent occasion to predicate any-
thing of.

But there is a sort of classes, for
the recognition of which no such
elaborate process is necessary ; be-
cause each of them is marked out
from all others not by some one pro-
perty, the detection of which may
depend on a difficult act of abstraction,

46o

OPERATIONS SUBSIDIARY TO INDUCTION.

but by its properties generally. I
mean, the Kinds of things, in the
sense which, in this treatise, has been
specially attached to that term. By
a Kind, it will be remembered, we
mean one of those classes which are
distinguished from all others not by
one or a few definite properties, but
by an unknown multitude of them ;
the combination of properties on which
the class is grounded being a mere
index to an indefinite number of other
distinctive attributes. The class horse
is a Kind, because the things which
agree in possessing the characters by
which we recognise a horse, agree in
a great number of other properties,
as we know, and, it cannot be doubted,
in many more than we know. Animal,
again, is a Kind, because no definition
that could be given of the name animal
could either exhaust the properties
common to all animals, or supply pre-
mises from which the remainder of
those properties could be inferred.
But a combination of properties which
does not give evidence of the existence
of any other independent peculiarities,
does not constitute a Kind. White
horse, therefore, is not a Kind ; be-
cause horses which agree in whiteness
do not agree in anything else, except
the qualities common to all horses,
and whatever may be the causes or
effects of that particular colour.

On the principle that there should
be a name for everything which we
have frequent occasion to make asser-
tions about, there ought evidently to
be a name for every Kind ; for as it
is the very meaning of a Kind that
the individuals composing it have an
indefinite multitude of properties in
common, it follows that, if not with
our present knowledge, yet with that
which we may hereafter acquire, the
Kind is a subject to which there will
have to be applied many predicates.
The third component element of a
philosophical language, therefore, is
that there shall be a name for every
Kind. In other words, there must
not only be a terminology, but also a
nomenclature.

The words Nomenclature and Ter-
minology are employed by most
authors almost indiscriminately ; Dr.
Whewell being, as far as I am aware,
the first writer who has regularly
assigned to the two words different
meanings. The distinction, however,
which he has drawn between them
being real and important, his example
is likely to be followed ; and (as is
apt to be the case when such innova-
tions in language are felicitously made")
a vague sense of the distinction is found
to have influenced the employment of
the terms in common practice, before
the expediency had been pointed out
of discriminating them philosophically.
Every one would say that the reform
effected by Lavoisier and Guy ton -
Morveau in the language of chemistry
consisted in the introduction of a new
nomenclature, not of a new termino-
logy. Linear, lanceolate, oval, or ob-
long, serrated, dentate, or crenate
leaves, are expressions forming part
of the terminology of botany while the
names " Viola odorata " and '* Ulex
Europseus" belong to its nomenclature.

A nomenclature may be defined,
the collection of the names of all the
Kinds with which any branch of know-
ledge is conversant ; or more properly,
of all the lowest Kinds, or infimce
species — those which may be sub-
divided indeed, but not into Kinds,
and which generally accord with what
in natural history are termed simply
species. Science possesses two splen-
did examples of a systematic nomen-
clature ; that of plants and animals,
constructed by Linnaeus and his suc-
cessors, and that of chemistry, which
we owe to the illustrious group oi
chemists who flourished in France to-
wards the close of the eighteenth cen-
tury. In these two departments, not
only has every known species, or low-
est Kind, a name assigned to it, but
when new lowest Kinds are discovered,
names are at once given to them on an
uniform principle. In other sciences
the nomenclature is not at present
constructed on any system, either be-
cause the species to be named are not

TERMINOLOGY AND NOMENCLATURE.

461

numerous enough to require one (as in
geometry, for example), or because no
one has yet suggested a suitable prin-
ciple for such a system, as in minera-
logy : in which the want of a scienti-
cally constructed nomenclature is now
the principal cause which retards the
progress of the science.

§ 5. A word which carries on its
face that it belongs to a nomen-
clature seems at first sight to differ
from other concrete general names in
this — that its meaning does not re-
side in its connotation, in the attri-
butes implied in it, but in its de-
notation, that is, in the particular
group of things which it is appointed
to designate ; and cannot, therefore, be
unfolded by means of a definition,
but must be made known in another
way. This opinion, however, appears
to me erx'oneous. Words belonging
to a nomenclature differ, I conceive,
from other words mainly in this, that
besides the ordinary connotation, they
have a peculiar one of their own :
besides connoting certain attributes,
they also connote that those attri-
butes are distinctive of a Kind. The
term *' peroxide of iron," for example,
belonging by its form to the syste-
matic nomenclature of chemistry,
bears on its face that it is the name
of a peculiar Kind of substance. It
moreover connotes, like the name of
any other class, some portion of the
properties common to the class ; in
this instance the property of being a
compound of iron and the largest
dose of oxygen with which iron will
combine. These two things, the fact
of being such a compound, and the
fact of being a Kind, constitute the
connotation of the name peroxide of
iron. When we say of the substance be-
fore us, that it is the peroxide of iron,
we thereby assert, first, that it is a
compound of iron and a maximum of
oxygen, and next, that the substance
so composed is a peculiar Kind of
substance.

Now, this second part of the con-
notatioa of any word belonging to a

nomenclature is as essential a portion
of its meaning as the first part, while
the definition only declares the first ;
and hence the appearance that the
signification of such terms cannot be
conveyed by a definition, which ap-
pearance, however, is fallacious. The
name Viola odorata denotes a Kind,
of which a certain number of char-
acters, sufficient to distinguish it, are
enunciated in botanical works. This
enumeration of characters is surely,
as in other cases, a definition of the
name. No, say some, it is not a
definition, for the name Viola odorata
does not mean those characters ; it
means that particular group of plants,
and the characters are selected from
among a miich greater number, merely
as marks by which to recognise the
group. But to this I reply, that the
name does not mean that group, for
it would be applied to that group no
longer than while the group is be-
lieved to be an injiina species ; if it
were to be discovered that several
distinct Kinds have been confounded
under this one name, no one would any
longer apply the name Viola odorata
to the whole of the group, but would
apply it, if retained at all, to )ne
only of the Kinds contained therein.
What is imperative, therefore, is not
that the name shall denote one par-
ticular collection of objects, but that
it shall denote a Kind, and a lowest
Kind. The form of the name declares
that, happen what will, it is to denote
an infima species; and that, therefore,
the properties which it connotes, and
which are expressed in the definition,
are to be connoted by it no longer
than while we continue to believe that
those properties, when found together,
indicate a Kind, and that the whole
of them are found in no more than
one Kind.

With the addition of this peculiar
connotation, implied in the form of
every word which belongs to a
systematic nomenclature, the set of
characters which is employed to dis-
criminate each Kind from all other
Kinds (and which is 9, re^l defioition)

462

OPERATIONS SUBSIDIARY TO INDUCTION.

constitutes as completely as in any
other case the whole meaning of the
term. It is no objection to say that
(as is often the case in natural history)
the set of characters may be changed,
and another substituted as being
better suited for the purpose of dis-
tinction, while the word, still conti-
nuing to denote the same group of
things, is not considered to have
changed its meaning. For this is no
more than may happen in the case of
any other general name : we may,
in reforming its connotation, leave
its denotation untouched ; and it is
generally desirable to do so. The
connotation, however, is not the less
for this the real meaning, for we at
once apply the name wherever the
characters set down in the definition
are found ; and that which exclusively
guides us in applying the term must
constitute its signification. If we
find, contrary to our previous belief,
that the characters are not peculiar
to one species, we cease to use the
term co-extensively with the char-
acters ; but then it is because the
other portion of the connotation fails ;
the condition that the class must be a
Kind. The connotation, therefore, is
stUl the meaning ; the set of descrip-
tive characters is a true definition ;
and the meaning is unfolded, not
indeed (as in other cases) by the
definition alone, but by the definition
and the form of the word taken to-
gether.

§ 6. We have now analysed what
is implied in the two principal re-
quisites of a philosophical language ;
first, precision, or definiteness, and
secondly, completeness. Any further
remarks on the mode of constructing
a nomenclature must be deferred
until we treat of Classification ; the
mode of naming the Kinds of things
being necessarily subordinate to the
mode of arranging those Kinds into
larger classes. With respect to the
minor requisites of terminology, some
of them are well stated and illus-
tr*t«i in the " Aphorisms concerning

the Language of Science," Included
in Dr. Whewell's Philosophy of the
Inductive Sciences. These, as being of
secondary importance in the peculiar
point of view of Logic, I shall not
further refer to, but shall confine my
observations to one more quality,
which, next to the two already treated
of, appears to be the most valuable
which the language of science can
possess. Of this quality a general
notion may be conveyed by the fol-
lowing aphorism : —

Whenever the nature of the sub-
ject permits our reasoning processes
to be, without danger, carried on
mechanically, the language should be
constructed on as mechanical prin-
ciples as possible : while in the con-
trary case, it should be so constructed
that there shall be the greatest pos-
sible obstacles to a merely mechanical
use of it.

I am aware that this maxim re-
quires much explanation, which I
shall at once proceed to give. And
first, as to what is meant by using
a language mechanically. The com-
plete or extreme case of the mechani-
cal use of language is when it is
used without any consciousness of a
meaning, and with only the conscious-
ness of using certain visible or audible
marks in conformity to technical
rules previously laid down. This
extreme case is nowhere realised
except in the figures of arithmetic,
and still more the symbols of algebra,
a language unique in its kind, and
approaching as nearly to perfection,
for the purposes to which it is des-
tined, as can, perhaps, be said of any
creation of the human mind. Its
perfection consists in the complete-
ness of its adaptation to a purely
mechanical use. The symbols are
mere counters, without even the sem-
blance of a meaning apart from the
convention, whicli is renewed each
time they are employed, and which
is altered at each renewal, the same
symbol a or a; being used on different
occasions to represent things which
(except that, like 9M things, they ar^

T

TERMINOLOGY AND NOMENCLATURE.

463

susceptible of being numbered) have
no property in common. There is
nothing, therefore, to distract the
mind from the set of mechanical
operations which are to be performed
upon the symbols, such as squaring
both sides of the equation, multiplying
or dividing them by the same or by
equivalent symbols, and so forth.
Each of these operations, it is true,
corresponds to a syllogism ; represents
one step of ratiocination, relating not
to the symbols, but to the things sig-
nified by them. But as it has been
found practicable to frame a technical
form, by conforming to which we can
make sure of finding the conclusion
of the ratiocination, our end can be
completely attained without our ever
thinking of anything but the symbols.
Being thus intended to work merely
as mechanism, they have the qualities
which mechanism ought to have.
They are of the least possible bulk,
so that they take up scarcely any
room, and waste no time in their
manipulation ; they are compact, and
fit so closely together that the eye
can take in the whole at once of
almost every operation which they
are employed to perform.

These admirable properties of the
symbolical language of mathematics
have made so strong an impression on
the minds of many thinkers, as to
have led them to consider the symbo-
lical language in question as the ideal
type of philosophical language gener-
ailly ; to think that names in general,
or (as they are fond of calling them)
signs, are fitted for the purposes of
thought in proportion as they can be
made to approximate to the compact-
ness, the entire unmeaningness, and
the capability of being used as counters
without a thought of what they repre-
.sent, which are characteristic of the a
and h, the x and y, of algebra. This
notion has led to sanguine views of
the acceleration of the progress of
science by means which, I conceive,
cannot possibly conduce to that end,
and forms part of that exaggerated
^timate of the influence of signs

which has contributed in no small
degree to prevent the real laws of
our intellectual operations from being
rightly understood.

In the first place, a set of signs by
which we reason without conscious-
ness of their meaning, can be service-
able, at most, only in our deductive
operations. In our direct inductions
we cannot for a moment dispense with
a distinct mental image of the pheno-
mena, since the whole operation turns
on a perception of the particulars in
which those phenomena agree and
differ. But, further, this reasoning
by counters is only suitable to a very
limited portion even of our deductive
processes. In our reasonings respect-
ing numbers, the only general prin-
ciples which we ever have occasion to
introduce are these : Things which
are equal to the same thing are equal
to one another, and The sums or dif-
ferences of equal things are equal ;
with their various corollaries. Not
only can no hesitation ever arise re-
specting the applicability of these
principles, since they are true of all
magnitudes whatever, but every pos-
sible application of which they are
susceptible may be reduced to a tech-
nical rule ; and such, in fact, the rules
of the calculus are. But if the sym-
bols represent any other things than
mere numbers, let us say even straight
or curve lines, we have then to apply
theorems of geometry not true of all
lines without exception, and to select
those which are true of the lines we
are reasoning about. And how can
we do this unless we keep completely
in mind what particular lines these
are? Since additional geometrical
truths may be introduced into the
ratiocination in any stage of its pro-
gress, we cannot suffer ourselves, dur-
ing even the smallest part of it, to use
the names mechanically (as we use
algebraical symbols) without an image
annexed to them. It is only after
ascertaining that the solution of a
question concerning lines can be made
to depend on a previous question con
cei-ning numbers, or, in other wt)rd8,

464

OPERATIONS SUBSIDIARY TO INDUCTION.

after the question has been (to speak
technically) reduced to an equation,
that the unmeaning signs become
available, and that the nature of the
facts themselves to which the investi-
gation relates can be dismissed from
the mind. Up to the establishment
of the equation, the language in which
mathematicians carry on their reason-
ing does not differ in character from
that employed by close reasoners on
any other kind of subject.

I do not deny that every correct
ratiocination, when thrown into the
syllogistic shape, is conclusive from
the mere form of the expression, pro-
vided none of the terms used be am-
biguous ; and this is one of the circum-
stances which have led some writers
to think that if all names were so
judiciously constructed and so care-
fully defined as not to admit of any
ambiguity, the improvement thus
made in language would not only give
to the conclusions of every deductive
science the same certainty with those
of mathematics, but would reduce all
reasonings to the application of a tech-
nical form, and enable their conclu-
siveness to be rationally assented to
after a merely mechanical process, as
is undoubtedly the case in algebra.
But, if we accept geometry the con-
clusions of which are already as cer-
tain and exact as they can be made,
there is no science but that of number,
in which the practical validity of a
reasoning can be apparent to any per-
son who has looked only at the reason-
ing itself. Whoever has assented to
what was said in the last book con-
cerning the case of the Composition
of Causes, and the still stronger case
of the entire supersession of one set
of laws by another, is aware that
geometry and algebra are the only
sciences of which the propositions are
categorically true ; the general propo-
sitions of all other sciences are true
only hypothetically, supposing that no
counteracting cause happens to inter-
fere. A conclusion therefore, however
correctly deduced, in point of form,
Uovfi admitted laws of nature, will

have no other than an hypothetical
certainty. At every step we must
assure ourselves that no other law of
nature has superseded or intermingled
its operation with those which are the
premises of the reasoning ; and how
can this be done by merely looking at
the words ? We must not only be
constantly thinking of the phenomena
themselves, but we must be constantly
studying them ; making ourselves ac-
quainted with the peculiarities of every
case to which we attempt to apply our
general principles.

The algebraicnotation, considered as
a philosophical language, is perfect in
its adaptation to the subjects for which
it is commonly employed, namely,
those of which the investigations have
already been reduced to the ascertain-
ment of a relation between numbers.
But, admirable as it is for its own
purpose, the properties by which it is
rendered such are so far from consti-
tuting it the ideal model of philoso-
phical language in general, that the
more nearly the language of any other
branch of science approaches to it, the
less fit that language is for its own
proper functions. On all other sub-
jects, instead of contrivances to pre-
vent our attention from being dis-
tracted by thinking of the meaning
of our signs, we ought to wish for
contrivances to make it impossible
that we should ever lose sight of that
meaning even for an instant.

With this view, as much meaning
as possible should be thrown into the
formation of the word itself ; the
aids of derivation and analogy being
made available to keep alive a con-
sciousness of all that is signified by
it. In this respect those languages
have an immense advantage which
form their compounds and derivatives
from native roots, like the German,
and not from those of a foreign or
dead language, as is so much the case
with English, French, and Italian ;
and the best are those which form
them according to fixed analogies,
corresponding to the relations between
the ide^ to be expressed, All la«-

I

CLASSIFICATION.

46:

guages do this more or less, but
especially, among modern European
languages, the German ; while even
that is inferior to the Greek, in which
the relation between the meaning of
a derivative word and that of its
primitive is in general clearly marked
by its mode of formation, except in
the case of words compounded with
prepositions, which are often, in both
those languages, extremely anoma-
lous.

But all that can be done, by the
mode of constructing words, to pre-
vent them from degenerating into
sounds passing through the mind
without any distinct apprehension of
what they signify, is far too little for
the necessity of the case. Words,
however well constructed originally,
are always tending, like coins, to have
their inscription worn off by passing
from hand to hand ; and the only
possible mode of reviving it is to be
ever stamping it afresh, by living in
the habitual contemplation of the plie-
nomena themselves, and not resting
in our familiarity with the words that
express them. If any one, having
possessed himself of the laws of phe-
nomena as recorded in words, whether
delivered to him originally by others,
or even found out by himself, is con-
tent from thenceforth to live among
these formulae, to think exclusively of
them, and of applying them to cases
as they arise, without keeping up his
acquaintance with the realities from
which these laws were collected — not
only will he continually fail in his
practical efforts, because he will apply
his formulae without duly considering
whether, in this case and in that,
other laws of nature do not modify
or supersede them ; but the formulae
themselves will progressively lose
their meaning to him, and he will
cease at last even to be capable of
recognising with certainty whether a
case falls within the contemplation of
his formula or not. It is, in short,
as necessary, on all subjects not
mathematical, that the things on
which we reason should be conceived

by us in the concrete, and " clothed
in circumstances," as it is in algebra
that we should keep all individua-
lising peculiarities sedulously out of
view.

With this remark we close our ob-
servations on the Philosophy of Lan-
guage.

.CHAPTER VII.

OP CLASSIFICATION, AS SUBSIDIARY TO
INDUCTION.

§ I. There is, as has been fre-
quently remarked in this work, a
classification of things, which is in-
separable from the fact of giving
them general names. Every name
which .connotes an attribute, divides,
by that very fact, all things whatever
into two classes, those which have
the attribute and those which have it
not ; those of which the name can be
predicated and those of which it can-
not. And the division thus made is
not merely a division of such things
as actually exist, or are known to
exist, but of all such as may hereafter
be discovered, and even of all which
can be imagined.

On this kind of Classification we
have nothing to add to what has pre-
viously been said. The Classification
which requires to be discussed as a
separate act of the mind is altogether
different. In the one, the arrange-
ment of objects in groups, and distri-
bution of them into compartments, is
a mere incidental effect consequent
on the use of names given for another
purpose, namely, that of simply ex-
pressing some of their qualities. In
the other, the arrangement and dis-
tribution are the main object, and
the naming is secondary to, and pur-
posely conforms itself to, instead of
governing, that more important ope-
ration.

Classification, thus regarded, is a
contrivance for the best possible order-
ing of the ideas of objects in our
minds ; for causing the ideas to ac-
company or succeed one another in

2G

466

OPERATIONS SUBSIDIARY TO INDUCTION.

gach a way as shall give us the
greatest command over our know-
ledge already acquired, and lead most
directly to the acquisition of more.
The general problem of Classification,
in reference to these purposes, may
be stated as follows : To provide that
things shall be thought of in such
groups, and those groups in such an
order, as will best conduce to the re-
membrance and to the ascertainment
of their laws.

Classification thus considered dif-
fers from classification in the wider
sense, in having reference to real
objects exclusively, and not to all
that are imaginable ; its object being
the due co-ordination in our minds of
those things only, with the properties
of which we have actually occasion to
make ourselves acquainted. But, on
the other hand, it embraces all really
existing objects. We cannot consti-
tute any one class properly, except in
reference to a general division of the
whole of nature ; we cannot deter-
mine the group in which any one ob-
ject can most conveniently be placed,
without taking into consideration all
the varieties of existing objects, all,
at least, which have any degree of
aflfinity with it. No one family of
plants or animals could have been
rationally constituted, except as part
of a systematic arrangement of all
plants or animals ; nor could such a
general arrangement have been pro-
perly made without first determining
the exact place of plants and animals
in a general division of nature.

§ 2. There is no property of ob-
jects which may not be taken, if we
please, as the foundation for a classi-
fication or mental grouping of those
objects ; and in our first attempts we
are likely to select for that purpose
properties which are simple, easily
conceived, and perceptible on a first
view, without any previous process of
thought. Thus Tournefort's arrange-
ment of plants was founded on the
shape and divisions of the corolla ;
and that which is commonly called

the Linnseaji (though Linnaeus
suggested another and more scientific
arrangement) was grounded chiefly
on the number of the stamens and
pistils.

But these classifications, which are
at first recommended by the facility
they afford of ascertaining to what
class any individual belongs, are sel-
dom much adapted to the ends of
that Classification which is the suli-
ject of our present remarks. The
Linnsean arrangement answers the
purpose of making us think together
of all those kinds of plants which
possess the same number of staniens
and pistils ; but to think of them in
that manner is of little use, since we
seldom have anything to affirm in
common of the plants which have a
given number of stamens and pistils.
If plants of the class Pentandria,
order Monogynia, agreed in any other
properties, the habit of thinking and
speaking of the plants under a com-
mon designation would conduce to
our remembering those common pro-
perties so far as they were ascertained,
and would dispose us to be on the
look-out for such of them as were not
yet known. But since this is not
the case, the only purpose of thought
which the Linnaean classification
serves is that of causing us to re-
member, better than we should other-
wise have done, the exact number of
stamens and pistils of every species
of plants. Now, as this property is
of little importance or interest, he
remembering it with any particular
accuracy is of no moment. And
inasmuch as, by habitually thinking
of plants in those groups, we are pre-
vented from habitually thinking of
them in groups which have a greater
number of properties in common, the
effect of such a classification, when
systematically adhered to, upon our
habits of thought, must be regarded
as mischievous.

The ends of scientific classification
are best answered when the objects
are formed into groups respecting
which a greater number of genera]

■

also

I

CLASSIFICATION.

467

propositions can be made, and those
propositions more important, than
could be made respecting any other
groups into which the same things
could be distributed. The properties,
therefore, according to which objects
are classified should, if possible, be
those which are causes of MEiny other
properties ; or, at any rate/which are
sure marks of them. Causes are pre-
ferable, both as being the surest and
most direct of marks, and as being
themselves the properties on which it
is of most use that our attention
should be strongly fixed. But the
pi'operty which is the cause of the
chief peculiarities of a class is un-
fortunately seldom fitted to serve
also as the diagnostic of the class.
Instead of the cause, we must gene-
rally select some of its more promi-
nent effects, which may serve as
marks of the other effects and of the
cause.

A classification thus formed is pro-
perly scientific or philosophical, and
is commonly called a Natural, in
contradistinction to a Technical or
Artificial, classification or arrange-
ment. The phrase Natural Classifi-
cation seems most peculiarly appro-
priate to such arrangements as corre-
spond, in the groups which they form,
to the spontaneous tendencies of the
mind, by placing together the objects
most similar in their general aspect ;
in opposition to those technical sys-
tems which, arranging things ac-
cording to their agreement in some
circumstance arbitrarily selected, often
throw into the same group objects
which in the general aggregate of
their properties present no resem-
blance, and into different and remote
groups others which have the closest
similarity. It is one of the most
valid recommendations of any classi-
fication to the character of a scientific
one, that it shall be a natural classifi-
cation in this sense also ; for the test
of its scientific character is the num-
ber and importance of the properties
which can be asserted in common of
all objects included in a group ; and

properties on which the general aspect
of the things depends are, if only on
that ground, important as well as, in
most cases, numerous. But, though
a strong recommendation, this cir-
cumstance ia not a sine qud non;
since the most obvious properties of
things may be of trifling importance
compared with others that are not
obvious. I have seen it mentioned as
a great absurdity in the Linnsean
classification, that it places (which, by
the way, it does not) the violet by the
side of the oak ; it certainly dissevers
natural affinities and brings together
things quite as unlike as the oak and
the violet are. But the difference,
apparently so wide, which renders the
juxtaposition of those two vegetables
so suitable an illustration of a bad
arrangement, depends, to the common
eye, mainly on mere size and texture ;
now if we made it our study to adopt
the classification which would involve
the least peril of similar rapjyi'oche-
merits, we should return to the obsolete
division into trees, shrubs, and herbs,
which, though of primary importance
with regard to mere general aspect,
yet (compared even with so petty and
unobvious a distinction as that into
dicotyledons and monocotyledons) an-
swers to so few differences in the
other properties of plants, that a
classification founded on it (indepen-
dently of the indistinctness of the
lines of demarcation) would be as
completely artificial and technical as
the Linnaean.

Our natural groups, therefore, must
often be founded not on the obvious,
but on the unobvious properties of
things, when these are of greater
importance. But in such cases it is
essential that there should be some
other property or set of properties,
more readily recognisable by the ob-
server, which co-exist with, and may
be received as marks of, the properties
which are the real groundwork of the
classification. A natural arrange-
ment, for example, of animals, must
be founded in the main on their
internal structure, but (as M. Comte

468

OPERATIONS SUBSIDIARY TO INDUCTION,

remarks) it would be absurd that we
should not be able to determine the
genus and species of an animal with-
out first killing it. On this ground,
the preference, among zoological clas-
sifications, is probably due to that of
M. de Blainville, founded on the dif-
ferences in the external integuments ;
differences which correspond much
more accurately than might be sup-
posed to the really important varieties,
both in the other parts of the struc-
ture, and in the habits and history of
the animals.

This shows, more strongly than
ever, how extensive a knowledge of
the properties of objects is necessary
for making a good classification of
them. And as it is one of the uses of
such a classification that by drawing
attention to the properties on which
it is founded, and which, if the classi-
fication be good, are marks of many
others, it facilitates the discovery of
those others ; we see in what manner
our knowledge of things, and our
classification of them, tend mutually
and indefinitely to the improvement
of each other.

We said just now that the classifi-
cation of objects should follow those
of their properties which indicate not
only the most numerous, but also the
most important peculiarities. What
is here meant by importance ? It has
reference to the particular end in
view ; and the same objects, there-
fore, may admit with propriety of
several different classifications. Each
science or art forms its classification
of things according to the properties
which fall within its special cognisance,
or of which it must take account in
order to accomplish its peculiar prac-
tical end. A farmer does not divide
plants, like a botanist, into dicotyle-
donous and monocotyledonous, but
into- useful plants and weeds. A
geologist divides fossils, not like a
zoologist, into families corresponding
to those of living species, but into
fossils of the paleeozoic, mesozoic, and
tertiary periods, above the coal and
below the coal, &;c. Whales are or

I

pose

are not fish, according to the purposi
for which we are considering them.
" If we are speaking of the internal
structure and physiology of the ani-
mal, we must not call them fish ; for
in these respects they deviate widely
from fishes : they have warm blood,
and prodoce and suckle their young
as land quadrupeds do. But this
would not prevent our speaking of
the %ohale Jishery, and calling such
animals fish on all occasions connected
with this employment ; for the rela-
tions thus arising depend upon the ani-
mal's living in the water, and being
caught in a manner similar to other
fishes. A plea that human laws which
mention fish do not apply to whales,
would be rejected at once by an in-
telligent judge." *

These different classifications are
all good for the purposes of their own
particular departments of knowledge
or practice. But when we are study-
ing objects not for any special practi-
cal end, but for the sake of extending
our knowledge of the whole of their
properties and relations, we must con-
sider as the most important attributes
those which contribute most, either by
themselves or by their effects, to ren-
der the things like one another, and
unlike other things ; which give to
the class composed of them the most
marked individuality ; which fill, as
it were, the largest space in their
existence, and would most impress
the attention of a spectator who knew
all their properties but was not speci-
ally interested in any. Classes formed
on this principle may be called, in
a more emphatic manner than any
others, natural groups.

§ 3. On the subject of these groups
Dr. Whewell lays down a theory,
grounded on an important truth,
which, he has, in some respects, ex-
pressed and illustrated very felici-
tously, but also, as it appears to me,
with some admixture of error. It
will be advantageous, for both these

* Nov. Org. Renov., pp. 286, 287.

I

f

I

CLASSIFICATION.

469

reasons, to extract the statement of
his doctrine in the very words he has
used.

" Natural groups," according to this
theory,* are " given by Type, not by
Definition." And this consideration
accounts for that " indefiniteness and
indecision which we frequently find
in the descriptions of such groups, and
which must appear so strange and in-
consistent to any one who does not
suppose these descriptions to assume
any deeper ground of connection than
an arbitrary choice of the botanist.
Thus in the family of the rose-tree,
we are told that the ovules are rcry
rarely erect,thestlgmatausuallt/s\TX)Tp\e.
Of what use, it might be asked, can
such loose accounts be? To which
the answer is, that they are not in-
serted in order to distinguish the
species, but in order to describe the
famil}', and the total relations of the
ovules and the stigmata of the family
are better known by this general state-
ment. A similar observation may be
made with regard to the Anomalies
of each group, which occur so com-
monly, that Dr. Lindley, in his In-
troduction to the Natural System of
Botany, makes the 'Anomalies' an
article in each family. Thus, part of
the character of the Rosacese is, that
they have alternate stipulate leaves,
and that the albumen is obliterated;
but yet in Lowea, one of the genera
of this family, the stipulae are absent,
and the albumen isj^resent in another,
NeiUia. This implies, as we have
already seen, that the artificial char-
acter (or diagnosis, as Mr. Lindley
calls it) is imperfect. It is, though
very nearly, yet not exactly, connnen-
surate with the natural group ; and
hence in certain cases this character
is made to yield to the general weight
of natural affinities.

"These view.s, — of classes deter-
mined by characters which cannot be
in words, — of propositions

which state, not what happens in all
cases, but only u.sually, — of particu-

* Hist. Sc. Id., ii. 120-122.

lars which are included in a class,
though they transgress the definition
of it, may probably surprise the reader.
They are so contrary to many of the
received opinions respecting the use
of definitions and the nature of scien-
tific propositions, that they will pro-
bably appear to many persons highly
illogical and lui philosophical. But a
disposition to such a judgment arises
in a great measure from this, that
the mathematical and mathematico-
physical sciences have, in a great de-
gree, determined men's views of the
general nature and form of scientific
truth, while Natural History .has not
yet had time or opportunity to exert
its due influence upon the current
habits of philosophising. The appa-
rent indefiniteness and incon.sistency
of the classifications and definitions
of Natural History belongs, in a far
higher degree, to all other except
mathematical speculations ; and the
modes in which approximations to
exact distinctions and general truths
have been made in Natural History
may be wortiiy our attention, even
for the light they throw upon the best
modes of pursuing truth of all kinds.

"Though in a Natural group of
objects a definition can no longer be
of any use as a regulative princij^le,
clas.ses are nottherefore left quite loose,
without any certain standard or guide.
The class is steadily fixed, though
not precisely limited ; it is given,
though not circumscribed ; it is de-
termined, not by a boundary line
without, but by a central point with-
in ; not by what it strictly excludes,
but by what it eminently includes ;
by an example, not by a precept ; in
short, instead of a Definition, we have
a Type for our director.

"A Type is an example of any
class, for instance a species of a genus,
which is considered as eminently pos-
sessing the character of the class. All
the species which have a greater
affinity with this type-species than
with any others form the genus, and
are arranged about it, deviating from
it in various directions and difi"erent

470

0I»ERATI0NS SUBSIDIARY TO INDUCTION.

degrees. Thus a genus may consist
of several species which approach
very near the type, and of which the
claim to a place with it is obvious ;
while there may be other species
which straggle farther from this cen-
tral knot, and which yet are clearly
more connected with it than with any
other. And even if there should be
some species of which the place is
dubious, and which appear to be
equally bound to two generic types,
it is easily seen that this would not
destroy the reality of the generic
groups, any more than the scattered
trees of the intervening plain prevent
our speaking intelligibly of the dis-
tinct forests of two separate hills.

" The type-species of every genus,
the type-genus of every family, is,
then, one which possesses all the cha-
racters and properties of the genaxs
in a marked and prominent manner.
The type of the Rose family has al-
ternate stipulate leaves, wants the
albumen, has the ovules not erect,
has the stigmata simple ; and besides
these features, which distinguish it
from the exceptions or varieties of its
class, it has the features which make
it prominent in its class. It is one
of those which possess clearly several
leading attributes ; and thus, though
we cannot say of any one genus that
it must be the type of the family, or
of any one species that it must be the
type of the genus, we are still not
wholly to seek ; the t^^pe must be
connected by many affinities with
most of the others of its group ; it
must be near the centre of the crowd,
and not one of the stragglers."

In this passage (the latter part of
which especially I cannot help noticing
as an admirable example of philo-
sophic style) Dr. Whewell has stated
very clearly and forcibly, but (I think)
without making all necessary distinc-
tions, one of the principles of a Natu-
ral Classification. What this principle
is, what are its limits, and in what
manner he seems to me to have over-
stepped them, will appear when we
have laid down another rule of Natu-

ral Arrangement, which appears
me still more fundamental.

§ 4. The reader is by this tim<ei
familiar with the general truth (which
I restate so often on account of the
great confusion in which it is com-
monly involved) that there are in
nature distinctions of Kind ; distinc-
tions not consisting in a given num-
ber of definite properties plus the
effects which follow from those pro-
perties, but running through the
whole nature, through the attributes
generally of the things so distin-
guished. Our knowledge of the pro-
perties of a kind is never complete.
We are always discovering, and ex-
pecting to discover, new ones. Where
the distinction between two classes of
things is not one of Kind, we expect
to find their properties alike, except
where there is some reason for then-
being different. On the contrary,
when the distinction is in Kind, wo
expect to find the properties different
unless there be some cause for their
being the same. All knowledge of a
Kind must be obtained by observation
and experiment upon the Kind itself ;
no inference respecting its properties
from the properties of things not con-
nected with it by Kind goes for more
than the sort of presumption usually
characterised as an analogy, and gene-
rally in one of its fainter degrees.

Since the common properties of a
true Kind, and consequently the gene-
ral assertions which can be made re-
specting it, or which are certain to be
made hereafter as our knowledge ex-
tends, are indefinite and inexhaustible;
and since the very first principle of na-
tural classification isthatof forming the
classes so that the objects composing
each may have the greatest number
of properties in common ; this prin-
ciple prescribes that every such classi-
fication shall recognise and adopt into
itself all distinctions of Kind which
exist among the objects it professes
to classify. To pass over any dis-
tinctions of Kind, and substitute defi-
nite distinctions, which, however con-

■

i

CtASSII^lCATiOX.

471

KuleraWe they may be, do not point to
ulterior unknown ditferences, would
be to replace classes with more by
classes with fewer attributes in coni-
njon, and would be subversive of the
Natural Method of Classification.

Accordingly all natural aiTange-
ments, whether the reality of the dis-
tinction of Kinds was felt or not by
their framers, have been led, by the
mere pursuit of their own proper end,
to conform themselves to the distinc-
tions of Kind, so far as these had been
ascertained at the time. The Species
of Plants are not only real Kinds, but
are probably, all of them, real lowest
Kinds, infimoi species; which, if we
vera to subdivide, as of course it is
open to us to do, into sub-classes,
the subdivision would necessarily be
founded on definite distinctions, not
pointing (apart from what may be
known of their causes or effects) to
any difference beyond themselves.

In so far as a natural classification
is grounded on real Kinds, its groups
are certainly not conventional : it is
perfectly true that they do not depend
npon an arbitrary choice of the natu-
ralist. But it does not follow, nor, I
conceive, is it true, that these classes
are determined by a tj^^*, and not by
characters. To determine them by a
type woiald be as sure a way of missing
the Kind, as if we were to select a set
of characters arbitrarily. They are
<letermined by characters, but these
are not arbitrary. The problem is,
to find a few definite characters which
point to the multitude of indefinite
one.s. Kinds are Classes between
which there is an impassable barrier ;
and what we have to seek is, marks
whereby we may determine on which
side of the barrier an object takes its
place. The characters which will best
do this should be chosen : if they are
also important in themselves, so much
the better. When we have selected
the characters, we parcel out the ob-
jects according to those characters,
and not, I conceive, according to re-
semblance to a type. We do not com-
ix>se the species Ranunculus acris of

all plants which bear a satisfactor}'
degree of resemblance to a model
buttercup, but of those which possess
certain characters selected as marks
by which we might recognise the pos-
sibility of a common parentage ; and
the enumeration of those characters
is the definition of the species.

The question next arises, whether,
as all Kinds must have a place among
the classes, so all the classes in a na-
tural arrangement must be Kinds 'i
And to this I answer, Certainly not.
The distinctions of Kinds are not
ninnerous enough to make up the
whole of a classification. Very few
of the genera of plants, or even of the
families, can be pronounced with cer-
tainty to be Kinds. The great dis-
tinctions of Vascular and Cellulai',
Dicotyledonous or Exogenous and
Monocotyledonous or Endogenous
plants, are perhaps differences of
kind ; the lines of demarcation which
divide those classes seem (though
even on this I would not pronounce
positively) to go through the whole
nature of the plants. But the differ-
ent species of a genus, or genera of
a family, usually have in common
only a lin)ited number of characters.
A Rose does not seem to differ from
a Rubus, or the Umbelliferse from
the Ranunculacese, in much else than
the characters botanically assigned to
those genera or those families. Un-
enumerated differences certainly do
exist in some cases ; there are families
of plants which have peculiarities of
chemical composition, or yield pro-
ducts having peculiar effects on the
animal economy. The Cruciferae and
Fungi contain an unusual proportion
of nitrogen ; the Labiatae are the chief
sources of essential oils, the SolaneaR
are very commonly narcotic, &c. In
these and similar cases thei-e are pos-
sibly distinctions of Kind ; but it is
by no means indispensable that there
should be. Genera and Families may
be eminently natural, though marked
out from one another by properties
limited in number, provided those
properties are important, and tlie

472

OPERATIONS StJBSlDlARY TO USTBUCTION.

objects contained in each genus or
family resemble each other more than
they resemble anything which is ex-
cluded from the genus or family.

After the recognition and defini-
tion, then, of the injimcu species, the
next step is to arrange those infimoe
species into larger groups : making
these groups correspond to Kinds
wherever it is possible, but in most
cases without any such guidance.
And in doing this it is true that we
are naturally and properly guided, in
most cases at least, by resemblance
to a type. We form our groups round
certain selected Kinds, each of which
serves as a sort of exemplar of its
group. But though the groups are
suggested by types, I cannot think
that a group when formed is deter-
mined by the type ; that in deciding
whether a species belongs to a group,
a reference is made to the type, and
not to the characters ; that the char-
acters "cannot be expressed in words."
This assertion is inconsistent with Dr.
Whewell's own statement of the fun-
damental principle of classification,
namely, that "general assertions shall
be possible." If the class did not
possess any characters in common,
what general assertions would be pos-
sible respecting it ? Except that they
all resemble each other more than
they resemble anything else, nothing
whatever could be predicated of the
class.

The truth is, on the contrary, that
every genus or family is framed with
distinct reference to certain characters,
and is composed, first and principally,
of species which agree in possessing
all those characters. To these are
added, as a sort of appendix, such
other species, generally in small num-
ber, as possess nearly all the properties
selected ; wanting some of them one
property, some another, and which,
while they agree with the rest almost
as much as they agree with one an-
other, do not resemble in an equal
degree any other group. Our con-
ception of the class continues to be
grounded on the characters ; and the

class might be defined, those things
which either possess that set of char-
acters, or resemble the things that
do so, more than they resemble any-
thing else.

And this resemblance itself is not,
like resemblance between simple sen-
sations and ultimate fact, unsuscep-
tible of analysis. Even the inferior
degree of resemblance is created by
the possession of common characters.
Whatever resembles the genus Rose
more than it resembles any other
genus, does so because it possesses
a greater number of the characters
of that genus than of the characters
of any other genus. Nor can there
be any real difficulty in representing,
by an enumeration of characters, the
nature and degree of the resemblance
which is strictly sufficient to include
any object in the class. There are
always some properties common to
all things which are included. Others
there often are, to which some things,
which are nevertheless included, are
exceptions. But the objects which
are exceptions to one character are
not exceptions to another : the re-
semblance which fails in some parti-
culars must be made up for in others.
The class, therefore, is constituted by
the possession of all the characters
which are universal, and most of those
which admit of exceptions. If a plant
had the ovules erect, the stigmata
divided, possessed the albumen, and
was without stipules, it possibly would
not be classed among the Rosacea;.
But it may want any one or moi*e
than one of these characters, and not
be excluded. The ends of a scientific
classification are better answered by
including it. Since it agrees so nearly
in its known properties with the sum
of the characters of the class, it is
likely to resemble that class more
than any other in those of its pro-
perties which are still undiscovered.

Not only, therefore, are natural
groups, no less than any artificial
classes, determined by characters ;
they are constituted in contemplation
of, and by reason of, characters. But

■

1

CLASSIFICATION.

47^

it is in contemplation not f>f those
characters only which are rigorotisly
common to all the objects included
in the group, but of the entire body
of characters, all of which are found
in most of those objects, and most of
them in all. And hence our concep-
tion of the class, the image in our
minds which is representative of it,
is that of a specimen complete in
all the characters ; most naturally a
specimen which, by possessing them
all in the greatest degree in which
they are ever found, is the best fitted
to exhibit clearly, and in a marked
manner, what they are. It is by a
mental reference to this standard,
not instead of, but in illustration of,
the definition of the class, that we
usually and advantageously determine
whether any individual or species
belongs to the class or not. And
this, as it seems to me, is the amount
of truth contained in the doctrine of
Types.

We shall see presently that where
the classification is made for the ex-
press purpose of a sj^ecial inductive
inc^uiry, it is not optional, but neces-
sary for fulfilling the conditions of a
correct Inductive Method, that we
should establish a type-species or
genus, namely, the one which exhibits
in the most eminent degree the par-
ticular phenomenon under investiga-
tion. But of this hereafter. It re-
niains, for completing the theory of
natural groups, that a few words
should be said on the principles of
the nomenclature adapted to them.

§ 5. A Nomenclature in science is,
as we have said, a system of the
names of Kinds. These names, like
other class-names, are defined by the
enumeration of the characters distinc-
tive of the class. The only merit
which a set of names can have beyond
this, is to convey, by the mode of
their construction, as much informa-
tion as possible, so that a person who
knows the thing may receive all the
assistance which the name can give
in remembering what he knows, while

he who knowa it not may receive as
much knowledge respecting it as the
case admits of by merely being told
its name.

There are two modes of giving to
the name of a Kind this sort of signi-
ficance. The best, but which unfor-
tunately is seldom practicable, is when
the word can be made to indicate,
by its formation, the very properties
which it is designed to connote. The
name of a Kind does not, of course,
connote all the properties of the Kind,
since these are inexhaustible, but such
of them as are sufficient to distinguish
it ; such as are sure marks of all the
rest. Now, it is very rarely that one
property, or even any two or three
properties, can answer this purpose.
To distinguish the common daisy from
all other species of plants would re-
quire the specification of many char-
acters. And a name cannot, without
being too cumbrous for use, give
indication, by its etymology or mode
of construction of more than a very
small number of these. The possi-
bility, therefore, of an ideally perfect
Nomenclature is probably confined to
the one case in which we are happily
in possession of something approach-
ing to it — the Nomenclature of Ele-
mentary Chemistry. The substances,
whether simple or compound, with
which chemistry is conversant, are
Kinds, and, as such, the properties
which distinguish each of them from
the rest are innumerable ; but in the
case of compound substances (the
simple ones are not numerous enough
to require a systematic nomenclature)
there is one property, the chemical
composition, which is of itself suffi-
cient to distinguish the Kind, and
is (with certain reservations not yet
thoroughly understood) a sure mark
of all the other proj?erties of the com-
pound. All that was needful, there-
fore, was to make the name of every
compound express on the first hearing
its chemical composition ; that is, to
form the name of the compound in
some uniform manner from the names
of the simple substances which enter

474

OPERATIONS SUBSIDIARY TO INDUCTION.

1

into it as elements. This was done,
most skilfully and successfully by the
French chemists, though their nomen-
clature has become inadequate to the
convenient expression of the very com-
])licated compounds now known to
chemists. The only thing left imex-
pressed by them was the exact pro-
portion in which the elements were
combined ; and even this, since the
establishment of the atomic theory, it
lias been found possible to express by a
simple adaptation of their phraseology.
But where the characters which
must be taken into consideration, in
order sufficiently to designate the
Kind, are too numerous to be all sig-
nified in the derivation of the name,
and where no one of them is of such
preponderant importance as to justify
its being singled out to be so indi-
cated, we may avail ourselves of a
subsidiary resource. Though we can-
not indicate the distinctive properties
of the Kind, we may indicate its
nearest natural affinities, by incor-
porating into its name the name of
the proximate natural group of which
it is one of the species. On this
l)rinciple is founded the admirable
binary nomenclature of botany and
zoology. In this nomenclature the
name of every species consists of the
name of the genus, or natural group
next above it, with a word added to
distinguish the particular species. The
last portion of the compound name is
sometimes taken from some one of the
jieculiarities in which that species
differs from others of the genus ; as
Clematis integrifolia, Potentilla alba,
Viola palustris, Artemisia vulgaris;
sometimes from a circumstance of an
lustorical nature, as Narcissus poeti-
cus, Potentilla tormentiUa (indicating
that the plant is that which was for-
merly known by the latter name),
Kxacum Candollii (from the fact that
I )e Candolle was its first discoverer) ;
:md sometimes the word is purely
conventional, as Thlaspi bursapastoris,
Kanunculus thora — it is of little con-
se<]uence which — since the second, or,
as it is usually called, the specific

inde-

name, Could at inost express,
pendently of convention, no more
than a very small portion of the con-
notation of the term. But by adding
to this the name of the superior genus,
we may make the best amends we
can for the impossibility of so con-
triving the name as to express all the
distinctive characters of the Kind.
We make it, at all events, express as
many of those characters as are com-
mon to the proximate natural group
in which the Kind is included. If
even those common characters are so
numerous or so little familiar as to
require a further extension of the
same resource, we might, instead of a
binary, adopt a ternary nomenclature,
employing not only the name of the
genus, but that of the next natural
group in order of generality above the
genus, commonly called the Family.
This was done in the mineralogical
nomenclature proposed by Professor
Mohs. " The names framed by him
were not composed of two, but of
three elements, designating respec-
tively the Species, the Genus, and the
Order ; thus he has such species as
Rhonibohedral Lime Ilaloide, Octohed-
ral Fluor Ilaloide, Prismatic Hal
Baryte." * The binary construction,
howe-^r, has been found sufficient in
botany and zoology, the only sciences
in which this general principle has
hitherto been successfully adopted in
the construction of a nomenclature.

Besides the advantage which this
principle of nomenclature possesses,
in giving to the names of species the
greatest quantity of independent sig-
nificance which the circumstances of
the case admit of, it answers the fur-
ther end of immensely economising the
use of names, and preventing an other-
wise intolerable burden on the me-
mory. When the names of species
become extremely numerous, some
artifice (as Dr. Whewellf observes)
becomes absolutely necessary to make
it possible to recollect or apply them.
" The known species of plants, for ex-

* Nov. Org. Renov., p, 274.
t nisi. Sc. Id., i. 133.

1

CLASSii'lCATlOX BY SERIES.

475

ample, were ten thousand in the time of
Linnaeus, and are now probably sixty
thousand. It would be useless to en-
deavour to frame and employ separate
names for each of these species. The
division of the objects into a sub-
ordinated system of classification en-
ables us to introduce a Nomenclature
which does not require this enormous
number of names. Each of the genera
has its name, and the species are
marked by the addition of some epi-
thet to the name of the genus. In
this manner about seventeen hundred
generic names, with a moderate num-
ber of specific names, were found by
Linnaeus sufficient to designate with
precision all the species of vegetables
known at his time." And though the
luimber of generic names has since
greatly increased, it has not increased
in anything like the proportion of the
multiplication of known species.

CHAPTER VIIL

OF CLASSIFICATION BY SERIES.

§ I. Thus far we liave considered
the principles of scientific classifica-
tion so far only as relates to the for-
mation of natural groups ; and at
this point most of those who have
attempted a theory of natural arrange-
n)ent, including among the rest Dr.
Whewell, have stopped. There re-
mains, however, another, and a not
less important portion of the theory,
which has not yet, as far as I am
aware, been systematically treated of
by any WTiter except M. Comte. This
is the arrangement of the natural
groups into a natural series.*

The end of classification, as an in-

* Dr. Whewell, in his reply (PhilosopJn/
of Discovenj, p. 270) says that he "stopped
sliort of, or rather passed by, the doctrine
of a series of organised beings," because he
"thought it bad and nan-ow philosophy."
If he did, it was evidentl}' without under-
standing this form of the doctrine ; for he
proceeds to quote a passage from his "His-
tory," in which the doctrine he condemns
is designated as that of "a mere linear
progression in nature, which would place

strument for the investigation of
nature, is (as before stated) to make
us think of those objects together
which have the greatest number of
important common properties, and
which, therefore, we have oftenest
occasion, in the course of our induc-
tions, for taking into joint considera-
tion. Our ideas of objects are thus
brought into the order most conducive
to the successful prosecution of induc-
tive inquiries generally. But when the
purpose is to facilitate some particular
inductive inquiry, more is required.
To be instrumental to that purj)ose,
the classification must bring those
objects together, the simultaneous
contemplation of which is likely to
throw most light upon the particular
subject. That subject being the Ia\\s
of some phenomenon or some set of
connected phenomena, the very phe-
nomenon or set of phenomena in ques-
tion must be chosen as the ground-
work of the classification.

The requisites of a classification
intended to facilitate the study of a
particular phenomenon, are, first, to
bring into one class all Kinds of
things which exhibit that pheno-
menon, in whatever variety of forms
or degrees ; and, secondly, to arrange
those Kinds in a series according to
the degree in which they exhibit it,
beginning with those which exhibit
most of it, and terminating with
those which exhibit least. The prin-
cipal example, as yet, of such a classi-
fication is afforded by conjparative
anatomy and physiology, from which,
therefore, our illustrations shall be
taken.

§ 2. The object being supposed to
be the investigation of the laws of

each genus in contact only with the pre-
ceding and succeeding ones." Now the
series treated of in the text agrees with
this linear progression in nothing whatever
but in being a progt ession.

It would svu-ely be possible to arrange
all places (for example) in the order of their
distance from the North Pole, though there
woulii lie not merely a plurality, but a
whole circle of places at every single grada-
tion in ttie scale.

476

OPERATIONS SUBSIDIARY TO INDUCTION.

animal life, the first step, after form-
ing the most distinct conception of
the phenomenon itself possible in the
existing state of our knowledge, is to
rrect into one great class (that of ani-
mals) all the known Kinds of beings
where that phenomenon presents it-
self, in however various combinations
with other properties, and in how-
ever different degrees. As some of
these Kinds manifest the general
phenomenon of animal life in a very
high degree, and others in an insig-
nificant degree, barely sufficient for
recognition, we must, in the next
place, arrange the various Kinds in a
series, following one another accord-
ing to the degrees in which they
severally exhibit the phenomenon ;
beginning therefore with man, and
ending with the most imperfect kinds
of zoophytes.

This is merely saying that we should
put the instances from which the law
is to be inductively collected into the
order which is implied in one of the
four Methods of Experimental In-
quiry discussed in the preceding Book,
the fourth Method, that of Concomi-
tant Variations. As formerly re-
marked, this is often the only method
to which recourse can be had, with
assurance of a true conclusion, in
cases in which we have but limited
means of effecting, by artificial ex-
periments, a separation of circum-
stances Tisually conjoined. The prin-
ciple of the method is, that facts
which increase or diminish together,
and disappear together, are either
cause and effect, or effects of a com-
mon cause. When it has been as-
certained that this relation really
subsists between the variations, a
connection between the facts them-
selves may be confidently laid down,
either as a law of nature or only as
an empirical law, according to cir-
cumstances.

That the application of this IMethod
must be preceded by the formation of
such a series as we have described, is
too obvious to need being pointed out;
and the mere arrangement of a set of

objects in a series, according to the
degrees in which they exhibit some
fact of which we are seeking the law,
is too naturally suggested by the
necessities of our inductive opera-
tions to require any lengthened illus-
tration here. But there are cases in
which the arrangement required for
the special purpose becomes the de-
termining principle of the classifica-
tion of the same objects for general
purposes. This will naturally and
properly happen when those laws of
the objects which are sought in the
special inquiry enact so principal a
part in the general character and
history of those objects — exercise so
much influence in determining all the
phenomena of which they are either
the agents or the theatre — that all
other differences existing among the
objects are fittingly regarded as mere
modifications of the one phenomenon
sought — effects determined by the
co-operation of some incidental cir-
cumstance with the laws of that phe-
nomenon. Thus in the case of ani-
mated beings, the differences between
one class of animals and another may
reasonably be considered as mere
modifications of the general pheno-
menon, animal life — modifications
arising either from the different de-
grees in which that phenomenon is
manifested in different animals, or
from the intermixture of the effects
of incidental causes peculiar to the
nature of each, with the effects pro-
duced by the general laws of life,
those laws still exercising a predomi-
nant influence over the result. Such
being the case, no other inductive in-
quiry respecting animals can be suc-
cessfully carried on, except in subor-
dination to the great inquiry into the
universal laws of animal life ; and the
classification of animals best suited to
that one purpose is the most suitable
to all the other purposes of zoological
science.

§ 3. To establish a classification of
this sort, or even to apprehend it when
established, requires the power of re-

■

I

CLASSIFICATION BY SERIES.

477

cognising the essential similarity of a
phenomenon, in its minuter degrees
and obscurer forms, with what is
called the same phenomenon in the
greatest perfection of its development ;
that is, of identifying with each other
all phenomena which differ only in
degree, and in properties which we
suppose to be caused by difference of
degree. In order to recognise this
identity, or, in other words, this exact
similarity of quality, the assumption
of a type-species is indispensable. We
must consider as the type of the class
that among the Kinds included in it
which exhibits the properties consti-
tutive of the class in the highest de-
gree, conceiving the other varieties as
instances of degeneracy, as it were,
from that type, deviations from it by
inferior intensity of the characteris-
tic property or properties. For every
phenomenon is best studied {ccBtei'is
paribus) where it exists in the greatest
intensity. It is there that the effects
which either depend on it, or depend on
the same causes with it, will also exist
in the greatest degree. It is there,
consequently, and only there, that
those effects of it, or joint effects with
it, can become fvilly known to us, so
that we may learn to recognise their
small degrees, or even their mere rudi-
ments, in cases in which the direct
study would have been difficult or
even impossible. Not to mention that
the phenomenon in its higher degrees
may be attended by effects or collateral
circumstances which in its smaller de-
grees do not occur at all, requiring
for their production in any sensible
amount a greater degree of intensity
of the cause than is there met with.
In man, for example, (the species in
which both the phenomenon of animal
and that of organic life exist in the
highest degree,) many subordinate
phenomena develop themselves in the
course of his animated existence, which
the inferior varieties of animals do not
show. The knowledge of these pro-
perties may nevertheless be of great
avail towards the discovery of the con-
ditions and laws of the general pheno-

menon of life, which is common to man
with those inferior animals. And
they are, even, rightly considered as
properties of animated nature itself ;
because they may evidently be affili-
ated to the general laws of animated
nature ; because we may fairly pre-
sume that some rudiments or feebl6
degrees of those properties would be
recognised in all animals by more per-
fect organs, or even by more perfect
instruments, than ours ; and because
those may be correctly termed pro-
perties of a class which a thing exhi-
bits exactly in proportion as it belongs
to the class, that is, in proportion as it
possesses the main attributes consti-
tutive of the class.

§ 4. It remains to consider how the
internal distribution of the series may
most properly take place : in what
manner it should be divided into
Orders, Families, and Genera.

The main principle of division must
of course be natural affinity ; the
classes formed must be natural groups;
and the formation of these has already
been sufficiently treated of. But the
principles of natural grouping must be
applied in subordination to the prin«
ciple of a natural series. The groups
must not be so constituted as to place
in the same group things which ought
to occupy different points of the gen-
eral scale. The precaution necessary
to be observed for this purpose is,
that the fHmary divisions must be
grounded not on all distinctions indis-
criminately, but on those which cor-
respond to variations in the degree of
the main phenomenon. The series of
Animated Nature should be broken
into parts at the points where the
variation in the degree of intensity of
the main phenomenon (as marked by
its principal characters, Sensation,
Thought, Voluntary Motion, &c.)
begins to be attended by conspicuous
changes in the miscellaneous proper-
ties of the animal. Such well-marked
changes take place, for example, where
the class Mammalia ends ; at the
points where Fishes are separated

478

OPERATIONS SUBSIDIARY TO INDUCTION.

from Insects, Insects from Mollusca,
&c. When so formed, the primary
natural groups will compose the series
by mere juxtaposition without redis-
tribution, each of them corresponding
to a definite portion of the scale. In
like manner each family should, if
possible, be so subdivided that one
portion of it shall stand higher and
the other lower, though >oi course con-
tiguous, in the general scale ; and only
when this is impossible is it allowable
to ground the remaining subdivisions
<m characters having no determinable
connection with the main phenomenon.
Whei'e the principal phenomenon
so far transcends in importance all
other properties on which a classifica-
tion could be grounded, as it does in
the case of animated existence, any
considerable deviation from the rule
last laid down is in general sufficiently
guarded against by the first princi-
ple of a natural arrangement, that of
forming the groups according to the
most important characters. All at-
tempts at a scientific classification of
animals, since first their anatomy and
physiology were successfully studied,
have been framed with a certain de-
gree of instinctive reference to a na-
tural series, and have accorded in
many more points than they have
differed, with the classification which
would most naturally have been
grounded on such a series. But the
accordance has not always been com-
plete ; and it still is often a matter
of discussion, which of several classi-
fications best accords with the true
scale of intensity of the main pheno-
menon. Cuvier, for example, has
been justly criticised for having
formed his natural groups with an
undue degree of reference to the
mode of alimentation, a circumstance
directly connected only with organic
life, and not leading to the arrange-
ment most appropriate for the pur-
poses of an investigation of the laws
of animal life, since both carnivorous
and herbivorous orfrugivorous animals
are found at almost every degree in
the scale of animal perfection. Blain-

I

ville's classification has been corv
sidered by high authorities to be free
from this defect, as representing cor-
rectly, by the mere order of the prin-
cipal groups, the successive degeneracy
of animal nature from its highest to
its most imperfect exemplification.

§ 5. A classification of any large
portion of the field of nature in con-
formity to the foregoing principles
has hitherto been found practicable
only in one great instance, that of
animals. In the case even of vege-
tables, the natural arrangement has
not been carried beyond the formation
of natural groups. Naturalists have
found, and probably will continue to
find, it impossible to form those groups
into any series, the terms of which
correspond to real gradations in the
phenomenon of vegetative or organic
life. Such a difference of degree may
be traced between the class of Vas-
cular Plants and that of Cellular,
which includes lichens, algae, and
other substances whose organisation
is simpler and more rudimentary than
that of the higher order of vegetables,
and which therefore approach nearer
to mere inorganic nature. But when
we rise much abovo this point, we do
not find any sufficient difference in the
degree in which different plants pos-
sess the properties of organisation and
life. The dicotyledons are of more
complex structure, and somewhat more
perfect organisation, than the mono-
cotyledons 5 and some dicotyledonous
families, such as the Compositae, are
rather more complex in their organisa-
tion than the rest. But the differences
are not of a marked character, and do
not promise to throw any particular
light upon the conditions and laws of
vegetable life and development. If
they did, the classification of vege-
tables would have to be made, like
that of animals, with reference to the
scale or series indicated.

Although the scientific arrange-
ments of organic nature afford as yet
the only complete example of the true
principles of rational classification,

CLASSIFICATION BY SERIES.

479

whether as to the formation of groups
or of series, those principles are ap-
plicable to all cases in which man-
kind are called upon to bring the
various parts of any extensive sub-
ject into mental co-ordination. They
are as much to the point when objects
are to be classed for purposes of art
r)r business as for those of science.
The proper arrangement, for example,
of a code of laws, depends on the same
scientific conditions as the classifica-
tions in natural history ; nor could
there be a better preparatory discip-
line for that important function than
the study of the principles of a natural
arrangement, not only in the abstract,

but in their actual application to the
class of phenomena for which they
were first elaborated, and which are
still the best school for learning their
use. Of this the great authority on
codification, Bentham, was perfectly
aware ; and his early Fragment on
Government, the admirable introduc-
tion to a series of writings unequalled
in their department, contains clear
and just views (as far as they go) on
the meaning of a natural arrange-
ment, such as could scarcely have
occurred to any one who lived an-
terior to the age of Linnaeus and
Bernard de Jussieu,

BOOK V.

ON FALLACIES

" Errare non modo affirmando et negaudo, sed etiam sentiendo, et in tacitA homi-
num cogitatione contingit." — Hobbes, Com-putaiio iivt Logica, ch. v.

" II leur semble qu'il n'y a qu'a douter par fantaisie, et qu'il n'y a qii'a dire en
general que notre nature est infirnie ; que notre esprit est plein d'aveuglement ; qu'il
faut avoir un grand soin de se defairc de ses prejuges, et autres choses semblables. lis
pensent que cela suffit pour ne plus se laisser s^duire a ses sens, et pour iie plus se
t romper du tout. 11 ne suffit pas de dire que I'esprit est foible, il faut lui faire sentir
ses foiblesses. Ce n'est pas assez de dire qu'il est sujet h I'erreur, il faut lui d^couvrir
«n quoi consistent ses erreurs." — Malebkanche, Recherche de la Verite.

CHAPTER I.

ON FALLACIES IN GENERAL.

§ I. It is a maxim of the school-
men that " contrariorum eadem est
scientia : " we never really know what
a thing is unless we are also able to
give a sufficient account of its oppo-
site. Conformably to this maxim,
one considerable section, in most
treatises on Logic, is devoted to the
subject of Fallacies ; and the practice
is too well worthy of observance to
allow of our departing from it. The
philosophy of reasoning, to be com-
plete, ought to comprise the theory of
bad as well as of good reasoning.

We have endeavoured to ascertain
the principles by which the sufficiency
of any proof can be tested, and by
which the nature and amount of evi-
dence needful to prove any given con-
clusion can be determined beforehand.
If these principles were adhered to,
then, although the number and value
of the truths ascertained would be
limited by the opportunities, or by
the industry, ingenuity, and patience
of the individual inquirer, at least
^rror would not be embraced instead

of truth. But the general consent of
mankind, founded on their experi-
ence, vouches for their being far in-
deed from even this negative kind of
perfection in the employment of their
reasoning powers.

In the conduct of life — in the prac
tical business of mankind — wrong
inferences, incorrect interpretations
of experience, unless after much cul-
ture of the thinking faculty, are ab-
solutely inevitable ; and with most
people, after the highest degree of
culture they ever attain, such errone-
ous inferences, producing correspond-
ing errors in conduct, are lamentably
frequent. Even in the speculations
to which eminent intellects have
systematically devoted themselves,
and in reference to which the col-
lective mind of the scientific world
is always at hand to aid the efforts
and correct the aberrations of indivi-
duals, it is only from the more perfect
sciences, from those of which the sub-
ject-matter is the least complicated,
that opinions not resting on a correct
induction have at length, generally
speaking, been expelled. In the de-
partments of inquiry relating to the

482

FALLACIES.'

more complex phenomena of nature,
and especially those of which the
subject is man, whether as a moral
and intellectual, a social, or even as
a physical being ; the diversity of
opinions still prevalent among in-
structed persons, and the equal con-
fidence with which those of the most
contrary ways of thinking cling to
their respective tenets, are proof not
only that right modes of philosophis-
ing are not yet generally adopted on
those subjects, but that wrong ones
are ; that inquirers have not only in
general missed the truth, but have
often embraced error ; that even the
most cultivated portion of our species
have not yet learned to abstain from
drawing conclusions which the evi-
dence does not warrant.

The only complete safeguard against
reasoning ill is the habit of reasoning
well ; familiarity with the principles
of correct reasoning, and practice in
applying those principles. It is, how-
ever, not unimportant to consider
what are the most common modes of
bad reasoning, by wliat appearances
the mind is most likely to be seduced
from the observance of true principles
of induction ; what, in short, are the
most common and most dangerous va-
rieties of Apparent Evidence, where-
by persons are misled into opinions
for which there does not exist evi-
dence really conclusive.

A catalogue of the varieties of ap-
parent evidence which are not real
evidence is an enumeration of Fal-
lacies. Without such an enumera-
tion, therefore, the present work
would be wanting in an essential
point. And while writers, who in-
cluded in their theory of reasoning
nothing more than ratiocination have,
in consistency with this limita,,tion,
confined their remarks to the fallacies
which have their seat in that portion
of the process of investigation, we,
who profess to treat of the whole pro-
cess, must add to our directions for
performing it rightly warnings against
performing it wrongly in any of its
parts : whether the ratiocinative or the

fS^'

experimental portion of it be in

or the fault lie in dispensing with rati

cination and induction altogethez*.

§ 2. In considering the sources of
unfounded inference, it is unnecessary
to reckon the errors which arise, not
from a wrong method, nor even from
ignorance of the right one, but from
a casual lapse, through hurry or in-
attention, in the application of the
true principles of induction. Such
en-ors, like the accidental mistakes in
casting up a sum, do not call for
philosophical analysis or classifica-
tion ; theoretical considerations can
throw no light upon the means of
avoiding them. In the present
treatise our attention is required,
not to mere inexpertness in perform-
ing the operation in the right Avay,
(the only remedies for which are in-
creased attention and more sedulous
practice,) but to the modes of per-
forming it in a way fundamentally
wrong ; the conditions under which
the human mind persuades itself that
it has sufficient grounds for a con-
clusion which it has not arrived at byJ 1
any of the legitimate methods of in-1 1
duction — which it has not, even care-
lessly or overhastily, endeavoured to
test by those legitimate methods.

§ 3. There is another branch
what may be called the Philosophy of
Error which must be mentioned here,
though only to be excluded from onr
subject. The sources of erroneous
opini(ms are twofold — moral and in-
tellectual. Of these, the moral do not
fall within the compass of this work.
They may be classed under two
general heads : Indifference to the
attainment of truth, and Bias ; of
which last the most common case is
that in which we are biassed by our
wishes ; but the liability is almost as
great to the undiie adoption of a con-
clusion which is disagreeable to us, as
of one which is agreeable, if it be
of a nature to bring into action any
of the stronger passions. Persons of
timid character are the more predis-

M

d

FALLACIES IN GENERAL.

483

posed to believe any statement, the
more it is calculated to alarm them.
Indeed it is a ps^'chological law de-
ducible from the most general laws of
the mental constitution of man, that
any strong passion rendei's us credu-
lous as to the existence of objects suit-
able to excite it.

But the moral causes of opinions,
though with most persons the most
})owerful of all, are but remote causes :
they do not act directly, but by means
()f the intellectual causes ; to which
they bear the same relation that the
(arcumstances called, in the theory of
medicine, predisposing causes, bear to
t'xcitimj causes. Indifference to truth
cannot, in and by itself, produce
erroneous belief ; it operates by pre-
venting the mind from collecting the
jn'oper evidences, or from applying to
them the te.st of a legitimate and
rigid induction ; by which omission
it is exposed improtected to the in-
fluence of any species of apparent
evidence which offers itself spontano-
ously, or which is elicited by that
smaller quantity of trouble which the
mind may be willing to take. As
little is Bias a direct source of wrong
conclusions. We cannot believe a
proposition only by wishing, or only
by dreading, to believe it. The most
violent inclinations to find a set of
propositions true will not enable the
weakest of mankind to believe them
without a vestige of intellectual
grounds — without any, even ap-
parent, evidence. It acts indirectly,
by placing the intellectual grounds
<tf belief in an incomplete or distorted
.shape before his eyes. It makes him
shrink from the irksome labour of a
rigorous induction, when he has a
misgiving that its results may be dis-
agreeable ; and in such examination
as he does institute, it makes him
exert that which is in a certain
measure voluntary, his attention, un-
fairly, giving a larger share of it to
the evidence which seems favourable
to the desired conclusion, a smaller to
that which seems unfavourable, it
operates, too, by making him look out

eagerly for reasons, or apparent rea-
sons, to support opinions which are
conformable, or resist those which are
repugnant, to his interests or feelings ;
and when the interests or feelings are
common to great numbers of pex'sons,
reasons ai-e accepted and pass current,
which would not for a moment be
listened to in that character if the
conclusion had notjjing more power-
ful than its reasons to speak in its
behalf. The natural or acquired
partialities of mankind are con-
tinually throwing up philosophical
theories, the sole recommendati<m of
which consists in the premises they
afford for proving cherished doc-
trines, or justifying favourite feel-
ings ; and when any one of these
theories has been so thoroughly
discredited as no longer to serve
the purpose, another is always ready
to take its place. This propensity,
when exercised in favour of any
widely-spread persuasion or senti-
ment, is often decorated with com-
plimentary epithets ; and the contrary
habit of keeping the judgment in
complete subordination to evidence
is stigmatised by various hard names,
as scepticism, immorality, coldness,
hard-heartedness, and similar ex-
pressions, according to the nature of
the case. But though the opinions
of the generality of mankind, when
not dependent on mere habit and
inculcation, have their root much
more in the inclinations than in the
intellect, it is a necessary condition
to the triumph of the moral bias
that it should first pervert the under-
standing. Every erroneous inference,
though originating in moral causes,
involves the intellectual operation of
admitting insufficient evidence as
sufficient ; and whoever was on his
guard against all kinds of incon-
clusive evidence which can be mis-
taken for conclusive, would be in no
danger of being led into error even
by the strongest bias. There are
minds so strongly fortified on the
intellectual side that they could not
blind themselves to the light of truth,

484

FALLACIES.

however really desirous of doing so ;
they could not, with all the inclina-
tion in the world, pass off upon
themselves bad arguments for good
ones. If the sophistry of the intellect
could be rendered impossible, that of
the feelings, having no instrument to
work with, would be powerless. A
comprehensive classification of all
those things which, not being evi-
dence, are liable to appear such to
the understanding, will, therefore, of
itself include all errors of judgment
arising from moral causes, to the ex-
clusion only of errors of practice com-
mitted against better knowledge.

To examine, then, the various kinds
of apparent evidence which are not
evidence at all, and of appai-ently
conclusive evidence which do not
really amount to conclusiveness, is
the object of that part of our inquiry
into which we are about to enter.

The subject is not beyond the com-
pass of classification and comprehen-
sive survey. The things, indeed,
which are not evidence of any given
conclusion, are manifestly endless,
and this negative property, having
no dependence on any positive ones,
cannot be made the groundwork of
a real classification. But the things
which, not being evidence, are suscep-
tible of being mistaken for it, are cap-
able of a classification having refer-
ence to the positive property which
they possess of appearing to be evi-
dence. We may arrange them, at our
choice, on either of two principles —
according to the caiise which makes
them appear to be evidence, not being
so ; or according to the particular
kind of evidence which they simulate.
The Classification of Fallacies which
will be attempted in the ensuing
chapter is founded on these considera-
tions jointly.

CHAPTER IL

CLASSIFICATION OP FALLACIES.

§ I. In attempting to establish cer-
tain general distinctions which shall

mark out from one another the various
kinds of Fallacious Evidence, we pro-
pose to ourselves an altogether dif-
ferent aim from that of several eminent
thinkers, who have given, under the
name of Political or other Fallacies,
a mere enumeration of a certain num-
ber of erroneous opinions ; false gene-
ral propositions which happen to be
often met with ; loci communes of bad
arguments on some particular subject.
Logic is not concerned with the false
opinions which people happen to en-
tertain, but with the manner in which
they come to entertain them. The
question is not, what facts have at
any time been erroneously supposed
to be proof of certain other facts, but
what property in the facts it was
which led any one to this mistaken
supposition.

When a fact is supposed, though
incorrectly, to be evidentiary of, or a
mark of, some other fact, there must
be a cause of the error ; the supposed
evidentiary fact must be connected in
some particular manner with the fact
of which it is deemed evidentiary, —
must stand in some particular relation
to it, without which relation it would
not be regarded in that light. The
relation may either be one resulting
from the simple contemplation of the
two facts side by side with one another,
or it may depend on some process of
mind, by which a previous associa-
tion has been established between
them. Some peculiarity of relation,
however, there must be ; the fact
which can, even by the wildest aber-
ration, be supposed to prove another
fact, must stand in some special posi-
tion with regard to it ; and if we could '
ascertain and define that special posi-
tion, we should perceive the origin of
the error.

We cannot regard one fact as evi-
dentiary of another unless we believe
that the two are always, or in the
majority of cases, conjoined. If we
believe A to be evidentiary of B, if
when we see A we are inclined to infer
B from it, the reason is because we be-
lieve that wherever A is, B also either

H

CLASSIFICATION OF FALLACIES.

485

alwaysorforthemost part exists, either
as an antecedent, a consequent, or a
concomitant. If when we see A we
are inclined not to expect B — if we
believe A to be evidentiary of the
absence of B— it is because we believe
that where A is, B either is never,
or at least seldom, found. Erroneous
conclusions, in short, no less than
correct conclusions, have an invariable
relation to a general formula, either
expressed or tacitly implied. When
we infer some fact from some other
fact which does not really prove it,
we either have admitted, or, if we
maintained consistency, ought to ad-
mit, some groundless general proposi-
tion respecting the conjunction of the
two phenomena.

For every property, therefore, in
facts, or in our mode of considering
facts, which leads us to believe that
they are habitually conjoined when
they are not, or that they are not
when in reality they are, there is a
corresponding kind of Fallacy ; and
an enumeration of fallacies would
consist in a specification of those
properties in facts, and those pecu-
liarities in our mode of considering
them, which give rise to this errone-
ous opinion.

§ 2. To begin, then ; the supposed
connection, or repugnance, between
the two facts, may either be a conclu-
sion from evidence, (that is, from some
jither proposition or propositions,) or
may be admitted without any such
ground ; admitted, as the phrase is,
on its own evidence ; embraced as
self-evident, as an axiomatic truth.
This gives rise to the first great dis-
tinction, that between Fallacies of
Inference and Fallacies of Simple
Inspection. In the latter division
must be included not only all cases in
which a proposition is believed and
held for true, literally without any
extrinsic evidence, either of specific
experience or general reasoning, but
those more frequent cases in which
simple inspection creates a presump-
tion in favour of a proposition ; not

sufficient for belief, but sufficient to
cause the strict principles of a regular
induction to be dispensed with, and
creating a predisposition to believe it
on evidence which would be seen to
be insufficient if no such presumption
existed. This class, comprehending
the whole of what may be termed
Natural Prejudices, and which I shall
call indiscriminately Fallacies of Sim-
ple Inspection or Fallacies a priori,
shall be placed at the head of our list.
Fallacies of Inference, or erroneous
conclusions from supposed evidence,
must be subdivided according to the
nature of the apparent evidence from
which the conclusions are drawn ; or
(what is the same thing) according to
the particular kind of sound argument
which the fallacy in question simu-
lates. But there is a distinction to
be first drawn, which does not answer
to any of the divisions of sound argu-
ments, but arises out of the nature
of bad ones. We may know exactly
what our evidence is, and yet draw a
false conclusion from it : we may con-
ceive precisely what our premises are,
what alleged matters of fact, or gene-
ral principles, are the foundation of
our inference ; and 3'et, because the
premises are false, or because we have
inferred from them what they will
not support, our conclusion may be
erroneous. But a case, perhaps even
more frequent, is that in which the
error arises from not conceiving our
premises with due clearness, that is,
(as shown in the preceding Book,*)
with due fixity ; forming one concep-
tion of our evidence when we collect
or receive it, and another when we
make use of it ; or unadvisedly, and
in general unconsciously, substituting,
as we proceed, different premises in the
place of those with which we set out,
or a different conclusion for that which
we undertook to prove. This gives
existence to a class of fallacies which
may be justly termed (in a phrase
borrowed from Bentham) Fallacies
of Confusion ; comprehending, among

* Supra, p. 431.

4§6

t-ALLACli:^.

others, all those which have their
source in language, whether arising
from the vagueness or ambiguity of
our terms, or from casual associations
with them. ,

When the fallacy is not one of Con-
fusion, that is, when the proposition
believed, and the evidetice on which it
is believed, are steadily apprehended
and unambiguously expressed, there
remain to be made two cross divisions.
The Apparent Evidence may be either
particular facts or foregone generali-
sations ; that is, the process may simu-
late either simple Induction or De-
duction ; and again, the evidence,
whether consisting of supposed facts
or of general propositions, may be
false in itself, or, being true, may fail
to bear out the conclusion attempted
to be founded on it. This gives us
first, Fallacies of Induction and Fal-
lacies of Deduction, and then a sub-
division of each of these, according as
the supposed evidence is false or true
but inconclusive.

Fallacies of Induction, where the
facts on which the induction proceeds
are erroneous, may be termed Fal-
lacies of Observation. The term is
not strictly accurate, or rather, not
accurately co-extensive with the class
of fallacies which I propose to desig-
nate by it. Induction is not always
grounded on facts immediately ob-
served, but sometimes on facts in-
ferred : and when these last are
erroneous, the error may not be, in
the literal sense of the term, an in-
stance of bad observation, but of bad
inference. It will be convenient, how-
ever, to make only one class of all
the inductions of which the error lies
in not sufficiently ascertaining the
facts on which the theory is grounded ;
whether the cause of failure be mal-
observation, or simple non-observa-
tion, and whether the mal-observation
be direct, or by means of intermedi-
ate marks which do not prove what
they are supposed to prove. And in
the absence of any comprehensive
term to denote the ascertainment, by
whatever means, of the facts on which

an induction is grounded, 1 will veil
ture to retain for this class of fallacies,
under the explanation now given, the
title of Fallacies of Observation.

The other class of inductive fal-
lacies, in which the facts are correct,
but the conclusion not warranted by
them, are properly denominated Fal-
lacies of Generalisation ; and these,
again, fall into the various subordi-
nate classes or natural groups, some
of which will be enumerated in their
proper place.

When we now turn to Fallacies of
Deduction, namely, those modes of
incorrect argumentation in which the
premises, or some of them, are general
propositions, and the argument a ra-
tiocination ; we may of course sub-
divide these also into two species
similar to the two preceding, namely,
those which proceed on false premises,
and those of which the premises,
though true, do not support the con-
clusion. But of these species, the
first nmst necessarily fail under some
one of the heads already enumerated.
For the error must be either in those
premises which are general proposi-
tions, or in those which assert indivi-
dual facts. In the former case it is
an Inductive Fallacy, of one or the
other class ; in the latter it is a Fal-
lacy of Observation : unless, in either
case, the erroneous premise has been
assumed on simple inspection, in which
case the fallacy is a priori Or finally,
the premises, of whichever kind they
are, may never have been conceived
in so distinct a manner as to produce
any clear consciousness by what means
they were arrived at ; as in the case
of what is called reasoning in a circle :
and then the fallacy is one of Confu-
sion.

There remain, therefore, as the only
class of fallacies having properly their
seat in deduction, those in which the
premises of the ratiocination do not
bear out its conclusion ; the various
cases, in short, of vicious argumenta-
tion provided against by the rules of
the syllogism. We shall call these
Fallacies of Ratiocination.

■

/en- 91
lies, H

I

I

CLASSIFICATION OF FALLACIES.

4S7

We have thus five distinguishable I pressed in the following synoptic
classes of fallacy, which may be ex- J table :^ —

'of Simple Inspection i. Fallacies a priori.

Fallacies {

distinctly I Fallacies 1 3-

j Deductive \
V Fallacies j *'

conceived

from evidence )

indistinctly ■

of Inference^ ^ conceived )

ij 3. We must not, however, expect
to find that men's actual errors always,
or even commonly, fall so unmi.stak-
ably under some one of these classes
as to be incapable of being referred
to any other. Erroneous arguments
do not admit of such a shai-ply cut
division as valid ai-guments do. An
argument fully stated, with all its
steps distinctly set out, in language
not susceptible of misunderstanding,
must, if it be erroneous, be so in some
one of these five modes unequivocally :
or indeed of the first four, since the
fifth, on such a supposition, would
vanish. But it is not in the nature
of bad reasoning to express itself thus
unambiguously. When a sophist, whe-
ther he is imposing on himself or
attempting to impose on others, can
be consti-ained to throw his sophistry
into so distinct a form, it needs, in a
large proportion of casej?, no further
exposure.

In all arguments, everywhere but
in the schools, some of the links are
suppressed ; d fortiori when the ar-
guer either intends to deceive, or is
a lame and inexpert thinker, little
accustomed to bring his reasoning
processes to any test : and it is in
those steps of the reasoning which
are made in this tacit and half-con-
scious, or even wholly unconscious
manner, that the error oftenest lurks.
In order to detect the fallacy, the pro-
position thus .silently assumed must
be supplied ; but the reasoner, most
likely, has never really asked himself
what he was assuming : his confuter,
unless permitted to extort it from him
by the Socratic mode of interrogation,

Fallacies of Observation.
Fallacies of Generalisation.

Fallacies of Ratiocination.

Fallacies of Confusion.

must liiniself judge what the sup-
pressed premise ought to be in order
to support the conclusion. And hence,
in the words of Archbishop Whately,
" it must be often a matter of doubt,
or rather of arbitrary choice, not only
to which genus each kind of fallacy
should be referred, but even to which
kind to refer anyone individual fal-
lacy ; for since, in any course of argu-
ment, one premise is usually suppressed,
it frequently happens in the case of a
fallacy, that the hearers are left to the
alternative of supplying either a pre-
mise which is not true, or ehe one
which does not prove the conclusion :
e.g. if a man expatiates on the distress
of the country, and thence argues that
the government is tyrannical, we must
suppose him to assume either 'that
every distressed country is under a
tyranny,' which is a manifest false-
hood, or merely that ' every country
under a tyranny is distressed,' which,
however true, proves nothing, the
middle term being undistributed."
The former would be ranked, in our
distribution, among Fallacies of Gene-
ralisation, the latter among those of
Ratiocination. *' Which are we to sup-
pose the speaker meant us to under-
stand? Surely" (if he understood
himself) " just whichever each of his
hearers might happen to prefer : some
might assent to the false premise :
others allow the unsound syllogism."

Almost all fallacies, therefore, might
in strictness be brought under our
fifth class, Fallacies of Confusion. A
fallacy can seldom be absolutely re-
ferred to any of the other classes : we
can only say that if all the links were

FALLACIES.

filled up which should be capable of
being supplied in a valid argument,
it would either stand thus, (forming a
fallacy of one class, ) or thus, (a fal-
lacy of another ;) or at furthest we
may say, that the conclusion is most
Likely to have originated in a fallacy
of such and such a class. Thus in
the illustration just quoted, the error
committed may be traced with most
probability to a Fallacy of Generalisa-
tion ; that of mistaking an uncertain
mark, or piece of evidence, for a cer-
tain one ; concluding from an effect
to some one of its possible causes,
when there are others which would
bave been equally capable of produc-
ing it.

Yet, though the five classes run
into each other, and a particular error
often seems to be arbitrarily assigned
to one of them rather than to any
of the rest, there is considerable use
in so distinguishing them. We shall
find it convenient to set apart, as
Fallacies of Confusion, those of which
confusion is the most obvious charac-
teristic ; in which no other cause can
be assigned for the mistake com-
mitted than neglect or inability to
state the question properly, and to
apprehend the evidence with defi-
niteness and precision. In the re-
maining four classes I shall place not
only the cases in which the evidence
is clearly seen to be what it is, and
yet a wrong conclusion drawn from it,
but also those in which, although
there be confusion, the confusion is
not the sole cause of the error, but
there is some shadow of a ground for
it in the nature of the evidence itself.
And in distributing these cases of
partial confusion among the four
classes, I shall, when there can be any
hesitation as to the precise seat of the
fallacy, suppose it to be in that part of
the process in which, from the nature
of the case and the tendencies of the
human mind, an error would in the
particular circumstances be the most
probable.

After these observations we shall
proceed, Avithout further preamble,

to consider the five classes in their
order.

CHAPTER IIL

FALIACIKS OF SIMPLE INSPECTION, OK
A PRIORI FALLACIES.

§ I. The tribe of errors of which
we are to treat in the first instance
are those in which no actual infer-
ence takes place at all : the proposi-
tion (it cannot in such cases be called
a conclusion) being embraced, not as
proved, but as requiring no proof ; as
a self-evident proof ; or else as having
such intrinsic verisimilitude, that ex-
ternal evidence not in itself amount-
ing to proof is sufficient in aid of the
antecedent presumption.

An attempt to treat this subject
comprehensively would be a trans-
gression of the bounds prescribed to
this work, since it would necessitate
the inquiry which, more than any
other, is the grand question of what
is called metaphysics, viz. What are
the propositions which may reason-
ably be received without proof ? That
there must be some such propositions
all are agreed, since there cannot be
an infinite series of proof, a chain
suspended from nothing. But to de-
termine what these propositions are
is the opus magnum of the more re-
condite mental philosophy. Two prin-
cipal divisions of opinion on the sub-
ject have divided the schools of philo-
sophy from its first dawn. The one
recognises no ultimate premises but
the facts of our subjective conscious-
ness ; our sensations, emotions, intel-
lectual states of mind, and volitions.
These, and whatever by strict rules
of mduction can be derived from these,
it is possible, according to this theory,
for us to know ; of all else we must
remain in ignorance. The opposite
school hold that there are other exist-
ences, suggested indeed to our minds
by these subjective phenomena, but
not inferrible from them by any pro-
cess either of deduction or of induc-
tion ; which, however, we must, by

I

FALLACIES OF SIMPLE INSPECTION.

489

the constitution of our mental nature,
recognise as realities ; and realities,
too, of a higher order than the pheno-
mena of our consciousness, being the
efficient causes and necessary sub-
strata of all Phenomena. Among
these entities they reckon Substances,
whether matter or spirit ; from the
dust under our feet to the soul, and
from that to Deity. All these, ac-
cording to them, are preternatural or
supernatural beings, having no like-
ness in experience, though experience
is entirely a manifestation of their
agency. Their existence, together
with more or less of the laws to
which they conform in their opera-
tions, are, on this theory, apprehended
and recognised as real by the mind
itself intuitively : experience (whether
in the form of sensation or of mental
feeling) having no other part in the
matter than as affording facts which
are consistent with these necessary
postulates of reason, and which are ex-
plained and accounted for by them.

As it is foreign to the purpose of
the present treatise to decide between
these conflicting theories, we are pre-
cluded from inquiring into the exist-
ence, or defining the extent and limits,
of knowledge d priori, and from char-
acterising the kind of correct assump-
tion which the fallacy of incorrect
assumption, now under consideration,
simulates. Yet, since it is allowed
on both sides that such assumptions
are often made improperly, we may
find it practicable, without entering
into theultimate metaphysical grounds
of the discussion, to state some specu-
lative propositions, and suggest some
practical cautions, respecting the forms
in which such unwarranted assump-
tions are most likely to be made.

§ 2. In the cases in which, accord-
ing to the thinkers of the ontological
school, the mind apprehends, by in-
tuition, things, and the laws of things,
not cognisable by our sensitive faculty,
those intuitive, or supposed intui-
tive, perceptions are undistinguishable
from what the opposite school are ac-

customed to call ideas of the mind.
When they themselves say that they
perceive the things by an immediate
act of a faculty given for that pur-
pose by their Creator, it would be
said of them by their opponents that
they find an idea or conception in
their own minds, and from the idea
or conception infer the existence of
a corresponding objective reality.
Nor would this be an unfair state-
ment, but a mere version into other
words of the account given by many
of themselves ; and one to which the
more clear-sighted of them might, and
generally do, without hesitation sub-
scribe. Since, therefore, in the cases
which lay the strongest claims to be
examples of knowledge d priori, the
mind proceeds from the idea of a
thing to the reality of the thing itself,
we cannot be surprised by finding
that illicit assumptions d priori con-
sist in doing the same thing errone-
ously : in mistaking subjective facta
for objective, laws of the percipient
mind for laws of the perceived object,
properties of the ideas or conceptions
for properties of the things conceived.

Accordingly, a large proportion of
the erroneous thinking which exists
in the world proceeds on a tacit as-
sumption that the same order must
obtain among the objects in nature
which obtains among our ideas of
them. That if we always think of
two things together, the two things
must always exist together ; that if
one thing makes us think of another
as preceding or following it, that
other must precede it or follow it in
actual fact. And, conversely, that
when we cannot conceive two things
together, they cannot exist together,
and that their combination may, with-
out further evidence, be rejected from
the list of possible occurrences.

Few persons, I am inclined to think,
have reflected on the great extent to
which this fallacy has prevailed, and
prevails, in the actual beliefs and ac-
tions of mankind. For a first illus-
tration of it, Ave may refer to a large
class of popular superstitions. If any

490 I^ALLACIKS.

one will examine in what circnm-
stances most of those things agree
which in different ages and by dif-
ferent portions of the human race
have been considei'ed as omens or
prognostics of some interesting event,
whether calamitous or fortunate, they
will be found very generally charac-
terised by this peculiarity, that they
cause the mind to think of that of
which they are therefore supposed to
forbode the actual occurrence. " Talk
of the devil and he will appear," has
passed into a proverb. Talk of the
devil, that is, raise the idea, and the
reality will follow. In times when
the appearance of that personage in
a visible form was thought to be no
Tinfrequent occurrence, it has doubt-
less often happened to persons of
vivid imagination and susceptible
nerves that talking of the devil has
caused them to fancy they saw him ;
as, even in our more incredulous days,
listening to ghost stories predisposes
us to see ghosts ; and thus, as a prop
to the a priori fallacy, there might
come to be added an auxiliary fallacy
of mal-observation, with one of false
generalisation grounded on it. Fal-
lacies of different orders often herd
or cluster together in this fashion,
one smoothing the way for another.
But the origin of the superstition is
evidently that which we have as-
signed. In like manner it has been
imiversally considered unlucky to
speak of misfortune. The day on
which any calamity happened has
been considered an unfortunate day,
and there has been a feeling every-
where, and in some nations a reli-
gious obligation, against transacting
any important business on that day ;
for on such a day our thoughts are
likely to be of misfortune. For a
similar reason any untoward occur-
rence in commencing an undertak-
ing has been considered ominous of
failure, and often, doubtless, has really
contributed to it, by putting the per-
sons engaged in the enterprise more
or less out of spirits : but the belief
has equally prevailed where the dis-

■

ide*

agreeable circumstance was, in
pendently of superstition, too insig-
nificant to depress the spirits by any
influence of its o^vn. All know the
story of Caesar's accidentally stum-
bling in the act of landing on the
African coast, and the presence 'of
mind with which he converted the
direful presage into a favourable one
by exclaiming, "Africa, I embrace
thee." Such omens, it is true, were
often conceived as warnings of the
future, given by a friendly or a hos-
tile deity ; but this very superstition
grew out of a pre-existing tendency :
the god was supposed to send, as an
indication of what was to come, some-
thing which people were already dis-
posed to consider in that light. So
in the case of lucky or unlucky names,
Herodotus tells us how the Greeks,
on the way to Mycale, were encoui-
aged in their enterprise by the arrival
of a deputation from Samos, one of
the members of which was named
Hegesistratus, the leader of armies.

Cases may be pointed out in whicli
something which could have no real
effect but to make persons think of
misfortune was regarded not merely
as a prognostic, but as something
approaching to an actual cause of it.
The ev-^tpfiei of the Greeks, and favete
Unguis or bona verba quc^so of the
Romans, evince the care with which
they endeavoured to repress the utter-
ance of any word expressive or sug-
gestive of ill-fortune ; not from notions
of delicate politeness, to which their
general mode of conduct and feeling
had very little reference, but from
bonu fide alarm lest the event so sug-
gested to the imagination should in
fact occur. Some vestige of a similar
superstition has been known to exist
among uneducated persons even in
our own day : it is thought an un-
christian thing to talk of or suppose
the death of any person while he is
alive. It is known how careful the
Romans were to avoid, by an indirect
mode of speech, the utterance of any
word directly expressive of death or
other calamity : how instead of mar-

fl

I

i'ALLACIES OF SIMPLK INSPECTIOX.

491

tuns est they said vixit ; nnJ "be the
event fortunate or otherwise,^' instead
of adverse. The name Malcventum,
«)f which Sahnasius so sagaciously de-
tected the Thessalian origin (MaXdeis,
MaXoeVros, ) they changed into the
liighly propitious denomination Bene-
ventum ; Egesta into Segesta ; and
Epidamnus, a name so interesting in
its associations to the reader of Thu-
cydides, they exchanged for Dyrrha-
chium, to escape the perils of a word
suggestive of damnum or detriment.

"If an hare cross the highway,"
says Sir Thomas Browne,* "there are
few above threescore that are n(jt
perplexed thereat ; which notwitli-
standing is but an augurial terror,
according to that received expres-
sion, Inuuspicatiuii dat iter ohlatus
lepus. And the ground of the conceit
was probably no greater than this,
that a fearful animal passing by us
portended unto us something to be
feared ; as upon the like considera-
tion the meeting of a fox presaged
some future imposture." Such super-
stitions as these last must be the
result of study ; they are too recon-
dite for natural or spontaneous growth.
But when the attempt was once made
to construct a science of predictions,
any association, though ever so faint
or remote, by which an object could
be connected, in however far fetched
a manner, with ideas either of pros-
perity or of danger and misfortune,
was enough to determine its being-
classed among good or evil omens.

An example of rather a different
kind from any of these, but falling
under the same principle, is the famous
attempt, on which so much labour and
ingenuity were expended by the al-
chemists, to make gold pq^able. Th^
motive to this was a conceit that
potable gold could be no other than
the universal medicine : and why
gold ? Because it was so precious.
It must have all marvellous properties
as a physical substance, because the
mind was already accustomed to mar-
vel at it.

* Vulgar Errors, book v. chap. 21.

From a similar feeling, "every
substance," says Dr. Paris,* "whose
origin is involved in mystery, has at
different times been eagerly applied
to the purposes of medicine. Not
long since, one of those showers which
are now known to consist of the ex-
crements of insects fell in the north
of Italy ; the inhabitants regarded it
as manna, or some supernatural pana-
cea, and they swallowed it with such
avidity, that it was only by extreme
address that a small quantity was
obtained for a chemical examination."
The superstition, in this instance,
though doubtless partly of a religious
character, probably in part also arose
from the prejudice that a wonderful
thing m\ist of course have wonderful
properties.

§ 3. The instances of a 2^riorl fal-
lacy w^hich we have hitherto cited
belong to the class of vulgar errors,
and do not now, nor in any but a
rude age ever could, impose upon
minds of any considerable attain-
ments. But those to which we are
about to proceed have been, and still
are, all but universally prevalent
among thinkers. The same disposi-
tion to give objectivity to a law of
the mind — to suppose that what is
true of our ideas of things must be
true of the things themselves — ex-
hibits itself in many of the most ac-
credited modes of philosophical in-
vestigation, both on physical and on
metaphysical subjects. In one of its
most undisguised manifestations it
embodies itself in two maxims, which
lay claim to axiomatic truth : Things
which we cannot think of together
cannot co-exisf; and Things which
we cannot help thinking of together
must CO- exist. I am not sure that
the maxims were ever expressed in
these precise words, but the history
both of philosophy and of popular
opinions abounds with exemplifica-
tions of both forms of the doctrine.

To begin with the latter of them :

* Pharmacologia, Historical Introduc-
tion, p. 16.

492

I'ALLACIES.

Things which we cannot think of ex-
cept together, must exist together.
This is assumed in the generally re-
ceived and accredited mode of reason-
ing which concludes that A must ac-
company B in point of fact, because
" it is involved in the idea," Such
thinkers do not reflect that the idea,
being a result of abstraction, ought to
conform to the facts, and cannot make
the facts conform to it. The argu-
ment is at most admissible as an
appeal to authority ; a surmise, that
what is now part of the idea must,
before it became so, have been found
by previous inquirers in the facts.
Nevertheless, the philosopher who
more than all others made professions
of rejecting authority, Descartes, con-
structed his system on this very iDasis.
His favourite device for arriving at
the truth, even in regard to outward
things, was by looking into his own
mind for it. " Credidi me," says his
celebrated maxim, " pro regul^ gene-
rali sum ere posse, omne id quod val-
de dilucid^ et distincte concipiebam,
verum esse ; " whatever can be very
clearly conceived must certainly exist;
that is, as he afterwards explains it, if
the idea includes existence. And on
this ground he infers that geometrical
figures really exist, because they can
be distinctly conceived. Whenever
existence is " involved in an idea," a
thing conformable to the idea must
really exist ; which is as much as to
say, whatever the idea contains must
have its equivalent in the thing ; and
•what we are not able to leave out of
the idea cannot be absent from the
reality.* This assumption pervades

* The author of one of the Bridgewater
Treatises has fallen, as it seems to me, into
a similar fallacy when, after arguing in
rather a curious way to prove that matter
may exist without any of the known pro-
perties of matter, and may therefore be
changeable, he concludes that it cannot be
eternal, because " eternal (passive) exist-
ence necessarily involves incapability of
change." I believe it would be diflBcult to
point out any other connection between
the facts of eternity and unchangeableness
than a strong association between the two
ideas. Most of the d priori arguments,

the philosophy not only of Descartes,
but of all the thinkers who received
their impulse mainly from him ; in
particular the two most remarkable
among them, Spinoza and Leibnitz,
from whom the modern German meta-
physical philosophy is essentially an
emanation, I am indeed disposed to jH
think that the fallacy now under con- S
sideration has been the cause of two-
thirds of the bad philosophy, and espe-
cially of the bad metaphysics, which
the human mind has never ceased to
produce. Our general ideas contain
nothing but what has been put into
them, either by our passive experience,
or by our active habits of thought ;
and the metaphysicians in all ages,
who have attempted to construct the
laws of the universe by reasoning from
our supposed necessities of thought,
have always proceeded, and only could
proceed, by laboriously finding in their
own minds what they themselves had ^M
formerly put there, and evolving from ^M
their ideas of things what they had
first involved in those ideas. In this
way all deeply-rooted opinions and
feelings are enabled to create apparent
demonstrations of their truth and rea-
sonableness, as it were out of their own
substance.

The other form of the fallacy —
Things which we cannot think of to-
gether cannot exist together, — includ-
ing, as one of its branches, that what
we cannot think of as existing cannot
exist at all, — may thus be briefly ex-
pressed : Whatever is inconceivable
must be false.

Against this prevalent doctrine I
have sufficiently argued in a former
Book,* and nothing is required in this
place but examples. It was long held
that Antipodes were impossible be-
cause of the difficulty which was found
in conceiving persons with their heads
in the same direction as our feet. And

both religions and anti-religious, on the
origin of things, are fallacies drawn from
the same source.

* Supra, book ii. chap. v. § 6, and ch. vii.
§ T, 2, 3, 4, See also Examination of Sir
Willinm Hamilton's Philotopfnj, chap. vi.
and elsewhere.

I

FALLACIES OF SIMPLE INSPECTIOX.

493

it was one of the received arguments
against the Copernican system, that
we cannot conceive so great a void
space as that system supposes to exist
in the celestial regions. When men's
imaginations liad always been used to
conceive the stars as firmly set in
•solid spheres, they naturally found
much difficulty in imagining them in
so different, and, as it doubtless ap-
peared to them, so precarious a situa-
tion. But they had no right to mis-
take the limitation (whether natural,
or, as it in fact proved, only artificial)
of their own faculties for an inherent
limitation of the possible modes of
existence in the universe.

It may be said in objection, that
the error in these cases was in the
minor premise, not the major ; an
error of fact, not of principle ; that it
did not consist in supposing that what
is inconceivable cannot be true, but in
supposing antipodes to be inconceiv-
able, when present experience proves
that they can be conceived. Even
if this objection were allowed, and the
proposition that what is inconceivable
cannot be true were suffered to remain
luiquestioned as a speculative truth, it
would be a truth on which no practi-
cal consequence could ever be founded,
since, on this showing, it is impossible
to affirm of any proposition, not being
a contradiction in terms, that it is in-
conceivable. Antipodes were really,
not fictitiously, inconceivable to our
ancestors : they are indeed conceiv-
able to us ; and as the limits of our
power of conception have been so
largely extended by the extension of
our experience and the more varied
exercise of our imagination, so may
posterity find many combinations per-
fectly conceivable to them which are
inconceivable to us. But, as beings
of limited experience, we must always
and necessarily have limited concep-
tive powers ; while it does not by any
means follow that the same limitation
obtains in the possibilities of nature,
nor even in her actual manifesta-
tions.

Bather more than a century and a

half ago it was a scientific maxim,
disputed by no one, and which no one
deemed to re([uire any proof, that "a
thing cannot act where it is not." *
With this weapon the Cartesians
waged a formidable war against the
theory of gravitation, which, accord-
ing to them, involving so obvious an
absurdity, must be rejected in limine :
the sun could not possibly act upon
the earth, not being there. It was
not surprising that the adherents of
the old systems of astronomy should
urge this objection against the new ;
but the false assumption imposed
equally on Newton himself, who, in
order to turn the edge of the objec-
tion, imagined a siibtle ether which
filled up the space between the sun
and the earth, and by its intermediate
agency was the proximate cause of
the phenomena of gravitation. " It
is inconceivable," said Newton, in one
of his letters to Dr. Bentley,t " that
inanimate brute matter should, with-
out the mediation of something else,
which is not material, operate upon
and affect other matter loithout mutual
contact. . . . That gravity should be
innate, inherent, and essential to mat-
ter, so that one body may act on
another at a distance, through a va-
cuum, without the mediation of any-
thing else, by and through which
their action and force may be con-
veyed from one to another, is to me
so great an absurdity, that I believe
no man, who in philosophical matters
has a competent faculty of thinking,
can ever fall into it." This passage
should be hung up in the cabinet of
every cultivator of science who is ever
tempted to pronounce a fact impos-
sible because it appears to him incon-
ceivable. In our own day one would
be more tempted, though with equal
injustice, to reverse the concluding
observation, and consider the seeing

* It seems that this doctrine was, before
the time I have mentioned, disputed by
.<^ome thinkers. Dr. Ward mentions Scotns,
Va-sqiiez, Biel, Francis Lugo, and Valentiu.

t I quote this passage from Playfair'.s
celebiated Dissertation on the Proijre-s of
Mathevmtical und J'hysical Science.

494

FALLACIES.

any absurdity at all in a thing so
simple and natural, to be what really
marks the absence of "a competent
faculty of thinking." No one now
feels any difficulty in conceiving gra-
vity to be, as much as any other pro-
perty is, " inherent and essential to
matter," nor finds the comprehension
of it facilitated in the smallest degree
uy the supposition of an ether, (though
some recent inquirers do give this as
an explanation of it,) nor thinks it
at all incredible that the celestial
bodies can and do act where they, in
actual bodily presence, are not. To
us it is not more wonderful that bodies
should act upon one another " with-
out mutual contact," than that they
should do so when in contact ; we are
familiar with both these facts, and we
find them equally inexplicable, but
equally easy to believe. To Newton,
the one, because his imagination was
familiar with it, appeared natural and
a matter of course, while the other, for
the contrary reason, seemed too absurd
to be credited.

It is strange that any one, after
such a warning, should rely implicitly
on the evidence a priori of such pro-
positions as these : that matter cannot
think ; that space, or extension, is
infinite ; that nothing can be made
out of nothing [ex nihilo nihil Jit).
Whether these propositions are true
or not this is not the place to deter-
mine, nor even whether. the questions
are soluble by the human faculties.
But such doctrines are no more self-
evident truths than the ancient maxim
that a thing cannot act where it is
not, which probably is not now be-
lieved by any educated person in
Europe.* Matter cannot think ; why ?
because we cannot conceive thought
to be annexed to any arrangement of
material particles. Space is infinite,
because having never known any part
of it which had not other parts be-

* This statement I must now correct, as
too tmqualified. The maxim in question
was maintained with full conviction by no
less an authority than Sir William Hamil-
ton, yee mjr Exarnination, chap. 3fxiv,

yond it, we cannot conceive an absolute
termination. Ex nihilo nihil fit, be-
cause having never known any phy-
sical product without a pre-existing
physical material, we cannot, or think
we cannot, imagine a creation out of
nothing. But these things may ia
themselves be as conceivable as gravi-
tation without an intervening medium,
which Newton thought too great an
absurdity for any person of a com-
petent faculty of philosophical think-
ing to admit : and even supposing
them not conceivable, this, for aught
we know, may be merely one of the
limitations of our very limited minds,
and not in nature at all.

No writer has more directly iden-
tified himself with the fallacy now
under consideration, or has embodied
it in more distinct terms, than Leib-
nitz. In his view, unless a thing
was not merely conceivable, but even
explainable, it could not exist in na-
ture. All 'natural phenomena, ac-
cording to him, nmst be susceptible
of being accounted for d priori. The
only facts of which no explanation
could be given but the will of God
were miracles properly so called.
" Je reconnais," says he,* "qu'il n'est
pas permis de nier ce qu'on n'entend
pas ; mais j'ajoute qu'on a droit de
nier (au moins dans I'ordre naturel)
ce que absolument n'est point in-
telligible ni explicable. Je soutiehs
aussi . . . qu'enfin la conception des
creatures n'est pas la mesure du
pouvoir de Dieu, mais que leur con-
ceptivite, ou force de concevoir, est
la mesure du pouvoir de la nature,
tout ce qui est conforme a I'ordre
naturel pouvant etre con^u ou en-
tendu par quelque creature."

Not content with assuming that
nothing can be true which we are un-
able to conceive, scientific inquire I's
have frequently given a still further
extension to the doctrine, and held
that, even of things not altogether
inconceivable, that which we can con-

'* Nouveaux Essais sar ' I'Entendement
Ilumain — Avant-propos. ((Euvres, Parii,
ed, 1842, vol. i. p. 19.)

FALLACIES OF SIMPLE INSPECTION.

495

ceive with the greatest ease is likeliest
to be true. It was long an admitted
axiom, and is not yet entirely dis-
credited, that *' nature always acts by
the simplest means," i.e. by those
which are most easily conceivable.*
A large proportion of all the errors
ever committed in the investigation
of the laws of nature have arisen
from the assumption that the most
familiar explanation or hypothesis
must be the truest. One of the most
instructive facts in scientific history
18 the pertinacity with which the
human mind clung to the belief that
the heavenly bodies must move in
circles, or be carried round by tbe
revolution of spheres, merely because
those were in themselves the simplest
suppositions ; though, to make them
accord with the facts which were
ever contradicting them more and
more, it became necessary to add
sphere to sphere and circle to circle,
tmtil the original simplicity was con-
verted into almost inextricable com-
plication.

§ 4. We pass to another a priori
fallacy or natural prejudice, allied
to the former, and originating, as
that does,- in the tendency to presume
an exact correspondence between the
laws of the mind and those of things
external to it. The fallacy may be
enunciated in this general form —
Whatever can be thought of apart
exists apart ; and its most remark-
able manifestation consists in the
personification of abstractions. Man-
kind in all ages have had a strong
propensity to conclude that wherever
there is a name there must be a dis-
tinguishable separate entity corre-
sponding to the name ; and every
complex idea which the mind has
formed for itself by operating upon
its conceptions of individual things,
was considered to have an outward
objective reality answering to it.

♦ This doctrine also was accepted as true,
.•md conclusions were gro\inded on it, bj'
ISir William Hamiltou. See L'xamination,
uliup. xxiv

Fate, Chance, Nature, Time, Space,
were real beings, nay, even gods. If
the analysis of qualities in the earlier
part of this work be correct, names
of qualities and names of substances
stand for the very same sets of facts
or phenomena ; whiteness and a white
thimj are only different phrases, re-
quired by convenience for speaking of
the same external fact under different
relations. Not such, however, was
the notion which this verbal distinc-
tion suggested of old, either to tht*
vulgar or to the scientific. Whiteness
was an entity inhering or sticking in
the white substance ; and so of all
other qualities. So far was this car-
ried, that even concrete general terms
were supposed to be, not names of
indefinite numbers of individual sub-
stances, but names of a peculiar kind
of entities termed Universal Sub-
stances. Because we can think and
speak of man in general, that is, of
uU persons in so far as possessing the
common attributes of the species,
without fastening our thoughts per-
manently on some one individual
person : therefore man in general was
supposed to be, not an aggregate of
individual persons, but an abstract
or universal man, distinct from these.
It may be imagined what havoc
metaphysicians trained in these ha-
bits made with philosophy when
they came to the largest generalisa-
tions of all. Substantice Secundce of
any kind were bad enough, but such
Substantiae Secundse as to 6v, for ex-
ample, and TO tv, standing for pecu-
liar entities supposed to be inherent
in all things which exist, or in all
which are said to be one, were enough
to put an end to all intelligible dis-
cussion ; especially since, with a just
perception that the truths which philo-
sophy pursues are general truths, it
was soon laid do^vn that these gene-
ral substances were the only subjects
of science, being immutable, while
individual substances cognisable by
the senses, being in a perpetual flux,
could not be the subject of real know-
ledge. This misapprehension of the

496

FALLACIES.

import of general language consti-
tutes Mysticism, a word so much
oftener written and spoken than
understood. Whether in the Vedas,
in the Platonists, or in the Hegelians,
mysticism is neither more nor less
than ascribing objective existence to
the subjective creations of our own
faculties, to ideas or feelings of the
mind ; and believing that by watch-
ing and contemplating these ideas of
its own making, it can read in them
what takes place in the world without,

§ 5. Proceeding with the enumera-
tion of a priori fallacies, and endea-
vouring to arrange them with as much
reference as possible to their natural
affinities, we come to another, which
is also nearly allied to the fallacy pre-
ceding the last, standing in the same
relation to one variety of it as the
fallacy last mentioned does to the
other. This, too, represents nature as
under incapacities corresponding to
those of our intellect ; but instead of
only asserting that nature cannot do
a thing because we cannot conceive it
done, goes the still greater length of
averring that nature does a particular
thing, on the sole ground that we can
see no reason why she should not.
Absurd as this seems when so plainly
stated, it is a received principle among
scientific authorities for demonstrat-
ing a priori the laws of physical phe-
nomena. A phenomenon must fol-
low a certain law, because we see no
reason why it should deviate from
that law in one way rather than in
another. This is called the Principle
of the Sufficient Keason ; * and by
means of it philosophers often flatter
themselves that they are able to es-
tablish, without any appeal to experi-
ence, the most general truths of ex-
perimental physics.

Take, for example, two of the most
elementary of all laws, the law of
inertia and the first law of motion.
A body at rest cannot, it is affirmed,

* Not that of Leibnitz, but the principle
commonly appealed to under that name by
wathematiciaug,

begin to move unless acted upon by
some external force ; because, if it
did, it must either move up or down,
forward or backward, and so forth ;
but if no outward force acts upon it,
there can be no reason for its moving
up rather than down, or down rather
than up, &c. ; ergo, it will not move
at all.

This reasoning I conceive to be en-
tirely fallacious, as indeed Dr. Brown,
in his treatise on Cause and Effect,
has shown with great acuteness and
justness of thought. We have before
remarked that almost every fallacy
may be referred to different genera
by different modes of filling up the
suppressed steps ; and this particular
one may, at our option, be brought
under petitio principii. It supposes
that nothing can be a "sufficient
reason " for a body's moving in one
particular direction except some ex-
ternal force. But this is the very
thing to be proved. Why not some
inteimal force ? Why not the law of
the thing's own nature ? Since these
philosophers think it necessary to
prove the law of inertia, they of
course do not suppose it to be self-
evident ; they must;, therefore, be of
opinion that, previously to all proof,
the supposition of a body's moving
by internal impulse is an admissible
hypothesis ; but if so, why is not the
hypothesis also admissible that the
internal impulse acts naturally in
some one particular direction, not in
another? If spontaneous motion
might have been the law of matter,
why not spontaneous motion towards
the sun, towards the earth, or to-
wards the zenith ? Why not, as the
ancients supposed, towards a parti-
cular place in the universe, appro-
priated to each particular kind of
substance? Surely it is not allow-
able to say that spontaneity of motion
is credible in itself, but not credible
if supposed to take place in any de-
terminate direction.

Indeed, if any one choose to assert
that all bodies when uncontrolled set
out in ^ direct line towards the north

FALLACIES OF SIMPLE INSPECTION.

497

pole, he might equally prove his point
by the principle of the Sufficient Rea-
son, By what right is it assumed
that a state of rest is the particular
state which cannot be deviated from
without special cause? Why not a
state of motion, and of some parti-
cular sort of motion ? Why may we
not say that the natural state of a
horse left to himself is to amble, be-
cause otherwise he must either trot,
gallop, or stand still, and because we
know no reason why he should do
one of these rather than another?
If this is to be called an unfair use
of the "sufficient reason," and the
other a fair one, there must be a
tacit assumption that a state of rest
is more natural to a horse than a
state of ambling. If this means that
it is the state which the animal will
assume when left to himself, that is
the very point to be proved ; and if it
does not mean this, it can only mean
that a state of rest is the simple.st
state, and therefore the most likely
to prevail in nature, which is one of
the fallacies or natural prejudices we
have already examined.

So again of the First Law of Mo-
tion ; that a body once moving will,
if left to itself, continue to move uni-
formly in a straight line. An attempt
is made to prove this law by saying,
that if not, the body must deviate
either to the right or to the left, and
that there is no reason why it should
do one more than the other. But
who could know, antecedently to ex-
perience, whether there was a reason
or not ? Might it not be the nature
of bodies, or of some particular bodies,
to deviate towards the right ? or if
the supposition is preferred, towards
the east or south ? It was long
thought that bodies, terrestrial ones
at least, had a natural tendency to
deflect downwards ; and there is no
shadow of anything objectionable in
the supposition, except that it is not
true. The pretended proof of the law
of motion is even more manifestly
untenable than that of the law of
inertia, for it is flagrantly inconsis-

tent ; it assumes that the continu-
ance of moti«)n in the direction first
taken is more natural than deviation
either to the right or to the left, but
denies that one of these can possibly
be more natural than the other. All
these fancies of the possibility of
knowing what is natural or not natu-
ral by any other means than experi-
ence, are, in truth, entirely futile.
The real and only proof of the laws
of motion, or of any other law of the
universe, is experience ; it is simply
that no other suppositions explain or
are consistent with the facts of uni-
versal nature.

Geometers have, in all ages, been
open to the imputation of endeavour-
ing to prove the most general facts
of the outward world by sophistical
reasoning, in order to avoid appeals
to the senses. Archimedes, says Pro-
fessor Play fair,* establi-shed some of
the elementary propositions of statics
by a process in which he " borrows no
principle from experiment, but estab-
lishes his ccmclusion entirely by rea-
soning d priori. He assumes, indeed,
that equal bodies, at the ends of the
equal arms of a lever, will balance
one another ; and also that a cylinder
or parallelepiped of homogeneous mat-
ter will be balanced about its centre
of magnitude. These, however, are
not inferences from experience ; they
are, properly speaking, conclusions
deduced from the principle of the
Sufficient Reason." And to this day
there are few geometers who would
not think it far more scientific to
establish these or any other premises
in this way than to rest their evidence
on that familiar experience which in
the case in question might have been
so safely appealed to.

§ 6. Another natural prejudice, of
most extensive prevalence, and which
had a great share in producing the
errors fallen into by the ancients in
thbir physical inquiries, was this :
That the dififerences in nature must

* Dittertation, ut supra, p. 37.
2 I

49S

FALLACIES.

I

correspond to our received distinc-
tions ; that effects which we are ac-
customed, in popular language, to call
by different names, and arrange in
different classes, must be of different
natures, and have different causes.
This prejudice, so evidently of the
same or'gin with those already treated
of, marks more especially the earliest
stage of science, when it has mjt yet
broken loose from the trammels of
everyday phraseology. The extra-
ordinary prevalence of the fallacy
among the Greek philosophers may
be accounted for by their generally
knowing no other language than their
own ; from w^hich it was a consequence
that their ideas followed the accidental
or arbitrary combinations of that lan-
guage more completely than can hap-
pen among the moderns to any but
illiterate persons. They had great
difficulty in distinguishing between
things which their language con-
founded, or in putting mentally to-
gether things which it distinguished,
and could hardly combine the objects
in nature into any classes but those
which were made for them by the
popular phrases of their own country ;
or at least could not help fancy-
ing those classes to be natural, and
all others arbitrary and artificial.
Accordingly, scientific investigation
among the Greek schools of specula-
tion and their followers in the Middle
Ages, was little more than a mere
sifting and analysing of the notions
attached to common language. They
thought that by determining the
meaning of words they could be-
come acquainted with facts. "They
took for granted," says Dr. Whewell,*
,*' that philosophy must result from the
relations of those notions which are
involved in the common use of lan-
guage, and they proceeded to seek it
by studying such notions." In his
next chapte", Dr. Whewell has so
well illustrated and exemplified this
error, that I shall take the liberty
of quoting him at some length.

« Hiit. Ind. Sc.y book i. chap. i.

** The propensity to seek for prin-
ciples in the common usages of lan-
guage may be discerned at a very
early period. Thus we have an ex-
ample of it in a saying which is re-
ported of Thales, the founder of Greek
philosophy. When he was asked,
* What is the (greatest thing ? ' he re-
plied, * Place; for all other things are
in the world, but the world is in it.*
In Aristotle we have the consumma-
tion of this mode of speculation. The
usual point from which he starts in
his inquiries is, that we say thus or
thus in common language. Thus,
when he has to discuss the question
whether there be, in any part of the
universe, a void, or space in which
there is nothing, he inquires first in
how many senses we say that one
thing is in another. He enumerates
many of these ; we say the part is
in the whole, as the finger is in the
hand ; again we say, the species is
in the genus, as man is included in
animal ; again, the government of
Greece is wi the king ; and various
other senses are described and ex-
emplified, but of all these the most
proper is when we say a thing is in
a vessel, and generally in plaice. He
next examines what place is, and
comes to this conclusion, that ' if
about a body there be another body
including it, it is in place, and if not,
not.' A body moves when it changes
its place ; but he adds, that if water
be in a vessel, the vessel being at rest,
the parts of the water may still move,
for they are included by each other ;
so that while the whole does not change
its place, the parts may change their
place in a circular order. Proceeding
then to the question of a void, he as
usual examines the different senses in
which the term is used, and adopts as
the most proper, place without matter : |l
with no useful result. ||

•' Again, in a question concerning
mechanical action, he says, ' When a
man moves a stone by pushing it with a
stick, we say both that the man moves
the stone, and that the stick moves the
stone, but the latter moj'e properly.

II

FALLACIES OF SIMPLE INSPECTION.

499

•' Again, we find the Greek philoso-
phers applying themselves to extract
their dogmas from the moj^t general
and abstract notions which they coulcl
detect : for example, from the con'
ception of the Universe as One or aa
Many things. They tried to deter-
mine how far we may, or must, com-,
bine with these conceptions that of a
whole, of parts, of number, of limits,
of place, of beginning or end, of full
or void, of rest, or motion, of cause
and effect, and the like. The ana-
lysis of such conceptions with such
a view occupies, for instance, almost
the whole of Aristotle's Treatise on
the Heavens. "

The following paragraph merits par-
ticular attention : — " Another mode
of reasoning, very widely applied in
these attempts, was the doctrine of
contrarieties, in which it was assumed
that adjectives or substances which
are in common language, or in some
abstract mode of conception, opposed
to each other, must point at some
fundamental antithesis in nature,
which it is important to study. Thus
Aristotle says that the Pythagoreans,
from the contrasts which number
suggests, collected ten principles —
Limited and Unlimited. Odd and
Even, One and Many, Right and
Left, Male and Female, Rest and
Motion, Straight and Curved, Light
and Darkness, Good and Evil, Square
and Oblong. . . . Aristotle himself
deduced the doctrine of four elements
and other dogmas by oppositions of
the same kind."

Of the manner in which, from pre-
mises obtained in this way, the ancients
attempted to deduce laws of nature,
an example is given in the same work
a few pages farther on. "Aristotle
decides that there is no void on such
arguments as this. In a void there
could be no difference of up and
down ; for as in nothing there are no
differences, so there are none in a
privation or negation; but a void is
merely a privation or negation of
matter ; therefore, in a void, bodies
could not move up and down, which

it is in their nature to do. It is easily
seen " (Dr. Whewell very justly adds)
" that such a mode of reasoning ele-
vates the familiar forms of language
and the intellectual connections of
terms to a supremacy over facts,
making truth depend upon whether
terms are or are not privative, and
whether we say that bodies fall natU'
rally y

The propensity to assume that the
same relations obtain between objects
themselves which obtain between our
ideas of them is here seen in the ex-
treme stage of its development. For
the mode of philosophising exempli-
fied in the foregoing instances assumes
no less than that the proper way of
arriving at knowledge of nature is to
study nature itself subjectively ; to
apply our observation and analysis
not to the facts, but to the common
notions entertained of the facts.

Many other equally striking ex-
amples may be given of the tendency
to assume that things which for the
convenience of common life are placed
in different classes, must differ in
every respect. Of this nature was
the universal and deeply-rooted pre-
judice of antiquity and the Middle
Ages, that celestial and terrestrial
phenomena must be essentially dif-
ferent, and could in no manner or
degree depend on the same laws. Of
the same kind, also, was the prejudice
against which Bacon contended, that
nothing produced by nature could be
successfully imitated by man : " Cal-
orem solis et ignis toto genere differre ;
ne scilicet homines putent se per opera
ignis, aliquid simile iis quie in Na-
tura,fiunt, educere et formare posse : "
and again, " Compositionem tantum
opus Honiinis, Mistionem vero opus
solius Naturae esse : ne scilicet homi-
nes sperent aliquam ex arte Corporum
naturalium generationem aut trans-
formationem." * The grand distinc-
tion in the ancient scientific specu-
lations, between natural and violent
motions, though not without a plau-

* Novum Organum, Aph. 75.

500

FALLACIES.

sible foundation in the appearances
themselves, was doubtless greatly re-
commended to adoption by its con-
formity to this prejudice.

§ 7. From the fundamental error of
the scientific inquirers of antiquity
we pass, by a natural association, to a
scarcely less fundamental one of their
great rival and successor, Bacon. It
has excited the surprise of philoso-
phers that the detailed sjrstem of in-
ductive logic which this extraordinary
man laboured to construct has been
turned to so little direct use by subse-
quent inquirers, having neither con-
tinued, except in a few of its gene-
ralities, to be recognised as a theory,
nor having conducted in practice to
any great scientific results. But this,
though not unfrequently remarked,
has scarcely received any plausible
explanation ; and some indeed have
preferred to assert that all rules of
induction are useless, rather than sup-
pose that Bacon's rules are grounded
on an insufficient analysis of the in-
ductive process. Such, however, will
be seen to be the fact, as soon as it is
considered that Bacon entirely over-
looked Plurality of Causes, All his
rules tacitly imply the assumption,
so contrary to all we now know of
nature, that a phenomenon cannot
have more than one cause.

When he is inquiring into what he
terms the forma caZidi aut frigidi,
gravis aut levis, sicci aut humidi^ and
the like, he never for an instant
doubts that there is some one thing,
some invariable condition or set of
conditions, which is present in all
cases of heat or cold, or whatever
other phenomenon he is considering ;
the only difficulty being to find what
it is, which accordingly he tries to do
by a process of elimination, rejecting
or excluding, by negative instances,
whatever is not the forma or cause, in
order to arrive at what is. But that
this forma or cause is one thing, and
that it is the same in all hot objects,
he has no more doubt of than another
person has that there is always some

■

state

cause or other. In the present
of knowledge it could not be neces-
sary, even if we had not already
treated so fully of the question, to
point out how widely this supposition
is at variance with the truth. It is
particularly unfortunate for Bacon
that, falling into this error, he should
have fixed almost exclusively upon a
class of inquiries in which it was
especially fatal ; namely, inquiries
into the causes of the sensible qua-
lities of objects. For his assump-
tion, groundless in every case, is false
in a peculiar degree with respect to
those sensible qualities. In regard to
scarcely any of them has it been
found possible to trace any unity of
cause, any set of conditions invari-
ably accompanying the quality. The
conjunctions of such qualities with
one another constitute the variety of
Kinds in which, as already remarked,
it has not been found possible to trace
any law. Bacon was seeking for what
did not exist. The phenomenon of
which he sought for the one cause
has oftenest no cause at all, and when
it has, depends (as far as hitherto
ascertained) on an unassignable va-
riety of distinct causes.

And on this rook every •ne must
split who represents to himself as the
first and fundamental problem of
science to ascertain what is the cause
of a given effect, rather than what
are the effects of a given cause. It
was shown, in an early stage of our
inquiry into the nature of Induction,*
how much more ample are the re-
sources which science commands for
the latter than for the former inquiry,
since it is upon the latter only that
we can throw any direct light by
means of experiment ; the power of
artificially producing an effect im-
plying a previous knowledge of a;t
least one of its causes. If we dis-
cover the causes of effects, it is gene-
rally by having previously discovered
the effects of causes ; the greatest
skill in devising crucial instances for

* Svipra, book iii. ch. vii. § 4.

/

FALLACIES OF SIMPLE INSPECTION.

591

the former purpose may only end, as
Bacon's physical inquiries did, in no
result at all. Was it that his eager-
ness to acquire the power of produc-
ing for man's benefit eflfects of practi-
cal importance to human life render-
ing him impatient of pursuing that
end by a circuitous route, made even
him, the champion of experiment, pre-
fer the direct mode, though one of
mere observation, to the indirect, in
which alone experiment was pos-
sible? Or had even Bacon not en-
tirely cleared his mind from the
notion of the ancients, that "rerum
cognoscere caiisas " was the sole ob-
ject of philosophy, and that to inquire
into the effects of things belonged to
servile and mechanical arts ?

It is worth remarking that, while
the only efficient mode of cultivating
speculative science was missed from
an undue contempt of manual opera
tions, the false speculative views thus
engendered gave in their turn a false
direction to such practical and me-
chanical aims as were suffered to exist.
The assumption xiniversal among the
ancients and in the Middle Ages, that
there were principles of heat and cold,
dryness and moisture, &c., led directly
to a belief in alchemy ; in a trans-
mutation of substances, a change from
one Kind into another. Why should
it not be possible to make goM? Each
of the characteristic properties of gold
has its fcmna, its essence, its set of
conditions, which if we could discover,
and learn how to realise, we could
superinduce that particular property
upon any other substance, upon wood,
or iron, or lime, or clay. If, then,
we could effect this with respect to
every one of the essential properties
of the precious metal, we should have
converted the other substance into
gold. Nor did this, if once the pre-
mises were granted, appear to trans-
cend the real powers of mankind. For
daily experience showed that almost
every one of the distinctive sensible
properties of any object, its conaist-
ence, its colour, its taste, its smell,
its shape, admitted of being totally

changed by fire, or water, or some
other chemical agent. The formce of
all those qualities seeming, therefore,
to be within human power either to
produce or to annihilate, not only did
the transmutation of substances ap-
pear abstractedly possible, but the em-
ployment of the power, at our choice,
for practical ends, seemed by no means
hopeless.*

A prejudice, universal in the ancient
world, and from which Bacon was so
far from being free, that it pervaded
and vitiated the whole practical part
of his system of logic, may with good
reason be ranked high in the order of
fallacies of which we are now treating.

§ 8. There remains one a priori
fallacy or natural prejudice, the most
deeply-rooted, perhaps, of all which
we have enumerated : one which not
only reigned supreme in the ancient
world, but still possesses almost un-
disputed dominion over many of the
most cultivated minds ; and some of
the most remarkable of the numerous
instances by which I shall think it
necessary to exemplify it will be
taken from recent thinkers. This is,
that the conditions of a phenomenon
must, or at least probably will, re-
semble the phenomenon itself.

Conformably to what we have before
remarked to be of frequent occurrence,
this fallacy might without much im-
propriety have been placed in a dif-
ferent class, among Fallacies of Gene-
ralisation ; for experience docs afford
a certain degree of countenance to the
assumption. The cause does, in very
many cases, resemble its effect ; like
produces like. Many phenomena have
a direct tendency to perpetuate their
own existence, or to give rise to other
phenomena similar to themselves. Not
to mention forms actually moulded

' • It is hardly needful to remark that
nothitiR i.s here intended to be said against
the possibility at some future period of
niaking gold, by first discovering it to be
a compound, and putting together its dif-
ferent elonients or ingredients. But this
ig a totally different idea from that of tha
seekers of the grand arcanum.

pi

FALLACIES.

on one another*, as impressions on wax
and the like, in which the closest re-
semblance between the effect and its
cause is the very law of the pheno-
menon ; all motion tends to continue
itself, with its own velocity, and in its
own original direction; and the mo-
tion of one body tends to set others
in motion, which is indeed the most
common of the modes in which the
motions of bodies originate. We need
scarcely refer to contagion, fermen-
tation, and the like ; or to the pro-
duction of effects by the growth or
expansion of a germ or rudiment re-
sembling on a smaller scale the com-
pleted phenomenon, as in the growth
of a plant or animal from an embryo,
that embryo itself deriving its origin
from another plant or animal of the
same kind. Again, the thoughts or
reminiscences which are effects of our
past sensations resemble those sen-
sations ; feelings produce similar feel-
ings by the way of sympathy ; acts
produce similar acts by involuntary or
voluntary imitation. With so many
appearances in its favour, no wonder
if a presumption naturally grew up
that causes must necessarily resemble
their effects, and that like could only
be produced by like.

This principle of fallacy has usually
presided over the fantastical attempts
to influence the course of nature by
conjectural means, the choice of which
was not directed by previous observa-
tion and experiment. The guess al-
most always fixed upon some means
which possessed features of real or
apparent resemblance to the end in
view. If a charm was wanted, as by
Ovid's Medea, to prolong life, all long-
lived animals, or what were esteemed
such, were collected and brewed into
a broth : —

.... n«c defuit llllo

Squamea Cinyphii tenuia membrana
ch«lydri

Vivacisqus j«cur cervi : quibus insup©r
addit

Ora capiitque tiovem coruicia sascula

pa8S89.

A similar notion was embodied in
the celebrated medical theory called

the "Doctrine of Signatures," " which
is no less," says Dr. Paris,* " than a
belief that every natural substance
which possesses any medicinal virtue
indicates by an obvious and well-
inarked external character the disease
for which it is a remedy, or the object
for which it should be employed."
This outward character was generally
some feature of resemblance, real or
fantastical, either to the effect it was
supposed to produce, or to the pheno-
menon over which its power was
thought to be exercised. " Thus the
lungs of a fox must be a specific for
asthma, because that animal is re-
markable for its strong powers of re-
spiration. Turmeric has a brilliant
yellow colour, which indicates that it
has the power of curing the jaundice ;
for the same reason, poppies must re-
lieve diseases of the head ; Agaricus
those of the bladder ; Cassia fistula
the affections of the intestines, and
Aristolochia the disorders of the
uterus : the polished surface and
stony hardness which so eminently
characterise the seeds of the Litho-
spermum officinale (common grom-
well) were deemed a certain indica-
tion of their efficacy in calculous and
gravelly disorders ; for a similar rea-
son, the roots of the Saxifraga granu-
lata (white saxifrage) gained reputa-
tion in the cure of the same disease ;
and the Euphrasia (eye -bright) ac-
quired fame as an application in com-
plaints of the eye, because it exhibits
a black spot in its corolla resembling
the pupil The bloodstone, the Helio-
tropium of the ancients, from the occa-
sional small specks or points of a
blood-red colour exhibited on its green
surface, is even at this very day em-
ployed in many parts of England and'
Scotland to stop a bleeding from the
hoso; and nettle -tea continues a popu-
lar remedy for the cure of Urticaria.
It is also asserted that some substances
bear the signatures of the humours,
as the petals of the red rose that of
tha bloody and the roots of rhubarb

* PharmacQlogia, p. 43-45.

i

FALLACIES OF SIMPLE INSPECTION

503

and the flowers of saffron that of the
bile."

The early speculations respecting
the chemical composition of bodies
were rendered abortive by no circum-
stance more than by their invariably
taking for granted that the properties
of the elements must resemble those
of the compounds \<?hich were formed
from them.

To descend to more modern in-
stances ; it was long thought, and
was stoutly maintained by the Carte-
sians, and even by Leibnitz, against
the Newtonian system, (nor did New-
ton himself, as we have 8een, contest
the assumption, but eluded it by an
arbitrary hypothesis,) that nothing
(of a physical nature at least) could
account for motion except previous
motion ; the impulse or impact of
some other body. It was very long
before the scientific world could pre-
vail upon itself to admit attraction
and repulsion {i.e. spontaneous ten-
dencies of particles to approach or
recede from one another) as ultiniate
laws, no more requiring to be ac-
counted for than impulse itself, if
indeed the latter were not, in truth,
resvolvable into the former. From the
same source arose the innumerable
hypotheses devised to explain those
classes of motion which appeared more
mysterious than others because there
was no obvious mode of attributing
them to impulse ; as, for example, the
voluntary motions of the human body.
Such were the interminable systems
of vibrations propagated along the
nerves, or animal spirits rushing up
and down between the muscles and
the brain, which, if the facts could
have been proved, would have been
aa important addition to our know-
ledge of physiological laws ; but the
mere invention or arbitrary supposi-
tion of them could not, unless by the
strongest delusion, be supposed to
render the phenomena of animal life
more comprehensible or less mysteri-
ous. Nothing, however seemed satis-
factory but to make out that motion
was caused by motion ; by something

like itself. If it was not one kind of
motion, it must be another. In like
manner it was supposed that the
physical qualities of objects must
arise from some simi-ar quality, or
perhaps only some quality bearing
the same name, in the particles or
atoms of which the objects were com-'
posed ; that a sharp taste, for ex-
ample, must arise from sharp par-
ticles. And reversing the inference,
the effects produced by a phenomenon
must, it was supposed, resemble in
their physical attributes the pheno-
menon itself. The influences of the
planets were supposed to be analo-
gous to their visible peculiarities :
Mars, being of a red colour, portended
fire and slaughter, and the like.

Passing from physics to meta-
physics, we may notice among the
most remarkable fruits of this d
priori fallacy two closely analogous
theories, employed in ancient and
modern times to bridge over the
chasm between the world of mind
and that of matter : the species sen-
sihilcs of the Epicureans, and the
modern doctrine of perception by
means of ideas. These theories are,
indeed, probably, indebted for their
existence not solely to the fallacy in
question, but to that fallacy combined
with another natural prejudice already
adverted to, that a thing cannot act
where it is not. In both doctrines
it is assumed that the phenomenon
which takes place in us when we see
or touch an object, and which v/e
regard as an effect of that object, or
rather of its presence to our organs,
must of necessity resemble very closely
the outward object itself. To fulfil
this condition, the Epicureans sup-
posed that objects were constantly
projecting in all directions impal-
pable images of themselves, which
entered at the eyes and penetrated
to the mind ; while modern meta-
physicians, though they rejected this
hypothesis, agreed in deeming it neces-
sary to suppose that not the thing
itself, but a mental image or repre-
sentation of it, was the direct object

504

FALLACIES.

of perception. Dr. Reid had to em-
ploy a world of argument and illus-
tration to familiarise people with the
truth that the sensations or impres-
sions on our minds need not neces-
sarily be copies of, or bear any re-
semblance to, the causes which pro-
duce them ; in opposition to the
natural prejudice which led people
to assimilate the action of bodies
upon our senses, and through them
upon oiir minds, to the transfer of
a given form from one object to an-
other by actual moulding. The works
of Dr. Reid are even now the most
effectual course of study for detaching
the mind from the prejudice of which
this was an example. And the value
of the service which he thus rendered
to popular philosophy is not much
diminished although wemay hold, with
Brown, that he went too far in im-
puting the "ideal theory," as an
actual tenet, to the generality of tlie
philosophers who preceded him, and
especially to Locke and Hume ; for
if they did not themselves consciously
fall into the error, unquestionably they
often led their readers into it.

The prejudice that the conditions
of a phenomenon nuist resemble the
phenomenon is occasionally exagger-
ated, at least verbally, into a still
more palpable absurdity ; the condi-
tions of the thing are spoken of as if
they were the very thing itself. In
Bacon's model inquiry, which occu-
pies so great a space in the Novum
Organum, the inquisitio in fwmam
^calidi, the conclusion which he fav-
ours is that heat is a kind of motion ;
meaning of course not the feeling of
heat, but the conditions of the feel-
ing ; meaning, therefore, only that
whenever there is heat, there must
first be a particular kind of motion ;
but he makes no distinction in his
language between these two ideas,
expressing himself as if heat, and the
conditions of heat, were one and the
same thing. So the elder Darwin, in
the beginning of his Zoow^mut, says,
"The word idea has various mean-
ings in the writers of metaphysics :

' no- ™1

it is here used simply for those no
tions of external things which our
organs of sense bring us acquainted
with originally," (thus far the pro-
position, though vague, is unexcep-
tionable in meaning,) " and is defined
a contraction, a motion, or configura-
tion of the fibres which constitute
the immediate organ of sense." Our
notions a configuration of the fibres !
What kind of logician must he be
who thinks that a phenomenon is de-
fined to he the condition on which he
supposes it to depend ? Accordingly
he says soon after, not that our ideas
are caused by, or consequent on, cer-
tain organic phenomena, but "our
ideas are animal motions of the organs
of sense." And this confusion runs
through the four volumes of the Zoono-
mia ; the reader never knows whether
the writer is speaking of the effect,
or of its supposed cause ; of the
idea, a state of mental consciousness,
or of the state of the nerves and
brain which he considers it to pre-
suppose.

I have given a variety of instances
in which the natural prejudice, that
causes and their effects must resemble
one another, has operated in practice
so as to give rise to serious errors. I
shall now go further, and produce
from writings even of the present or
very recent times, instances in which
this prejudice is laid down as an es-
tablished principle. M. Victor Cou-
sin, in the last of his celebrated lec-
tures on Locke, enunciates the maxim
in the following unqualified terms :
" Tout ce qui est vrai de I'effet, est
vrai de la cause." A doctrine to which,
unless in some peculiar and technical
meaning of the words cause and effect,
it is not to be imagined that any per-
son would literally adhere ; but he who
could so write must be far enough from
seeing that the very reverse might
be the effect ; that there is nothing
impossible in the supposition that no
one property which is true of the effect
might be true of the cause. Without
going quite so far in point of expres-
sion, Coleridge, in his Bioyraphia Lite-

J'ALLACIES OF SIMlPtU INSPECTION.

5^5

farta,* affirms as an "evident truth,"
that "the law of causality holds only
between, homogeneous things, i.e.
things having some common pro-
perty," and therefore " cannot extend
from one world into another, its op-
posite : " hence, as mind and matter
have no common property, mind can-
not act upon matter, nor matter upon
mind. What is this but the d pinori
fallacy of which we are speaking ?
The doctrine, like many others of
Coleridge, is taken from Spinoza, in
the first book of whose Ethica (De
Deo) it stands as the Third Proposi-
tion, " Quae res nihil commune inter
se habent, earum una alterius causa
esse non potest," and is there proved
from two so-called axioms, equally
gratuitous with itself ; but Spinoza,
ever systematically consistent, pur-
siied the doctrine to its inevitable
consequence, the materiality of God.

The same conception of impossi-
bility led the ingenious and subtle
mind of Leibnitz to his celebrated
doctrine of a pre-established har-
mony. He, too, thought that mind
could not act upon matter, nor mat-
ter upon mind, and that the two,
therefore, must have been arranged
by their Maker like two clocks, which,
though unconnected with one another,
strike simultaneously, and always
point to the same hour. Malebranche's
equally famous theory of Occasional
Causes was another form of the same
conception : instead of supposing the
clocks originally arranged to strike
together, he held that when the one
strikes, God interposes, and makes
the other strike in correspondence
with it.

Descartes, in like manner, whose
works are a rich mine of almost every
description of d priori fallacy, says
that the Efficient Cause must at least
have all the perfections of the effect,
and for this singular reason : "Si
enim ponamus aliquid in ide4 reperiri
quod non fuerit in ejus caus^, hoc
igitur habet a nihilo ; " of which it is

• Vol. i. chap. 8.

scarcely a parody to say, that if there
be pepper in the soup there must be
pepper in the cook who made it, since
otherwise the pepper would be with-
out a cause. A similar fallacy is com-
mitted by Cicero in his second book
De Finibus, where, speaking in his
own person against the Epicureans,
he charges them with inconsistency
in saying that the pleasures of the
mind had their origin from those of
the body, and yet that the former
were more valuable, as if the effect
could surpass the cause. " Animi
voluptas oritur propter voluptatem
corporis, et major est animi voluptas
quam corporis ? ita fit ut gratulator,
Isetior sit quam is cui gratulatur."
Even that, surely, is not an impos-
sibility : a person'.s good fortune has
often given more pleasure to others
than it gave to the person himself.

Descartes, with no less readiness,
applies the same principle the con-
verse way, and infers the nature of
the effects from the assumption that
they must, in this or that property or
in all their properties, resemble their
cause. To this class belong his specu-
lations, and those of so many others
after him, tending to infer the order
of the universe, not from observation,
but by d priori reasoning from sup-
posed qualities of the Godhead. This
sort of inference was probably never
carried to a greater length than it
was in one particular instance by
Descartes, when, as a proof of one
of his physical principles, that the
quantity of motion in the universe
is invariable, he had recourse to the
immutability of the Divine Nature.
Reasoning of a very similar character
is, however, nearly as common now
as it was in his time, and does duty
largely as a means of fencing off dis-
agreeable conclusions. Writers have
not yet ceased to oppose the theory
of divine benevolence to the evidence
of physical facts, to the principle of
population, for example. And people
seem in general to think that they
have used a very powerful argument
when they have said, that to suppose

5o6

FALLACIES.

some proposition true, would be a re-
flection on the goodness or wisdom
ot the Deity. Put into the simplest
possible terms, their argument is, "If
it had depended on me, I would not
have made the proposition true, there-
fore it is not true." Put into other
words it stands thus : " God is per-
fect, therefore (what I think) perfec-
tion must obtain in nature." But
since in reality every one feels that
nature is very far from perfect, the
doctrine is never applied consistently.
It furnishes an argument which (like
many others of a similar character)
people like to appeal to when it makes
for their own side. Nobody is con-
vinced by it, but each appears to
think that it puts religion on his side
of the question, and that it is a useful
weapon of ofifence for wounding an
adversary.

Although several other varieties of
a priori fallacy might probably be
added to those here specified, these
are all against which it seems neces-
sary to give any special caut^'on. Our
object is to open, without attempting
or affecting to exhaust, the subject.
Having illustrated, therefore, this
first class of Fallacies at sufficient
length, I shall proceed to the second.

CHAPTER IV.

FALLACIES OP OBSERVATION.

§ I. From the fallacies which are
properly Prejudices, or presumptions
antecedent to, and superseding proof,
we pass to those which lie in the
incorrect performance of the proving
process. And as Proof, in its widest
extent, embraces one or more, or all,
of three processes, Observation, Gene-
ralisation, and Deduction, we shall
consider in their order the errora
capable of being committed in these
three operations. And first, of the
first mentioned.

A fallacy of misobservation may
be either negative or positive ; either
Non-observation or Mal-observation.

It is non-observation when all the
error consists in overlooking or ne-
glecting facts or particulars which
ought to have been observed. It is
mal-observation when something is
not simply unseen, but seen wrong ;
when the fact or phenomenon, instead "
of being recognised for what it is
in reality, is mistaken for something
else.

§ 2. Non-observation may either
take place by overlooking instances,
or by overlooking some of the cir-
cumstances of a given instance. If
we were to conclude that a fortune-
teller was a true prophet, from not
adverting to the cases in which his
predictions had been falsified by the
event, this would be non-observation
of instances ; but if we overlooked
or remained ignorant of the fact that
in cases where the predictions had
been fulfilled, he had been in collusion
with some one who had given him
the information on which they were
grounded, this would be non-observa-
tion of circumstances.

The former case, in so far as the
act of induction from insufficient evi-
dence is concerned, does not fall under
this second class of Fallacies, but
under the third, Fallacies of Genera-
lisation. In every such case, however,
there are two defects or errors instead
of one : there is the error of treating
the insufficient evidence as if it were
sufficient, which is a Fallacy of the
third class ; and there is the insuffi-
ciency itself, the not having better
evidence ; which, when such evidence,
or, in other words, when other in-
stances, were to be had, is Non-
observation ; and the erroneous infer-
ence, so far as it is to be attributed '
to this cause, is a Fallacy of the
second class.

It belongs not to o\ir purpose to
treat of non-observation as arising
from casual inattention, from general
slovenliness of mental habits, want of
due practice in the use of the observ-
ing faculties, or insufficient interest
in the subject. The question per-

FALLACIES OF OBSERVATION.

507

tinent to logic is — Granting the want
of complete competency in the d)-
server, on what point is that insuffi-
ciency on his part likely to lead him
wrong? or rather, what sorts of in-
stances, or of circumstances in any
given instance, are most likely to
escape the notice of observers gene-
rally— of mankind at large.

§ 3. First, then, it is evident that
when the instances on one side of a
question are more likely to be remem-
bered and recorded than those on the
other, especially if there be any strong
motive to preserve the memory of the
first, but not of the latter, these last
are likely to be overlooked, and escape
the observation of the mass of man-
kind. This is the recognised explana-
tion of the credit given, in spite of
reason and evidence, to many classes
of impostors — to quack doctors and
fortune-tellers in all ages, to the
" cunning man " of modem times, and
the oracles of old. Few have con-
sidered the extent to which this fal-
lacy operates in practice, even in the
teeth of the most palpable negative
evidence. A striking example of it
is the faith which the uneducated
, portion of the agricultural classes, in
this and other countries, continue to
repose in the prophecies as to weather
supplied by almanac-makers, though
every season affords to them nume-
rous cases of completely erroneous
prediction ; but as every season also
furnishes some cases in which the
prediction is fulfilled, this is enough
to keep up the credit of the prophet
with people who do not reflect on the
immber of instances requisite for
what we have called, in our induc-
tive terminology, the Elimination of
Chance ; since a certain number of
casual coincidences not only may, but
will happen, between any two uncon-
nected events.

Coleridge, in one of the essays in
the Friend, has illustrated the ujatter
we are now considering, in discussing
the origin of a proverb, " which, dif-
ferently worded, is to bo found in all

the languages of Europe," viz. " For-
tune favours fools." He ascribes it
partly to the " tendency to exaggerate
all effects that seem disproportionate
to their visible cause, and all circum-
stances that are in any way strongly
contrasted with our notions of the
persons under them." Omitting some
explanations which would refer the
error to mal-observation or to the
other species of non-observation, (that
of circumstances,) I take up the quo-
tation farther on. *' Unforeseen co-
incidences may have greatly helped a
man, yet if they have done for him
only what possibly from his own
abilities he might have effected for
himself, his good luck will excite less
attention, and the instances be less
remembered. That clever men should
attain their objects seems natural,
and we neglect the circumstances
that perhaps produced that success of
themselves, without the intervention
of skill or foresight ; but we dwell on
the fact and remember it as some-
thing strange, when the same happens
tt> a weak or ignorant man. So too,
though the latter should fail in his
undertakings from concurrences that
might have happened t(i the wisest
man, yet his failure being no more
than might have been expected and
accounted for from his folly, it lays
no hold on our attention, but fleets
away among the other undistinguished
waves in which the stream of ordinary
life murmurs by us, and is forgotten.
Had it been as true as it was notoriously
false, that those all-embracing disco-
veries, which have shed a dawn of
science on the art of chemistry, and
give no obscure promise of some one
great constitutive law, in the light of
which dwell dominion and the power
of prophecy ; if these discoveries, in-
stead of having been, as they really
were, preconcerted by meditation, and
evolved out of his own intellect, had
occurred by a set of lucky accidents
to the illustrious father and founder
of philosophic alchemy ; if they had
presented themselves to Professor
Davy exclusively in consequence of

sod

:p'allacies.

his luch in possessing a particular gal-
vanic battery ; if this battery, as far
as Davy was concerned, had itself
been an accident, and not (as in point
of fact it was) desired and obtained
by him for the purpose of ensuring
the testimony of experience to his
principles, and in order to bind down
material nature under the inquisition
of reason, and force from her, as by
torture, unequivocal answers to 'pre-
pared and preconceived questions, —
3'et still they would not have been
talked of or described as instances of
luck, but as the natural results of his
admitted genius and known skill. But
should an accident have disclosed
similar discoveries to a mechanic at
Birmingham or Sheffield, and if the
man should grow rich in consequence,
and, partly by the envy of his neigh-
bours and partly with good reason,
be considered by them as a man below
par in the general powers of his under-
standing ; then, ' O what a lucky fel-
low ! Well, Fortune does favour fools
-^that's for certain ! It is always so ! '
And forthwith the exclaimer relates
half a dozen similar instances. Thus
accumulating the one sort of facts and
never collecting the other, we do, as
poets in their diction, and quacks of
all denominations do in their reason-
ing, put a part for the whole."

This passage very happily sets forth
the manner in which, under the loose
mode of induction which proceeds per
enumerationem simpUcem, not seeking
for instances of such a kind as to be
decisive of the question, but generalis-
ing from any which occur, or rather
which are remembered, opinions grow
up with the apparent sanction of ex-
perience, which have no foundation in
the laws of nature at all. "Itaque
recte respond it ille," (we may say
with Bacon,*) "qui cum suspensa
tabula in templo ei monstraretur
eorum, qui vota solverant, quod nau-
f ragii periculo elapsi sint, atque inter-
rogando premeretur, anne tum qxiidem
Deorum numen agnosceret, qusesivit

* Kcv. Org., Aph. 46.

denuo, At uhi sunt iUi depicti qui post
vota nuncupata perierunt 1 Eadem
ratio est fere omnis superstitionis, ut
in Astrologicis, in Somniis, Ominibus,
Nemesibus, et hujusmodi ; in quibus,
homines delectati hujusmodi vanita-
tibus, advertunt eventus, ubi implen-
tur ; ast ubi fallunt, licet multo fre-
quentius, tamen negligunt, et praete-:
reunt." And he proceeds to say, that
independently of the love of the m.ar-
vellous, or any other bias in the in-'
clinations, there is a natural tendency
in the intellect itself to this kind of
fallacy, since the mind is more moved
by affirmative instances, though nega-
tive ones are of most use in philoso-
phy : " Is tamen humano intellectui
error est proprius et perpetuus, ut
magis moveatur et excitetur Affirma-
tivis quam Negativis ; cum rite et
ordine sequum se utrique praebere de-
beat ; quin contra, in omni Axiomate
vero constituendo, major vis est in-
stantise negativae."

But the greatest of all causes of
non - observation is a preconceived
opinion. This it is which, in all
ages, has made the whole race of
mankind, and every separate section
of it, for the most part unobservant
of all facts, howev*>r abundant, even
when passing under their own eyes,
which are contradictory to any first
appearance or any received tenet.
It is worth while to recall occasion-
ally to the oblivious memorj* of man-
kind some of the striking instances
in which opinions that the simplest
experiment would have shown to be
erroneous continued to be entertained
because nobody ever thought of try-
ing that experiment. One of the
most remarkable of these was exhi-
bited in the Copernican controversy.
The opponents of Copernicus argued
that the earth did not move, because
if it did, a stone let fall from the top
of a high tower would not reach the
ground at the foot of the tower, but
at a little distance from it, in a con-
trary direction to the earth's course ;
in the same manner (said they) as, if
a ball is let drop from the mast-head

FALLACIES OF OBSERVATION.

509

while the ship is in full sail, it does
not fall exactly at the foot of the
mast, but nearer to the stem of the
vessel. The Copernicans would have
silenced these objectors at once if they
had tried dropping a ball from the
mast-head, since they would have
found that it does fall exactly at the
foot, as the theory requires : but no ;
they admitted the spurious fact and
struggled vainly to make out a dif-
ference between the two cases. " The
ball was no part of the ship — and
the motion forward was not natural,
either to the ship or to the ball. The
stone, on the other hand, let fall from
the top of the tower was a part of
the earth, and, therefore, the diurnal
and annular revolutions which were
natural to the earth were also natural
to the stone : the stone would, there-
fore, retain the same motion with the
tower, and strike the ground precisely
at the bottom of it." *

Other examples, scarcely less strik-
ing, are recorded by Dr. Whewell,t
where imaginary laws of nature have
continued to be received as real,
merely because no person had steadily
looked at facts which almost every one
had the opportunity of observing. "A
vague and loose mode of looking at
facts very easily observable, left men
for a long time under the belief that
a body ten times as heavy as another
falls ten times as fast ; that objects
immersed in water are always magni-
fied, without regard to the form of
the surface ; that the magnet exerts
an irresistible force ; that crystal is
always found associated with ice, and
the like. These and many others are
examples how blind and careless man
can be even in observation of the
plainest and commonest appearances,
and they show us that the mere facul-
ties of perception, although constantly
exercised upon innumerable objects,
may long fail in leading to any exact
knowledge."

If even on physical facts, and these
of the most obvious character, the

* Play fair's Diisertation, sect. 4.
t Nov. Org. Renov., p. 61.

observing faculties of mankind can
be to this degree the passive slaved
of their preconceived impressions, w6
need not be surprised that this should
be so lamentably true as all experi-
ence attests it to be, on things more
nearly connected with their stronger
feelings— on moral, social, and reli-
gious subjects. The information
which an ordinary traveller bring.'*
back from a foreign country, as the
result of the evidence of his senses^
is almost always such as exactly con-
firms the opinions with which he sets
out. He has had eyes and ears for
such things only as he expected to
see. Men read the sacred books of
their religion, and pass unobserved
therein multitudes of things utterly
irreconcilable with even their own
notions of moral excellence. With
the same authorities before them, dif-
ferent historians, alike innocent of in-
tentional misrepresentation, see only
what is favourable to Protestants or
Catholics, Royalists or Republicans,
Charles I. or Cromwell ; while others,
having .set out with the preconception
that extremes must be in the wrong,
are incapable of seeing truth and jus-
tice when these are wholly on one side.
The influence of a preconceived the-
ory is well exemplified in the super-
stitions of barbarians respecting the
virtues of medicaments and charms.
The negroes, among whom coral, as
of old among ourselves, is worn as an
amulet, affirm, according to Dr. Paris,*
that its colour " is always affected by
the state of health of the wearer, it
becoming paler in disease." On a
matter open to universal observation, '
a general proposition which has not
the smallest vestige of truth is re- '
ceived as a result of experience ; the
preconceived opinion preventing, it
would seem, any observation what-
ever on the subject

§ 4. For illustration of the first
species of non-observation, that of In-
stances, what has now been stated

* Pharmacologia, p. 21. '

5IO

FALLACIES.

may suflRce. But there may also he
non -observation of some material cir-
cum tances in instances which have
not been altogether overlooked — nay,
which may be the very instances on
which the whole superstructure of a
theory has been founded. As, in the
cases hitherto examined, a general
proposition was too rashly adopted,
on the evidence of particulars, true
indeed, but insufficient to support it ;
so in the cases to which we now turn,
the particulars themselves have been
imperfectly observed, and the singular
propositions on which the generalisa-
tion is grounded, or some at least of
those singular propositions, are false.

Such, for instance, was one of the
mistakes committed in the celebrated
phlogistic theory — a doctrine which
accounted for combustion by the ex-
trication of a substance called phlo-
giston, supposed to be contained in all
combustible matter. The hjrpothesis
accorded tolerably well with superfi-
cial appearances : the ascent of flame
naturally suggests the escape of a sub-
stance ; and the visible residuum of
ashes, in bulk and weight, generally
falls extremely short of the combus-
tible material. The error was, non-
observation of an important portion
of the actual residue, namely, the
gaseous products of combustion.
When these were at last noticed and
brought into account, it appeared to
be an universal law that all substances
gain instead of losing weight by under-
going combustion ; and after the usual
attempt toaccommodatethe old theory
to the new fact by means of an arbi-
trary hypothesis, (that phlogiston had
the quality of positive levity instead
of gravity,) chemists were conducted
to the true explanation, namely, that
instead of a substance separated, there
was, on the contrary, a substance ab-
sorbed.

Many of the absurd practices which
have been deemed to possess medi-
cinal efficacy have been indebted for
their reputation to non-observance
of some accompanying circumstance
which was the real agent in the cures

ascribed to them. Thus, of the sym-
pathetic powder of Sir Kenelm Digby :
*' Whenever any wound had been in-
flicted, this powder was applied to the
weapon that had inflicted it, which
was, moreover, covered with ointment,
and dressed two or three times a day.
The wound itself, in the meantime,
was directed to be brought together,
and carefully bound up with clean
linen rags, but ab(»;e all, to he let alone
for seven days, at the end of which
period the bandages were removed,
when the wound was generally found
perfectly united. The triumph of the
cure was decreed to the mysterious
agency of the sympathetic powder
which had been so assiduously ap-
plied to the weapon, whereas it is
hardly necessary to observe that the
promptness of the cure depended on
the total exclusion of air from the
wound, and upon the sanative opera-
tions of nature not having received
any disturbance from the officious in-
terference of art. The result, beyond
all doubt, furjiished the first hint
which led surgeons to the improved
practice of healing wounds by what is
technically called the,^rs^ intention." *
" In all records," adds Dr. Paris, " of
extraordinary cures performed by mys-
terious agents, there is a great desire
to conceal the remedies and other
curative means which were simultane-
ously administered with them ; thus
Oribasius commends in high terms a
necklace of Paeony root for the cure
of epilepsy ; but we learn that he al-
ways took care to accompany its use
with copious evacuations, although he
assigns to them no share of credit in
the cure. In later times we have
a good specimen of this species of
deception presented to us in a work
on scrofula by Mr. Morley, written,
as we are informed, for the sole pur-
pose of restoring the much injured
character and use of the Vervain ; in
which the author directs the root of
this plant to be tied with a yard of
white satin riband round the neck,'

* Pharmacologia, p. 23-24.

FALLACIES OF OBSERVATION.

where it is to remain until the patient
is cured ; but mark — during this in-
terval he calls to his aid the most
active medicines in the materia me-
dica." *

In other cases the cures really pro-
duced by rest, regimen, and amuse-
ment, have been ascribed to the
medicinal, or occasionally to the su-
pernatural, means which were put
in requisition. "The celebrated John
Wesley, while he commemorates the
triumph of sulphur and supplication
over his bodily infirmity, fors^ets to
appreciate the resuscitating influence
of four months' repose from his apos-
tolic labours ; and such is the disposi-
tion of the human mind to place con-
fidence in the operation of mysterious
agents, that we find him more dis-
posed to attribute his cure to a brown
paper plaister of egg and brimstone,
than to Dr. Fothergiirs salutary pre-
scription of country air, rest, asses'
milk, and liorse exercise." +

In the following example, the cir-
cumstance overlooked was of a some-
what different character. "When
the yellow fever raged in America,
the practitioners trusted exclusively
to the copious use of mercury ; at
first this plan was deemed so univers-
ally efficacious, that, in the enthusiasm
of the moment, it was triumphantly
proclaimed that death never took
place after the mercury had evinced
its effect upon the system ; all this
was very true, but it furnished no
proof of the efficacy of that metal,
since the disease in its aggravated
form was so rapid in its career, that
it swept away its victims long before
the system could be brought under
mercurial influence, while in its milder
shape it passed off equally well with-
out any assistance from art." t

In these examples the circumstance
overlooked was cognisable by the
senses. In other cases, it is one the
knowledge of which could only be
arrived at by reasoning ; but the

* Pharmacologia, p. 38.
t Jbid., p. 62.
t Jbid., p. 6i-6».

fallacy may still be classed under
the head to which, for want of a
more appropriate name, we have given
the appellation Fallacies of Non -ob-
servation. It is not the nature of
the faculties which ought to ha\ e been
employed, but the non-employment of
them, which constitutes this Natural
Order of Fallacies. Wherever the
error is negative, not positive ; wher-
ever it consists especially in overlook-
ing, in being ignorant or unmindful
of some fact which, if known and
attended to, would have made a differ-
ence in the conclusion arrived at ;
the error is properly placed in the
class which we are considering. In
this class there is not, as in all other
fallacies there is, a positive mis-esti-
mate of evidence actually had. The
conclusion would be just, if the por-
tion which is seen of the case were
the whole of it ; but there is another
portion overlooked, which vitiates the
result.

For instance, there is a remarkable
doctrine which has occasionally found
a vent in the public speeches of un-
wise legislators, but which only in
one instance that I am aware of has
received the sanction of a philosophi-
cal writer, namely M. Cousin, who in
his preface to the Gorgias of Plato,
contending that punishment must
have some other and higher justifi-
cation than the prevention of crime,
makes use of this argument— that if
punishment were only for the sake
of example, it would be indifferent
whether we punished the innocent or
the guilty, since the punishment, con-
sidered as an example, is equally effi-
cacious in either case. Now we must,
in order to go along with this reason-
ing, suppose, that the person who
feels himself under temptation, ob-
serving somebody punished, concludes
himself to be in danger of being
punished likewise, and is terrified ac-
cordingly. But it is forgotten that
if the person punished is supposed to
be innocent, or even if there be any
doubt of his guilt, the spectator will
reflect that his own danger, whatever

512

FALLACIES.

it may be, is not contingent on his
guiltiness, but threatens him equally
it he remains innocent, and how there-
fore is he deterred from guilt by the
apprehension of such punishment?
M. Cousin supposes that people will
be dissuaded from guilt by whatever
renders the condition of the guilty
more perilous, forgetting that the
condition of the innocent (also one of
the elements in the calculation) is, in
the case supposed, made perilous in
precisely an equal degree. This is a
fallacy of overlooking ; or of non-
observation, within the intent of our
classification.

Fallacies of this description are
the great stumbling-block to correct
thinking in political economy. The
economical workings of society afford
numerous cases in which the effects
of a cause consist of two sets of phe-
nomena : the one immediate, concen-
trated, obvious to all eyes, and pass-
ing, in common apprehension, for the
whole effect ; ♦he other widely dif-
fused, or lying deeper under the sur-
face, and which is exactly contrary to
the former. Take, for instance, the
common notion, so plausible at the
first glance, of the encouragement
given to industry by lavish expendi-
ture. A, who spends his whole in-
come, and even his capital, in expen-
sive living, is supposed to give great
employment to labour. B, who lives
on a small portion, and invests the
remainder in the funds, is thought
to give little or no employment ; for
everybody sees the gains which are
made by A's tradesmen, servants, and
others, while his money is spending.
B's savings, on the contrary, pass into
the hands of the person whose stock
he purchased, who with it pays a debt
he owed to some banker, who lends
it again to some merchant or manu-
facturer ; and the capital being laid
out in hiring spinners and weavers,
or carriers and the crews of merchant
vessels, not only gives immediate em-
ployment to at least as much industry
as A employs during the whole of his
career, but, coming back with increase

by the sale of the goods which have
been manufactured or imported, forms
a fund for the employment of the
same, and perhaps a greater quantity
of labour in perpetuity. But the ob-
server does not see, and therefore does
not consider what becomes of B's
money ; he does see what is done with
A's ; he observes the amount of in-
dustry which A's profusion feeds ; he
observes not the far greater quantity
which it prevents from being fed ;
and thence the prejudice, universal to
the time of Adam Smith, that prodi-
gality encourages industry, and par-
simony is a discouragement to it.

The common argument against free
trade was a fallacy of the same na-
ture. The purchaser of British silk
encourages British industry ; the pur-
chaser of Lyons silk encourages only
French ; the former conduct is patrio-
tic, the latter ought to be prevented
by law. The circumstance is over-
looked that the purchaser of any
foreign commodity necessarily causes,
directly or indirectly, the export of
an equivalent value of some article of
home production (beyond what would
otherwise be exported) either to the
same foreign country or to some
other ; which fact, though from the
complication of the circumstances it
cannot always be verified by specific
observation, no observation can pos-
sibly be brought to contradict, while
the evidence of reasoning on which it
rests is irrefragable. The fallacy is,
therefore, the same as in the preced-
ing case, that of seeing a part only of
the phenomena, and imagining that
part to be the whole, and may be
ranked among Fallacies of Non-ob-
servation.

§ 5. To complete the examination
of the second of our five classes, we
have now to speak of mal-observa-
tion, in which the error does not lie
in the fact that something is unseen,
but that something seen is seen wrong.

Perception being infallible evidence
of whatever is really perceived, the
error now under consideration can be

FALLACIES OF OBSERVATION.

513

committed no otherwise than by mis-
taking for conception what is in fact
inference. We have formerly shown
how intimately the two are blended
in almost everything which is called
observation, and still more in every
Description.* What is actually on
any occasion perceived by our senses
being so minute in amount, and gene-
rally so unimportant a portion of the
state of facts which we wish to ascer-
tain or to communicate, it would be
absurd to say that either in our ob-
servations or in conveying their result
to others, we ought not to mingle in-
ference with fact ; all that can be
said is, that when we do so we ought
to be aware of what we are doing,
and to know what part of the asser-
tion rests on consciousness, and is
therefore indisputable, what part on
inference, and is therefore question-
able.

One of the most celebrated ex-
amples of an universal error pro-
duced by mistaking an inference for
the direct evidence of the senses was
the resistance made, on the ground
of common sense, to the Copernican
system. People fancied they saw the
sun rise and set, the stars revolve in
circles round the pole. We now
know that they saw no such thing ;
what they really saw was a set of ap-
pearances equally reconcilable with
the theory they held and with a to-
tally different one. It seems strange
that such an instance as this, of the
testimony of the senses pleaded with
the most entire conviction in favour
of something which was a mere infer-
ence of the judgment, and, as it turned
out, a false inference, should not have
opened the eyes of the bigots of com-
mon sense, and inspired them with a
more modest distrust of the compe-
tency of mere ignorance to judge the
conclusions of cultivated thought.

In proportion to any person's defi-
ciency of knowledge and mental culti-
vation is generally his inability to
discriminate between his inferences

* Supra, p. 42».

and the perceptions on which they
were grounded. Many a marvellous
tale, many a scandalous anecdote,
owes its origin to this incapacity.
The narrator relates, not what he
saw or heard, but the impression
which he derived from what he saw
or heard, and of which perhaps the
greater part consisted of inference,
though the whole is related not as
inference but as matter of fact. The
difficulty of inducing witnesses to
restrain within any moderate limits
the intermixture of their inferences
with the narrative of their percep-
tions is well known to experienced
cross-examiners ; and still more is
this the case when ignorant persons
attempt to describe any natural phe-
nomenon. " The simplest narrative,"
says Dugald Stewart,* '*of the nio.<t
illiterate observer involves more or
less of hypothesis ; nay, in general it
will be found that, in proportion to
his ignorance, the greater is the num-
ber of conjectural principles involved
in his statements. A village apothe-
cary (and, if possible, in a still greater
degree, an experienced nurse) is sel-
dom able to describe the plainest case
without employing a phraseology of
which every word is a theory ; where-
as a simple and genuine specifica-
tion of the phenomena which mark
a particular disease, a specification
unsophisticated by fancy or by pre-
conceived opinions, may be regarded
as unequivocal evidence of a mind
trained by long and successful study
to the most difficult of all arts, that
of the faithful interpretation of na-
ture."

The universality of the confusion
between perceptions and the infer-
ences drawn from them, and the
rarity of the power to discriminate
the one from the other, ceases to sur-
prise us when we consider that in the
far greater number of instances the
actual perceptions of our senses are of
no importance or interest to us except
as marks from which we infer some-

' Elements of the Philosophy of the Mind,
ToL ii. cU. 4, sect. 5.

2^

5M

FALLACIES.

thing beyond them. It is not the
colour and superficial extension per-
ceived by the eye that are important
to us, but the object of which those
visible appearances testify the pre-
sence ; and where the sensation itself
is indifferent, as it generally is, we
have no motive to attend particularly
to it, but acquire a habit of passing it
over without distinct consciousness,
and going on at once to the inference.
So that to know what the sensation
actually was is a study in itself, to
which painters, for example, have to
train themselves by special and long-
continued discipline and application.
In things further removed from the
dominion of the outward senses, no
one who has not great experience in
psychological analysis is competent to
break this intense association ; and
when such analytic habits do not
exist in the requisite degree, it is
hardly possible to mention any of the
habitual judgments of mankind on
subjects of a high degree of abstrac-
tion, from the being of a God and the
immortality of the soul down to the
multiplication table, which are not,
or have not been, considered as mat-
ter of direct intuition. So strong is
the tendency to ascribe an intuitive
chaiacter to judgments which are
mere inferences, and often false ones.
No one can doubt that many a de-
luded visionary has actually believed
that he was directly inspired from
Heaven, and that the Almighty had
conversed with him face to face ;
which yet was only, on his part, a
conclusion drawn from appearances
to his senses, or feelings in his inter-
nal consciousness, which afforded no
warrant for any such belief. A cau-
tion, therefore, against this class of
errors is not only needful but indis-
pensable ; though to determine whe-
ther, on any of the great questions of
metaphysics, such errors are actually
committed, belongs not to this place,
but, as I have so often said, to a dif-
ferent science.

CHAPTER V.

FALLACIES OF GENERALISATION.

§ I. The class of Fallacies of which
we are now to speak is the most ex-
tensive of all; embracing a greater
number and variety of unfounded in-
ferences than any of the other classes,
and which it is even more difficult to
reduce to sub-classes or species. If
the attempt made in the preceding
Books to define the principles of well-
grounded generalisation has been suc-
cessful, all generalisations not con-
formable to those principles might, in
a certain sense, be brought under the
present class : when, however, the
rules are known and kept in view, but
a casual lapse committed in the appli-
cation of them, this is a blunder, not
a fallacy. To entitle an error of gene-
ralisation to the latter epithet, it must
be committed on principle; there must
lie in it some erroneoxis general con-
ception of the inductive process ; the
legitimate mode of drawing conclu-
sions from observation and experi-
ment must be fundamentally miscon-
ceived.

Withoxit attempting anything so
chimerical as an exhaustive classifica-
tion of all the misconceptions which
can exist on the subject,, let us con-
tent ourselves with noting, among the
cautions which might be suggested, a
few of the most useful and needful.

§ 2. In the first place, there are cer-
tain kinds of generalisation which,
if the principles already laid down be
correct, must be groundless : experi-
ence cannot afford the necessary con-
ditions for establishing them by a cor-
rect induction. Such, for instance,
are all inferences from the order of
nature existing on the earth, or in
the solar system, to that which may
exist in remote parts of the universe ;
where the phenomena, for aught we
know, may be entirely different, or
may succeed one another according to
different laws, or even according to no
fixed Jaw ^t all. Such, again, in mat-

I

I

I

FALLACIES OF GENERALISATION.

51S

ters dependent on causation, are all
* universal negatives, all propositions
that assert impossibility. The non-
existence of any given phenomenon,
however uniformly experience may as
yet have testified to the fact, proves
at most that no cause adequate to its
production has yet manifested itself ;
but that no such causes exist in nature
can only be inferred if we are so fotJ-
ish as to suppose that we know all
the forces in nature. The supposition
would at least be premature while our
acquaintance with some, even of those
which we do know, is so extremely re-
cent. And, however much our know-
ledge of nature may hereafter be ex-
tended, it is not easy to see how that
knowledge could ever be complete, or
how, if it were, we could ever be as-
sured of its being so.

The only laws of nature which afford
sufficient warrant for attributing im-
possibility (even with reference to the
existing order of nature, and to our
own region of the universe) are, first,
those of number and extension, which
are paramount to the laws of the suc-
cession of phenomena, and not exposed
to the agency of counteracting causes ;
and, secondly, the universal law of
causality itself. That no variation in
any effect or consequent will take place
while the whole of the antecedents re-
main the same, may be affirmed with
full assurance. But that the addition
of some new antecedent might not
entirely alter and subvert the accus-
tomed consequent, or that antecedents
competent to do this do not exist in
nature, we are in no case empowered
positively to conclude.

§ 3. It is next to be remarked that
all generalisations which pi-ofess, like
the theories of Thales, Democritus,
and others of the early Greek specula-
tors, to resolve all things into some one
element, or, like many modern theories,
to resolve phenomena radically differ-
ent into the same, are necessarily false.
By radically different phenomena T
mean impressions on our senses which
differ in quality, and not merely in de-

gree. On this subject what appeared
necessary was said in the chapter on
the Limits to the Explanation of Laws
of Nature ; but as tlie fallacy is even
in our own times a common one, I
shall touch on it somewhat further ia
this place.

When we gay that the force which
retains the planets in their orbits is
resolved into gravity, or that tlie
force which makes substances combine
chemically is resolved into electricity,
we assert in the one case what is, and
in the other case what might, and
probably will ultimately, be a legiti-
mate result of induction. In both
these cases motion is resolved into
motion. The assertion is, that a case
of motion, which was supposed to be
special and to follow a distinct law of
its own, conforms to and is included in
the general law which regulates an-
other class of motions. But, from these
and similar generalisations, counten-
ance and currency have been given to
attempts to resolve, not motion into
motion, but heat into motion, light into
motion, sensation itself into motion ;
states of consciousness into states of
the nervous system, as in the ruder
forms of the Materialist philosophy ;
vital phenomena into mechanical or
chemical processes, as in some schools
of physiology.

Now I am far from pretending that
it may not be capable of proof, or that
it is not an important addition to
our knowledge if proved, that cer-
tain motions in the particles of bodies
are the conditions of the production
of heat or light ; that certain assign-
able physical modifications of the
nerves may be the conditions not only
of our sensations and emotions, but
even of our thoughts ; that certain
mechanical and chemical conditions
may, in the order of nature, be suf-
ficient to determine to action the phy-
siological laws of life. All, I insist
upon, in common with every thinker
who entertains any clear idea of the
logic of science, is that it shall not be
supposed that by proving these things
one step would be niade towards fv re^J

Si6

fallacies;

explanation of heat, light, or sensa-
tion ; or that th6 generic peculiarity
of those phenomena can be in the least
degree evaded by any such discoveries,
however well established. Let it be
shown, for instance, that the most
complex series of physical causes and
effects succeed one another in the eye
and in the brain to produce a sensa-
tion of colour ; rays falling on the eye,
refracted, converging, crossing one an-
other, making an inverted image on
the retina, and after this a motion —
let it be a vibration, or a rush of ner-
vous fluid, or whatever else you are
pleased to suppose, along the optic
nerve — a propagation of this motion
to the brain itself, and as many more
dififerent motions as you choose ; still
at the end of these motions there is
something which is not motion — there
is a feeling or sensation of colour.
Whatever number of motions we may
be able to interpolate, and whether
they be real or imaginary, we shall
still find, at the end of the series, a
motion antecedent and a colour con-
sequent. The mode in which any one
of the motions produces the next may
possibly be susceptible of explanation
by some general law of motion ; but
the mode in which the last motion
produces the sensation of colour can-
not be explained by any law of mo-
tion ; it is the law of colour, which
is, and must always remain, a peculiar
thing. Where our consciousness re-
cognises between two phenomena an
inherent distinction ; where we are
sensible of a difference which is not
merely of degree, and feel that no add-
ing one of the phenomena to itself
would produce the other ; any theory
which attempts to bring either under
the laws of the other must be false ;
though a theory which merely treats
the one as a cause or condition of the
other may possibly be true.

§ 4. Among the remaining forms
of erroneoiis generalisation, several of
those most worthy of and most re-
quiring notice have fallen under our
examination in former places, where,

in investigating the rules of correct
induction, we have had occasion to
advert to the distinction between it
and some common mode of the incor-
rect. In this number is what I have
formerly called the natural induction
of uninquiring minds, the induction
of the ancients, which proceeds 'per
ennmerationein simplicem : "This, that,
and the other A are B, I cannot think
of any A which is not B, therefore
every A is B." As a final condemna-
tion of this rude and slovenly mode
of generalisation, I will quote Bacon's
emphatic denunciation of it ; the most
important part, as I have more than
once ventured to assert, of the perma-
nent service rendered by him to philo-
sophy. " Inductio quae procedit per
enumerationem simplicem, res puerilis
est, et precario concludit," (concludes
only by yourleave, or provisionally,) " et
periculo exponitor ab instantia con-
tradictori^ et plerumque secundum
pauciora quam parest, et exhistantwn-
modoquceprcEsto sunt pronunciat. At ^m
Inductio quae ad inventionem et de- fl
monstrationem Scientiarum et Artium V
erit utilis, Naturam separare debet, per
rejectiones et exclusiones debitas ; ac
deinde post negativas tot quot suffi-
ciunt, super affirmativas concludere."

I have already said that the mode h
of Simple Enumeration is still the flj
common and received method of In- ™l
duction in whatever relates to man
and society. Of this a very few in-
stances, more by way of memento than
of instruction, may suffice. What,
for example, is to be thought of all
the " common - sense " maxims for
which the following may serve as the
universal formula, "Whatsoever has
never been, will never be " ? As, for
example : Negroes have never been as
civilised as whites sometimes are,
therefore it is impossible they should
be so. Women, as a class, are sup-
posed not to have hitherto been equal
in intellect to men, therefore they are
necessarily inferior. Society cannot
prosper without this or the other insti-
tution ; e.g, in Aristotle's time, with-
out slavery ; in later times, without

FALLACIES OF GENERALISATION.

5J7

an established priesthood, without arti-
ficial distinctions of rank, &c One
poor person in a thousand educated,
while the nine hundred and ninety-
nine remain uneducated, has usually
aimed at raising himself out of his
class, therefore education makes people
dissatisfied with the condition of a
labourer. Bookish men, taken from
speculative pursuits and set to work
on something they know nothing
about, have generally been found or
thought to do it ill ; therefore pliilo-
sophers are unfit for business, &c., &c.
All these are inductions by simple
enumeration. Reasons having some
reference to the canons of scientific
investigation have been attempted to
be given, however unsuccessfully, for
some of these propositions ; but to the
multitude of those who parrot them,
the cnumeratio simplex, ex his tan-
tummodo quce prcesto sunt pronuncians,
is the sole evidence. Their fallacy
consists in this, that they are induc-
tions without elimination : there has
been no real comparison of instances,
nor even ascertainment of the material
facts in any given instance. There is
also the further error of forgetting
that such g»eneralisations, even if well
established, could not be ultimate
truths, but must be results of laws
much more elementary ; and there-
fore, until deduced from such, could
at most be admitted as empirical
laws, holding good within the limits
of space and time by which the par-
ticular observations that suggested
the generalisations were bounded.

This error of placing mere empirical
laws, and laws in which there is no
direct evidence of causation, on the
same footing of certainty as laws of
cause and effect, an error which is
at the root of perhaps the greater
number of bad inductions, is exempli-
fied only in its grossest form in the
kind of generalisations to which we
have now referred. These, indeed,
do not possess even the degree of
evidence which pertains to a well-
ascertained empirical law, but admit
of refutation on the empirical ground

itself, without ascending to casual
laws. A little reflection, indeed, will
show that mere negations can only
form the ground of the lowest and
least valuable kind of empirical law.
A phenomenon has never been no-
ticed : this only proves that the con-
ditions of that phenomenon have not
yet occurred in experience, but does
not prove that they may not occur
hereafter. There is a better kind
of empirical law than this, namely,
when a phenomenon which is observed
presents within the limits of observa-
tion a series of gradations, in which a
regularity, or something like a ma-
thematical law, is perceptible, from
which, therefore, something may be
rationally presumed as to those terms
of the series which are beyond the
limits of observation. But in nega-
tion there are no gradations and no
series : the generalisations, therefore,
which deny the possibility of any
given condition of man and society
merely because it has never yet been
witnessed, cannot possess this higher
degree of validity even as empirical
laws. What is more, the minuter
examination which that higher order
of empirical laws presupposes, being
applied to the subject-matter of these,
not only does not confirm, but actually
refutes them. For in reality the past
history of Man and Society, instead
of exhibiting them as immovable, un-
changeable, incapable of ever present-
ing new phenomena, shows them on
the contrary to be, in many most im-
portant particulars, not only change-
able, but actually \mdergoing a pro-
gressive change. The empirical law,
therefore, best expressive, in most
cases, of the genuine result of ob-
servation, would be, not that sucli
and such a phenomenon will continue
unchanged, but that it will continue
to change in some particular manner.
Accordingly, while almost all gene-
ralisations relating to Man and So-
ciety, antecedent to the last fifty or
sixty years, have erred in the gross
way which we have attempted to
characterise, namely, by implicitly

5i8

FAL^ACtES.

assuming that human nature arid so-
ciety will for ever revolve in the same
orbit, and exhibit essentially the same
phenomena — which is also the vul-
gar error of the ostentatiously practi-
cal, the votaries of so-called common
sense, in our day, especially in Great
Britain — the more thinking minds
of the present age, having applied a
more minute analysis to the past re-
cords of our race, have for the most
part adopted a contrary opinion, that
the human species is in a state of ne-
cessary progression, and that from the
terms of the series which are past we
may infer positively those which are
yet to come. Of this doctrine, con-
sidered as a philosophical tenet, we
shall have occasion to speak more
fully in the concluding Book. If not,
in all its forms, free from error, it is
at least free from the gross and stupid
error which we previously exemplified.
But, in all except the most eminently
philosophical minds, it is infected with
precisely the same kind of fallacy as
that is. For we must remember that
even this other and better generalisa-
tion, the progressive change in the
condition of the human species, is,
after all, bxit an empirical law, to
which, too, it is not difficult to point
out exceedingly large exceptions; and
even if these could be got rid of, either
by disputing the facts or by explaining
and limiting the theory, the general
objection remains valid against the
supposed law, as applicable to any
other than what, in our Third Book,
were termed Adjacent Cases. For
not only is it no ultimate, but not
even a causal law. Changes do in-
deed take place in human affairs, but
every one of those changes depends on
determinate causes ; the *' progres-
siveness of the species " is not a cause,
but a summary expression for the
general result of all the causes. So
soon as, by a quite different sort of
induction, it shall be ascertained what
causes have produced these successive
changes from the beginning of his-
tory, in so far as they have really
taken place, and by what cauBes of a

contrary tendency they haV6 been-
occasionally checked or entirely coun-
teracted, we may then be prepared to
predict the future with reasonable
foresight ; we may be in possession of
the real laxv of the future, and may
be able to declare on what circum-
stances the continuance of the same
onward movement will eventually de-
pend. But this it is the error of many
of the more advanced thinkers in the
jiresent age to overlook, and to ima-
gine that the empirical law collected
from a mere comparison of the condi-
tion of our species at different past
-imes is a real law, is the law of its
changes, not only past, but also to
come. The truth is, that the causes
on which the phenomena of the moral
world depend are in every age, and
almost in every coimtry, combined in
some different proportion ; so that it
is scarcely to b* expected that the
general result of them all should con-
form very closely, in its details at
least, to any uniformly progressive
series. And all generalisations which
affirm that mankind have a tendency
to grow better or worse, richer or
poorer, more cultivated or more barba-
rous ; that population increases faster
than subsistence, or subsistence than
population ; that inequality of fortune
has a tendency to increase or to break
down, and the like — propositions of
considerable value as empirical laws
within certain (but generally rather
narrow) limits — are in reality true or
false according to times and circum-
stances.

What we have said of empirical
generalisations from times past to
times still to come, holds equally true
of similar generalisations from present
times to times past ; when persons
whose acquaintance with moral and
social facts is confined to their own
age, take the men and the things of
that age for the type of men and
things in general, and apply without
scruple to the interpretation of the
events of history the empirical laws
which represent suflSciently for daily
guidance the common phenomena of

I

FALLACIES OF GENEKALISATIOK.

51^

human nature at that time and in
that particular state of society. If
examples are wanted, almost every
historical work, until a very recent
period, abounded in them. The same
may be said of those who generalise
empirically from the people of their
own country to the people of other
countries, as if human beings felt,
judged, and acted everywhere in the
same manner.

§ 5. In the foregoing instances, the
distinction is confounded between em-
pirical laws, which express merely
the customary order of the succession
of effects, and the laws of causation
on which the effects depend. There
may, however, be incorrect generali-
sation when this mistake is not com-
mitted ; when the invebtigation takes
its proper direction, that of causes,
and the result erroneously obtained
purports to be a really causal law.

The most vulgar form of this fal-
lacy is that which is commonly called
2wst hoc, ergo propter hoc, or cum hoc,
ergo propter hoc. As when it was in-
ferred that England owed her indus-
trial pre-eminence to her restrictions
on commerce ; as when the old school
of financiers and some speculative
writers maintained that the national
debt was one of the causes of national
prosperity ; as when the excellence of
the Church, of the Houses of Lords
and Commons, of the procedure of the
law courts, &c., were inferred from
the mere fact that the country had
prospered under them. In such cases
as these, if it can be rendered pro-
bable by other evidence that the sup-
posed causes have some tendency to
produce the effect ascribed to them,
the fact of its having been produced,
though only in one instance, is of
some value as a verification by spe-
cific experience ; but in itself it goes
scarcely any way at all towards estab-
lishing such a tendency, since, admit-
ting the effect, a hundred other ante-
cedents could show an equally strong
title of that kind to be considered as
the cause.

In these examples we see bad
generalisation d posteriori, or empiri-
cism properly so called : causation in-
ferred from casual conjunction, with-
out either due elimination, or any
presumption arising from known pro-
perties of the supposed agent. But
bad generalisation d priori is fully
as common, which is properly called
false theory ; conclusions drawn, by
way of deduction, from properties of
some one agent which is known or
supposed to be present, all other co-
existing agents being overl(X)ked. As
the former is the error of sheer ig-
norance, so the latter is especially
that of semi-instructed minds, and is
mainly committed in attempting to
explain complicated phenomena by a
simpler theory than their nature ad-
mits of. As when one school of phy-
sicians sought for the universal prin-
ciple of all disease in "lentor and
morbid viscidity of the blood," and
imputing most bodily derangements
to mechanical obstructions, thought
to cure them by mechanical reme-
dies ; * while another, the chemical
school, "acknowledged no source of
disease but the presence of some hos-
tile acid or alkali, or some deranged
condition in the chemical composi-
tion of the fluid or solid parts," and
conceived, therefore, that "all reme-
dies must act by producing chemical
changes in the body. We find Toume-
fort busily engaged in testing every

* "Thus Fonrcroy," says Dr. Paris, "ex-
plained the operation of mercury Ijy its
specific gravit}', and the advocates of this
doctrine favoured the genei-al introduction
of the preparations of iron, especially' in
schirrus of the spleen or liver, upon the
same hypothetical principle ; for. s:iy they,
whatever is most forcible in removing tho
obstruction must be the most proper in-
strument of cure ; such is steel, which,
besides the attenuating power with which
it is furnished, has still a greater force in
this case from the gravity of its ) articles,
which, being seven times specifically hea-
vier than any vegetable, acts in propor-
tion with a stronger impulse, and there-
fore is a more powerful deobstruent. Tliis
may be taken as a spec men of the styl^
in which these mechanical physicians
reasoned and practised."— P/itt?-»i«coiooia,
p. 38-39.

520

fULLACIES.

vegetable juice, in order to discover
in it some traces of an acid or alkaline
ingredient, which might confer upon
it medicinal activity. The fatal errors
into which such an hypothesis was
liable to betray the practitioner re-
ceived an awful illustration in the
history of the memorable fever that
raged at Ley den in the year 1699,
and which consigned two-thirds of
the population of that city to an un-
timely grave ; an event which in a
great measure depended upon the
Professor Sylvius de la Boe, M'ho
having just embraced the chemical
doctrines of Van Helniont, assigned
the origin of the distemper to a pre-
vailing acid, and declared that its
cure could alone [only] be effected by
the copious administration of absor-
bent and testaceous medicines." *

These aberrations in medical theory
have their exact parallels in politics.
All the doctrines which ascribe ab-
solute goodness to particular forms
of government, particular social ar-
rangements, and even to particular
modes of education, without reference
to the state of civilisation and the
various distinguishing characters of
the society for which they are in-
tended, are open to the same objec-
tion— that of assuming one class of
influencing circumstances to be the
paramount rulers of phenomena which
depend in an equal or greater degree
on many others. But on these con-
siderations it is the less necessary
that we should now dwell, as they
will occupy our attention more largely
in the concluding Book.

§ 6. The last of the modes of
erroneous generalisation to which I
shall advert is that to which we may
give the name of False Analogies.
This Fallacy stands distinguished
from those already treated of by the
peculiarity that it does not even
simulate a complete and conclusive
induction, but consists in the mis-
application of an argument which is

* Pharmacologia, p. 39-40-

at best only admissible as an incon-
clusive presumption where real proof
is unattainable.

An argument from analogy is an
inference that what is true in a cer-
tain case is true in a case known to
be somewhat similar, but not known
to be exactly parallel, that is, to be
similar in all the material circum-
stances. An object has the property
B ; another object is not known to
have that property, but resembles
the first in a property A, not known
to be connected with B ; and the
conclusion to which the analogy
points is that this object has the
property B also. As, for example,
that the planets are inhabited because
the earth is so. The planets resem-
ble the earth in describing elliptical
orbits round the sun, in being at-
tracted by it and by one another, in
being nearly spherical, revolving on
their axes, &c., and, as we have now
reason to believe from the revelations
of the spectroscope, are composed, iii
great part at least, of similar mate-
rials ; but it is not known that any of
these properties, or all of them to-
gether, are the conditions on which
the possession of inhabitants is de-
pendent, or are marks of those condi-
tions. Nevertheless, so long as we
do not know what the conditions are,
they viay be connected by some law
of nature with those common proper-
ties ; and to the extent of that possi-
bility the planets are more likely to
be inhabited than if they did not re-
semble the earth at all. This non-
assignable and generally small in-
crease of probability beyond what
would otherwise exi t is all the evi-
dence which a conclusion can derive
from analogy. For if we have the
slightest reason to suppose any real
connection between the two proper-
ties A and B, the argument is no
longer one of analogy. If it had
been ascertained (I purposely put an
absurd supposition) that there was a
connection by causation between the
fact of revolving on an axis and
the existence of animated beings, OJ?

I'ALLACIES OF GENERALISATION.

521

if there were any reasonable ground
for even suspecting such a connection,
a probability would arise of the exist-
ence of inhabitants in the planets,
which might be of any degree of
strength, up to a complete induction;
but we should then infer the fact
from the ascertained or presumed
law of causation, and not from the
analogy of the earth.

The name analogy, however, is
sometimes employed by extension to
denote those arguments of an induc-
tive character, but not amounting to
a real induction, which are employed
to strengthen the argument drawn
from a simple resemblance. Though
A, the property common to the two
cases, cannot be shown to be the cause
or effect of B, the analogical reasoner
will endeavour to show that there is
some less close degree of connection
between them ; that A is one of a set
of conditions from which, when all
united, B would result ; or is an occa-
sional effect of some cause which has
been known also to produce B ; and
the like. Any of which things, if
shown, would render the existence of
B by so much more pn^bable than if
there had not been even that amount
of known connection between B and A.

Now an error or fallacy of analc^
may occur in two ways. Sometimes
it consists in employing an argument
of either of the above kinds, with cor-
rectness indeed, but overrating its
probative force. This very common
aberration is sometimes supposed to
be particularly incident to persons
distinguished for their imagination ;
but in reality it is the characteristic
intellectual vice of those whose ima-
ginations are barren, either from want
of exercise, natural defect, or the nar-
rowness of their range of ideas. To
such minds objects present themselves
clothed in but few properties ; and as,
therefore, few analogies between one
object and another occur to them, they
almost invariably overrate the degree
of importance of those few ; while one
whose fancy takes a wider range per-
ceives and remembers so many analo-

gies tending to conflicting conclusions,
that he is much less likely to lay
undue stress on any of them. We
always find that those are the greatest
slaves to metaphorical language who
have but one set of metaphors.

But this is only one of the modes
of error in the employment of argu-
ments of analogy. There is another,
more properly deserving the name of
fallacy, namely, when resemblance in
one point is inferred from resemblance
in another point, though there is not
only no evidence to connect the two
circumstances by way of causation,
but the evidence tends positively to
disconnect them. This is properly
the Fallacy of False Analogies.

As a first instance, we may cite
that favourite argument in defence of
absolute power drawn from the ana-
Jogy of paternal government in a
family, which government, however
much in need of control, is not and
cannot be controlled by the children
themselves, while they remain chil-
dren. Paternal government, says the
argument, works well, therefore de-
spotic government in a state will
work well. I waive, as not pertinent
in this place, all that could be said in
qualification of the alleged excellence
of paternal government. However
this might be, the argument from the
family to the state would not the less
proceed on a false analogy, implying
that the beneficial working of parental
government depends, in the family,
on the only point which it has in com-
mon with political despotism, namely,
irresponsibility. Whereas it depends,
when real, not on that, but on two
other circumstances of the case, the
affection of the parent for the chil-
dren, and the superiority of the parent
in wisdom and ej^erience ; neither
of which properties can be reckoned
on, or are at all likely to exist, be-
tween a political despot and his sub-
jects ; and when either of these cir-
cumstances fails even in the family,
and the influence of the irresponsi-
bility is allowed to work uncorrected,
the result is anything but good gov*

524

FAILLACIES.

ernment. This, therefore, is a false
analogy.

Another example is the not un-
common dictum, that bodies politic
have youth, maturity, old age, and
death, like bodies natural ; that after
a certain duration of prosperity, they
tend spontaneously to decay. This
also is a false analogy, because the
decay of the vital powers in an ani-
mated body can be distinctly traced to
the natural progress of those very
changes of structure which, in their
earlier stages, constitute its growth
to maturity ; while in the body politic
the progress of those changes cannot,
generally speaking, have any effect
but the still further continuance of
growth : it is the stoppage of that
progress, and the commencement of
retrogression, that alone would con-
stitute decay. Bodies politic die, but
it is of disease or violent death ; they
have no old age.

The following sentence from Hook-
er's Ecclesiastical Polity is an instance
of a false analogy from physical bodies
to what are called bodies politic : " As
there could be in natural bodies no
motion of anything unless there were
some which moveth all things, and
continueth immovable : even so in
politic societies there must be some
unpunishable, or else no man shall
suffer punishment." There is a double
fallacy here, for not only the analogy,
but the premise from which it is
drawn, is untenable. The notion
that there must be something im-
movable which moves all other things,
is the whole scholastic error of a pri-
mum mobile.

The following instance I quote from
Archbishop Whately's Rhetoric: "It
would be admitted that a great and
permanent diminution in the quantity
of some useful commodity, such as
corn, or coal, or iron, throughout the
world, would be a serious and lasting
loss ; and again, that if the fields and
coal-mines yielded regularly double
quantities, with the same labour, we
should be so much the richer ; hence
it might be inferred, that if the quan-

tity of gold and silver in the world
were diminished one-half, or were
doubled, like results would follow ;
the utility of these metals, for the
pmrposes of coin, being very great.
Now there are many points of re-
semblance and many of difference,
between the precious metals on the
one hand, and corn, coal, &c., on the
other ; but the important circum-
stance to the supposed argument is,
that the utility of gold and silver (as
coin, which is far the chief) depends
on their value, which is regulated by
their scarcity ; or rather, to speak
strictly, by the difficulty of obtaining
them ; whereas, if corn and coal were
ten times as abundant, {i.e. more
easily obtained,) a bushel of either
would still be as useful as now. But
if it were twice as easy to procure
gold as it is, a sovereign would be
twice as large ; if only half as easy
it would be of the size of a half-
sovereign, and this (besides the trifl-
ing circumstance of the cheapness or
dearness of gold ornaments) would
be all the difference. The analogy,
therefore, fails in the point essential
to the argument."

The same author notices, aftei
Bishop Copleston, the case of False
Analogy which consists in inferring
from the similarity in many respects
between the metropolis of a country
and the heart of the animal body,
that the increased size of the metro-
polis is a disease

Some of the false analogies on which
systems of physics were confidently
grounded in the time of the Greek
philosophers, are such as we now call
fanciful, not that the resemblances are
not often real, but that it is long since
any one has been inclined to draw
from them the inferences which were
then drawn. Such, for instance, are
the curious speculations of the Pytha-
goreans on the subject of numbers.
Finding that the distances of the
planets bore and seemed to bear to
one another a proportion not varying
much from that of the divisions of
the monochord, they inferred from it

I'ALLACIES OF GENERALISATION.

523

ihe existence of an inaudible music,
that of the spheres : as if the music
of a harp had depended solely on the
numerical proportions, and not on the
material, nor even on the existence of
any material — any strings at all. It
has been similarly imagined that cer-
tain combinations of numbers, which
were found to prevail in some natural
phenomena, must run through the
whole of nature : as that there must
be four elements, because there are
four possible combinations of hot and
cold, wet and dry : that there must
be seven planets, because there were
seven metals, and even because there
were seven days of the week. Kepler
himself thought that there could be
only six planets because there were
only five regular solids. With these
we may class the reasonings, so com-
mon in the speculations of the an-
cients, founded on a supposed perfec-
tion in nature : meaning by nature
the customary order of events as they
take place of themselves without
human intei-ference. This also is a
rude guess at an analogy supposed to
pervade all phenomena, however dis-
similar. Since what was thought to
be perfection appeared to obtain in
some phenomena, it was inferred (in
opposition to the plainest evidence) to
obtain in all. "We always suppose
that which is better to take place in
nature, if it be possible," says Aris-
totle ; and the vaguest and most
heterogeneous qualities being con-
founded together under the notion of
being better, there was no limit to the
wildness of the inferences. Thus,
because the heavenly bodies were
'•perfect," they must move in circles
and uniformly. Eor "they" (the
Pythagoreans) "would not allow,"
says Geminus,* " of any such disorder
among divine and eternal things, as
that they should sometimes move
quicker and sometimes slower, and
sometimes stand still; for no one would
tolerate such anomaly in the move-
ments even of a man, who was decent

* I quote from Dr. Whewell's Hist. Ind.
Sc, 3d ed. i. 129. <

and orderly. The occasions of life, how-
ever, are often reastms for men going
quicker or slower ; but in the incor-
ruptible nature of the stars, it is not
possible that any cause can be alleged
of quickness or slowness." It is seek-
ing an argument of analogy very far
to suppose that the stars must observe
the rules of decorum in gait and car-
riage, prescribed for themselves by
the long-bearded philosophers sati-
rised by Lucian.

As late as the Copernican contro-
versy it was urged as an argument in
favour of the true theory of the solar
system, that it placed the fire, the
noblest element, in the centre of the
universe. This was a. remnant of the
notion that the order of nature must
be perfect, and that perfection con-
sisted in conformity to niles of pre-
cedency in dignity, either real or con-
ventional. Again, reverting to num-
bers : certain numbers were perfect,
therefore those numbers must obtain
in the great phenomena of nature.
Six was a perfect number, that is,
equal to the sum of all its factors ;
an additional reason why there must
be exactly six planets. The Pythago-
reans, on the other hand, attributed
perfection to the number ten ; but
agreed in thinking that the perfect
number must be somehow realised in
the heavens : and knowing only of
nine heavenly bodies, to make up
the enumeration, they asserted " that
there was an antichthon or counter-
earth on the other side of the sun,-
invisible to us." * Even Huygens
was persuaded that when the number
of the heavenly bodies had reached
twelve, it could not admit of any
further increase. Creative power
could not go beyond that sacred
number.

Some curious instances of false
analogy are to be found in the argu-
ments of the Stoics to prove the
equality of all crimes, and the equal
wretchedness of all who had not re-,
alised their idea of perfect virtue*

* Hist. Ind. Sc, i. 52. =

524

FALLACIES.

Cicero, towards the end of his Fourth
Book De Finibus, states some of these
as follows. "Ut inquit, in fidibus
pliirimis, si nulla earum ita contenta
numeris sit, ut concentum servare
possit, omnes aequo incontentae sunt ;
sic peccata, quia discrepant, seque
discrepant ; paria sunt igitur." To
which Cicero himself aptly answers,
" aequo contingit omnibus fidibus, ut
incontentae sint ; illud non continuo,
ut aeque incontentae." The Stoic re-
sumes : " Ut enim, inquit, gubernator
aeque peccat, si palearum navem ever-
tit, et si auri ; item seque peccat qui
parentem, et qui servum, injuria ver-
berat ; " assuming, that because the
magnitude of the interest at stake
makes no difference in the mere de-
fect of skill, it can make none in the
moral defect : a false analogy. Again,
" Quis ignorat, si plures ex alto emer-
gere velint, propius fore eos quidem
ad respirandum, qui ad summam
jam aquam appropinquant, sed nihilo
magis respirare posse, quam eos, qui
sunt in profundo ? Nihil ergo adju-
vat procedere, et progi'edi in virtute,
quominus miserrimus sit, antequam
ad earn pervenerit, quoniam in aqu4
nihil adjuvat : et quoniam catuli, qui
jam despecturi sunt, caeci aeque, et ii
qui modo nati ; Platonem quoque ne-
cesse est, quoniam nondum videbat
sapientiam, aeque caecum animo, ac
Phalarim fuisse." Cicero, in his own
person, combats these false analogies
by other analogies tending to an
opposite conclusion. "Ista similia
non sunt, Cato. .... Ilia sunt sim-
ilia ; hebes acies est cuipiam ocu-
lorum : corpore alius languescit : hi
curatione adhibitd levantur in dies :
alter valet plus quotidie : alter videt.
Hi similes sunt omnibus, qui virtuti
student; levantur vitiis, levantur erro-
ribus."

§ 7. In these and all other argu-
ments drawn from remote analogies,
and from metaphors, which are cases
of analogy, it is apparent (especially
when we consider the extreme facility
of raising iip contrary analogies and

conflicting metaphors) that so far from
the metaphor or analogy proving any-
thing, the applicability of the meta-
phor is the very thing to be made
out. It has to be shown that in the
two cases asserted to be analogous,
the same law is really operating ;
that between the known resemblance
and the inferred one there is some
connection by means of causation.
Cicero and Cato might have bandied
opposite analogies for ever ; it rested
with each of them to prove by just
induction, or at least to render pro-
bable, that the case resembled the
one set of analogous cases and not
the other, in the circumstances on
which the disputed question really
hinged. Metaphors, for the most
part, therefore, assume the proposi-
tion which they are brought to prove :
their use is, to aid the apprehension
of it ; to make clearly and vividly
comprehended what it is that the
person who employs the metaphor is
proposing to make out ; and some-
times also, by what media he pro-
poses to do so. For an apt metaphor,
though it cannot prove, often suggests
the proof.

For instance, when D'Alembert (I
believe) remarked that in certain
governments, only two creatures find
their way to the highest places, the
eagle and the serpent ; the metaphor
not only conveys with great vividness
the assertion intended, but contributes
towards substantiating it, by suggest-
ing, in a lively manner, the means by
which the two opposite charactersthus
typified effect their I'ise. When it is
said that a certain person misunder-
stands another because the lesser of
two objects cannot comprehend the
greater, the application of what is
true in the literal sense of the word
comprehend, to its metaphorical sense,
points to the fact which is the ground
and justification of the assertion, viz.
that one mind cannot thoroughly
understand another unless it can con-
tain it in itself, that is, unless it pos-
sesses all that is contained in the
other. When it is urged as an argu-

FALLACIES OF GENERALISATION.

525

ment for education, that if the soil is
left uncultivated, weeds will spring
up, the metaphor, though no proof,
but a statement of the thing to be
proved, states it in terms which, by
suggesting a parallel case, put the
mind upon the track of the real proof.
For the reason why weeds grow in an
uncultivated soil is that the seeds of
worthless products exist everywhere,
and can germinate and grow in almost
all circumstances, while the reverse is
the case with those which are valu-
able ; and this being equally true of
mental products, this moide of convey-
ing an argument, independently of its
rhetorical advantages, has a logical
value, since it not only suggests the
grounds of the conclusion, but points
to another case in which those grounds
have been found, or at least deemed to
be, sufficient.

On the other hand, when Bacon,
who is equally conspicuous in the use
and abuse of figurative illustration,
says that the stream of time has
brought down to us only the least
valuable part of the writings of the
ancients, as a river carries froth and
straws floating on its surface, while
more weighty objects sink to the bot-
tom ; this, even if the assertion illus-
trated by it were true, would be no
good illustration, there being no parity
of cause. The levity by which sub-
stances float on a stream, and the
levity which is synonymous with
worthlessness, have nothing in com-
mon except the name ; and (to show
how little value there is in the meta-
phor) we need only change the word
into buoyancy, to turn the semblance
of argument involved in Bacon's illus-
tration against himself.

A metaphor, then, is not to be con-
sidered as an argument, but as an
assertion that an argument exists ;
that a parity subsists between the case
from which the metaphor is drawn
and that to which it is applied. This
parity may exist though the two cases
be apparently \evy remote from one
another ; the only resemblance exist-
ing between them may be a resem-

blance of relations, an analogy in
Ferguson's and Archbishop Whately's
sense : as in the preceding instance,
in which an illustration from agricul-
ture was applied to mental cultiva-
tion.

§ 8. To terminate the subject of
Fallacies of Generalisation, it re-
mains to be said that the most fer-
tile source of them is bad classifica-
tion : bringing together in one group,
and under one name, things which
have no common properties, or none
but such as are too unimportant to
allow general propositions of any con-
siderable value to be made respecting
the class. The misleading effect is
greatest when a word which in com-
mon use expresses some definite fact
is extended by slight links of connec-
tion to cases in which that fact does
not exist, but some other or others,
only slightly resembling it. Thus
Bacon,* in speaking of the Idola or
Fallacies arising from notions temere
et inaqualitei'- a rebus abstractce, exem-
plifies them by the notion of Humi-
dum or Wet, so familiar in the physics
of antiquity and of the Middle Ages.
" Invenietur verbum istud, Humidum
nihil aliud quam nota confusa diver-
sarum actionum, quae nullam con-
stantiam aut reductionem patiuntur.
Significat enim, et quod circa aliud
corpus facile se circumf undit ; et quod
in se est indeterminabiie, nee con-
sistere potest : et quod facile cedit
undique ; et quod facile se dividit et
dispergit ; et quod facile se unit et
colligit ; et quod facile fluit, et in
motu ponitur ; et quod alteri corpori
facile adhseret, idque madefacit ; et
quod facile reducitur in liquidum,
sive colliquatur, cum antea consiste-
ret. Itaque quum ad hujus nominis
prsedicationem et impositionem ven-
tum sit ; si alia accipias, flamma
humida est ; si alia accipias, aer
humidus non est ; si alia, pulvis mi-
nutus huuiidus est ; si alia, vitrum
humidum est : ut facile appareat,

* ^Yoi'. Org., Apb. 69.

526

FALLACIES.

istam notionem ex aquH tantum, et
communibus et vulgaribus liquoribus,
absque ulla debita veriticatione, te-
mere abstractam esse."

Bacon himself is not exempt from a
similar accusation when inquiring into
the nature of heat : where he occa-
sionally proceeds like one who, seek-
ing for the cause of hardness, after
examining that quality in iron, flint,
and diamond, should expect to find
that it is something which can be
traced also in hard water, a hard
knot, and a hard heart.

The word Kivrjais in the Greek phi-
losophy, and the words Generation
and Corruption, both then and long
afterwards, denoted such a multitude
of heterogeneous phenomena, that any
attempt at philosophising in which
those words were used was almost as
necessarily abortive as if the word
hard had been taken to denote a class
including all the things mentioned
above. Kivrjais, for instance, which
properly signified motion, was taken
to denote not only all motion, but
even all change ; aXXoiioais being re-
cognised as one of the modes of
KivT^ais, The effect was, to connect
with every form of dWoiwais or
change, ideas drawn from motion in
the proper and literal sense, and
which had no real connection with
any other kind of Kiv-rjais than that.
Aristotle and Plato laboured under a
continual embarrassment from this
misuse of terms. But if we proceed
further in this direction we shall en-
croach upon the Fallacy of Ambiguity,
which belongs to a different class, the
last in order of our classification, Fal-
lacies of Confusion.

CHAPTER VL

FALLACIES OP RATIOCINATION.

§ I. We have now, in our progress
through the classes of Fallacies, ar-
rived at those to which, in the com-
jjjQn books of logic, the appellation is

in general exclusively appropriated ;
those which have their seat in the
ratiocinative or deductive part of the
investigation of truth. Of these fal-
lacies it is the less necessary for us
to insist at any length, as they have
been most satisfactorily treated in a
work familiar to almost all, in this
country at least, who feel any in^
terest in these speculations. Arch-
bishop Whately's Logic. Against the
more obvious forms of this class of
fallacies, the rules of the syllogism
are a complete protection. Not (as
we have so often said) that ratiocina-
tion cannot be good unless it be in
the form of a syllogism ; but that, by
showing it in that form, we are sure
to discover if it be bad, or at least if
it contain any fallacy of this class.

§ 2. Among Fallacies of Ratiocina-
tion, we ought perhaps to include the
errors committed in processes which
have the appearance only, not the
reality, of an inference from premises —
the fallacies connected with the con-
version and sequipollency of proposi-
tions. I believe errors of this de-
scription to be far more frequently
committed than is generally sup-
posed, or than their extreme obvious-
ness might seem to admit of. For 91
example, the simple conversion of an VI
universal affirmative proposition. All
A are B, therefore all B are A, I take
to be a very common form of error :
though committed, like many other
fallacies, oftener in the silence of
thought than in express words, for
it can scarcely be clearly enunciated
without being detected. And so with
another form of fallacy, not substanr
tially different from the preceding :
the erroneous conversion of an hypo-
thetical proposition. The proper con-
verse of an hypothetical proposition
is this : If the consequent be false,
the antecedent is false ; but this. If AM
the consequent be true, the ante- ■■
cedent is true, by no means holds
good, but is an erior corresponding
to the simple conversion of an uni-
yers£<,l affirmative. Yet hardly auy-

II

FALLACIES OF RATIOCINATION.

527

thing is more common than for people
in their private thoughts to draw this
inference. As when the conclusion
is accepted, which it so often is, for
proof of the premises. That the pre-
mises cannot be true if the conclusion
is false, is the unexceptionable foun-
dation of the legitimate mode of rea-
soning called reductio ad absurdum.
But people continually think and
express themselves as if they also
believed that the premises cannot be
false if the conclusion is trne. The
truth, or supposed truth, of the in-
ferences which follow from a doctrine,
often enables it to find acceptance in
spite of gross absurdities in it. How
many philosophical systems which had
scarcely any intrinsic recommendation
have been received by thoughtful men
because they were supposed to lend
additional support to religion, mora-
lity, some favourite view of politics,
or some other cherished persuasion ;
not merely because their wishes were
thereby enlisted on its side, but be-
cause its leading to what they deemed
sound conclusions appeared to them
a strong presumption in favour of its
truth, though the presumption, when
viewed in its true light, amounted
only to the absence of that particular
evidence of falsehood which would
have resulted fron» its leading by cor-
rect inference to something already
known to be false.

Again, the very frequent error in
conduct of mistaking reverse of wrong
for right, is the practical form of a
logical error with respect to the Oppo-
sition of Propositions. It is com-
mitted for want of the habit of dis-
tinguishing the contrary of a proposi-
tion from the contradictory of it, and
of attending to the logical canon that
contrary propositions, though they
cannot both be true, may both be
false. If the error were to express
itself in words, it would run distinctly
counter to this canon. It generally,
however, does not so express itself,
and to compel it to do so is the most
effectual method of detecting and ex-
posing it.

§ 3. Among Fallacies of Ratiocina-
tion are to be ranked in the first place
all the cases of vicious syllogism laid
down in the books. Tliese generally re-
solve themselves into having more than
three terms to the syllogism, either
avowedly, or in the covert mode of an
undistributed middle term, or an illi-
cit process of one of the two extremes.
It is not, indeed, very easy fully to
convict an argument of falling under
any one of these vicious cases in par-
ticular ; for the reason already more
than once referred to, that the pre-
mises are seldom formally set out :
if they were, the fallacy would impose
upon nobody ; and while they are not
it is almost always to a certain degree
optional in what manner the sup-
pressed link should be filled up. The
rules of the syllogism are rules for
compelling a person to be aware of
the whole of what he must undertake
to defend if he persists in maintain-
ing his conclusion. He has it almost
always in his power to make his syllo-
gism good by introducing a false pre-
mise ; and hence it is scarcely ever
possible decidedly to affirm that any
argument involves a bad syllogism :
but this detracts nothing from the
value of the syllogistic rules, since it
is by them that a reasoner is compelled
distinctly to make his election what
premises he is pi-epared to maintain.
The election made, there is generally
so little difficulty in seeing whether
the conclusion follows from the pre-
mises set out, that we might without
much logical impropriety have merged
this fourth class of fallacies in the
fifth, or Fallacies of Confusion.

§ 4. Perhaps, however, the com-
monest and certainly the most dan-
gerous fallacies of this class, are those
which do not lie in a single syllogism,
but slip in between one syllogism and
another in a chain of argument, and
are committed by changing the pre-
mises. A proposition is proved, or an
acknowledged truth laid down, in the
first part of an argumentation, and
in the second a further argument i?

528

FALLACIES.

founded not on the same proposition,
but on some other, resembling it suffi-
ciently to be mistaken for it. In-
stances of this fallacy will be found
in almost all the argumentative dis-
courses of unprecise thinkers, and we
need only here advert to one of the
obscurer forms of it, recognised by
the schoolmen as the fallacy d dicto
secundum quid ad dictum simpliciter.
This is committed when, in the pre-
mises, a proposition is asserted with a
qualification, and the qualification lost
sight of in the conclusion ; or oftener,
when a limitation or condition, though
not asserted, is necessary to the truth
of the proposition, but is forgotten
when that proposition comes to be
employed as a premise. Many of the
bad arguments in vogue belong to
this class of error. The premise is
Bome admitted truth, some common
maxim, the reasons or evidence for
which have been forgotten, or are not
thought of at the time, but if they had
been thought of would have shown the
necessity of so limiting the premise
that it would no longer have sup-
ported the conclusion drawn from it.
Of this nature is the fallacy in what
is called, by Adam Smith and others,
the Mercantile Theory in Political
Economy. That theory sets out from
the common maxim, that whatever
brings in money enriches ; or that
every one is rich in proportion to the
quantity of money he obtains. From
this it is concluded that the value of
any branch of trade, or of the trade
of the country altogether, consists in
the balance of money it brings in ;
that any trade which carries more
money out of the country than it
draws into it is a losing trade ; that
therefore money should be attracted
into the country and kept there, by
prohibitions and bounties ; and a train
of similar corollaries. All for want of
reflecting that if the riches of an indi-
vidual are in proportion to the quan-
tity of money he can command, it is
because that is the measure of his
power of purchasing money's worth ;
^pd is therefore subject to the proviso

that he is not debarred from employ-
ing his money in such purchases. The
premise, therefore, is only true secun-
dum quid; but the theory assumes
it to be true absolutely, and infers
that increase of money is increase of
riches, even when produced by means
ubversi ve of thecondition under which
alone money can be riches.

A second instance is, the argument
by which it used to be contended, be-
fore the commutation of tithe, that
tithes fell on the landlord, and were
a deduction from rent ; because the
rent of tithe - free land was always
higher than that of land of the same
quality, and the same advantages of
situation, subject to tithe. Whether
it be true or not that a tithe falls on
rent, a treatise on Logic is not the
place to examine ; but it is certain
that this is no proof of it. Whether
the proposition be true or false, tithe-
free land must, by the necessity of the
case, pay a higher rent. For if tithes
do not fall on rent, it must be because
they fall on the consumer ; because
they raise the price of agricultural
produce. But if the produce be raised
in price, the farmer of tithe-free as
well as the farmer of tithed land gets
the benefit. To the latter the rise is
but a compensation for the tithes he
pays ; to the first, who pays none, it
is clear gain, and therefore enables
him, and if there be freedom of com-
petition forces him to pay so much
more rent to his landlord. The ques-
tion remains, to what class of fallacies
this belongs. The premise is, that the
owner of tithed land receives less rent
than the owner of tithe-free land ; the
conclusion is, that therefore he re-
ceives less than he himself would re-
ceive if tithe were abolished. But the
premise is only true conditionally ; the
owner of tithed land receives less than
what the owner of tithe-free land is
enabled to receive when other lands are
tithed ; while the conclusion is applied
to a state of circumstances in which
that condition fails, and in which,
by consequence, the premise will not
be true, The fallacy, therefore, is a

I

FALLACIES OF RATIOCINATION.

529

dido secundum quid ad dictum sim-
jpliciter.

A third example is the opposition
sometiines made to legitimate interfer-
ences of government in the econi)mical
affairs of society, grounded on a mis-
application of the maxim, that an in-
dividual is a better judge than the
government of what i.s for his own pe-
cuniary interest. This objection was
urged to Mr. Wakefield's principle of
colonisation ; the concentration of the
settlers, by fixing such a price on un-
occupied land as may preserve the
most desirable proportion between the
quantity of land in culture and the
labouring population. Against this it
was argued, that if individuals found
it for their advantage to occupy exten-
sive tracts of land, they, being better
judges of their own interest than the
Legislature, (which can only proceed
on general rules,) ought not to be re-
strained from doing so. But in this
argument it was forgotten that the
fact of a person's taking a large tract of
land is evidence only that it is his in-
terest to take as much as other people,
but not that it might not be for his
interest to content himself with less, if
he could be assured that other people
would do so too ; an assurance which
nothing but a government regulation
can give. If all other people took
much, and he only a little, he would
reap none of the advantages derived
from the concentration of the popula-
tion and the consequent possibility of
procuring labour for hire, but would
have placed himself, without equiva-
lent, in a situation of voluntary in-
feriority. The proposition, therefore,
that the quantity of land which people
will take when left to themselves is
that which is most for their interest to
take, is true only secundum quid : it
is only their interest while they have
no guarantee for the conduct of one
another. But the argument disre-
gards the limitation, and takes the
proposition for true simpliciter.

One of the conditions oftenest
dropped, when what would otherwise
be a true proposition is employed as a

premise for proving others, is the con-
dition of ti)ue. It is a principle of
political economy that prices, profits,
wages, &c., "always find their level ;"
but this is often interpreted M if it
meant that they are always, or gene-
rally, at their level ; while the truth
is, as Coleridge epigraujmatically ex-
presses it, that they are always >'//(/i«5'
their level, " which might be taken as
a paraphrase or ironical definition of
a storm."

Under the same head of fallacy (d
dicto secundum quid ad dictum sim-
pliciter) might be placed all the errors
which are vulgarly called misapplica-
tions of abstract truths : that is, where
a principle, true (as the common ex-
pression is) in the abstract, that is, all
modif} ing causes being supposed ab-
sent, is reasoned on as if it were true
absolutely, and no modifying circum-
stance could ever by possibility exi-L
This very common form of error it is
not requisite that we should exem-
plify here, as '*' vill be particularly
treated of hereatter in its application
to the subjects on which it is most
frequent and most fatal, those of poli-
tics and society.*

* "An advocate," My* Mr. De Morgan,
(Formal Logic, p. 270,) "ia ^^omeriIne8 guilty
of the arguinent d dicto Mecundvin quid ad
dictum tiviplicitev : it in his business to do
lor his client all that his client might
hoiuttly do for himself. Is not the word
in italics frequently o-nitted? Might axij
man honestly ti y to do for himself all that
counsel frequently try to do for him ? W«
are often reminded of the two men who
stole the leg of mutton ; one could swear
he had not got, it, the other that he had not
taken it. The coun.sel is doing his duty by
his client, the client has left the matter to
his coimsel. Between tiie unexecuted in-
tention of the client and the unintended
execution of the counsel there may be a
wroi g done, and, v we are t<» bclieTe tho
usual maxims, no wrong-doer."

The hame wi iter jus ly remarka (p. 251)
that there is a coo verse fallacy, d dicto
timpliciter ad dictum xecundum quid, called
by the scholastic lofficiana fallacia oeci'
dentis; and another, which may be called
d dicto tecundum quid od dictum tecundum,
alterum quid (p. 265). For >ipt instances of
both, I must refer the reader to Mr. !)•
Morgan's able chapter on Fallacies.

2 L

530

FALLACIES.

CHAPTER VII.

FALLACIES OF CONFUSION.

§ I. Under this fifth and last class
it is convenient to arrange all those
fallacies in which the source of error
is not so much a false estimate of
the probative force of known evi-
dence, as an indistinct, indefinite, and
fluctuating conception of what the
evidence is.

At the head of these stands that
multitudinous body of fallacious rea-
sonings in which the source of error
is the ambiguity of terms : when
something which is true, if a word be
used in a particular sense, is reasoned
on as if it were true in another sense.
In such a case there is not a mal-
estimation of evidence, because there
is not properly any evidence to the
point at all ; there is evidence, but to
a different point, which, from a con-
fused apprehension of the meaning of
the terms used, is supposed to be the
same. This error will naturally be
oftener committed in our ratiocina-
tions than in our direct inductions,
because in the former we are decipher-
ing our own or other people's notes,
while in the latter we have the things
themselves present, either to the
senses or to the memory. Except,
indeed, when the induction is not
from individual cases to a generality,
but from generalities to a still higher
generalisation ; in that case the fal-
lacy of ambiguity may affect the in-
ductive process as well as the ratioci-
native. It occurs in ratiocination in
two ways : when the middle term is
ambiguous, or when one of the terms
of the syllogism is taken in one sense
in the premises and in another sense
in the conclusion.

Some good exemplifications of this
fallacy are given by Archbishop
Whately. "One case," says he, " which
may be regarded as coming under the
head of Ambiguous Middle, is (what
I believe logical writers mean by 'Fal-
lacia Figxrce Dictionis ') the fallacy
built on the grammatical structure of

language, from men's usually taking
for granted that paronymous (or con-
jugate) words, i.e. those belonging to
each other, as the substantive, adjec-
tive, verb, &c., of the same root, have
a precisely corresponding meaning ;
which is by no means universally the
case. Such a fallacy could not indeed
be even exhibited in strict logical form,
which would preclude even the at-
tempt at it, since it has two middle
terms in sound as well as sense. But
nothing is more common in practice
than to vary continually the terms
employed, with a view to grammatical
convenience ; nor is there anything
unfair in such a practice, as long as
the meaning is preserved unaltered ;
e.g. * murder should be punished with
death ; this man is a murderer, there-
fore he deserves to die,' &c. Here we
proceed on the assumption (in this
case just) that to commit murder,
and to be a murderer, — to deserve
death, and to be one who ought to
die, are, respectively, equivalent ex-
pressions ; and it would frequently
prove a heavy inconvenience to be
debarred this kind of liberty ; but
the abuse of it gives rise to the fal-
lacy in question ; e.g. projectors are \
unfit to be trusted ; this man has]
formed a project, therefore he is unfit
to be trusted : here the sophist pro-
ceeds on the hypothesis that he whojj
forms a project must be a projector ;
whereas the bad sense that commonlyj
attaches to the latter word, is not at j
all implied in the former. This fal-,
lacy may often be considered as lying j
not in the Middle, but in one of thej
terms of the Conclusion ; so that!
the conclusion drawn shall not be, in|
reality, at all warranted by the pre-
mises, though it will appear to be so,
by means of the grammatical affinity!
of the words : e.g. to be acquainted
with the guilty is a presumption ofj
guilt ; this man is so acquaintec"
therefore we may presume that he ia
guilty : this argument proceeds on'
the supposition of an exact corre-
spondence between presume and pre-
sumption, which, however, does not

FALLACIES OF CONFUSION.

531

really exist ; for * presumption * is
commonly used to express a kind
of slight suspicion ; whereas, to ' pre-
sume ' amounts to actual belief. There
are innumerable instances of a non-
correspondence in paronymous words,
similar to that above instanced ; as
between art and artful, design and
designing, faith BXid faithful , &c.: and
the more slight the variation of the
meaning, the more likely is the fal-
lacy to be successful ; for when the
words have become so widely removed
in sense as 'pity' and 'pitiful,' every
one would perceive such a fallacy, nor
would it be employed but in jest*

"The present Fallacy is nearly
allied to, or rather, perhaps, may be
regarded as a branch of, that founded
on etymology ; viz. when a terra is
used at one time in its customary,
and at another in its etymological
sense. Perhaps no example of this
can be found that is more extensively
and mischievously employed than in
the case of the word representative:
assuming that its right meaning must
correspond exactly with the strict and
original sense of the verb * represent,'
the sophist persuades the multitude
that a member of the House of Com-
mons is bound to be guided in all
points by the opinion of his constitu-
ents ; and, in short, to be merely their
spokesman; whereas law and custom,
which in this case may be considered

" scarcity of money." In the language
of commerce "money" has two mean-
ings : currency, or the circulating
medium ; and capital seeking invest-
ment, especially investment on loan.
In tills last sense the word is used
when the " money market " is spoken
of, and when the " value of money "
is said to be high or low, the rate
of interest being meant. The con-
sequence of this an)biguity is, that as
soon as scarcity of money in the latter
of these senses begins to be felt, — as
soon as there is difficulty of obtaining
loans, and the rate of interest is high,
— it is concluded that this must arise
from causes acting upon the quantity
of money in the other and more popu-
lar sense ; that the circulating medium
must have diminished in quantity, or
ought to be increased. I am aware
that, independently of the double
meaning of the term, there are in the
facts themselves some peculiarities,
giving an apparent support to this
error ; but the ambiguity of the lan-
guage stands on the very threshold
of the subject, and intercepts all at-
tempts to throw light upon it.

Another ambiguous expression
which continually meets us in the
political controversies of the present
time, especially in those which relate
to organic changes, is the phrase "in-
fluence of property," which is some-
times used for the influence of respect

as fixing the meaning of the term, { for superior intelligence, or gratitude
require no such thing, but enjoin the for the kind offices which persons of
representative to act according to the
best of his own judgment, and on his
own responsibility."

The following are instances of great
practical imporlance, in which argu-
ments are habitually founded on a
verbal ambiguity.

The mercantile public are frequently
led into this fallacy by the phrase

* An example of this fallacy is the popu-
lar erior that strong drink must be a cause
of strenfjth. There is here fallacy with-
in fallacy ; for granting that the words
"strong-" and "strength" were not (as
they are) applied in a totally different
sense to fermented liquors and to the hu-
man body, there would still be involved

large property have it so much m
their power to bestow ; at other times
for the influence of fear ; fear of the
worst sort of power, which large pro-
perty also gives to its possessor, the
power of doing mischief to depen-
dents. To confound these two is the
standing fallacy of ambiguity brought
against those who seek to purify the

the error of sur^posing that an eflfect must
be like its cause ; that the conriiTioiis of a
phenomenon are likely to resemble the
phenomenon itself; wiiich we have already
treated of as an a priori fallacy of tlie first
rank. As well might it be .--upposed thut
a strong poison would make the person
who takes it strong.

532

FALLACIES.

electoral system from corruption and
intimidation. Persuasive influence,
acting through the conscience of the
voter, and carrying his heart and
mind with it, is beneficial ; therefore
(it is pretended) coercive influence,
which compels him to forget that he
is a moral agent, or to act in opposi-
tion to his moral convictions, ought
not to be placed under restraint.

Another word which is often turned
into an instrument of the fallacy of
ambiguity is Theory. In its most
proper acceptation, theory means the
completed result of philosophical in-
duction from experience. In that
sense, there are erroneous as well as
true theories, for induction may be
incorrectly performed, but theory of
some sort is the necessary result of
knowing anything of a subject, and
having put one's knowledge into the
form of general propositions for the
guidance of practice. In this, the
proper sense of the word. Theory is
the explanation of practice. In an-
other and a more vulgar sense, theory
means any mere fiction of the ima-
gination, endeavouring to conceive
how a thing may possibly have been
produced, instead of examining how
it was produced. In this sense only
are theory and theorists unsafe guides;
but because of this, ridicule or dis-
credit is attempted to be attached to
theory in its proper sense, that is, to
legitimate generalisation, the end and
aim of all philosophy ; and a conclu-
sion is represented as worthless, just
because that has been done which, if
done correctly, constitutes the highest
worth that a principle for the guid-
ance of practice can possess, namely,
to comprehend in a few words the
real law on which a phenomenon de-
pends, or some property or relation
which is universally- true of it.

" The Church " is sometimes under-
stood to mean the clergy alone, some-
times the whole body of believers, or
at least of communicants. The de-
clamations respecting the inviolability
of Church property are indebted for
the greater part of their apparent

force to this ambiguity. The clergy,
being called the Church, are supposed
to be the real owners of what is called
Church property, whereas they are in
truth only the managing members of
a much larger body of proprietors,
and enjoy on their own part a mere
usufruct, not extending beyond a life
interest.

The following is a Stoical argument
taken from Cicero, De Finihus, book
the third : " Quod est bonum, omne
laudabile est. Quod autem laudabile
est, omne honestum est. Bonum
igitur quod est, honestum est." Here
the ambiguous word is laudabile, which
in the minor premise means anything
which mankind are accustomed, on
good grounds, to admire or value ;
as beauty, for instance, or good for-
tune ; but in the major it denotes
exclusively moral qualities. In much
the same manner the Stoics endea-
voured logically to justify as philo-
sophical truths their figurative and
rhetorical expressions of ethical senti-
ment : as that the virtuous man is
alone free, alone beautiful, alone a
king, &c. Whoever has virtue has
Good, (because it has been previously
determined not to call anything else
good;) but, again. Good necessarily
includes freedom, beauty, and even
kingship, all these being good things ;
therefore whoever has virtue has all
these.

The following is an argument of
Descartes to prove, in his d priori
manner, the being of a God. The
conception, says he, of an infinite
Being proves the real existence of
such a being. For if there is not
really any such being, / must have
made the conception ; but if I could
make it, I can also unmake it ; which
evidently is not true ; therefore there
must be, externally to myself, an
archetype, from which the conception
was derived. In this argument (which,
it may be observed, would equally
prove the real existence of ghosts and
of witches) the ambiguity is in the
pronoun /, by which, in one place, is
to be understood my wiU, in another

FALLACIES OF CONFUSION.

533

the laws of my nature. If the con-
ception, existing as it does in my
mind, had no original without, the
conclusion would unquestit)nably fol-
low that / made it ; that is, the laws
of my nature must have somehow
evolved it ; but that my will made
it, would not follow. Now when
Descartes afterwards adds that I can-
not unmake the conception, he means
that I cannot get rid of it by an act
of my will : which is true, but is not
the proposition required. I can as
much unmake this conception as I
can any other : no conception which
I have once had, can I ever dismiss
by mere volition ; but what some of
the laws of my nature have produced,
other laws, or those same laws in
other circumstances, may, and often
do, subsequently efface.

Analogous to this are some of the
ambiguities in the free-will contro-
versy, which, as they will come
under special consideration in the
concluding Book, I only mention me-
moi'ice causd. In that discussion, too,
the word / is often shifted from one
meaning to another, at one time
standing for my volitions, at another
time for the actions which are the
consequences of them, or the mental
dispositions from which they proceed.
The latter ambiguity is exemplified
in an argument of Coleridge (in his
Aids to Reflection) in support of the
freedom of the will. It is not true,
he says, that a man is governed by
motives ; " the man makes the mo-
tive, not the motive the man ; " the
proof being that "what is a strong
motive to one man is no motive at all
to another." The premise is true,
but only amounts to this, that dif-
ferent persons have different degrees
of susceptibility to the same motive ;
as they have also to the same intoxi-
cating liquid, which, however, does not
prove that they are free to be drunk
or not drunk, whatever quantity of
the fluid they may drink. What is
proved is, that certain mental condi-
tions in the person himself must co-
operate in the production of the act,

with the external inducement ; but
those mental conditions also are the
effect of causes ; and there is no-
thing in the argument to prove that
they can arise without a cause — that
a spontaneous determination of the
will, without any cause at all, ever
takes place, as the free-will doctrine
supposes.

The double use, in the free-will
controversy, of the word Necessity,
which sometimes stands only for Cer-
tainty, at other times for Compulsion,
sometimes for what cannot be pre-
vented, at other times only for what
we have reason to be assured xoill
not, we shall have occasion hereafter
to pursue to some of its ulterior con-
sequences.

A most important ambiguity, both
in common and in metaphysical lan-
guage, is thus pointed out by Arch-
bishop Whately in the Appendix to
his Logic : " Same (as well as One,
Identical, and other words derived
from them) is used frequently in a
sense very different from its primary
one, as applicable to a tingle object ;
being employed to denote great simi-
larity. When several objects are un-
distinguishably alike, one single de-
scription will apply equally to any of
them ; and thence they are said to be
all of one and the same nature, appear-
ance, &c. As, e.g., when we say ' this
house is built of the same stone with
such another,' tve only mean that the
stones are undistinguishable in their
qualities ; not that the one building
was pulled down, and the other con-
structed with the materials. Whereas
sameness, in the primary sense, does
not even necessarily imply similarity ;
for if we say of any man that he is
greatly altered since such a time, we
understand, and indeed imply by the
very expression, that he is one person,
though different in several qualities.
It is worth observing also, that Same,
in the secondary sense, admits, ac-
cording to popular usage, of degrees :
we speak of two things being nearly
the same, but not entirely : personal
identity does not admit of degrees.

534

FALLACIES.

Nothing, perhaps, has contributed
more to the error of Realism than
inattention to this ambiguity. When
several persons are said to have one
and the same opinion, thought, or
idea, many men, overlooking the true
simple statement of the case, which
is, that they are aU thinking alike,
look for something more abstruse and
mystical, and imagine there must be
some One Thing, in the primary sense,
though not an individual, which is
present at once in the mind of each
of these persons ; and thence readily
sprung Plato's theory of Ideas, each
of which was, according to him, one
real, eternal object, existing entire
and complete in each of the individual
objects that are known by one name."
It is, indeed, not a matter of infer-
ence, but of authentic history, that
Plato's doctrine of Ideas, and the
Aristotelian doctrine (in this respect
similar to the Platonic) of substantial
forms and second substances, grew up
in the precise way here pointed out,
from the supposed necessity of find-
ing in things which were said to have
the same nature or the same qualities
something which was the same in the
very sense in which a man is the same
as himself. All the idle speculations
respecting rb 6v, rb ^v, rb Sfxolov, and
similar abstractions, so common in the
ancient and in some modern schools
of thought, sprang from the same
source. The Aristotelian logicians
saw, however, one case of the ambi-
guity, and provided against it with
their peculiar felicity in the invention
of technical language, when they dis-
tinguished things which differed both
specie and numero from those which
differed numero tantum, that is, which
were exactly alike, ( in some particular
respect at least,) but were distinct
individuals. An extension of this
distinction to the two meanings of
the word Same, namely, things which
are the same specie tantum, and a
thing which is the same numero as
well as specie, would have prevented
the confusion, which has been a source
of so much darkness and such an

abundance of positive error in meta-
physical philosophy.

One of the most singular examples
of the length to which a thinker of
eminence may be led away by an am-
biguity of language is afforded by
this very case. I refer to the famous
argument by which Bishop Berkeley
flattered himself that he had for ever
put an end to "scepticism, atheism,
and irreligion," It is briefly as fol-
lows : — I thought of a thing yesterday ;
I ceased to think of it ; I think of it
again to-day. I had, therefore, in
my mind yesterday an idea of the
object ; I have also an idea of it to-
day ; this idea is evidently not another,
but the very same idea. Yet an in-
tervening time elapsed in which 1 had
it not. Where was the idea during
this interval? It must have been
somewhere ; it did not cease to exist ;
otherwise the idea I had yesterday
could not be the same idea ; no more
than the man I see alive to-day can
be the same whom I saw yesterday if
the man has died in the meanwhile.
Now an idea cannot be conceived to
exist anywhere except in a mind ;
and hence there must exist an Uni-
versal Mind, in which all ideas have
their permanent residence during the
intervals of their conscious presence
in our own minds.

It is evident that Berkeley here
confounded sameness numero with
sameness specie, that is, with exact
resemblance, and assiimed the former
where there was only the latter ; not
perceiving that when we say we have
the same thought to-day which we
had yesterday, we do not mean the
same individual thought,but a thought
exactly similar ; as we say that we
have the same illness which we had
last year, meaning only the same sort
of illness.

In one remarkable instance the
scientific world was divided into two
furiously hostile parties by an am-
biguity of language affecting a branch
of science which, more completely
than most others, enjoys the advan-
tage of a precise and well-defined

FALLACIES OF CONFUSION.

535

terminology. I refer to the famous
dispute respecting the vis viva, the
history of which is given at large in
Professor Playfair's Dissertation. The
question was whether the force of a
moving body was proportional (its
mass being given) to its velocity sim-
ply, or to the square of its velocity ;
and the ambiguity was in the word
Force. "One of the efifects," says
Playfair, " produced by a moving
body is proportional to the square of
the velocity, while another is propor-
tional to the velocity simply ; " from
whence clearer thinkers were subse-
quently led to establish a double
measure of the efficiency of a moving
power, one being called vis viva, and
the other momentum. About the
facts both parties were from the first
agreed ; the only question was, with
which of the two effects the term
force should be, or could most con-
veniently be, associated. But the
disputants were by no means aware
that this was all ; they thought that
force was one 'thing, the production
of effects another ; and the question,
by which set of effects the force which
produced both the one and the other
should be measured, was supposed to
be a question not of terminology, but
of fact.

The ambiguity of the word Infinite
is the real fallacy in the amusing logi-
cal puzzle of Achilles and the Tortoise,
a puzzle which has been too hard for
the ingenuity or patience of many
philosophers, and which no less a
thinker than Sir William Hamilton
considered as insoluble, as a sound
argument though leading to a palpable
falsehood. The fallacy, as Hobbes
hinted, lies in the tacit assumption
that whatever is infinitely divisible is
infinite ; but the following solution
(to the invention of which I have
no claim) is more precise and satis-
factory.

The argument is, let Achilles run
ten times as fast as the tortoise, yet
if the tortoise has the start, Achilles
will never overtake him. For sup-
pose them to be at fii-st separated by

an interval of a thousand feet : when
Achilles has run these thousand feet,
the tortoise will have got on a hun-
dred ; when Achilles has run those
hundred, the tortoise will have run
ten, and so on for ever ; therefore
Achilles may run for ever without
overtaking the tortoise.

Now the " for ever " in the conclu-
sion means, for any length of time
that can be supposed ; but in the pre-
mises, " ever" does not mean any
length of time ; it means any number
of subdivisions of time. It means
that we may divide a thousand feet
by ten, and that quotient again by
ten, and so on as often as we please ;
that there never needs bean end to the
subdivisions of the distance, nor conse-
quently to those of the time in which
it is performed. But an unlimited
number of subdivisions may be made
of that which is itsdf limited. The
argument proves no other infinity of
duration than may be embraced within
five minutes. As long as the five
minutes are not expired, what re-
mains of them may be divided by
ten, and again by ten, as often as
we like, which is perfectly compatible
with their being only five minutes
altogether. It proves, in short, that
to pass through this finite space re-
quires a time which is infinitely divi-
sible, but not an in finite time — thecon-
founding of which distinction Hobbes
had already seen to be the gist of the
fallacy.

The following ambiguities of the
word right (in addition to the obvious
and familiar one of a right and the
adjective right) are extracted from a
forgotten paper of my own, in a perio-
dical : —

" Speaking morally, you are said to
have a right to do a thing, if all per-
sons are morally bound not to hinder
you from doing it. But, in another
sense, to have a right to do a thing is
the opposite of having no right to do
it, i.e. of being under a moral obliga-
tion to forbear doing it. In this
sense, to say that you have a right to
do a thing means that you may do it

536

FALLACIES.

without any breach of duty on your
part ; that other persons not only
ought not to hinder you, but have no
cause to think worse of you for doing
it. This is a perfectly distinct pro-
position from the preceding. The
right which you have by virtue of a
duty incumbent upon other persons is
obviously quite a different thing from
a right consisting in the absence of
any duty incumbent upon yourself.
Yet the two things are perpetually
confounded. Thus a man will say he
has a right to publish his opinions,
which may be true in this sense, that
it would be a breach of duty in any
other person to interfere and prevent
the publication ; but he assumes there-
upon that in publishing his opinions
he himself violates no duty, which
may either be true or false, depending
as it does on his having taken due
pains to satisfy himself, first, that the
opinions are true, and, next, that their
publication in this manner, and at
this particular juncture, will probably
be beneficial to the interests of truth
on the whole.

" The second ambiguity is that of
confounding a right of any kind with
a right to enforce that right by re-
sisting or punishing a violation of it.
People will say, for example, that they
have a right to good government,
which is undeniably true, it being the
moral duty of their governors to govern
them well. But in granting this you
are supposed to have admitted their
right or liberty to turn out their gov-
ernors, and perhaps to punish them,
for having failed in the performance
of this duty ; which, far from being
the same thing, is by no means uni-
versally true, but depends on an im-
mense number of varying circum-
stances," requiring to be conscien-
tiously weighed before adopting or
acting on such a resolution. This
last example is (like others which have
been cited) a case of fallacy within
fallacy ; it involves not only the second
of the two ambiguities pointed out,
but the first likewise.

One not unusual form of the Fal-

lacy of Ambiguous Terms is known
technically as the Fallacy of Compo-
sition and Division : when the same
term is collective in the premises,
distributive in the conclusion, or vice
versa; or when the middle term is
collective in one premise, distributive
in the other. As if one were to say,
(I quote from Archbishop Whately,)
" All the angles of a triangle are
equal to two right angles : ABC is an
angle of a triangle ; therefore ABC
is equal to two right angles. . . .
There is no fallacy more common, or
more likely to deceive, than the one
now before us. The form in which it
is most usually employed is to estab-
lish some truth separately concern-
ing each single member of a certain
class, and thence to infer the same of
the whole collect, vely. " As in the argu-
ment one sometimes hears to prove
that the world could do without great
men. If Columbus (it is said) had
never lived, America would still have
been discovered, at most only a few
years later ; if Newton had never
lived, some other person would have
discovered the law of gravitation ;
and so forth. Most tnae ; these
things would have been done, but in
all probability not till some one had
again been found with the qualities
of Columbus or Newton. Because
any one great man might have had
his place .supplied by other great men,
the argument concludes that all great
men could have been dispensed with.
The term *' great men" is distributive
in the premises and collective in the
conclusion.

"Such also is the fallacy which
proi)ably operates on movst adven-
turers in lotteries : e.g. ' the gaining
of a high prize is no uncommon oc-
currence ; and what is no uncommon
occurrence may reasonably be ex-
])ected ; therefore the gaining of a
high prize may reasonably be ex-
pected : ' the ctmdusiou when applied
to the individual (as in practice it is)
must be understood in the sense of
' reasonably expected by a certain in-
dividual; ' therefore for the major

1

)wn ^1

FALLACIES OF CONFUSION.

537

premise to be true, the middle term
must be understood to mean, ' no un-
common occurrence to some one pai'-
ticular person ; ' whereas for the
minor (which has been placed first)
to be true, you must understand it of
* no xmcommon occurrence to some one
or othei' ; ' and thus you will have the
Fallacy of Composition.

" This is a Fallacy with which
men are extremely apt to deceive
themselves; for when a multitude of
particulars are presented to the mind,
many are too weak or too indolent to
take a comprehensive view of them,
but confine their attention to each
single point by turns ; and then de-
cide, infer, and act accordingly : e.g.
the imprudent spendthrift, finding
that he is able to afford this, or that,
or the other expense, forgets that all
of them together will ruin him." The
debauchee destroys his health by suc-
cessive acts of intemperance, because
no one of those acts would be of itself
BuflBcient to do him any serious harm.
A sick person reasons with himself,
"one, and another, and another of
my symptoms do not prove that I
have a fatal disease ; " and practi-
cally concludes that all taken together
do not prove it.

§ 2. We have now sufficiently ex-
emplified one of the principal Genera
in this Order of Fallacies, where, the
source of error being the ambiguity
of terms, the premises are verbally
what is required to support the con-
clusion, but not really so. In the
second great Fallacy of Confusion
they are neither verbally nor really
sufficient, though, from their multi-
plicity and confused arrangement,
and still oftener from defect of me-
mory, they are not seen to be what
they are. The fallacy I mean is that
of Petitio Principii, or begging tlie
question, including the more com-
plex and not uncommon variety of
it which is termed Reasoning in a
Circle.

Petitio Principii, as defined by
Archbishop Whately, is the fallacy

" in which the premise either appears
manifestly to be the same as the con-
clusion, or is actually proved from the
conclusion, or is such as would natur-
ally and properly so be proved." By
the last clause I presume is meant, that
it is not susceptible of any other proof ;
for otherwise there would be no fal-
lacy. To deduce from a proposition
propositions from which it would
itself more naturally be deduced, is
often an allowable deviation from the
usual didactic order ; or at most what,
by an adaptation of a phrase familiar
to mathematicians, may be called a
logical inelegance*

The employment of a proposition to
prove that on which it is itself depen-
dent for proof, by no means implies
the degree of mental imbecility which
might at first be supposed. The diffi-
culty of comprehending how this fal-
lacy could possibly be committed dis-
appears when we reflect that all per-
sons, even the instructed, hold a great
number of opinions without exactly
recollecting how they came by them.
Believing that they have at some for-
mer time verified them by sufficient
evidence, but having forgotten what
the evidence was, they may easily be
betrayed into deducing from them the
very propositions which are alone cap-
able of serving as premises for their
establishment. "As if," says Arch-
bishop Whately, " one should attempt
to prove the being of a God from
the authority of Holy Writ ; " which
might easily happen to one with
whom both doctrines, as fundamental
tenets of his religious creed, stand on
the same ground of familiar and tra-
ditional belief.

* In his later editions. Archbishop
Wliate y confines tho n;ime of Petitio
Privcipii "to those cjiaes in whicii one of
the premises either is manifestly the sai?ie
in siiise with the conclusion, or is actunlly
proved from it, or is such as the ])er8on8
vou are •• ddiessing are not likely to know,
or to admit, except a-^ an inference from
the conclusion: as, eg. if anyone should
infer ti e authenricity of a certain history
from its recf)rding such and such facts, the
reality of which rosts on th« •videuco of
that history."

538

FALLACIES.

Arguing in a circle, however, is a
stronger case of the fallacy, and im-
plies more than the mere passive re-
ception of a premise by one who does
not remember how it is to be proved.
It implies an actual attempt to prove
two propositions reciprocally from one
another ; and is seldom resorted to,
at least in express terms, by any per-
son in his own speculations, but is
committed by those who, being hard
pressed by an adversary, are forced
into giving reasons for an opinion of
which, when they began to argue, they
had not sufficiently considered the
grounds. As in the following example
from Archbishop Whately : * ' Some
mechanicians attempt to prove (what
they ought to lay down as a probable
but doubtful hypothesis *) that every
particle of matter gravitates equally :
'why?' 'because those bodies which
contain more particles ever gravitate
more strongly, i.e. are heavier : ' * but,
(it may be urged,) those which are
heaviest are not always more bulky ; *
' no, but they contain more particles,
though more closely condensed :' 'how
do you know that?' ' because they are
heavier : ' ' how does that prove it ? '
• because all particles of matter gravi-
tating equally, that mass which is
specifically the heavier must needs
have the more of them in the same
space.' " It appears to me that the
fallacious reasoner, in his private
thoughts, would not be likely to pro-
ceed beyond the first step. He would
acquiesce in the sufficiency of the rea-
son first given, " bodies which contain
more particles are heavier." It is
when he finds this questioned, and is
called upon to prove it, without know-
ing how, that he tries to establish his
premise by supposing proved what he
is attempting to prove by it. The
most effectual way, in fact, of expos-
ing a Petitio Principii, when circum-
stances allow of it, is by challenging

* No longer even a probable hyrothesis,
oince the establishment of the atomic the-
ory ; it l)eiiig now cei tuin that the integral
particles of different substances gravitate
uueijually. It is true that these particles,

the reasoner to prove his premises ;
which if he attempts to do, he is
necessarily driven into arguing in a
circle.

It is not uncommon, however, for
thinkers, and those not of the lowest
description, to be led even in their
own thoughts, not indeed into for-
mally proving each of two propo-
sitions from the other, but into ad-
mitting propositions which can only
be so proved. In the preceding ex-
ample the two together form a com-
plete and consistent, though hypothe-
tical, explanation of the facts con-
cerned. And the tendency to mistake
mutual coherency for truth, to trust
one's safety to a strong chain though
it has no point of support, is at the
bottom of much which, when reduced
to the strict forms of argumentation,
can exhibit itself no otherwise than as
reasoning in a circle. All experience
bears testimony to the enthralling
effect of neat concatenation in a sys-
tem of doctrines, and the difficulty
with which people admit the persua-
sion that anything which holds so
well together can possibly fall.

Since every case where a conclusion
which can only be proved from cer-
tain premises is used for the proof of
those premises is a case of petitio
principii, that fallacy includes a very
great proportion of all incorrect rea-
soning. It is necessary, for complet-
ing our view of the fallacy, to ex-
emplify some of the disguises under
which it is accustomed to mask itself,
and to escape exposure.

A proposition would not be ad-
mitted by any person in his senses
as a corollary from itself, unless it
were expressed in language which
made it seem different. One of the
commonest modes of so expressing it
is to present the proposition itself in
abstract terms, as a proof of the same
proposition expressed in concrete lan-

thongh real minima for the purposes of '.
CI emical combination, may not be the ulti-
mate particles of the su Instance ; and this
doTibt alone renders the hypothesis admis-
sible, even as au hypothesis.

FALLACIES OF CONFUSION.

539

guage. This is a very frequent mode,
not only of pretended proof, but of
pretended explanation, and is paro-
died when Moli^re makes one of his
absurd physicians say —

" Mihi k docto doctore,

Doiutmdatur causam et rationem
qiiare
Opium facit dormire.

A qnoi respuudeo,

Quia est in eo

Virtus doimitiva,
Cujus est iiatura

Sensua assoupire."

The words Nature and Essence are
grand instruments of this mode of
begging the question ; as in the well-
known argument of the scholastic
theologians, that the mind thinks
always, because the essence of the
mind is to think. Locke had to
point out that if by essence is here
meant some property which must
manifest itself by actual exercise at
all times, the premise is a direct as-
sumption of the conclusion ; while if
it only means that to think is the
distinctive property of a mind, there
is no connection between the premise
and the conclusion, since it is not
necessary that a distinctive property
should be perpetually in action.

The following is one of the modes
in which these abstract terms. Nature
and Essence, are used as instruments
of this fallacy. Some particular pro-
perties of a thing are selected, more
or less arbitrarily, to be termed its
nature or essence ; and when this
has been done, these properties are
supposed to be invested with a kind
of indefeasibleness, to have become
paramoxmt to all the other properties
of the thing, and incapable of being
prevailed over or counteracted by
them. As when Aristotle, in a pas-
sage already cited, "decides that
there is no void on such arguments
as this ; in a void there could be no
difference of up and down ; for as in
nothing there are no differences, so
there are none in a privation or nega-
tion ; but a void is merely a privation
or negation of matter ; therefore, in a
void, bodie» could not move up and

down, which it is in their nature to
do." * In other words, it is in the
natu7'e of bodies to move up and
down, ergo any physical fact which
supposes them not so to move can-
not be authentic. This mode of rea-
soning, by which a bad generalisation
is made to overrule all facts which
contradict it, is petitto principii in
one of its most palpable forms.

None of the modes of assuming
what should be proved are in more
frequent use than what are termed
by Bentham "question- begging ap-
pellatives," names which beg the
question under the disguise of stating
it. The most potent of these are
such as have a laudatory or vitupe-
rative character. For instance, in
politics, the word Innovation. The
dictionary meaning of this term being
merely "a change to something new,"
it is difficult for the defenders even
of the most salutary improvement to
deny that it is an innovation ; yet
the word having acquired in common
usage a vituperative connotation in
addition to its dictionary meaning,
the admission is always construed as
a large concession to the disadvan-
tage of the thing proposed.

The following passage from the
argument in refutation of the Epicu-
reans, in the second book of Cicero de
Finibus, affords a fine example of this
sort of fallacy : — '* Et quidem illud
ipsum non nin>ium probo (et tantum
patior) philosophum loqui de cupidi-
tatibus finiendis. An potest cupiditas
finiri ? toUenda est, atque extrahenda
radicitus. Quis est enim, in quo sit
cupiditas, quin recte cupidus dici
possit ? Ergo et avarus erit, sed finite :
adulter, verum habebit modum : et
luxuriosus eodem modo. Qualis ista
philosophia est, quae non interitum
afferat pravitatis, sed sit contenta
mediocritate vitiorum?" The ques-
tion was, whether certain desires,
when kept within bounds, are vices
or not ; and the argument decides the
point by applying to them a word

» Hisi. Ind. Sc, 1. 34.

540

FALLACIES.

{cupiditas) which implies vice. It is
shown, however, in the remarks which
follow, that Cicero did not intend this
as a serious argument, but as a criti-
cism on what he deemed an inappro-
priate expression. " Rem ipsam pror-
sus probe : elegantiam desidero. Ap-
pellet hsec desideria naturce; cupidi-
tatis nomen servet alio," &c. But
many persons, both ancient and mo-
dern, have employed this, or some-
thing equivalent to it, as a real and
conclusive argument. We may re-
mark that the passage respecting
cupiditas and cupidus is also an ex-
ample of another fallacy already no-
ticed, that of Paronymous Terms.

Many more of the arguments of the
ancient moralists, and especially of
the Stoics, fall within the definition
of Petitio Principii. In the De Fini-
bus, for example, which I continue to
quote as being probably the best ex-
tant exemplification at once of the
doctrines and the methods of the
schools of philosophy existing at that
time ; of what value as arguments are
such pleas as those of Cato in the
third book : That if virtue were not
happiness, it could not be a thing to
boast of : that if death or pain were
evils, it would be impossible not to
fear them, and it could not, therefore,
be laudable to despise them, &c. In
one way of viewing these arguments,
they may be regarded as appeals to
the authority of the general sentiment
of mankind which had stamped its
approval upon certain actions and
characters by the phrases referred to ;
but that such could have been the
meaning intended is very unlikely,
considering the contempt of the an-
cient philosophers for vulgar opinion.
In any other sense they are clear
cases of Petitio Principii, since the
word laudable and the idea of boast-
ing imply principles of conduct ; and
practical maxims can only be proved
by speculative truths, namely, from
the properties of the subject-matter,
and cannot, therefore, be employed
to prove those properties. As well
might it be argued that a government

is good because we ought to support
it, or that there is a God because it is
our duty to pray to him.

It is assumed by all the disputants
in the De Finibus as the foundation
of the inquiry into the siimmum bo-
numthsit "sapiens semper beatus est."
Not simply that wisdom gives the
best chance of happiness, or that wis-
don consists in knowing what happi-
ness is, and by what things it is pro-
moted— these propositions would not
have been enough for them — but that
the sage always is, and must of neces-
sity be, happy. The idea that wisdom
could be consistent with unhappiness
was always rejected as inadmissible:
the reason assigned by one of the in-
terlocutors, near the beginning of the
third book, being, that if the wise
could be unhappy, there was little use
in pursuing wisdom. But by un-
happiness they did not mean pain or
suffering ; to that it was granted that
the wisest person was liable in com-
mon with others : he was happy, be-
cause in possessing wisdom he had the
most valuable of all possessions, the
most to be sought and prized of all
things, and to possess the most valu-
able thing was to be the most happy.
By laying it down, therefore, at the
commencement of the inquiry, that
the sage must be happy, the disputed
question respecting the summmn bo-
num was in fact begged ; with the
further assumption that pain and
suffering, so far as they can co-exist
with wisdom, are not unhappiness, and
are no evil.

The following are additional in-
stances of Petitio Principii, under
more or less of disguise.

Plato, in the Sophides, attempts
to prove that things may exist which
are incorporeal by the argument that
justice and wisdom are incorporeal,
and justice and wisdom must be
something. Here, if by some king be
meant, as Plato did in fact mean, a
thing capable of existing in and by it-
self, and not as a quality of some other
thing, he begs the question in assert-
ing that justice and wisdom muat be

FALLACIES OF CONFUSION.

541

something : if he means anything else,
his conclusion is not proved. This
fallacy might also be classed under
ambiguous middle term : something,
in the one premise, meaning some
substance, in the other merely some
object of thought, whether substance
or attribute.

It was formerly an argiiment em-
ployed in proof of what is now no
longer a popular doctrine, the infinite
divisibility of matter, that every por-
tion of matter, however small, must at
least have an upper and an under sur-
face. Those who used this argument
did not see that it assumed the very
point in dispute, the impossibility of
arriving at a minimum of thickness ;
for if there be a minimum, its upper
and under surface will of course be
one : it will be itself a surface, and no
more. The argument owes its very
considerable plausibility to this, that
the premise does actually seem more
obvious than the conclusion, though
really identical with it. As expressed
in the premise, the proposition appeals
directly and in concrete language to
the incapacity of the human imagi-
nation for conceiving a minimum.
Viewed in this light, it becomes a
case of the d priori fallacy or natural
prejudice, that whatever cannot be
conceived cannot exist. Every Fal-
lacy of Confusion (it is almost un-
necessary to repeat) will, if cleared up,
become a fallacy of some other sort ;
and it will be found of deductive or
ratiocinative fallacies generally, that
when they mislead, there is mostly, as
in this case, a fallacy of some other
description lurking under them, by
virtue of which chiefly it is that the
verbal juggle, which is the outside or
body of this kind of fallacy, passes
undetected.

Euler's Algebra, a book otherwise
of great merit, but full to overflow-
ing of logical errors in respect to the
foundation of the science, contains
the following argument to prove that
minus multiplied by minus gives plus,
a. doctrine the opprobrium of all mere
mathematicians, and which Euler had

not a glimpse of the true method of
proving. He says minus multiplied
by minvs cannot give minus ; for
minus multiplied hy plus gives mivns,
and minus nmltiplied by minus can-
not give the same product as minus
multiplied by plus. Now one is ob-
liged to ask why minus multiplied
by minus must give any product at
all ? and if it does, why its product
cannot be the same as that of minus
multiplied by plus ; for this would
seem, at the first glance, not more ab-
surd than that minus by minus should
give the same as jlus by plus, the
proposition which Euler prefers to it.
The premise requires proof as much as
the conclusion ; nor can it be proved ex-
cept by that more comprehensive view
of the nature of multiplication and
of algebraic processes in general which
would also supply a far better proof
of the mysterious doctrine which Euler
is here endeavouring to demonstrate.

A striking instance of reasoning in
a circle is that of some ethical writers,
who first take for their standard of
moral truth what, being the general,
they deem to be the natural or in-
stinctive sentiments and perceptions
of mankind, and then explain away
the numerous instances of divergence
from their assumed standard, by re-
presenting them as Teases in which the
perceptions are unhealthy. Some par-
ticular mode of conduct or feeling is
affirmed to be unnatural ; why ? be-
cause it is abhorrent to the universal
and natural sentiments of mankind.
Finding no such sentiment in your-
self, you question the fact ; and the
answer is, (if your antagonist is polite,)
that you are an exception, a peculiar
case. But neither (say you) do I find
in the people of some other country,
or of some former age, any such feel-
ing of abhorrence : " Ay, but their
feelings were sophisticated and un-
healthy."

One of the most notable specimens
of reasoning in a circle is the doctrine
of Hobbes, Rousseau, and others,
which rests the obligations by which
human beings are bound as members

542

FALLACIES.

of society, on a supposed social com-
pact. I waive the consideration of
the fictitious nature of the compact
itself ; but when Hobbes, through
the whole Leviathan, elaborately de-
duces the obligation of obeying the
sovereign, not from the necessity or
utility of doing so, but inmi a pro-
mise supposed to have been made by
our ancestors, on renouncing savage
life and agreeing to establish political
society, it is impossible not to retort
by the question, why are we bound
to keep a promise made for us by
others, or why bound to keep a pro-
mise at all ? No satisfactory ground
can be assigned for the obligation,
except the mischievous consequences
of the absence of faith and mutual
confidence among mankind. We are,
therefore, brought round to the in-
terests of society, as the ultimate
ground of the obligation of a pro-
mise ; and yet those interests are not
admitted to be a sufficient justifica-
tion for the existence of government
and law. Without a promise it is
thought that we should not be bound
to that which is implied in all modes
of living in society, namely, to yield a
general obedience to the laws therein
established ; and so necessary is the
promise deemed, that if none has
actually been made, some additional
safety is supposed to be given to the
foundations of society by feigning

§ 3. Two principal subdivisions of
the class of Fallacies of Confusion
having been disposed of, there re-
mains a third, in which the c<mfusion
is not, as in the Fallacy of Ambiguity,
in misconceiving the import of the
premises, nor as in Petitio Principii,
in forgetting what the premises are,
but in mistaking the conclusion which
is to be proved. This is the fallacy
of Ignoratio Elenchi, in the widest
sense of the phrase ; also called by
Archbishop Whately the Fallacy of
Irrelevant Conclusion. His examples
and remarks are highly worthy of
citation.

" Various kinds of propositions are,
according to the occasion, substituted
for the one of which proof is required :
sometimes the particular for the uni-
versal ; someiimes a proposition with
different terms ; and various are tlie
contrivances employed to effect and
to conceal this substitution, and to
make the conclusion which the sophist
has drawn answer practically the
same purpose as the one he oiight
to have established. We say, 'prac-
tically the same purpose,' because it
will very often happen that some
emotion will be excited, some senti-
ment impressed on the mind, (by a
dexterous employment of this fallacy,)
such as shall bring men into the dis-
position requisite for your purpose ;
though they may not have assented
to, or even stated distinctly in their
own minds, the proposition which it
was your business to establish. Thus
if a sophist has to defend one who
has been guilty of some serious offence,
which he wishes to extenuate, though
he is unable distinctly to prove that
it is not such, yet if he can succeed
in making the audience laugh at some
casual matter, he has gained practi-
cally the same point. So also if any
one has pointed out the extenuating
circumstances in some particular case
of offence so as to show that it differs
widely from the generality of the same
class, the sophist, if he finds himself
unable to disprove these circum-
stances, may do away the force of
them by simply referring the action
to that very class which no one can
deny that it belongs to, and the very
name of which will excite a feeling of
disgust sufficient to counteract the
extenuation : e.g. let it be a case of
peculation, and that many mitigating
circumstances have been brought for-
ward which cannot be denied ; the
sophistical opponent will reply, 'Well,
but after all, the man is a rogue, and
there is an end of it ; ' now in reality
this was (by hypothesis) never the
question ; and the mere assertion of
what was never denied ought not, in
fairness, to be regarded as decisive :

FALLACIES OF CONFUSION.

543

but, practically, the odiousness of the
word, arising in great measure from
the association of those very circum-
stances which belong to most of the
class, but which we have supposed to
be absent in this particular instance,
excites precisely that feeling of dis-
gust which in effect destroys the
force of the defence. In like manner
we may refer to this head all cases
of improper appeal to the passions,
and everything else which is men-
tioned by Aristotle as extraneous to
the matter in hand (i^u roO irpdyfia-

TOJ)."

Again, "instead of proving that
'this prisoner has committed an at-
rocious fraud,' you prove that the
fraud he is accused of is atrocious :
instead of proving (as in the well-
known tale of Cyrus and the two
coats) that the taller boy had a right
to force the other boy to exchange
coats with him, you prove that the
exchange would have b.^en advantage-
ous to both : instead of proving that
the poor ought to be relieved in this
way rather than in that, you prove
that the poor ought to be relieved :
instead of provin,^ that the irrational
agent — whether a brute or a mad-
man —can never be deterred from any
act by apprehension of punishment,
(as, for instance, a dog from sheep-
biting by fear of being beaten,) you
prove that the beating of one dog
does not operate as an example to
other dogs, &c.

" It is evident that ignoratio elenchi
may be employed as well for the ap-
parent refutation of your opponent's
proposition as for the apparent estab-
lishment of your own ; for it is sub-
stantially the same thing to prove
what was not denied or to disprove
what was not asserted. The latter
practice is not less common, and it is
more offensive, because it frequently
amounts to a personal affront, in attri-
buting to a person opinions, &c., which
he perhaps holds in abhorrence. Thus,
when in a discussion one party vin-
dicates, on the ground of general ex-
pediency, a particular instance of re-

sistance to government in a case of
intolerable oppression, the opponent
may gravely maintain * that we ought
not to do evil that good may come ' —
a proposition which of course had • ever
been denied, the point in dispute be-
ing, * whether resistance in this parti-
cular case were doing evil or not.' Or
again, by way of disproving the asser-
tion of the right of private judgment
in religion, one may hear a grave ar-
gument to prove that ' it is impossible
every one can be riyht in his judg-
ment: "

The works of controversial writers
are seldom free from this fallacy. The
attempts, for instance, to disprove the
population doctrines of Maltlms have
been mostly cases of vjnoratio elenchL
Malthus has been supposed to be re-
futed if it could be shown that in
some countries or ages population ha.s
been nearly stationary, as if he had
asserted that population always in-
creases in a given ratio, or had not
expressly declared that it increases
only in so far as it is not restrained
by prudence or kept down by poverty
and disease. Or, perhaps, a collection
of facts is produced to prove that in
some one country the people are better
off with a dense population than they
are in another country with a thin
one, or that the people have become
more numerous and better off at the
same time ; as if the assertion were
that a dense population could not pos-
sibly be well off — as if it were not part
of the very doctrine, and essential to
it, that where there is a more abun-
dant production there may be a greater
population without any increase of
poverty, or even with a diminution
of it.

The favourite argument against Ber-
keley's theory of the non-existence of
matter, and the most popularly effec-
tive, next to a "grin"* — an argu-
ment, moreover, which is not confined
to "coxcombs," nor to men like Samuel
Johnson, whose greatly overrated abi-
lity certainly did not lie in the direc-

* "And coxcombs vanquish Berkeley
with agiiu"

544

FALLACIES.

tion of metaphysical speculation, but
is the stock argument of the Scotch
school of metaphysicians — is a pal-
pable ignoratio elenchi. The argu-
ment is perhaps as frequently ex-
pressed by gesture as by words, and
one of its commonest forms consists
in knocking a stick against the ground.
This short and easy confutation over-
looks the fact that, in denying mat-
ter, Berkeley did not deny anything
to which our senses bear witness,, and
therefore cannot be answered by any
appeal to them. His scepticism re-
lated to the supposed substratum, or
hidden cause of the appearances per-
ceived by our senses, the evidence of
which, whatever may be thought of
its conclusiveness, is certainly not the
evidence of sense ; and it will always
remain a signal proof of the want
of metaphysical profundity of Reid,
Stewart, and, I am porrv to add, of
Brown, that they should have per-
sisted in asserting that Berkeley, if
he believed his own doctrine, was
bound to walk into the kennel or run

his head against a post. As if per-
sons who do not recognise an occult
cause of their sensations could not
possibly believe that a fixed order
subsists among the sensations them-
selves. Such a want of comprehen-
sion of the distinction between a thing
and its sensible manifestation, or, in
metaphysical language, between the
noumenon and the phenomenon, would
be impossible to even the dullest dis-
ciple of Kant or Coleridge.

It would be easy to add a greater
number of examples of this fallacy,
as well as of the others which I have
attempted to characterise. But a
more copious exemplification does not
seem to be necessary ; and the intelli-
gent reader will have little difficulty
in adding to the catalogue from his
own reading and experience. We
shall therefore here close our exposi-
tion of the general principles of logic,
and proceed to the supplementary
inquiry which is necessary to com-
plete our deiign.

BOOK VI.

ON THE LOGIC OF THE MOEAL
SCIENCES.

•• SI ITiomme peut predire, avec une assurance presqiie entiire, les ph^nomines dont
il connait lea lois ; si lors meme qu'elles lui sont inconnues, il pent, d'aprba I'exp^ri-
ence, prevoir avec une grande prooabilite les eveneniena de I'aveiur; pourqiioi regar*
derait-on comme une eutreprise chim^rique, celle de tracer avec quelque vrai>eniblance
le tableau des destinies futures de I'esj^ce humauie, d'apres les idsultats de son hi»-
toire? Le seul fondement de croyance dans les sciences naturelles, est cette id6e,
que les loia generates, connues ou iguor^es, qui rfeglent les phenonifenes de I'univers,
sont n^ces.-aires et constantes ; et p,.r quelle rai-on ce principe serait-il m<'ins vrai
pour le developpement des facult^s intellectuelles et morales de rhomme, que pour
les autres operations, de la nature? Enfin, puisque des opinions fornixes dapifesl'ex-
p6rience . . . sont )a seule rfegle de la conduite des honimes les plus sages, pourquoi
Interdirait-on an philosophy d'appuyer ses conjectures sur cette mfiine base, pourvu
qu'il ne leur attribue pas une certitude sup^rieure ^ celle qui pout maitre du nonibre,
de la Constance, de I'exactitude des observations ? "—Condorcjct, Eiquitit d'wn Tabltayi,
Historique des Progrh de V Esprit Haniain.

CHAPTER I.

INTRODUCTORY REMARKS.

§ 1. Principles of Evidence and
Theories of Method are not to be
constructed d prioiH, The laws of
our rational faculty, like those of
every other natural agency, are only
learnt by seeing the agent at work.
The earlier achievements of science
were made without the conscious ob-
servance of any Scientific Method ;
and we should never have known by
what process truth is to be ascertained
if we had not previously ascertained
many truths. But it was only the
easier problems which could be thus
resolved : natural sagacity, when it
tried its strength ag:ain.st the more
difficult ones, either failed altogether,
or if it succeeded here and there in
obtaining a solution, had no sure
means of convincing others that its

solution was correct. In scientific
investigation, as in all other v/orks of
human skill, the way of obtaining the
end is seen as it were instinctively by
superior minds in some comparatively
simple case, and is then, by judicious
generalisation, adapted to the variety
of complex cases. We learn to do
a thing in difficult circumstances by
attending to the manner in which
we have spontaneously done the same
thing in easier ones.

This truth is exemplified by the
history of the various branches of
knowledge which have successively,
in the ascending oider of their com-
plication, assumed the character of
sciences ; and will doubtless receive
fresh confirmation from those of which
the final scientific constitution is yet
to come, and which are still aban-
doned to the uncertainties of vague
and popular discussion. Although

2M

546

LOGIC OF THE MORAL SCIENCES.

several other sciences have emerged
from this state at a comparatively
recent date, none now remain in it
except those which relate to man
himself, the most complex and most
difficult subject of study on which
the human mind can be engaged.

Concerning the physical nature of
man as an organised being, — though
there is still much uncertainty and
much controversy, which can only be
terminated by the general acknow-
ledgment and employment of stricter
rules of induction than are commonly
recognised, — there is, however, a con-
siderable body of truths which all
who have attended to the subject
consider to be fully established ; nor
is there now any radical imperfection
in the method observed in this de-
partment of science by its most dis-
tinguished modem teachers. But the
laws of Mind, and, in even a greater
degree, those of Society, are so far
from having attained a similar state
of even partial recognition, that it is
still a controversy whether they are
capable of becoming subjects of science
in the strict sense of the term ; and
among those who are agreed on this
point there reigns the most irrecon-
cilable diversity on almost every other.
Here, therefore, if anywhere, the prin-
ciples laid down in the preceding Books
may be expected to be useful.

If, on matters so much the most
important with which human intel-
lect can occupy itself, a more general
agreement is ever to exist among
thinkers ; if what has been pronounced
" the proper study of mankind " is not
destined to remain the only subject
which Philosophy cannot succeed in
rescuing from Empiricism ; the same
process through which the laws of
many simpler phenomena have by
general acknowledgment been placed
beyond dispute must be consciously
and deliberately applied to those more
difficult inquiries. If there are some
subjects on which the results obtained
have finally received the unanimous
assent of all who have attended to
the proof, ftud others on which man-

kind have not yet been equally suc-
cessful ; on which the most sagacious
minds have occupied themselves from
the earliest date, and have never suc-
ceeded in establishing any consider-
able body of truths, so as to be beyond
denial or doubt ; it is by generalising
the methods successfully followed in
the former inquiries, and adapting
them to the latter, that we may hope
to remove this blot on the face of
science. The remaining chapters are
an endeavour to facilitate this most
desirable object

§ 2. In attempting this, I am not
unmindful how little can be done
towards it in a mere treatise on Logic,
or how vague and unsatisfactory all
precepts of Method must necessarily
appear when not practically exempli-
fied in the establishment of a body of
doctrine. Doubtless, the most effec-
tual mode of showing how the sciences
of Ethics and Politics may be con-
structed would be to construct them :
a task which, it needs scarcely be
said, I am not about to undertake.
But even if there were no other ex-
amples, the memorable one of Bacon
would be sufficient to demonstrate
that it is sometimes both possible and
iiseful to point out the way, tl]ough
without being oneself prepared to ad-
venture far into it. And if more were
to be attempted, this at least is not a
proper place for the attempt.

In substance, whatever can be done
in a work like this for the Logic of
the Moral Sciences, has been or ought
to have been accomplished in the five
preceding Books ; to which the present
can be only a kind of supplement or
appendix, since the methods of in-
vestigation applicable to moral and
social science must have been already
described, if I have succeeded in enu-
merating and characterising those
of science in general. It remains,
however, to examine which of those
methods are more especially suited to
the various branches of moral inc^uiry ;
under what peculiar faculties or diffi-
culties they are there employed ; how

LIBERTY AND NECESSITY.

547

far the unsatisfactory state of those
inquiries is owing to a wrong choice
of methods, how far to want of skill
in the application of right ones ; and
what degree of ultimate success may
be attained or hoped for by a better
choice and more careful emplojmaent
of logical processes appropriate to the
case. In other words, whether moral
sciences exist, or can exist ; to what
degree of perfection they are suscep-
tible of being carried ; and by what
selection or adaptation of the methods
brought to view in the previous part
of this work that degree of perfection
is attainable.

At the threshold of this inquiry we
are met by an objection, which, if not
removed, would be fatal to the at-
tempt to treat human conduct as a
subject of science. Are the actions
of human beings, like all other na-
tural events, subject to invariable
laws ? Does that constancy of causa-
tion, which is the foundation of every
scientific theory of successive phe-
nomena, really obtain among them?
This is often denied ; and, for the
sake of systematic completeness, if not
from any very urgent practical neces-
sity, the question should receive a
deliberate answer in this place. We
shall devote to the subject a chapter
apart.

CHAPTER II.

OP LIBERTY AND NKCKSSITT.

§ I. The question whether the law
of causality applies in the same strict
sense to human actions as to other
phenomena, is the celebrated contro-
versy concerning the freedom of the
will, which, from at least as far back
as the time of Pelagius, has divided
both the philosophical and the reli-
gious world. The affirmative opinion
is commonly called the doctrine of
Necessity, as asserting human voli-
tions and actions to be necessary and
inevitable. The negative maintains
that the will is not determined, like
ptber phenomena, by antecedents, but

determines itself ; that our volitions
are not, properly speaking, the effects of
causes, or at least have no causes which
they uniformly and implicitly obey.

I have already made it sufficiently
apparent that the former of these
opinions is that which I consider the
true one ; but the misleading terms
in which it is often expressed, and
the indistinct manner in which it is
usually apprehended, have both ob-
structed its reception and perverted
its influence when received. The
metaphysical theory of free-will, as
held by philosophers, (for the practi-
cal feeling of it, common in a greater
or less degree to all mankind, is in no
way inconsistent with the contrary
theory,) was invented because the
supposed alternative of admitting
human actions to be necessary was
deemed inconsistent with every one's
instinctive consciousness, as well as
humiliating to the pride, and even de-
grading to the moral nature, of man.
Nor do I deny that the doctrine, as
sometimes held, is open to these im-
putations ; for the misapprehension
in which I shall be able to show that
they originate unfortunately is not
confined to the opponents of the doc-
trine, but is participated in by many,
perhaps we might say by most, of its
supporters.

§ 2. Correctly conceived, the doc-
trine called Philosophical Necessity
is simply this : that, given the mo-
tives which are present to an indi-
.vidual's mind, and given likewise the
character and disposition of the indi-
vidual, the manner in which he will
act might be unerringly inferred ;
that if we knew the person thor-
oughly, and knew all the induce-
ments which are acting upon him, we
could foretell his conduct with as
much certainty as we can predict any
physical event. This proposition I
take to be a mere interpretation of
universal experience, a statement in
words of what every one is internally
convinced of. No one who believed
that he knew thoroughly the cir^^uji^"

548

LOGIC OF TftE MORAL SCIENCES.

stances of any case, and the charac-
ters of the different persons concerned,
would hesitate to foretell how all of
them would act. Whatever degree
of doubt he may in fact feel arises
from the uncertainty whether he
really knows the circumstances, or
the character of some one or other of
the persons, with the degree of accu-
racy required ; but by no means from
thinking that if he did know these
things, there could be any uncertainty
what the conduct would be. Nor
does this full assurance conflict in
the smallest degree with what is
called our feeling of freedom. We
do not feel ourselves the less free be-
cause those to whom we are inti-
mately known are well assured how
we shall will to act in a particular
case. We often, on the contrary, re-
gard the doubt what our conduct will
be as a mark of ignorance of our cha-
racter, and sometimes even resent
it as an imputation. The religious
metaphysicians who have asserted
the freedom of the will have always
maintained it to be consistent with
divine foreknowledge of our actions ;
and if with divine, then with any
other foreknowledge. We may be
free, and yet another may have rea-
son to be perfectly certain what use
we shall make of our freedom. It is
not, therefore, the doctrine that our
volitions and actions are invariable
consequents of our antecedent states
of mind, that is either contradicted
by our consciousness or felt to be de-
grading.

But the doctrine of causation, when
considered as obtaining between our
volitions and their antecedents, is al-
most universally conceived as involv-
ing more than this. Many do not
believe, and very few practically feel,
that there is nothing in causation but
invariable, certain, and unconditional
sequence. There are few to whom
mere constancy of succession appears
a sufficiently stringent bond of union
for so peculiar a relation as that of
cause and effect. Even if the reason
repudiates, the imagination retains,

the feeling of some more intimate
connection, of some peculiar tie or
mysterious constraint exercised by
the antecedent over the consequent.
Now this it is which, considered as
applying to the human will, conflicts
with our consciousness and revolts
our feelings. We are certain that,
in the case of our volitions, there is
not this mysterious constraint. We
know that we are not compelled, as
by a magical spell, to obey any parti-
cular motive. We feel that if we
wished to prove that we have the
power of resisting the motive, we
could do so, (that wish being, it needs
scarcely be observed, a new antece-
dent;) and it would be humiliating
to our pride, and (what is of more
importance) paralysing to our desire
of excellence, if we thought other-
wise. But neither is any such myste-
rious compulsion now supposed, by
the best philosophical authorities, to
be exercised by any other cause over
its effect. Those who think that
causes draw their effects after them
by a mystical tie are right in believing
that the relation between volitions
and their antecedents is of another
nature. But they should go farther,
and admit that this is also true of all
other effects and their antecedents.
If such a tie is considered to be in-
volved in the word necessity, the doc-
trine is not true of human actions ;
but neither is it then true of inani-
mate objects. It would be more cor-
rect to say that matter is not bound
by necessity, than that mind is so.

That the free-will metaphysicians,
being mostly of the school which rejects
Hume's and Brown's analysis of Cause
and Effect, should miss their way for
want of the light which that analy-
sis affords, cannot surprise us. The
wonder is, that the Necessitarians,
who usually admit that philosophical
theory, should in practice equally lose
sight of it. The very same miscon-
ception of the doctrine called Philo-
.sophical Necessity which prevents the
opposite party from recognising its
truth, I believe to exist more or leu|

LIBERTY AND NECESSITY.

549

obscurely m the minds of most Neces-
sitarians, however they may in words
disavow it. I am much mistaken if
they habitually feel that the necessity
which they recognise in actions is but
uniformity of order, and capability of
being predicted. They have a feeling
as if there were at bottom a stronger
tie between the volitions and their
causes : as if, when they asserted that
the will is governed by the balance of
motives, they meant something more
cogent than if they had only said, that
whoever knew the motives, and our
habitual susceptibilities to them, could
predict how we should will to act.
They commit, in opposition to their
own scientific system, the very same
mistake which their adversaries com-
mit in obedience to theirs ; and in
consequence do really in some in-
stances suffer those depressing conse-
quences which their opponents erro-
neously impute to the doctrine itself.

§ 3. I am inclined to think that this
error is almost wholly an effect of the
associations with a word, and that
it would be prevented by forbearing
to employ, for the expression of the
simple fact of causation, so extremely
inappropriate a term as Necessity.
That word, in its other acceptations,
involves much more than mere uni-
formity of sequence : it implies irre-
sistibleness. Applied to the will, it
only means that the given cause will
be followed by the effect, subject to
all possibilities of counteraction by
other causes ; but in common use it
stands for the operation of those causes
exclusively, which are supposed too
powerful to be counteracted at all.
When we say that all human actions
take place of necessity, we only mean
that they will certainly happen if no-
thing prevents : — when we say that
dying of want, to those who cannot get
food, is a necessity, we mean that it
will certainly happen, whatever may be
done to prevent it. The application of
the same term to the agencies on which
human actions depend as is used to ex-
press those agencies of nature which

are really uncontrollable, cannot fail,
when habitual, to create a feeling of
uncontrollableness in the former also.
This, however, is a mere illusion.
There are physical sequences which
we call necessary, as death for want
of food or air ; there are others which,
though as much cases of causation as
the former, are not said to be neces-
sary, as death from poison, which an
antidote, or the use of the stomach-
pump, will sometimes avert. It is
apt to be forgotten by people's feel-
ings, even if remembered by their un-
derstandings, that human actions are
in this last predicament : they are
never (except in some cases of mania)
ruled by any one motive with such
absolute sway that there is no room
for the influence of any other. The
causes, therefore, on which action de-
pends are never uncontrollable, and
any given effect is only necessary pro-
vided that the causes tending to pro-
duce it are not controlled. That what-
ever happens could not have happened
otherwise unless something had taken
place which was capable of preventing
it, no one surely needs hesitate to admit.
But to call this by the name necessity
is to use the term in a sense so different
from its primitive and familiar mean-
ing, from that which it bears in the
common occasions of life, as to amount
almost to a play upon words. The as-
sociations derived from the ordinary
sense of the term will adhere to it in
spite of all we can do; and though
the doctrine of Necessity, as stated
by most who hold it, is very remote
from fatalism, it is probable that most
Necessitarians are Fatalists, more or
less, in their feelings.

A Fatalist believes, or half believes,
(for nobody is a consistent Fatalist,)
not only that whatever is about to
happen will be the infallible result of
the causes which produce it, (which is
the true Necessitarian doctrine,) but,
moreover, that there is no use in
struggling against it ; that it will
happen however we may strive to
prevent it. Now, a Necessitarian,
believing that our actions follow from

550

LOGIC OF THE MORAL SCIENCES*

our characters, and that our charac-
ters follow from our organisation, our
education, and our circumstances, is
apt to be, with more or less of con-
sciousness on his part, a Fatalist as to
his own actions, and to believe that
his nature is such, or that his edu-
cation and circumstances have so
moulded his character, that nothing
can now prevent him from feeling
and acting in a particular way, or at
least that no effort of his own can
hinder it. In the words of the sect
which in our own day has most per-
severingly inculcated and most per-
versely misunderstood this great doc-
trine, his character is formed for him,
and not hy him; therefore his wishing
that it had been formed differently is
of no use ; he has no power to alter
it. But this is a grand error. He
has, to a certain extent, a power to
alter his character. Its being, in the
ultimate resort, formed for him, is
not inconsistent with its being, in
part, formed hy him as one of the
intermediate agents. His character
is formed by his circumstances, (in-
cluding among these his particular
organisation,) but his own desire to
mould it in a particular way is one
of those circumstances, and by no
means one of the least influential.
We cannot, indeed, directly will to
be different from what we are ; but
neither did those who are supposed
to have formed our characters directly
will that we should be what we are.
Their will had no direct power except
over their own actions. They made
us what they did make us by willing,
not the end, but the requisite means ;
and we, when our habits are not too
inveterate, can, by similarly willing
the requisite means, make ourselves
different. If they could place us
under the influence of certain cir-
cumstances, we in like manner can
place ourselves under the influence of
other circumstances. We are exactly
as capable of making our own char-
acter, if ive wiU, as others are of
making it for us.

Yes, (answers the Owenite,) but

these words, "if we will,'* surrender
the whole point, since the will to
alter our own character is given us,
not by any efforts of ours, but by cir-
cumstances which we cannot help ;
it comes to us either from external
causes or not at all. Most true : if
the Owenite stops here, he is in a
position from which nothing can ex-
pel him. Our character is formed by
us as well as for us ; but the wish
which induces us to attempt to form
it is formed for us ; and how ? Not,
in general, by our organisation, nor
wholly by our education, but by our
experience — experience of the painful
consequences of the character we pre-
viously had, or by some strong feeling
of admiration or aspiration accident-
ally aroused. But to think that we
have no power of altering our char-
acter, and to think that we shall not
use our power unless we desire to use
it, are very different things, and have
a very different effect on the mind.
A person who does not wish to alter
his character cannot b© the person
who is supposed to feel discouraged
or paralysed by thinking himself un-
able to do it. The depressing effect
of the Fatalist doctrine can only be
felt where there is a wish to do what
that doctrine represents as impossible.
It is of no consequence what we think
forms our character, when we have
no desire of our own about forming
it, but it is of great consequence that
we should not be prevented from
forming such a desire by thinking
the attainment impracticable, and
that if we have the desire we should
know that the work is not so irre-
vocably done as to be incapable of
being altered.

And, indeed, if we examine closely,
we shall find that this feeling, of our
being able to modify our own char-
acter if we wish, is itself the feeling
of moral freedom which we are con-
scious of. A person feels morally
free who feels that his habits or his
temptations are not his masters, but
he theirs : who even in yielding to
them knows that he could resist ; that

LIBERTY AND NECESSITY.

551

Were he desirous of altogether throw-
ing them off, there would not be re-
quired for that purpose a stronger
desire than he knows himself to be
capable of feeling. It is of course
necessary, to render our consciousness
of freedom complete, that we should
have succeeded in making our char-
acter all we have hitherto attempted
to make it ; for if we have wished
and not attained, we have, to that
extent, not power over our own char-
acter— we are not free. Or at least,
we must feel that our wish, if not
strong enough to alter our character,
is strong enough to conquer our char-
acter when the two are brought into
conflict in any particular case of con-
duct. And hence it is said with truth,
that none but a person of confirmed
virtue is completely free.

The application of so improper a
term as Necessity to the doctrine of
cause and effect in the matter of
human character seems to me one
of the most signal instances in philo-
sophy of the abuse of terms, and its
practical conseqiiences one of the
most striking examples of the power
of language over our associations.
The subject will never be generally
understood until that objectionable
term is dropped. The free-will doc-
trine, by keeping in view precisely
that portion of the truth which the
word Necessity puts out of sight,
namely, the power of the mind to
co-operate in the formation of its own
character, has given to its adherents
a practical feeling much nearer to the
truth than has generally (I believe)
existed in the minds of Necessitarians.
The latter may have had a stronger
sense of the importance of what human
beings can do to shape the characters
of one another ; but the free-will doc-
trine has, I believe, fostered in its
supporters a much stronger spirit of
self -culture.

§ 4. There is still one fact which
requires to be noticed (in addition to
the existence of a power of self-forma-
tion) before the doctrine of the causa-

tion of human actions can be freed
from the confusion and misapprehen-
sions which surround it in many
minds. When the will is said to be
determined by motives, a motive does
not mean always, or solely, the anti-
cipation of a pleasure or of a pain.
I shall not here inquire whether it be
true that, in the commencement, all
our voluntary actions are mere means
consciously employed to obtain some
pleasure or avoid some pain. It is
at least certain that we gradually,
thnmgh the influence of association,
come to desire the means without
thinking of the end : the action itself
becomes an object of desire, and is
performed without reference to any
motive beyond itself. Thus far, it
may still be objected, that the action
having through association become
pleasurable, we are, as much as be-
fore, moved to act by the anticipa-
tion of a pleasure, namely, the pleasure
of the action itself. But granting
this, the matter does not end here.
As we proceed in the formation of
habits, and become accustomed to
will a particular act or a particular
course of conduct because it is pleasur-
able, we at last continue to will it
without any reference to its being
pleasurable. Although, from some
change in us or in our circumstances,
we have ceased to find any pleasure
in the action, or perhaps to anticipate
any pleasure as the consequence of it,
we still continue to desire the action,
and consequently to do it. In this
manner it is that habits of hurtful
excess continue to be practised al-
though the}' have ceased to be plea-
surable ; and in this manner also it
is that the habit of willing to per-
severe in the course which he has
chosen does not desert the moral
hero, even when the reward, however
real, which he doubtless receives from
the consciousness of well-doing, is
anything but an equivalent for the
sufferings he undergoes or the wishes
which he may have to renounce.

A habit of willing is commonly
called a purpose ; and among the

552

LOGIC OF THE MORAL SCIENCES.

causes of our volitions, and of the
actions which flow from them, must
be reckoned not only likings and aver-
sions, but also purposes. It is only
when our purposes have become inde-
pendent of the feelings of pain or
pleasure from which they originally
took their rise that we are said to
have a confirmed character. " A char-
acter," says Novalis, "is a completely
fashioned will ; " and the will, once
so fashioned, may be steady and con-
stant, when the passive susceptibili-
ties of pleasure and pain are greatly
weakened or materially changed.

With the corrections and explana-
tions now given, the doctrine of the
causation of our volitions by motives,
and of motives by the desirable ob-
jects offered to us, combined with our
particular susceptibilities of desire,
may be considered, I hope, as suffi-
ciently established for the purposes of
this treatise.*

CHAPTER III.

THAT THERE IS, OR MAY BE, A SCIENCE
OF HUMAN NATURE.

§ I. It is a common notion, or at
least it is implied in many common
modes of speech, that the thoughts,
feelings, and actions of sentient beings
are not a subject of science, in the
same strict sense in which this is true
of the objects of outward nature. This
notion seems to involve some confu-
sion of ideas, which it is necessary to
begin by clearing up.

Any facts are fitted, in themselves,
to be a subject of science, which fol-
low one another according to constant
laws ; although those laws may not
have been discovered, nor even be
discoverable by our existing resources.
Take, for instance, the most familiar
class of meteorological phenomena,
those of rain and sunshine. Scientific

* Some arguments and explanations,
Bupplementaiy to those in the text, will be
found in An Examination of Sir William
Hamilton'i Philoiophy, chap. xxvi.

inquiry has not yet succeeded in
ascertaining the order of antecedence
atjd consequence among these pheno-
mena, so as to be able, at least in our
regions of the earth, to predict them
with certainty or even with any high
degree of probability. Yet no one
doubts that the phenomena depend
on laws, and that these must be deri-
vative laws resulting from known
ultimate laws, those of heat, elec-
tricity, vaporisation, and elastic fluids.
Nor can it be doubted that if we were
acquainted with all the antecedent
circumstances, we could, even from
those more general laws, predict (sav-
ing difficulties of calculation) the state
of the weather at any future time.
Meteorology, therefore, not only has
in itself every natural requisite for
being, but actually is, a science ;
though, from the difficulty of observ-
ing the facts on which the phenomena
depend, (a difficulty inherent in the
peculiar nature of those phenomena, )
the science is extremely imperfect ;
and were it perfect, might probably
be of little avail in practice, since the
data requisite for applying its prin-
ciples to particular instances would
rarely be procurable.

A case may be conceived of an
intermediate character between the
perfection of science and this its ex-
treme imperfection. It may happen
that the greater causes, those on
which the principal part of the pheno-
mena depends, are within the reach
of observation and measurement ; so
that if no other causes intervened, a
complete explanation could be given
not only of the phenomenon in gene-
ral, but of all the variations and
modifications which it admits of.
But inasmuch as other, perhaps many
other causes, separately insignificant
in their effects, co-operate or conflict
in many or in all cases with those
greater causes, the effect, accordingly,
presents more or less of aberration
from what would be produced by the
greater causes alone. Now if these
minor causes are not so constantly
accessible, or not accessible at all

HUMAN NATURE A SUBJECT OF SCIENCE.

553

to accurate observation, the principal
mass of the effect may still, as before,
be accounted for, and even predicted ;
but there will be variations and modi-
fications which we shall not be com-
petent to explain thoroughly, and our
predictions will not be fulfilled accur-
ately, but only approximately.

It is thus, for example, with the
theory of the tides. No one doubts
that Tidology (as Dr. Whewell pro-
poses to call it) is really a science.
As much of the phenomena as depends
on the attraction of the sun and moon
is completely understood, and may in
any, even unknown, part of the earth's
surface be foretold with certainty ;
and the far greater part of the pheno-
mena depends on those causes. But
circumstances of a local or casual
nature, such as the configuration of
the bottom of the ocean, the degree
of confinement from shores, the direc-
tion of the wind, &c., influence in
many or in all places the height and
time of the tide ; and a portion of
these circumstances being either not
accurately knowable, not precisely
measurable, or not capable of being
certainly foreseen, the tide in known
places commonly varies from the cal-
culated result of general principles by
some difiference that we cannot ex-
plain, and in unknown ones may vary
from it by a difiference that we are
not able to foresee or conjecture.
Nevertheless, not only is it certain
that these variations depend on causes,
and follow their causes by laws of
unerring uniformity ; not only, there-
fore, is tidology a science, like meteo-
rology, but it is what, hitherto at
least, meteorology is not, a science
largely available in practice. Gene-
ral laws may be laid down respecting
the tides ; predictions may be founded
on those laws, and the result will in
the main, though often not with com-
plete accuracy, correspond to the pre-
dictions.

And this is what is or ought to be
meant by those who speak of sciences
which are not exact sciences. Astro-
nomy was once a science, without

being an exact science. It could not
become exact until not only the gene-
ral course of the planetary motions, but
the perturbations also, were accounted
for, and referred to their causes.
It has become an exact science,
because its phenou)ena have been
brought under laws comprehending
the whole of the causes by which the
phenomena are influenced, whether
in a great or only in a trifling degree,
whether in all or only in some cases,
and assigning to each of those causes
the share of effect which really belongs
to it. But in the theory of the tides,
the only laws as yet accurately ascer-
tained are those of the causes which
aflfect the phenomenon in all cases,
and in a considerable degree ; while
others which afiFect it in some cases
only, or, if in all, only in a slight
degree, have not been sufficiently
ascertamed and studied to enable us
to lay down their laws, still less to
deduce the completed law of the
phenomenon, by compounding the
effects of the greater with those of
the minor causes. Tidology, there-
fore, is not yet an exact science ; not
from any inherent incapacity of being
so, but from the difficulty of ascer-
taining with complete precision the
real derivative uniformities. By com-
bining, however, the exact laws of the
greater causes, and of such of the
minor ones as are sufficiently known,
with such empirical laws or such
approximate generalisations respect-
ing the miscellaneous variations as
can be obtained by specific observa-
tion, we can lay down general pro-
positions which will be true in the
main, and on which, with allowance
for the degree of their probable in-
accuracy, we may safely ground our
expectations and our conduct.

§ 2. The science of human nature
is of this description. It falls far
short of the standard of exactness
now realised in Astronomy ; but
there is no reason that it should not
be as much a science as Tidology is,
or as Astronomy was when its calcula«

554

LOGIC OF THE MORAL SCIENCES.

tions had only mastered the main
phenomena, but not the perturbations.
The phenomena with which this
science is conversant being the
thoughts, feelings, and actions of
human beings, it would have at-
tained the ideal perfection of a
science if it enabled us to foretell
how an individual would think, feel,
or act throughout life, with the same
certainty with which astronomy en-
ables us to predict the places and the
occultations of the heavenly bodies.
It needs scarcely be stated that no-
thing approaching to this can be done.
The actions of individuals could not
be predicted with scientific accuracy,
were it only because we cannot fore-
see the whole of the circumstances in
which those individuals will be placed.
But further, even in any given combi-
nation of (present) circumstances, no
assertion, which is both precise and
universally true, can be made respect-
ing the manner in which human beings
will think, feel, or act. This is not,
however, because every person's modes
of thinking, feeling, and acting do
not depend on causes ; nor can we
doubt that if, in the case of any indi-
vidual, our data could be complete,
we even now know enough of the ulti-
mate laws by which mental pheno-
mena are determined to enable us in
many cases to predict, with tolerable
certainty, what, in the greater number
of supposable combinations of circum-
stances, his conduct or sentiments
would be. But the impressions and
actions of human beings are not solely
the result of their present circum-
stances, but the joint result of those
circumstances and of the characters
of the individuals; and the agencies
which determine human character are
Eo numerous and diversified, (nothing
which has happened to the person
throughout life being without its por-
tion of influence,) that in the aggre-
gate they are never in any two cases
exactly similar. Hence, even if our
science of human nature were theore-
tically perfect, that is, if we could
calculate any character a** we can cal-

culate the orbit of any planet, froiA
given data; still, as the data are
never all given, nor ever precisely
alike in different cases, we could
neither make positive predictions, nor
lay down universal propositions.

Inasmuch, however, as many of
those effects which it is of most im-
portance to render amenable to hu-
man foresight and control are deter-
mined, like the tides, in an incompar-
ably greater degree by general causes,
than by all partial causes taken to-
gether ; depending in the main on
those circumstances and qualities
which are common to all mankind,
or at least to large bodies of them,
and only on a small degree on the
idiosyncrasies of organisation or the
peculiar history of individuals ; it
evidently possible, with regard to al
such effects, to make predictior
which will almost always be verifiec
and general propositions which ar
almost always true. And whenevei
it is sufficient to know how the grea
majority of the human race, or ol
some nation or class of persons, wil
think, feel, and act, these propositioi
are equivalent to universal ones. Yoi
the purposes of political and socis
science this is sufficient. As we foH
merly remarked,* an approximat
generalisation is, in social inquiries
for most practical purposes equivs
lent to an exact one ; that which
only probable when asserted of inc
vidual human beings indiscriminately
selected, being certain when affirme
of the character and collective conduc
of masses.

It is no disparagement, therefor
to the science of Human Nature tha
those of its general propositions whic
descend sufficiently into detail to serv
as a foundation for predicting phenc
mena in the concrete are for the moi
part only approximately true. But i^
order to give a genuinely scientif
character to the study, it is indispen-
sable that these approximate genera-
lisations, which in themselves would
amount only to the lowest kind of
« Supra, p. 394.

I

Laws ot mind.

555

etopirical laws, should be connected
deductively with the laws of nature
from which they result — should be
resolved into the properties of the
causes on which the phenomena de-
pend. In other words, the science of
Human Nature may be said to exist in
proportion as the approximate truths
which compose a practical knowledge
of mankind can be exhibited as
corollaries from the universal laws of
human nature on which they rest,
whereby the proper limits of those ap-
proximate truths would be shown, and
we should be enabled to deduce others
for any new state of circumstances, in
anticipation of specific experience.

The proposition now stated is the
text on which the two succeeding
chapters will furnish the comment.

CHAPTER IV.

OF THE LAWS OF MIND.

§ I. What the Mind is, as well as
what Matter is, or any other question
respecting Things in themselves, as
distinguished from their sensible mani-
festations, it would be foreign to the
purposes of this treatise to consider.
Here, as throughout our inquiry, we
shall keep clear of all speculations re-
specting the mind's own nature, and
shall understand by the laws of mind
those of mental phenomena — of the
various feelings or states of conscious-
ness of sentient beings. These, accord-
ing to the classification we have uni-
formly followed, consist of Thoughts,
Emotions, Volitions, and Sensations ;
the last being as truly states of Mind
as the three former. It is usual, in-
deed, to speak of sensations as states
of body, not of mind. But this is the
common confusion of giving one and
the same name to a phenomenon and
to the proximate cause or conditions
of the phenomenon. The immediate
antecedent of a sensation is a state of
body, but the sensation itself is a state
of mind. If the word mind means
anything, it means that which feels.

Whatever opinion we hold respecting
the fundamental identity or diversity
of matter and mind, in any case the
distinction between mental and physi-
cal facts, between the internal and
the external world, will always re-
main as a matter of classification ;
and in that classification, sensations,
like all other feelings, must be ranked
as mental phenomena. Themechanism
of their production, both in the body
itself and in what is called outward
nature, is all that can with any pro-
priety be classed as physical.

The phenomena of mind, then, are
the various feelings of our nature,
both those improperly called physical
and those peculiarly designated aa
mental ; and by the laws of mind I
mean the laws according to which
those feelings generate one another.

§ 2. All states of mind are imme-
diately caused either by other states
of mind or by states of body. When
a state of mind is produced by a state
of mind, I call the law concerned in
the case a law of Mind When a
state of mind is produced directly by
a state body, the law is a law of Body,
and belongs to physical science.

With regard to those states of mind
which are called sensations, all are
agreed that these have for their im-
mediate antecedents states of body.
Every sensation has for its proximate
cause some afifection of the portion of
our frame called the nervous system,
whether this affection originate in the
action of some external object, or in
some pathological condition of the
nervous organisation itself. The laws
of this portion of our nature — the
varieties of our sensations and the phy-
sical conditions on which they proxi-
mately depend — manifestly belong to
the province of Physiology.

Whether the remainder of our men-
tal states are similarly dependent on
physical conditions, is one of the vexa-
tcB questiones in the science of human
nature. It is still disputed whether
our thoughts, emotions, and volitions
are generated through the intervene

556

LOGIC OF THE MORAL SCIENCES.

tion of material mechanism ; whether
we have organs of thought and of emo-
tion in the same sense in which we
have organs of sensation. Many emi-
nent physiologists hold the affirma-
tive. These contend that a thought
(for example) is as much the result of
nervous agency as a sensation ; that
some particular state of our nervous
system, in particular of that central
portion of it called the brain, invari-
ably precedes, and is presupposed by,
every state of our consciousness. Ac-
cording to this theory, one state of mind
is never really produced by another ;
all are produced by states of body.
When one thought seems to call up
another by association, it is not really
a thought which recalls a thought ; the
association did not exist between the
two thoughts, but between the two
states of the brain or nerves which
preceded the thoughts : one of those
states recalls the other, each being at-
tended, in its passage, by the particu-
lar state of consciousness which is con-
sequent on it. On this theory the uni-
formities of succession among states
of mind would be mere derivative
uniformities, resulting from the laws
of succession of the bodily states
which cause them. There would be
no original mental laws, no Laws
of Mind in the sense in which I use
the term, at all ; and mental science
would be a mere branch, though the
highest and most recondite branch, of
the science of Physiology. M. Comte,
accordingly, claims the scientific cog-
nisance of moral and intellectual phe-
nomena exclusively for physiologists ;
and not only denies to Psychology, or
Mental Philosophy properly so called,
the character of a science, but places
it, in the chimerical nature of its ob-
jects and pretensions, almost on a par
with astrology.

But, after all has been said which
can be said, it remains incontestable
that there exist uniformities of suc-
cession among states of mind, and
that these can be ascertained by ob-
servation and experiment. Further,
that every mental state has a nervous

state for its immediate antecedent att
proximate cause, though extreme!;
probable, cannot hitherto be said
be proved, in the conclusive mann
in which this can be proved of sensa-"
tions ; and even were it certain, yet
every one must admit that we are
wholly ignorant of the characteristics
of these nervous states ; we kno\nr
not, and at present have no mea
of knowing, in what respect one ol
them differs from another ; and oi
only mode of studying their succes
sions or co-existences must be b
observing the successions and co-ex
istences of the mental states of whic-
they are supposed to be the generate:
or causes. The successions, therefoi
which obtain among mental pheno
mena do not admit of being dedu
from the physiological laws of o
nervous organisation ; and all rei
knowledge of them must continu
for a long time at least, if not alwa;
to be sought in the direct study, b;
observation and experiment, of th
mental successions themselves. Sin
therefore, the order of our menti
phenomena must be studied in th
phenomena, and not inferred froi
the laws of any phenomena moi
general, there is a distinct and se
rate Science of Mind.

The relations, indeed, of that scieni
to the science of physiology must nev
be overlooked or imdervalued
must by no means be forgotten t
the laws of mind may be derivative
laws resulting from laws of ani
life, and that their truth therefo:
may ultimately depend on physic
conditions ; and the influence of physi
logical states or physiological chang(
in altering or counteracting the mei
tal successions is one of the most i
portant departments of psychologi
study. But, on the other hand,
reject the resource of psychological
analysis, and construct the theory of
the mind solely on such data as phy-
siology at present affords, seems to
me as great an error in principle, and
an even more serious one in practice.
Imperfect as is the science of mindf

I

I

LAWS OF MIND.

I do not scruple to affirm that it is in
a considerably more ."dvanced state
than the porticm of physiology which
corresponds to it ; and to discard the
former for the latter appears to me
an infringement of the true canons
of inductive philosophy, which nmst
produce, and which does produce, erro-
neous conclusions in some very im-
portant departments of the science of
human nature.

§ 3. The subject, then, of Psycho-
logy is the uniformities of succession,
the laws, whether ultimate or deri-
vative, according to which one mental
state succeeds another — is caused by,
or at least is caused to follow, another.
Of these laws, some are general, others
more special. The following are ex-
amples of the most general laws.

First, Whenever any state of con-
sciousness has once been excited in
us, no matter by what cause, an in-
ferior degree of the same state of con-
sciousnessj a state of consciousness
resembling the former, but inferior in
intensity, is capable of being repro-
duced in us, without the presence of
any such cause as excited it at first.
Thus, if we have once seen or touched
an object, we can afterwards think of
the object though it be absent from
our sight or from our touch. If we
have been joyful or grieved at some
event, we can think of or remember
our past joy or grief, though no new
event of a happy or painful nature
has taken place. When a poet has
put together a mental picture of an
imaginary object, a Castle of Indo-
lence, a Una, or a Hamlet, he can
afterwards think of the ideal object
he has created without any fresh act
of intellectual combination. This law
is expressed by saying, in the language
of Hume, that every mental impres-
sion has its idea.

Stfcondly, These ideas, or secondary
mental states, are excited by our im-
pressions, or by other ideas, according
to certain laws which are called Laws
of Association. Of these laws the
^st is, that simiUu: ideas tend to ex*

557

cite one another. The second is, that
when tw'o impressions have been fre-
quently experienced (or even thought
of), either sinmltaneously or in imme-
diate succession, then whenever one
of these impressions, or the idea of it,
recurs, it tends to excite the idea of
the other. The third law is, that
greater intensity in either or both of
the impressions is equivalent, in ren-
dering them excitable by one another,
to a greater frequency of conjunction.
These are the laws of ideas, on which
I shall not enlarge in this place, but
refer the reader to works professedly
psychological, in particular to Mr.
James Mill's Analysis of the Pheno-
mena of the Human Mind, where the
principal laws of association, along
with many of their applications, are
copiously exemplified, and with a mas-
terly hand.*

These simple or elementary Laws
of Mind have been ascertained by the
ordinary methods of experimental in-
quiry ; nor could they have been as-
certained in any other manner. But
a certain number of elementary laws
having thus been obtained, it is a fair
subject of scientific inquiry how far
those laws can be made to go in ex-
plaining the actual phenomena. It is
obvious that complex laws of thought
and feeling not only may, but must
be generated from these simple laws.

* When this chapter was written. Pro-
fessor Bain had not yet published even the
first part ("The Senses and the Intellect")
of his profotind Treatise on the Mind. In
this the laws of association have been more
comprehensively stated and more largely
exemplified than by any previous writer ;
and the work, having been completed by
the publication of " The Emotions and the
Will," may now be referred to as incom-
parably the most complete analytical ex-
position of the mental phenomena, on the
basis of a legitimate induction, which has
yet been produced. More recently still,
Mr. Ba n h;is joined with me in api'endlng
to a new edition of the " Analysis " notes
intended to bring up the analytic science
of Mind to its latest improvements.

Many striking app ications of the laws of
association to the exiilanation of complex
mental phenomena are also to be found in
Mr. Herbert 8penctr'§ "Principle* «f Psy-
chology."

558

LOGIC OF THE MORAL SCIENCES.

And it is to be remarked that the
case is not always one of Composition
of Causes : the effect of concurring
causes is not always precisely the
sum of the effects of those causes
when separate, nor even always an
effect of the same kind with them.
Reverting to the distinction which
occupies so prominent a place in the
theory of induction, the laws of the
phenomena of mind are sometimes
analogous to mechanical, but some-
times also to chemical laws. When
many impressions or ideas are operat-
ing in the mind together, there some-
times takes place a process of a simi-
lar kind to chemical combination.
When impressions have been so often
experienced in conjunction that each
of them calls up readily and instan-
taneously the ideas of the whole
group, those ideas sometimes melt
and coalesce into one another, and
appear not several ideas, but one, in
the same manner as, when the seven
prismatic colours are presented to the
eye in rapid succession the sensation
produced is that of white. But as in
this last case it is correct to say that
the seven colours when they rapidly
follow one another generate white, but
not that they actually are white ; so it
appears to me that the Complex Idea,
("ormed by the blending together of
several simpler ones, should, when it
really appears simple, (that is, when
the separate elements are not con-
sciously distinguishable in it,) be said
to result from, or he generated by, the
simple ideas, not to consist of them.
Our idea of an orange really consists
of the simple ideas of a certain colour,
a certain form, a certain taste and
smell, &c., because we can, by inter-
rogating our consciousness, perceive
all these elements in the idea. But
we cannot perceive, in so apparently
simple a feeling as our perception of
the shape of an object by the eye, all
that multitude of ideas derived from
other senses, without which it is well
ascertained that no such visual per-
ception would ever have had exist-
ence ; nor, in our idea of Extension,

can we discover those elemenl
ideas of resistance derived from oi
muscular frame in which it has beei
conclusively bhown that the idea ori^
ginates. These, therefore, are ca
of mental chenjistry, in which it ii
proper to say that the simple ides
generate, rather than that they com-'
pose, the complex ones.

With respect to all the other con*^
stituents of the mind, its beliefs, ita^
abstruser conceptions, its sentimenta,j
emotions, and volitions, there ai
some (among whom are Hartley an<3
the author of the Analysis) who thinl
that the whole of these are generat
from simple ideas of sensation by
chemistry similar to that which we]
have just exemplified. These philo-i
sophers have made out a great par
of their case, but I am not satisfie
that they have established the whok
of it. They have shown that ther
is such a thing as mental chemistry :
that the heterogeneous nature of
feeling A, considered in relation
B and C, is no conclusive argumeni
against its being generated from "
an^ C. Having proved this, thej
proceed to show that where A it
found B and C were or may hav<
been present ; and why, therefore,!
they ask, should not A have beei
generated from B and C ? But evei
if this evidence were carried to th<
highest degree of completeness whic
it admits of ; if it were shown (whic
hitherto it has not, in all cases, been)
that certain groups of associated ides
not only might have been, but actu-j
ally were present whenever the mor
recondite mental feeling was experij
enced, this would amount only to
the Method of Agreement, and could
not prove causation until confirmed
by the more conclusive evidence of
the Method of Difference. If thej
question be whether Belief is a mei
case of close association of ideas, is
would be necessary to examine ex|
perimentally if it be true that an]
ideas whatever, provided they ar
associated with the required degr
of closeness, ^ive rise to belief.

LAWS OF MIND.

559

the inquiry be into the origin of
moral feelings, the feeling, for ex-
ample, of moral reprobation, it is
necessary to compare all the varieties
of actions or states of mind which
are ever morally disapproved, and see
whether in all these cases it can be
shown, or reasonably surmised, that
the action or state of mind had be-
come connected by association, in the
disapproving mind, with some parti-
cular class of hateful or disgtisting
ideas ; and the method employed is,
thus far, that of Agreement. But
this is not enough. Supposing this
proved, we must try further by the
Method of Difference whether this
particular kind of hateful or disgust-
ing ideas, when it becomes associated
with an action previously indifferent,
will render that action a subject of
moral disapproval. If this question
can be answered in the affirmative, it
is shown to be a law of the human
mind that an association of that par-
ticular description is the generating
cause of moral reprobation. That all
this is the case has been rendered
extremely probable, but the experi-
ments have not been tried with the
degree of precision necessary for a
complete and absolutely conclusive in-
duction.*

It is further to be remembered, that
even if all which this theory of mental
phenomena contends for could be
proved, we should not be the more
enabled to resolve the laws of the
more complex feelings into those of
the simpler ones. The generation of
one class of mental phenomena from
another, whenever it can be made out,
is a highly interesting fact in psy-
chological chemistry ; but it no more
supersedes the necessity of an experi-

* In the case of the moral sentiments,
the place of direct expennient is to a con-
siderable extent supphed by historical ex-
perience, and we are able to trace with a
tolerable appronch to cer'ainty the parti-
cular associations by which those senti-
ments are engendered. This has been
attempted, so far as i-espects the senti-
ment of justice, in a httle work by the
present author, cuUtlfd Utilitarianurn,

mental study of the generated pheno-
menon, than a knowledge of the
properties of oxygen and sulphur
enables us to deduce those of sulphuric
acid without specific observation and
experiment. Whatever, therefore,
may be the final issue of the attempt
to account for the origin of our judg-
ments, our desires, or our volitions,
from simpler mental phenomena, it,ia
not the less imperative to ascertain
the sequences of the complex pheno-
mena themselves by special study in
conformity to the canons of Induction,
Thus, in respect to Belief, psycho-
logists will always have to inquire
what beliefs we have by direct con-
sciousness, and according to what
laws one belief produces another ;
what are the laws in virtue of which
one thing is recognised by the mind,
either rightly or erroneously, as evi-
dence of another thing. Jn regard
to Desire, they will have to examine
what objects we desire naturally, and
by what causes we are made to desire
things originally indifferent, or even
disagreeable to us ; and so forth. It
may be remarked, that the general
laws of association prevail among
these more intricate states of mind,
in the same manner as among the
simpler ones. A desire, an emotion,
an idea of the higher order of abstrac-
tion, even our judgments and volitions
when they have become habitual, are
called up by association, according to
precisely the same laws as our simple
ideas.

§ 4. In the course of these inquiries
it will be natural and necessary to
examine how far the production of
one state of mind by another is in-
fluenced by any assignable state of
body. The commonest observation
shows that different minds are sus-
ceptible in very different degrees to
the action of the same psychological
causes. The idea, for example, of a
given desirable object will excite in
different minds very different degrees
of intensity of desire. The same sub-
ject of meditation preseiited to differ-

56o

LOGIC OF THE MORAL SCIENCES.

ent minds, will excite in them very
unequal degrees of intellectual action.
These differences of mental suscepti-
bility in different individuals may be,
first, ori_^inal and ultimate facts, or,
secondly, they may be consequences of
the previous mental history of those
individuals, or, thirdly and lastly, they
may depend on varieties of physical
organisation. That the previous men-
tal history of the individuals must
have some share in producing or in
modifying the whole of their mental
character is an inevitable consequence
of the laws of mind ; but that differ-
ences of bodily structure also co-
operate is the opinion of all physi-
ologists, confirmed by common expe-
rience. It is to be regretted that
hitherto this experience, being accepted
in the gross without due analysis, has
been made the groundwork of em-
pirical generalisations most detrimen-
tal to the progress of real knowledge.
It is certain that the natural differ-
ences which really exist in the men-
tal predispositions or susceptibilities of
different persons, are often not uncon-
nected with diversities in their organic
constitution. But it does not there-
fore follow that these organic differ-
ences must in all cases influence the
mental phenomena directly and im-
mediately. They often affect them
through the medium of their psycho-
logical causes. For example, the idea
of some particular pleasure may ex-
cite in different persons, even inde-
pendently of habit or education, very
different strengths of desire, and this
may be the effect of their different
degrees or kinds of nervous suscepti-
bility ; but these organic differences,
we must remember, will render the
pleasurable sensation itself more in-
tense in one of these persons than in
the other ; so that the idea of the
pleasure will also be an intenser
feeling, and will, by the operation
of mere mental laws, excite an in-
tenser desire, without its being neces-
sary to suppose that the desire itself
is directly influenced by the physical
peculiftrit^. As ia this, »o in many

cases, such differences in the kind or
in the intensity of the physical sensa-
tions as must necessarily result from
differences of bodily organisation will
of them.selves account for many differ-
ences, not only in the degree, but even
in the kind, of the other mental
phenomena. So true is this, that
even different qualities of mind, differ-
ent types of mental character, will
naturally be produced by mere differ-
ences of intensity in the sensations
generally : as is well pointed out in
the able essay on Dr. Priestley by
Mr. Martineau, mentioned in a, former
chapter : —

"The sensations which form the
elements of all knowledge are received
either simultaneously or successively ;
when several are received simulta-
neously, ae the smell, the taste, the
colour, the form, &c., of a fruit, their
association together constitutes our
idea of an object ; when received suc-
cessively, their association makes up
the idea of an event. Anything, then,
which favours the associations of syn-
chronous ideas will tend to produce
a knowledge of objects, a perception
of qualities ; while anything which
favours association in the successive
order will tend to produce a know-
ledge of events, of the order of occur-
rences, and of the connection of cause
and effect : in other words, in the
one case a perceptive mind, with a
discriminate feeling of the pleasur-
able and painful properties of things,
a sense of the grand and the beauti-
ful will be the result ; in the other,
a mind attentive to the movements
and phenomena, a ratiocinative and
philosophic intellect. Now it is an
acknowledged principle that all sensa-
tions experienced during the pre-
sence of any vivid impression become
strongly associated with it and with
each other, and does it not follow
that the synchronous feelings of a
sensitive constitution {i.e. the one
which has vivid impressions) will be
more intimately blended than in a
differently formed mind ? If this
suggestion has any foundation in

LAWS OF MIND.

561

truth, it leads to an inference not
unimportant ; that when nature has
endowed an individual with great
original susceptibility, he will pro-
bably be distinguished by fondness
for natural history, a relish for the
beautiful and great, and moral en-
thusiasm ; where there is but a medio-
crity of sensibility, a love of science,
of abstract truth, with a deficiency of
taste and of fervour, is likely to be
the result."

We see from this example that
when the general laws of mind are
more accurately known, and, above
all, more skilfully applied to the de-
tailed explanation of mental peculia-
rities, they will account for many
more of those peculiarities than is
ordinarily supposed. Unfortunately
the reaction of the last and present
generation against the philosophy of
the eighteenth century has produced
a very general neglect of this great
department of analytical inquiry, of
which, consequently, the recent pro-
gress has been by no means propor-
tional to its early promise. The
majority of those who speculate on
human nature prefer dogmatically
to assume that the mental differences
which they perceive, or think they
perceive, among human beings are
ultimate facts, incapable of being
either explained or altered, rather
than take the trouble of fitting them-
selves, by the requisite processes of
thought, for referring those mental
differences to the outward causes by
which they are for the most part pro-
duced, and on the removal of which
they would cease to exist. The Ger-
man school of metaphysical specula-
tion, which has not yet lost its tem-
porary predominance in European
thought, has had this among many
other injurious influences ; and at the
opposite extreme of the psychological
scale, no writer, either of early or of
recent date, is chargeable in a higher
degree with this aberration from the
true scientific spirit than M. Comte.

It is certain that, in human beings
at least, differences in education and

in outward circumstances are capable
of affording an adequate explanation
of by far the greatest portion of char-
acter, and that the remainder may
be in great part accounted for by
physical differences in the sensations
produced in different individuals by
the same external or internal cause.
There are, however, some mental facts
which do not seem to admit of these
modes of explanation. Such, to take
the strongest case, are the various
instincts of animals, and the portion
of human nature which corresponds
to those instincts. No mode has been
suggested, even by way of hypothesis,
in which these can receive any satis-
factory, or even plausible, explanation
from psychological causes alone ; and
there is great reason to think that
they have as positive, and even as
direct and immediate, a connection
with physical conditions of the brain
and nerves as any of our mere sensa-
tions have. A supposition which (it
is perhaps not superfluous to add) in
no way conflicts with the indisputable
fact that these instincts may be modi-
tied to any extent, or entirely con-
quered, in human beings, and to no
inconsiderable extent even in some
of the domesticated animals, by other
mental influences, and by education.
Whether organic causes exercise a
direct influence over any other classes
of mental phenomena is hitherto as
far from being ascertained as is the
precise nature of the organic condi-
tions even in the case of instincts.
The physiology, however, of the brain
and nervous system is in a state of
such rapid advance, and is continually
bringing forth such new and interest-
ing results, that if there be really a
connection between mental peculiari-
ties and any varieties cognisable by
our senses in the structure of the
cerebral and nervous apparatus, the
nature of that connection is now in
a fair way of being found out. The
latest discoveries in cerebral physio-
logy appear to have proved that any
such connection which may exist is of
a radically different character from

2 N

562

LOGIC OF THE MORAL SCIENCES.

that contended for by Gall and his
followers, and that whatever may
hereafter be found to be the true
theory of the subject, phrenology at
least is untenable.

CHAPTER V.

OP ETHOLOGY, OR THE SCIENCE OF
THE FORMATION OF CHARACTER.

§ I. The laws of mind, as char-
acterised in the preceding chapter,
compose the universal or abstract
portion of the philosophy of human
nature ; and all the truths of common
experience, constituting a practical
knowledge of mankind, must, to the
extent to which they are truths, be
results or consequences of these. Such
familiar maxims, when collected d
posteriori from observation of life,
occupy among the truths of the science
the place of what, in our analysis of
Induction, have so often been spoken
of under the title of Empirical Laws.

An Empirical Law (it will be re-
membered) is an uniformity, whether
of succession or of co-existence, which
holds true in all instances within our
limits of observation, but is not of a
nature to afford any assurance that
it would hold beyond those limits,
either because the consequent is not
really the effect of the antecedent, but
forms part along with it of a chain of
effects, flowing from prior causes not
yet ascertained, or because there is
ground to believe that the sequence
(though a case of causation) is re-
solvable into simpler sequences, and,
depending therefore on a concurrence
of several natural agencies, is exposed
to an unknown multitude of pos-
sibilities of counteraction. In other
words, an empirical law is a gene-
ralisation, of which, not content with
finding it true, we are abliged to ask
why is it true ? knowing that its
truth is not absolute, but dependent
on some more general conditions, and
that it can only be relied on in so far

as there is ground of assurance that
those conditions are realised.

Now, the observations concerning
human affairs collected from common
experience are precisely of this na-
ture. Even if they were universally
and exactly true within the bounds of
experience, which they never are, still
they are not the ultimate laws of
human action ; they are not the prin-
ciples of human nature, but results
of those principles under the circum-
stances in which mankind have hap-
pened to be placed. When the Psal-
mist " said in his haste that all men
are liars," he enunciated what in some
ages and countries is borne out by
ample experience ; but it is not a law
of man's nature to lie, though it is
one of the consequences of the laws of
human nature that lying is nearly
universal when certain external cir-
cumstances exist universally, espe-
cially circumstances productive of
habitual distrust and fear. When
the character of the old is asserted to
be cautious, and of the young im-
petuous, this, again, is but an empiri-
cal law ; for it is not because of their
youth that the young are impetuous,
nor because of their age that the old
are cautious. It is chiefly, if not
wholly, because the old, during their '
many years of life, have generally had
much experience of its various evils,
and having suffered or seen others
suffer much from incautious exposure
to them, have acquired associations
favourable to circumspection ; while
the young, as well from the absence
of similar experience as from the !
greater strength of the inclinations
which urge them to enterprise, en-
gage themselves in it more readily.
Here, then, is the explanation of the
empirical law ; here are the conditions
which ultimately determine whether
the law holds good or not. If anoldman
has not been oftener than most young
men in contact with danger and diffi-
culty, he will be equally incautious :
if a youth has not stronger inclina-
tions than an old man, he probably
will be as little enterprising^. The

ETHOLOGY.

563

empirical law derives whatever truth
it has from the causal laws of which
it is a consequence. If we know
those laws, we know what are the
limits to the derivative law ; while,
if we have not yet accounted for the
empirical law — if it rests only on
observation — there is no safety in
applying it far beyond the limits of
time, place, and circumstance in which
the observations were made.

The really scientific truths, then,
aire not these empirical laws, but the
causal laws which explain them. The
empirical laws of those phenomena
which depend on known causes, and
of which a general theory can there-
fore be constructed, have, whatever
may be their value in practice, no
other function in science than that of
verifying the conclusions of theory.
Still more must this be the case when
most of the empirical laws amount,
even within the limits of observation,
only to approximate generalisations.

§ 2. This, however, is not, so much
as is sometimes supposed, a peculi-
arity of the sciences called moral. It
is only in the simplest branches of
science that empirical laws are ever
exactly true, and not always in those.
Astronomy, for example, is the sim-
plest of all the sciences which ex-
plain, in the concrete, the actual
course of natural events. The causes
or forces on which astronomical phe-
nomena depend are fewer in number
than those which determine any other
of the great phenomena of nature.
Accordingly, as each efifect results
from the conflict of but few causes, a
great degree of regularity and uni-
formity might be expected to exist
among the effects ; and such is really
the case : they have a fixed order and
return in cycles. But propositions
which should express with absolute
correctness all the successive positions
of a planet until the cycle is com-
pleted would be of almost unmanage-
able complexity, and could be obtained
from theory alone. The generalisa-
tions which can be collected on the i

subject from direct observation, even
such as Kepler's law, are mere ap-
proximations : the planets, owing to
their perturbations by one another,
do not move in exact ellipses. Thus
even in astronomy perfect exactness
in the mere empirical laws is not to be
looked for ; much less, then, in more
complex subjects of inquiry.

The same example shows how little
can be inferred against the univer-
sality, or even the simplicity of the
ultimate laws, from the impossibility
of establishing any but approximate
empirical laws of the effects. The
laws of causation according to which
a class of phenomena are produced
may be very few and simple, and yet
the effects themselves may be so
various and complicated that it shall
be impossible to trace any regularity
whatever completely through them.
For the phenomena in question may
be of an eminently modifiable charac-
ter ; insomuch that innumerable cir-
cumstances are capable of influencing
the effect, although they may all do it
according to a very small number of
laws. Suppose that all which passes
in the mind of man is determined by
a few simple laws : still, if those
laws be such that there is not one of
the facts surrounding a human being,
or of the events which happen to him,
that does not influence in some mode
or degree his subsequent mental his-
tory, and if the circumstances of dif-
ferent human beings are extremely
different, it will be no wonder if very
few propositions can be made respect-
ing the details of their conduct or
feelings which will be true of ail
mankind.

Now, without deciding whether the
ultimate laws of our mental nature
are few or many, it is at least certain
that they are of the above description.
It is certain that our mental states, and
our mental capacities and suscepti-
bilities, are modified, either for a time
or permanently, by everything which
happens to us in life. Considering,
therefore, how much these modifying
causes differ in the case of any two

564

LOGIC OF THE MORAL SCIENCES.

individuals, it would be unreasonable
to expect that the empirical laws of
the human mind, the generalisations
which can be made respecting the
feelings or actions of mankind with-
out reference to the causes that de-
termine them, should be anything but
approximate generalisations. They
are the common wisdom of common
life, and as such are invaluable ; espe-
cially as they are mostly to be ap-
plied to cases not very dissimilar to
those from which they were collec-
ted. But when maxims of this sort,
collected from Englishmen, come to
be applied to Frenchmen, or when
those collected from the present day
are applied to past or future genera-
tions, they are apt to be very much
at fault. Unless we have resolved
the empirical law into the laws of the
causes on which it depends, and as-
certained that those causes extend to
the case which we have in view, there
can be no reliance placed in our infer-
ences. For every individual is sur-
rounded by circumstances different
from those of every other individual ;
every nation or generation of mankind
from every other nation or generation;
and none of these differences are with-
out their influence in forming a dif-
ferent type of character. There is,
indeed, also a certain general resem-
blance ; but peculiarities of circum-
stances are continually constituting
exceptions even to the propositions
which are true in the great majority
of cases.

Although, however, there is scarcely
any mode of feeling or conduct which
is, in the absolute sense, common to
all mankind ; and though the genera-
lisations which assert that any given
variety of conduct or feeling will be
found universally, (however nearly
they may approximate to truth with-
in given limits of observation,) will
be considered as scientific propositions
by no one who is at all familiar with
scientific investigation ; yet all modes
of feeling and conduct met with among
mankind have causes which produce
them ; and in the propositions which

assign those causes will be found the
explanation of the empirical laws, and
the limiting principle of our reliance
on them. Human beings do not all
feel and act alike in the same circum-
stances ; but it is possible to deter-
mine what makes one person, in a
given position, feel or act in one way,
another in another ; how any given
mode of feeling and conduct, com-
patible with the general laws (physi-
cal and mental) of human nature, has
been, or may be, formed. In other
words, mankind have not one univer-
sal character, but there exist universal
laws of the Formation of Character.
And since it is by these laws, com-
bined with the facts of each particular
case, that the whole of the phenomena
of human action and feeling are pro-
duced, it is on these that every rational
attempt to construct the science of
human nature in the concrete and for
practical purposes must proceed.

§ 3. The laws, then, of the forma-
tion of character being the principal
object of scientific inquiry into human
nature, it remains to determine the
method of investigation best fitted for
ascertaining them. And the logical
principles according to which this
question is to be decided must be
those which preside over every other
attempt to investigate the laws of
very complex phenomena For it is
evident that both the character of any
human being, and the aggregate of
the circumstances by which that char-
acter has been formed, are facts of a
high order of complexity. Now to
such cases we have seen that the
Deductive Method, setting out from
general laws, and verifying their con-
sequences by specific experience, is
alone applicable. The grounds of this
great logical doctrine have formerly
been stated, and its truth will derive
additional support from a brief exami-
nation of the specialities of the present
case.

There are only two modes in which
laws of nature can be ascertained :
deductively and experimentally, in-

ethologv.

5«5

eluding under the denomination of
experimental inquiry, observation as
well as artificial experiment. Are the
laws of the formation of character sus-
ceptible of a satisfactory investigation
by the method of experimentation ?
Evidently not ; because, even if we
suppose unlimited power of varying
the experiment, (which is abstractedly
possible, though no one but an Oriental
despot has that power, or, if he had,
would probably be disposed to exer-
cise it,) a still more essential condi-
tion is wanting — the power of per-
forming any of the experiments with
scientific accuracy.

The instances requisite for the pro-
secution of a directly experimental
inquiry into the formation of char-
acter would be a number of human
beings to bring up and educate from
infancy to mature age ; and to per-
form any one of these experiments
with scientific propriety, it would be
necessary to know and record every
sensation or impressed received by the
young pupil from a period long before
it could speak, including its own no-
tions respecting the sources of all those
sensations and impressions. It is not
only impossible to do this completely,
but even to do so much of it as should
constitute a tolerable approximation.
One apparently trivial circumstance
which eluded our vigilance might let
in a train of impressions and associa-
tions sufficient to vitiate the experi-
ment as an authentic exhibition of the
effects flowing from given causes. No
one who has sufficiently reflected on
education is ignorant of this truth :
and whoever has not will find it most
instructively illustrated in the writ-
ings of Rousseau and Helvetius on
that great subject.

Under this impossibility of study-
ing the laws of the formation of char-
acter by experiments purposely con-
trived to elucidate them there remains
the resource of simple observation.
But if it be impossible to ascertain
the influencing circumstances with
any approach to completeness even
when we have the shaping of them

ourselves, much more impossible is it
when the cases are further removed
from our observation, and altogether
out of our control. Consider the diffi-
culty of the very first step — of ascer-
taining what actually is the character
of the individual in each particular
case that we examine. There is hardly
any person living, concerning some
essential part of whose character
there are not differences of opinion
even among his intimate acquain-
tances ; and a single action, or con-
duct continued only for a short time,
goes a very little way towards ascer-
taining it. We can only make our
observations in a rough way and en
masse, not attempting to ascertain
completely in any given instance
what character has been formed, and
still less by what causes ; but only
observing in what state of previous
circumstances it is found that cer-
tain marked mental qualities or defi-
ciencies qftenest exist. These conclu-
sions, besides that they are mere
approximate generalisations, deserve
no reliance, even as such, unless the
instances are sufficiently numerous to
eliminate not only chance, but every
assignable circumstance in which a
number of the cases examined may
happen to have resembled one an-
other. So numerous and various, too,
are the circumstances which form in-
dividual character, that the conse-
quence of any particular combination
is hardly ever some definite and
strongly marked character, alwa5rs
found where that combination exists,
and not otherwise. What is obtained,
even after the most extensive and ac-
curate observation, is merely a com-
parative result ; as, for example, that
in a given number of Frenchmen,
taken indiscriminately, there will be
found more persons of a particular
mental tendency, and fewer of the
contrary tendency, than among an
equal number of Italians or English,
similarly taken ; or thus : of a hun-
dred Frenchmen and an equal number
of Englishmen, fairly selected, and
arranged according to the degree in

S66

LOGIC Of Ttifi MORAL SCIENCES.

which they possess a particular mental
characteristic, each number i, 2, 3,
&c., of the one series will be found to
possess more of that characteristic
than the corresponding number of
the other. Since, therefore, the com-
parison is not one of kinds, but of
ratios and degrees ; and since in pro-
portion as the differences are slight,
it requires a greater number of in-
stances to eliminate chance ; it can-
not often happen to any one to know
a suflBcient number of cases with the
accuracy requisite for making the sort
of comparison last mentioned ; less
than which, however, would not con-
stitute a real induction. Accordingly
there is hardly one current opinion
respecting the characters of nations,
classes, or descriptions of persons,
which is universally acknowledged as
indisputable.*

And finally, if we could even obtain

* The most favourable cases for malclng
such apiiroximate generalisations are what
may be termed collective instances, where
we are fortunately enabled to see the whole
class respecting which we are inquiring
in action at once, and, from the qualities
displayed by the collective body, are able
to judge what must be the qualities of the
majority of the individuals composing it
Thus the character of a nation is ••hown in
its acts as a nation ; not so much in the
acts of its government, for those are much
influenced by other causes ; but iu the cur-
rent popular maxims, and other marks of
the general direction of public opinion ; in
the character of the persons or writings
that are held in permanent esteem or ad-
miration ; in laws and institutions, so far
as they are tlie work of the nation itself, or
are acknowledged and supported by it ;
and so forth. But even here there is a
large margin of doubt and uncertainty.
These things are liable to be influenced by
many circumstances : they are partly de-
termined by ihe distinctive qualities of
that nation or body of persons but partly
also by external causes which would in-
fluence any other body of persons, in the
same manner. In order, therefore, to
make the experiment really complete, we
ought to b« able to try it without variation
upon othci- nation* : to try how English-
men would act or feel if placed in the same
•ircumatanc*'! in which w« have lupposed
Frenchmen to be placed ; to apply, in
abort, the Method of Difference as well as
that of Agreement. Now these experi-
ments we caunot try, nor even approxi-
mate to.

by way of experiment a much more sat-
isfactory assurance of these generalisa-
tions than is really possible, they would
still be only empirical laws. They
would show, indeed, that there was
some connection between the type of
character formed and the circum-
stances existing in the case, but not
what the precise connection was, nor
to which of the peculiarities of those
circumstances the effect was reaUy
owing. They could only, therefore,
be received as results of causation, re-
quiring to be resolved into the general
laws of the causes : until the deter-
mination of which, we could not judge
within what limits the derivative laws
might serve as presumptions in cases
yet unknown, or even be depended
on as permanent in the very cases
from which they were collected. The
French people had, or were supposed
to have, a certain national character ;
but they drive out their royal family
and aristocracy, altertheir institutions,
pass through a series of extraordinary
events for the greater part of a cen-
tury, and at the end of that time their
character is found to have undergone
important changes. A long list of
mental and moral differences are ob-
served, or supposed to exist, between
men and women ; but at some future,
and, it may be hoped, not distant
period, equal freedom and an equally
independent social position come to
be possessed by both, and their differ-
ences of character are either removed
or totally altered.

But if the differences which we
think we observe between French and
English, or between men and women,
can be connected with more general
laws ; if they be such as might be
expected to be produced by the differ-
ences of government, former customs,
and physical peculiarities in the two
nations, and by the diversities of
education, occupations, personal inde-
pendence, and social privileges, and
whatever original differences thewi
may be in bodily strength and nervous
sensibility between the two sexes ;
then, indeed, the coincidence of the

):jTHOLOGY.

S6?

two kinds of evidence justifies lis in
believing that we have both reasoned
rightly and observed rightly. Our
observation, though not sufficient as
proof, is ample as verification. And
having ascertained not only the em-
pirical laws, but the causes of the
peculiarities, we need be under no
difficulty in judging how far they may
be expected to be permanent, or by
what circumstances they would be
modified or destroyed.

§ 4. Since, then, it is impossible to
obtain really accurate propositions
respecting the formation of character
from observation and experiment
alone, we ar'^ driven perforce to that
which, ev?n if it had not been the in-
dispensable, would have been the most
perfect mode of investigation, and
which it is one of the principal aims
of philosophy to extend ; namely, that
which tries its experiments not on the
complex facts, but on the simple ones
of which they are compounded, and
after ascertaining the laws of the
causes, the composition of which gives
rise to the complex phenomena, then
considers whether these will not ex-
plain and account for the approxi-
mate generalisations which have been
framed empirically respecting the
sequences of those complex pheno-
mena. The laws of the formation of
character are, in short, derivative
laws, resulting from the general laws
of mind, and are to be obtained by
deducing them from those general
laws by supposing any given set of
circumstances, and then considering
what, according to the laws of mind,
will be the influence of those circum-
stances on the formation of character.

A science is thus formed, to which
I would propose to give the name of
Ethology, or the Science of Char-
acter, from ^doi, a word more nearly
corresponding to the term " char-
acter," as I here use it, than any
other word in the same language.
The name is perhaps etymologically
applicable to the entire science of our
mental and moral nature ; but if, as

is usual and convenient, we employ
the name Psychology for the science
of the elementary laws of mind, Etho-
logy will serve for the ulterior science
which determines the kind of char-
acter produced in conformity to those
general laws, by any set of circum-
stances, physical and moral. Accord-
ing to this definition, Ethology is the
science which corresponds to the act
of education, in the widest sense of
the term, including the formation of
national or collective character as
well as individual. It would indeed
be vain to expect (however completely
the laws of the formation of character
might be ascertained) that we could
know so accurately the circumstances
of any given case as to be able posi-
tively to predict the character that
would be produced in that case. But
we must remember that a degree of
knowledge far short of the power of
actual prediction is often of much
practical value. There may be great
power of influencing phenomena, with
a very imperfect knowledge of the
causes by which they are in any given
instance determined. It is enough
that we know that certain means have
a tendency to produce a given effect,
and that others have a tendency to
frustrate it. When the circumstances
of an individual or of a nation are in
any considerable degree under our
control, we may, by our knowledge
of tendencies, be enabled to shape
those circumstances in a manner much
more favourable to the ends we desire
than the shape which they would of
themselves assume. This is the limit
of our power, but within this limit
the power is a most important one.

This science of Ethology may be
called the Exact Science of Human
Nature ; for its truths are not, like
the empirical laws which depend on
them, approximate generalisations,
but real laws. It is, however, (as
in all cases of complex phenomena,)
necessary to the exactness of the pro-
positions that they should be hypo-
thetical only, and affirm tendencies,
not facts. They must not assert that

568

LOGIC OF THE MORAL SCIENCES.

something will always or certainly
happen, but only that such and such
will be the effect of a given cause,
so fg-r as it operates uncounteracted.
It is a scientific proposition that
bodily strength tends to make men
courageous ; not that it always makes
them so : that an interest on one side
of a question tends to bias the judg-
ment ; not that it invariably does so :
that experience tends to give wisdom;
not that such is always its effect.
These propositions, being assertive
only of tendencies, are not the less
universally true because the tenden-
cies may be frustrated.

§ 5. While, on the one hand. Psy-
chology is altogether, or principally,
a science of observation and experi-
ment, Ethology, as I have conceived
it, is, as I have already remarked,
altogether deductive. The one ascer-
tains the simple laws of Mind in
general, the other traces their opera-
tion in complex combinations of cir-
cumstances. Ethology stands to Psy-
chology in a relation very similar to
that in which the various branches of
natural philosophy stand to mechanics.
The principles of Ethology are properly
the middle principles, the axiomata
media (as Bacon would have said) of
the science of mind : as distinguished,
on the one hand, from the empirical
laws resulting from simple observa-
tion, and on the other from the highest
generalisations.

And this seems a suitable place for
a logical remark, which, though of
general application, is of peculiar im-
portance in reference to the present
subject. Bacon has judiciously ob-
served that the axiomata media of
every science principally constitute
its value. The lowest generalisations,
until explained by and resolved into
the middle principles of which they
are the consequences, have only the
imperfect accuracy of empirical laws ;
while the most general laws are too
general, and include too few circum-
etances, to give sufficient indication
of what happens in individual cases

where the circumstances are almost
always immensely numerous. In the
importance, therefore, which Bacon
assigns in every science to the middle
principles, it is impossible not to
agree with him. But I conceive him
to have been radically wrong in his
doctrine respecting the mode in which
these axiomata media should be ar-
rived at ; though there is no one pro-
position laid down in his works for
which he has been more extravagantly
eulogised. He enunciates as an uni-
versal rule that induction should pro-
ceed from the lowest to the middle
principles, and from those to the
highest, never reversing that order,
and consequently, leaving no room
for the discovery of new principles by
way of deduction at all. It is not
to be conceived that a man of his
sagacity could have fallen into this
mistake if there had existed in his
time, among the sciences which treat
of successive phenomena, one single in-
stance of a deductive science, such as
mechanics, astronomy, optics acous-
tics, &c., now are. In those sciences
it is evident that the higher and
middle principles are by no means
derived from the lowest, but the re-
verse. In some of them the very
highest generalisations were those
earliest ascertained with any scien-
tific exactness ; as, for example, (in
mechanics, ) the laws of motion . Those
general laws had not indeed at first
the acknowledged universality which
they acquired after having been suc-
cessfully employed to explain many
classes of phenomena to which they
were not originally seen to be appli-
cable ; as when the laws of motion
were employed, in conjunction with
other laws, to explain deductively the
celestial phenomena. Still the fact
remains that the propositions which j|
were afterwards recognised as the
most general truths of the science
were, of all its accurate generalisa-
tions, those earliest arrived at. Ba-
con's greatest merit cannot therefore
consist, as we are so often told that it
did, in exploding the vicious method

ETHOLOGY.

569

pursued by the ancients of flying to
the highest generalisations first, and
deducing the middle principles from
them ; since this is neither a vicious
nor an exploded, bat the universally
accredited method of modern science,
and that to which it owes its greatest
tiiumphs. The error of ancient spe-
culation did not consist in making
the largest generalisations first, but
in making them without the aid or
warrant of rigorous inductive me-
thods, and applying them deductively
without the needful use of that im-
portant part of the Deductive Method
termed Verification.

The order in which truths of the
various degrees of generality should
be ascertained cannot, I apprehend,
be preserved by any unbending rule.
I know 01 no maxim which can be
laid down on the subject, but to ob-
tain those first in respect to which
the conditions of a real induction can
be first and most completely realised.
Now, wherever our means of investi-
gation can reach causes, without stop-
ping at the empirical laws of the
effects, the simplest cases being those
in which fewest causes are simul-
taneously concerned, will be most
amenable to the inductive process ;
and these are the cases which elicit
laws of the greatest comprehensive-
ness. In every science, therefore,
which has reached the stage at which
it becomes a science of causes, it will
be usual, as well as desirable, first to
obtain the highest generalisations,
and then deduce the more special
ones from them. Nor can I dis-
cover any foundation for the Baconian
maxim, so much extolled by subse
quent writers, except this : That
before we attempt to explain de
ductively from more general laws
any new class of phenomena, it is
desirable to have gone as far as is
practicable in ascertaining the em-
pirical laws of those phenomena, so as
to compare the results of deduction
not with one individual instance after
another, but with general propositions
expressive of the points of agreement

which have been found among many
instances. For if Newton had been
obliged to verify the theory of gravi-
tation, not by deducing from it Kep-
ler's laws, but by deducing all the
observed planetary positions which
had served Kepler to establish those
laws, the Newtonian theory would
probably never have emerged from
the state of an hjrpothesis.*

The applicability of these remarks
to the special case under considera-
tion cannot admit of question. The
science of the formation of character
is a science of causes. The subject
is one to which those among the
canons of induction, by which laws of
causation are ascertained, can be rigo-
rously applied. It is, therefore, both
natural and advisable to ascertain the
simplest, which are necessarily the
most general, laws of causation first,
and to deduce the middle principles
from them. In other words, Etho-
logy, the deductive science, is a sys-
tem of corollaries from Psychology,
the experimental science.

* "To which," says Dr. Wliewell, "we
may add, that it is certain from the
history of the subject, that in that case
the hypothesis would never have been
framed at all. "

Dr. Whewell (Philosophy of Discovery,
pp. 277-282) defends Bacon's rule against
the preceding strictiires. But his defence
consists only in asserting and exemplify-
ing a proposition which I had myself
stated, viz. that though the largest gene-
ralisations may be the earliest made, they
are not at first seen in their entire gene-
rality, but acquire it by degrees, as ihey
are found to explain one class after another
of phenomena. The laws of motion, for
example, were not known to extend to the
celestial regions until the motions of the
celestial bodies had been deduced from
them. This, however, does not in any
way affect the fact that the middle prin-
ciples of astronomy, the central force, for
example, and the law of the inverse
square, could not have been discovered if
the laws of motion, wiiich are so much
more universal, had not been known first.
Ou Bacon's system of step-by-siep genera-
lisation, it would be impossible in any
science to ascend higher than the empiri-
cal laws ; a remark which Dr. Whewell's
own Inductive Tables, referred to by him
in support of his argument, amply bear
out.

570

LOGIC OF THE MOBAL SCIENCES.

§ 6. Of these, the earlier alone has
been, as yet, really conceived or studied
as a science ; the other, Ethology, is
Btill to be created. But its creation
has at length become practicable. The
empirical laws, destined to verify its
deductions, have been formed in abun-
dance by every successive age of hu-
manity, and the premises for the
deductions are now sufficiently com-
plete. Excepting the degree of un-
certainty which still exists as to the
extent of the natural differences of
individual minds, and the physical
circumstances on which these may be
dependent, (considerations which are
of secondary importance when we are
considering mankind in the average,
or enmasse,) I believe most competent
judges will agree that the general
laws of the different constituent ele-
ments of human nature are even now
sufficiently understood to render it
possible for a competent thinker to
deduce from those laws, with a con-
siderable approach to certainty, the
particular type of character which
would be formed in mankind generally
by any assumed set of circumstances.
A science of Ethology, founded on
the laws of Psychology, is therefore
possible, though little has yet been
done, and that little not at all sys-
tematically, towards forming it. The
progress of this important but most
imperfect science will depend on a
double process : first, that of deducing
theoretically the ethological conse-
quences of particular circumstances
of position, and comparing them with
the recognised results of common ex-
perience ; and secondly, the reverse
operation — increased study of the
various types of human nature that
ure to be found in the world, con-
ducted by persons not only capable of
analysing and recording the circum-
■tances in which these types severally
prevail, but also sufficiently acquainted
with psychological laws to be able to
explain and account for the charac-
teristics of the type by the peculiari-
ties of the circumstances, the residuum
alone, when there proves to be any,

being set down to the account of con-
genital predispositions.

For the experimental or d 'posteriori
part of this process, the materials are
continually accumulating by the ob-
servation of mankind. So far as
thought is concerned, the great pro-
blem of Ethology is to deduce the
requisite middle principles from the
general laws of Psychology. The sub-
ject to be studied is, the origin and
sources of all those qualities in human
beings which are interesting to us,
either as facts to be produced, to be
avoided, or merely to be understood ;
and the object is to determine, from
the general laws of mind, combined
with the general position of our species
in the universe, what actiial or pos-
sible combinations of circumstances
are capable of promoting or of pre-
venting the production of those quali-
ties. A science which possesses m* Idle
principles of this kind, arranged in
the order, not of causes, but of the
effects which it is desirable to produce
or to prevent, is duly prepared to be
the foundation of the corresponding
Art. And when Ethology shall be
thus prepared, practical education will
be the mere transformation of those
principles into a parallel system of
precepts, and the adaptation of these
to the sum total of the individual
circumstances which exist in each
particular case.

It is hardly necessary again to re-
peat, that, as in every other deductive
science, verification d posteriori must
proceed 'pari passu with deduction d
priori. The inference given by theory
as to the type of character which
would be formed by any given cir-
cumstances must be tested by speci-
fic experience of those circumstances
whenever obtainable ; and the con-
clusions of the science as a whole
must undergo a perpetual verification
and correction from the general re-
marks afforded by common experi-
ence respecting human nature in our
own age, and by history respecting;
times gone by. The conclusions of
theory cannot be trusted, unless con-

SOCIAL SCIJEKCE.

S7i

firmed by observation ; nor those of
observation, unless they can be affili-
ated to theory, by deducing them
from the laws of human nature, and
from a close analysis of the circum-
stances of the particular situation.
It is the accordance of these two
kinds of evidence separately taken —
the consilience of d priori reasoning
and specific experience — which forms
the only sufficient ground for the prin-
ciples of any science so " immersed in
matter," dealing with such complex
and concrete phenomena, as Ethology.

CHAPTER VI.

GENKBAL CONSIDERATIONS ON THE
SOCIAL SCIENCE.

§ I. Next after the science of in-
dividual man comes the science of
man in society ; of the actions of col-
lective masses of mankind, and the
various phenomena which constitute
social life.

If the formation of individual char-
acter is already a complex subject of
study, this subject must be, in ap-
pearance at least, still more complex ;
because the number of concurrent
causes, all exercising more or less in-
fluence on the total eflFect, is greater,
in the proportion in which a nation,
or the species at large, exposes a
larger surface to the operation of
agents, psychological and physical,
than any single individual. If it
was necessary to prove, in opposition
to an existing prejudice, that the
simpler of the two is capable of being
a subject of science ; the prejudice is
likely to be yet stronger against the
possibility of giving a scientific char-
acter to the study of Politics, and of
the phenomena of Society. It is, ac-
cordingly, but of yesterday that the
conception of a political or social
science ha» exiited anywhere but
in the mind of here and there an
insulated thinker, generally very ill
prepared for its realisation : though
the subject itself has of all others

engaged the most general attention,
and been a theme of interested and
earnest discussions, almost from the
beginning of recorded time.

The condition indeed of politics, as
a branch of knowledge, was until
very lately, and has scarcely even
yet ceased to be, that which Bacon
animadverted on, as the natural state
of the sciences while their cultivation
is abandoned to practitioners ; not
being carried on as a branch of specu-
lative inquiry, but only with a view
to the exigencies of daily practice,
and the fructifera experimenta, there-
fore, being aimed at, almost to the
exclusion of the lucifera. Such was
medical investigation before physio-
logy and natural history began to be
cultivated as branches of general
knowledge. The only questions exa-
mined were, what diet is wholesome,
or what medicine will cure some given
disease, without any previous system-
atic inquiry into the laws of nutrition,
and of the healthy and morbid action
of the different organs, on which laws
the effect of any diet or medicine must
evidently depend. And in politics,
the questions which engaged general
attention were similar : — Is such an
enactment, or such a form of govern-
ment, beneficial or the reverse — either
universally, or to some particular com-
munity? without any previous inquiry
into the general conditions by which
the operation of legislative measures,
or the effects produced by forms of
government, are determined. Students
in politics thus attempted to study
the pathology and therapeutics of the
social body before they had laid the
necessary foundation in its physio-
logy ; to cure disease without under-
standing the laws of health. And
the result was such as it must always
be when persons, even of ability, at-
tempt to deal with the complex ques-
tions of a science before its simpler
and more elementary truths hav« been
established.

No wonder that when the pheno-
mena of society have so rarely been
contemplated in the point of view

572

LOGIC OF THE MOHAL SCIENCES.

characteristic of science, the philo-
sophy of society should have made
little progress ; should contain few
general propositions sufficiently pre-
cise and certain for common inquirers
to recognise in them a scientific cha-
racter. The vulgar notion accord-
ingly is, that all pretension to lay
dovm general truths on politics and
society is quackery ; that no univer-
sality and no certainty are attainable
in such matters. What partly excuses
this common notion is, that it is really
not without foundation in one parti-
cular sense. A large proportion of
those who have laid claim to the cha-
racter of philosophic politicians have
attempted, not to ascertain universal
sequences, but to frame universal pre-
cepts. They have imagined some one
form of government, or system of laws,
to fit all cases ; a pretension well
meriting the ridicule with which it is
treated by practitioners, and wholly
unsupported by the analogy of the
art to which, from the nature of its
subject, that of politics must be the
most nearly allied. No one now sup-
poses it possible that one remedy can
cure all diseases, or even the same
disease in all constitutions and habits
of body.

It is not necessary even to the per-
fection of a science that the corre-
sponding art should possess universal,
or even general rules. The phenomena
of society might not only be completely
dependent on known causes, but the
mode of action of all those causes might
be reducible to laws of considerable
simplicity, and yet no two cases might
admit of being treated in precisely the
same manner. So great might be the
variety of circumstances on which the
results in different cases depend, that
the art might not have a single general
precept to give, except that of watch-
ing the circumstances of the particular
case, and adapting our measures to
the effects which, according to the
principles of the science, result from
those circumstances. But although,
in so complicated a class of subjects,
it is impossible to lay down practical

maxims of universal application, it
does not follow that the phenomena
do not conform to universal laws.

§ 2. All phenomena of society are
phenomena of human nature, gene-
rated by the action of outward cir-
cumstances upon masses of human
beings : and if, therefore, the pheno-
mena of human thought, feeling, and
action, are subject to fixed laws, the
phenomena of society cannot but con-
form to fixed laws, the consequence of
the preceding. There is, indeed, no
hope that these laws, though our
knowledge of them were as certain
and as complete as it is in astronomy,
would enable us to predict the history
of society, like that of the celestial
appearances, for thousands of years
to come. But the difference of cer-
tainty is not in the laws themselves,
it is in the data to which these laws
are to be applied. In astronomy the
causes influencing the result are few,
and change little, and that little ac-
cording to known laws ; we can ascer-
tain what they are now, and thence
determine what they will be at any
epoch of a distant future. The data,
therefore, in astronomy, are as certain
as the laws themselves. The circum-
stances, on the contrary, which influ-
ence the condition and progress of
society, are innumerable, and perpe-
tually changing ; and though they all
change in obedience to causes, and
therefore to laws, the multitude of
the causes is so great as to defy our
limited powers of calculation. Not
to say that the impossibility of apply-
ing precise numbers to facts of such a
description, would set an impassable
limit to the possibility of calculating
them beforehand, even if the powers
of the human intellect were otherwise
adequate to the task.

But, as before remarked, an amount
of knowledge quite insufficient for
prediction may be most valuable for
guidance. The science of society
would have attained a very high
point of perfection if it enabled us, in
any given condition of social affairs, —

I

THE CHEMICAL METHOD.

573

In the condition, for instance, of
Europe or any European country at
the present time, — to understand by
what causes it had, in any and every
particular, been made what it was ;
whether it was tending to any, and
to what, changes ; what effects each
feature of its existing state was likely
to produce in the future ; and by
what means any of those effects might
be prevented, modified, or accelerated,
or a different class of effects superin-
duced. There is nothing chimerical
in the hope that general laws, suffi-
cient to enable us to answer these
various questions for any country or
time with the individual circumstances
of which we are well acquainted, do
really admit of being ascertained ;
and that the other branches of human
knowledge, which this undertaking
presupposes, are so far advanced that
the time is ripe for its commencement.
Such is the object of the Social
Science.

That the nature of what I consider
the true method of the science may
be made more palpable, by first show-
ing what that method is not, it will
be expedient to characterise briefly
two radical misconceptions of the
proper mode of philosophising on
society and government, one or other
of which is, either explicitly or more
often unconsciously, entertained by
almost all who have meditated or
argued respecting the logic of politics
since the notion of treating it by strict
rules, and on Baconian principles, has
been current among the more advanced
thinkers. These erroneous methods,
if the word method can be applied to
erroneous tendencies arising from the
absence of any sufficiently distinct
conception of method, may be termed
the Experimental or Chemical mode
of investigation, and the Abstract or
Geometrical mode. We shall begin
with the former.

CHAPTER VII.

OP THE CHEMICAL, OR EXPERIMENTAL,
METHOD IN THE SOCIAL SCIENCE.

§ I. The laws of the phenomena of
society are, and can be, nothing but
the laws of the actions and passions
of human beings united together in
the social state. Men, however, in a
state of society, are still men ; their
actions and passions are obedient to
the laws of individual human nature.
Men are not, when brought together,
converted into another kind of sub-
stance, with different properties ; as
hydrogen and oxygen are different from
water, or as hydrogen, oxygen, carbon,
and azote are different from nerves,
muscles, and tendons. Human be-
ings in society have no properties but
those which are derived from, and
may be resolved into, the laws of the
nature of individual man. In social
phenomena the Composition of Causes
is the universal law.

Now, the method of philosophising
which may be termed chemical over-
looks this fact, and proceeds as if the
nature of man as an individual were
not concerned at all, or were con-
cerned in a very inferior degree, in
the operations of human beings in
society. All reasoning in political or
social affairs, grounded on principles
of human nature, is objected to by
reasoners of this sort, under such
names as "abstract theory." For the
direction of their opinions and con-
duct they profess to demand, in all
cases without exception, specific ex-
perience.

This mode of thinking is not only
general with practitioners in politics,
and with that very numerous class
who (on a subject which no one, how-
ever ignorant, thinks himself incom-
petent to discuss) profess to guide
themselves by common sense rather
than by science, but is often counte-
nanced by persons with greater pre-
tensions to instruction — persons who,
having sufficient acquaintance with
books and with the current ideas to

574

LOGIC OF THE MORAL SCIENCES.

have heard that Bacon taught man-
kind to follow experience, and to
ground their conclusions on facts
instead of metaphysical dogmas —
think that, by treating political facts
in as directly experimental a method
as chemical facts, they are showing
themselves true Baconians, and prov-
ing their adversaries to be mere syllo-
gisers and schoolmen. As, however,
the notion of the applicability of ex-
perimental methods to political philo-
sophy cannot co-exist with any just
conception of these methods them-
selves, the kind of arguments from
experience which the chemical theory
brings forth as its fruits (and which
form the staple, in this country es-
pecially, of parliamentary and hust-
ings oratory) are such as, at no time
since Bacon, would have been ad-
mitted to be valid in chemistry itself,
or in any other branch of experimental
science. They are such as these : that
the prohibition of foreign commodi-
ties must conduce to national wealth,
because England has flourished under
it; or because countries in general which
have adopted it have flourished ; that
our laws, or our internal adminstra-
tion, or our constitution, are excellent
for a similar reason ; and the eternal
arguments from historical examples,
from Athens or Rome, from the fires
in Smithfield or the French Revolu-
tion.

I will not waste time in contending
against modes of argumentation which
no person, with the smallest practice
in estimating evidence, could possibly
be betrayed into ; which draw con-
clusions of general application from a
single unanalysed instance, or arbi-
trarily refer an effect to some one
among its antecedents, without any
process of elimination or comparison
of instances. It is a rule both of jus-
tice and of good sense to grapple not
with the absurdest, but with the most
reasonable form of a wrong opinion.
We shall suppose our inquirer ac-
quainted with the true conditions of
experimental investigation, and com-
petent in point of acquirements for

realising them, so far as they can be
realised. He shall know as much of
the facts of history as mere erudition
can teach — as much as can be proved
by testimony without the assistance
of any theory ; and if those mere facts,
properly collated, can fulfil the condi-
tions of a real induction, he shall be
qualified for the task.

But that no such attempt can have
the smallest chance of success, has
been abundantly shown in the tenth
chapter of the Third Book.* We
there examined whether effects which
depend on a complication of causes
can be made the subject of a true
induction by observation and experi-
ment ; and concluded, on the most
convincing grounds, that they cannot.
Since, of all effects, none depend on
so great a complication of causes as
social phenomena, we might leave our
case to rest in safety on that previous
showing. But a logical principle as
yet so little familiar to the ordinary
run of thinkers requires to be insisted
on more than once in order to make
the due impression ; and the present
being the case which of all others
exemplifies it the most strongly, there
will be advantage in re-stating the
grounds of the general maxim, as
applied to the specialities of the class
of inquiries now under consideration.

§ 2. The first difficulty which meets
us in the attempt to apply experi-
mental methods for ascertaining the
laws of social phenomena, is that we
are without the means of making
artificial experiments. Even if we
could contrive experiments at leisure,
and try them without limit, we should
do so under immense disadvantage ;
both from the impossibility of ascer-
taining and taking note of all the
facts of each case, and because (those
facts being in a perpetual state of
change) before sufficient time had
elapsed to ascertain the result of the
experiment, some material circum-
stances would always have ceased to be

Page 291 to th« end of the chapter.

«

THE CHEMICAL METHOD.

575

the same. But it is unnecessary to
consider the logical objections which
would exist to the conclusiveness of
our experiments, since we palpably
never have the power of trying any.
We can only watch those which nature
produces, or which are produced for
other reasons. We cannot adapt our
logical means to our wants by varying
the circumstances as the exigencies of
elimination may require. If the spon-
taneous instances formed by cotem-
porary events and by the successions
of phenomena recorded in history
afford a sufficient variation of circum-
stances, an induction from specific ex-
perience is attauiable ; otherwise not.
The question to be resolved is, there-
fore, whether the requisites for induc-
tion respecting the causes of political
effects or the properties of political
agents are to be met with in history ?
including under the term cotempo-
rary history. And in order to give
fixity to our conceptions, it will be
advisable to suppose this question
asked in reference to some special
subject of political inquiry or contro-
versy ; such as that frequent topic of
debate in the present century, the
operation of restrictive and prohibitory
commercial legislation upon national
wealth. Let this, then, be the scien-
tific question to be investigated by
specific experience.

§ 3. In order to apply to the case
the most perfect of the methods of
experimental inquiry, the Method of
Difference, we require to find two
instances which tally in every par-
ticular except the one which is the
subject of inquiry. If two nations
can be found which are alike in all
natural advantages and disadvan-
tages ; whose people resemble each
other in every quality, physical and
moral, spontaneous and acquired ;
whose habits, usages, opinions, laws
and institutions are the same in all
respects, except that one of them has
a more protective tariff, or in other
respects interferes more with the free-
dom of industry ; if one of these

nations is found to be rich and the
other poor, or one richer than the
other, this will be an experimentum
crucis — a real proof by experience
which of the two systems is most
favourable to national riches. But the
supposition that two such instances
can be met with is manifestly absurd. •
Nor is such a concurrence even
abstractedly possible. Two nations
which agreed in everything except
their commercial policy would agree
also in that. Differences of legisla-
tion are not inherent and ultimate
diversities — are not properties of
Kinds. They are effects of pre-exist-
ing causes. If the two nations differ
in this portion of their institutions, it
is from some difference in their posi-
tion, and thence in their apparent
interests, or in some portion or other
of their opinions, habits, and ten-
dencies ; which opens a view of fur-
ther differences without any assignable
limit, capable of operating on their
industrial prosperity, as well as on
every other feature of their condition,
in more ways than can be enumerated
or imagined. There is thus a de-
monstrated impossibility of obtaining,
in the investigations of the social
science, the conditions required for
the most conclusive form of inquiry
by specific experience.

In the absence of the direct, we
may next try, as in other cases, the
supplementary resource, called in a
former place the Indirect Method of
Difference, which, instead of two in-
stances differing in nothing but the
presence or absence of a given circum-
stance, compares two classes of in-
stances respectively agreeing in no-
thing but the presence of a circum-
stance on the one side and its absence
on the other. To choose the most
advantageous case conceivable, (a case
far too advantageous to be ever ob-
tained,) suppose that we compare one
nation which has a restrictive policy,
with two or more nations agreeing in
nothing but in permitting free trade.
We need not now suppose that either
of these nations agrees with the first

576

LOGIC OF THE MORAL SCIENCES.

in all its circumstances ; one may
agree with it in some of its circum-
stances, and another in the remainder.
And it may be argued, that if these
nations remain poorer than the re-
strictive nation, it cannot be for want
either of the first or of the second set
of circumstances, but it must be for
want of the protective system. If (we
might say) the restrictive nation had
prospered from the one set of causes,
the first of the free-trade nations
would have prospered equally : if, by
reason of the other, the second would :
but neither has : therefore the pros-
perity was owing to the restrictions.
This will be allowed to be a very
favourable specimen of an argument
from specific experience in politics,
and if this be inconclusive, it would
not be easy to find another preferable
to it.

Yet that it is inconclusive scarcely
requires to be pointed out. Why must
the prosperous nation have prospered
from one cause exclusively ? National
prosperity is always the collective re-
sult of a multitude of favourable cir-
cumstances ; and of these, the restric-
tive nation may unite a greater num-
ber than either of the others, though
it may have all of those circumstances
in common with either one or the
other of them. Its prosperity may be
partly owing to circumstances common
to it with one of those nations, and
partly with the other, while they,
having each of them only half the
number of favourable circumstances,
have remained inferior. So that the
closest imitation which can be made
in the social science of a legitimate
induction from direct experience gives
but a specious semblance of conclusive-
ness, without any real value.

§ 4. The Method of Difference in
either of its forms being thus com-
pletely out of the question, there re-
mains the Method of Agreement.
But we are already aware of how
little value this method is in cases
admitting Plurality of Causes ; and
social phenomena are those in which

the plurality prevails in the utmost
possible extent.

Suppose that the observer makes
the luckiest hit which could be given
by any conceivable combination of
chances : that he finds two nations
which agree in no circumstance what-
ever, except in having a restrictive
system and in being prosperous ; or
a number of nations, all prosperous,
which have no antecedent circum-
stances common to them all but that
of having a restrictive policy. It is
unnecessary to go into the considera-
tion of the impossibility of ascertaining
from history, or even from contempo-
rary observation, that such is really
the fact : that the nations agree in no
other circumstance capable of influ-
encing the case. Let us suppose this
impossibility vanquished, and the fact
ascertained that they agree only in a
restrictive system as an antecedent,
and industrial prosperity as a con-
sequent. What degree of presump-
tion does this raise, that the restric-
tive system caused the prosperity?
One so trifling as to be equivalent to
none at all. That some one antece-
dent is the cause of a given effect,
because all other antecedents have
been ioundT capable of being elimi-
nated, is a just inference only if the
effect can have but one cause. If it
admits of several, nothing is more na-
tural than that each of these should
separately admit of being eliminated.
Now, in the case of political pheno-
mena, the supposition of unity of cause
is not only wide of the truth, but at
an immeasurable distance from it.
The causes of every social phenome-
non which we are particularly inte-
rested about, security, wealth, freedom,
good government, public virtue, gene-
ral intelligence, or their opposites, are
infinitely numerous, especially the ex-
ternal or remote causes, which alone
are, for the most part, accessible to
direct observation. No one cause suf-
fices of itself to produce any of these
phenomena ; while there are countless
causes which have some influence over
them, and may co-operate either in

THE CHEMICAL METHOD.

577

their production or in their preven-
tion. From the mere fact, therefore,
of our having been able to ehminate
some circumstance, we can by no
means infer that this circumstance
was not instrumental to the effect
in some of the very instances from
which we have eliminated it. We
can conclude that the effect is some-
times produced without it, but not
that, when present, it does not con-
tribute its share.

Similar objections will be found to
apply to the Method of Concomitant
Variations. If the causes which act
upon the state of any society pro-
duced effects differing from one an-
other in kind ; if wealth depended
on one cause, peace on another, a
third made people virtuous, a fourth
intelligent, we might, though unable
to sever the causes from one another,
refer to each of them that property
of the effect which waxed as it waxed,
and which waned as it waned. But
every attribute of the social body is
influenced by innumerable causes ;
and such is the mutual action of the
co-existing elements of society, that
whatever affects any one of the more
important of them, will by that alone,
if it does not affect the others directly,
affect them indirectly. The effects,
therefore, of different agents not being
different in quality, while the quan-
tity of each is the mixed result of all
the agents, the variations of the ag-
gregate cannot bear an uniform pro-
portion to those of any one of its com-
ponent parts.

§ 5. There remains the Method of
Residues, which appears, on the first
view, less foreign to this kind of in-
quiry than the three other methods,
because it only requires that we
should accurately note the circum-
stances of some one country, or state
of society. Making allowance, there-
upon, for the effect of all causes
whose tendencies are known, the re-
sidue which those causes are inade-
quate to explain may plausibly be
imputed to the remainder of the oir-

cumstances which are known to have
existed in the case. Something simi-
lar to this is the method which Cole^
ridge * describes himself as having
followed in his political Essays in
the Mwming Post. *' On every great
occurrence I endeavoured to discover
in past history the event that most
nearly resembled it. I procured,
whenever it was possible, the con-
temporary historians, memorialists,
and pamphleteers. Then fairly sub-
tracting the points of difference from
those of likeness, as the balance
favoured the former or the latter, I
conjectured that the result would be
the same or different. As, for in-
stance, in the series of essays en-
titled *A Comparison of France under
Napoleon with Rome under the first
Caesars,' and in those which followed,
*on the probable final restoration of
the Bourbons.' The same plan I
pursued at the commencement of the
Spanish Revolution, and with the
same success, taking the war of the
United Provinces with Philip II. as
the groundwork of the comparison."
In this inquiry he no doubt employed
the Method of Residues, for, in
*' subtracting the points of difference
from those of likeness," he doubtless
weighed, and did not content himself
with numbering, them : he doubtless
took those points of agreement only
which he presumed from their own
nature to be capable of influencing
the effect, and, allowing for that in-
fluence, concluded that the remainder
of the result would be referable to
the points of difference.

Whatever may be the efficacy of
this method, it is, as we long ago re-
marked, not a method of pure obser-
vation and experiment ; it concludes,
not from a comparison of instances,
but from the comparison of an in-
stance with the result of a previous
deduction. Applied to social pheno-
mena, it presupposes that the causes
from which part of the effect pro-
ceeded are already knowna ; and as

* Biographia literaria, i. 214.
2 O

LOGIC OF THE MORAL SCIENCES.

578

we have shown that these cannot
have been known by specific experi-
ence, they must have been leamt by
deduction from principles of human
nature, experience being called in
only as a supplementary resource, to
determine the causes which produced
an unexplained residue. But if the
principles of human nature may be
had recourse to for the establishment
of some political truths, they may for
all. If it be admissible to say, Eng-
land must have prospered by reason
of the prohibitory system, because
after allowing for all the other ten-
dencies which have been operating,
there is a portion of prosperity still
to be accounSted for ; it must be ad-
missible to go to the same source for
the effect of the prohibitory system,
and examine what account the laws
of human motives and actions will
enable us to give of its tendencies.
Nor, in fact, will the experimental
argument amount to anything, ex-
cept in verification of a conclusion
drawn from those general laws. For
we may subtract the effect of one,
two, three, or four causes, but we
shall never succeed in subtracting
the effect of all causes except one ;
while it would be a curious instance
of the dangers of too much caution,
if, to avoid depending on d priori
reasoning concerning the effect of a
single cause, we should oblige our-
selves to depend on as many separate
d priori reasonings as there are causes
operating concurrently with that par-
ticular cause in some given instance.
We have now sufficiently charac-
terised the gross misconception of
the mode of investigation proper to
political phenomena, which I have
termed the Chemical Method. So
lengthened a discussion would not
l>ave been necessary if the claim to
decide authoritatively on political
doctrines were confined to persons
who had competently studied any
one of the higher departments of phy-
wcal science. But since the genera-
lity of those who reason on political
subjects, satisfactorily to then^selvee

and to a more or less numerous body
of admirers, know nothing whatever
of the methods of physical investiga-
tion beyond a few precepts which
they continue to parrot after Bacon,
being entirely unaware that Bacon's
conception of scientific inquiry has
done its work, and that science has
now advanced into a higher stage,
there are probably many to whom
such remarks as the foregoing may
still be useful. In an age in which
chemistry itself, when attempting U)
deal with the more complex chemical
sequences, those of the animal, or even
the vegetable organism, has found
it necessary to become, and has suc-
ceeded in becoming, a Deductive
Science, it is not to be apprehended
that any person of scientific habits,
who has kept pace with the general
progress of the knowledge of nature,
can be in danger of applying the me
thods of elementary chemistry to ex-
plore the sequences of the most com-
plex order of phenomena in existence.

CHAPTER VIIL

OF THE GKOMETRICAI,, OB ABSTRACT
METHOD.

§ I. The misconception discussed
in the preceding chapter is, as we said,
chiefly committed by persons not much
accustomed to scientific investigation :
practitioners in politics, who rather
employ the commonplaces of philo-
sophy to justify their practice, than
seek to guide their practice by philo-
sophic principles : or imperfectly edu-
cated persons, who, in ignorance of
the careful selection and elaborate
comparison of instances required for
the formation of a sound theory, at-
tempt to found one upon a few coin-
cidences which they have casually
noticed.

The erroneous method of which we
are now to treat, is, on the contrary,
peculiar to thinking and studious
minds. It never could have suggested
itself but to persons of son^e f airxiliarity

THE GEOMETRICAL METHOD.

579

with the nature of scientific research ;
who, — being aware of the impossi-
bility of establishing, by casual obser-
vation or direct experimentation, a
true theory of sequences so complex
as are those of the social phenomena,
— have recourse to the simpler laws
which are immediately operative in
those phenomena, and which are no
other than the laws of the nature of
the human beings therein concerned.
These thinkers perceive (what the
partisans of the chemical or experi-
mental theory do not) that the science
of society must necessarily be deduc-
tive. But, from an insufficient con-
sideration of the specific nature of the
subject-matter, — and often because
(their own scientific education having
stopped short in too early a stage)
geometry stands in their minds as the
type of all deductive science, — it is to
geometry, rather than to astronomy
and natural philosophy, that they un-
consciously assimilate the deductive
science of society.

Among the differences between
geometry (a science of co-existent
facts, altogether independent of the
laws of the succession of phenomena)
and those physical Sciences of Causa-
tion which have been rendered deduc-
tive, the following is one of the most
conspicuous : That geometry affords
no room for what so constantly occurs
in mechanics and its applications, the
case of conflicting forces ; of causes
which counteract or modify one an-
other. In mechanics we continually
find two or more moving forces pro-
ducing, not motion, but rest ; or
motion in a different direction from
that which would have been produced
by either of the generating forces. It
is true that the effect of the joint
forces is the same when they act
simultaneously, as if they had acted
one after another, or by turns ; and
it is in this that the difference between
mechanical and chemical law consists.
But still the effects, whether produced
by successive or by simultaneous ac-
tion, do, wholly or in part, cancel one
pother ; what the one force does the

other, partly or altogether, undoes.
There is no similar state of things in
geometry. The result which follows
from one geometrical principle has
nothing that conflicts with the result
which follows from another. What
is proved true from one geometrical
theorem, what would be true if no
other geometrical principles existed,
cannot be altered and made no longer
true by reason of some other geomet-
rical principle. What is once proved
true is true in all cases, whatever sup-
position may be made in regard to any
other matter.

Now a conception, similar to this
last, would appear to have been
formed of the social science, in the
minds of the earlier of those who have
attempted to cultivate it by a deduc-
tive method. Mechanics would be a
science very similar to geometry if
every motion resulted from one force
alone, and not from a conflict of forces.
In the geometrical theory of society,
it seems to be supposed that this is
really the case with the social pheno-
mena ; that each of them results al-
ways from only one force, one single
property of human nature.

At the point which we have now
reached, it cannot be necessary to say
anything either in proof or in illustra-
tion of the assertion that such is not
the true character of the social pheno-
mena. There is not, among these
most complex and (for that reason)
most modifiable of all phenomena, any
one over which innumerable forces do
not exercise influence ; which does
not depend on a conjunction of very
many causes. We have not, there-
fore, to prove the notion in question
to be an error, but to prove that the
error has been committed ; that so
mistaken a conception of the mode in
which the phenomena of society are
produced has actually been ascer-
tained.

§ 2. One numerous division of the
reasoners who have treated social facts
according to geometrical methods, not
admitting any modification of one law

58o

LOGIC OF THE MORAL SCIENCES.

by another, must for the present be
left out of consideration ; because in
them this error is complicated with,
and is the effect of another funda-
mental misconception, of which we
have already taken some notice, and
which will be further treated of before
we conclude. I speak of those who
deduce political conclusions not from
laws of nature, not from sequences of
phenomena, real or imaginary, but
from unbending practical maxims.
Such, for example, are all who found
their theory of politics on what is
called abstract right, that is to say,
on universal precepts ; a pretension of
which we have already noticed the
chimerical nature. Such, in like man-
ner, are those who make the assump-
tion of a social contract, or any other
kind of original obligation, and apply
it to particular cases by mere inter-
pretation. But in this the funda-
mental error is the attempt to treat an
art like a science, and to have a de-
ductive art ; the irrationality of which
will be shown in a future chapter. It
will be proper to take our exemplifica-
tion of the geometrical theory from
those thinkers who have avoided this
additional error, and who entertain, so
far, a juster idea of the nature of poli-
tical inquiry.

We may cite, in the first instance,
those who assume as the principle of
their political philosophy that govern-
ment is founded on fear ; that the
dread of each other is the one motive
by which human beings were origin-
ally brought into a state of society,
and are still held in it. Some of the
earlier scientific inquirers into politics,
in particular Hobbes, assumed this
proposition, not by implication, but
avowedly, as the foundation of their
doctrine, and attempted to build a
complete philosophy of politics there-
upon. It is true that Hobbes did not
find this one maxim sufficient to carry
him through the whole of his subject,
but was obliged to eke it out by the
double sophism of an original con-
tract. I call this a double sophism ;
first, as passing off a fiction for a fact.

and, secondly, assuming a practical
principle! or precept as the basis of a
theory ; which is a petitio pnncipii,
since (as we noticed in treating of that
Fallacy) every rule of conduct, even
though it be so binding a one as the
observance of a promise, must rest its
own foundations on the theory of the
subject, and the theory, therefore, can-
not rest upon it.

§ 3. Passing over less important in-
stances, I shall come at once to the
most remarkable example afforded by
our own times of the geometrical me-
thod in politics ; emanating from per-
sons who are well aware of the dis-
tinction between science and art ; who
knew that rules of conduct must fol-
low, not precede, the ascertainment of
laws of nature, and that the latter,
not the former, is the legitimate field
for the application of the deductive
method. I allude to the interest-
philosophy of the Bentham school.

The profound and original thinkers
who are commonly known under this
description, founded their general
theory of government on one compre-
hensive premise, namely, that men's
actions are always determined by their
interests. There is an ambiguity in
this last expression ; for, as the same
philosophers, especially Bentham, gave
the name of an interest to anything
which a person likes, the proposition
may be understood to mean only this,
that men's actions are always deter-
mined by their wishes. In this sense,
however, it would not bear out any of
the consequences which these writers
drew from it ; and the word, there-
fore, in their political reasonings, must
be understood to mean (which is also
the explanation they themselves, on
such occasions, gave of it) what is
commonly termed private or worldly
interest.

Taking the doctrine, then, in this
sense, an objection presents itself in
limine which might be deemed a fatal
one, namely, that so sweeping a proposi-
tion is far from being universally true.
Human beings are not governed in all

i

THE GEOMETRICAL METaoD.

58«

their actions by their worldly interests.
This, however, is by no means so con-
clusive an objection as it at first ap-
pears ; because in politics we are for
the most part concerned with the con-
duct, not of individual persons, but
either of a series of persons (as a suc-
cession of kings), or a body or mass
of persons, as a nation, an aristocracy,
or a representative assembly. And
whatever is true of a large majority
of mankind, may without much error
be taken for true of any succession of
persons, considered as a whole, or of
any collection of persons in which the
act of the majority becomes the act of
the whole body. Although, therefore,
the maxim is sometimes expressed in a
manner unnecessarily paradoxical, the
consequences drawn from it will hold
equally good if the assertion be limited
as follows : Any succession of persons,
or the majority of any body of per-
sons, will be governed in the bulk of
their conduct by their personal inte-
rests. We are bound to allow to this
school of thinkers the benefit of this
more rational statement of their funda-
mental maxim, which is also in strict
conformity to the explanations which,
when considered to be called for, have
been given by themselves.

The theory goes on to infer, quite
correctly, that if the actions of man-
kind are determined in the main by
their selfish interests, the only rulers
who will govern according to the in-
terest of the governed are those whose
selfish interests are in accordance with
it. And to this is added a third pro-
position, namely, that no rulers have
their selfish interest identical with
that of the governed, unless it be ren-
dered so by accountability, that is, by
dependence on the will of the governed.
In other words (and as the result of
the whole), that the desire of retain-
ing or the fear of losing their power,
and whatever is thereon consequent,
is the sole motive which can be relied
on for producing on the part of rulers
a course of conduct in accordance with
the general interest.

We have thus a fundamental theo-

rem of political science, consisting of
three syllogisms, and depending chiefly
on two general premises, in each of
which a certain effect is considered as
determined only by one cause, not by
a concurrence of causes. In the one,
it is assumed that the actions of ave-
rage rulers are determined solely by
self-interest ; in the other, that the
sense of identity of interest with the
governed, is produced and producible
by no other cause than responsibility.

Neither of these propositions is by
any means true ; the last is extremely
wide of the truth.

It is not true that the actions even
of average rulers are wholly, or any-
thing approaching to wholly, deter-
mined by their personal interest, or
even by their own opinion of their
personal interest. I do not speak of
the influence of a sense of duty, or
feelings of philanthropy, motives never
to be mainly relied on, though (except
in countries or during periods of great
moral debasement) they influence al-
most all rulers in some degree, and
some rulers in a very great degree.
But I insist only on what is true of
all rulers, viz. that the character and
course of their actions is largely in-
fluenced (independently of personal
calculation) by the habitual senti-
ments and feelings, the general mod^s
of thinking and acting, which prevail
throughout the community of which
they are members, as well as by the
feelings, habits and modes of thought
which characterise the particular class
in that community to which they
themselves belong. And no one will
understand or be able to decipher
their system of conduct who does not
take all these things into account.
They are also much influenced by the
maxims and traditions which have
descended to them from other rulers,
their predecessors ; which maxims
and traditions have been known to
retain an ascendancy during long
periods, even in opposition to the pri-
vate interests of the rulers for the
time being. I put aside the influence
of other less general causes. Although,

5^2

LOGIC OF THE MORAL SCIENCES.

therefore, the private interests of the
rulers or of the ruling class is a very
powerful force, constantly in action,
and exercising the most important
influence upon their conduct, there
is also in what they do a large por-
tion which that private interest by
no means affords a sufficient expla-
nation of ; and even the particulars
which constitute the goodness or bad-
ness of their government are in some,
and no small degree, influenced by
those among the circumstances act-
ing upon them, which cannot, with
any propriety, be included in the term
self-interest.

Turning now to the other proposi-
tion, that responsibility to the governed
is the only cause capable of producing
in the rulers a sense of identity of in-
terest with the community ; this is
still less admissible as an universal
truth, than even the former. I am
not speaking of perfect identity of in-
terest, which is an impracticable chi-
mera, which, most assuredly, responsi-
bility to the people does not give. I
epeak of identity in essentials ; and
the essentials are different at different
places and times. There are a large
number of cases in which those things
which it is most for the general in-
terest that the rulers should do, are
also those which they are prompted to
do by their strongest personal interest,
the consolidation of their power. The
suppression, for instance, of anarchy
and resistance to law, — the complete
establishment of the authority of the
central government, in a state of so-
ciety like that of Europe in the middle
ages, — is one of the strongest interests
of the people, and also of the rulers
simply because they are the rulers :
and responsibility on their part could
not strengthen, though in many con-
ceivable ways it might weaken, the
motives prompting them to pursue this
object. During the greater part of the
reign of Queen Elizabeth, and of many
other monarchs who might be named,
the sense of identity of interest be-
tween the sovereign and the majority
of the people was probably stronger

than it usually is in responsible gov-
ernments : everything that the people
had most at heart, the monarch had
at heart too. Had Peter the Great,
or the rugged savages whom he began
to civilise, the truest inclination to-
wards the things which were for the
real interest of those savages ?

I am not here attempting to esta-
blish a theory of government, and am
not called upon to determine the pro-
portional weight which ought to be
given to the circumstances which this
school of geometrical politicians left
out of their system, and those which
they took into it. I am only concerned
to show that their method was un-
scientific ; not to measure the amount
of eiTor which may have affected their
practical conclusions.

It is but justice to them, however,
to remark that their mistake was not
so much one of substance as of form ;
and consisted in presenting in a sys-
tematic shape, and as the scientific
treatment of a great philosophical
question, what should have passed for
that which it really was, the mere
polemics of the day. Although the
actions of rulers are by no means
wholly determined by their selfish
interests, it is chiefly as a security
against those selfish interests that
constitutional checks are required ;
and for that purpose such checks, in
England and the other nations of
modern Europe, can in no manner be
dispensed with. It is likewise true,
that in these same nations, and in the
present age, responsibility to the gov-
erned is the only means practically
available to create a feeling of identity
of interest, in the cases, and on the
points, where that feeling does not
sufficiently exist. To all this, and to
the arguments which may be founded
on it in favour of measures for the
correction of our representative sys-
tem, I have nothing to object ; but I
confess my regret, that the small
though highly important portion of
the philosophy of government, which
was wanted for the immediate pur-
pose of serving the cause of parlia-

TftE PHYSICAL METHOD.

583

hientary reform, should have been
held forth by thinkers of such emi-
nence as a complete theory.

It is not to be imagined possible,
nor is it true in point of fact, that
these philosophers regarded the few
premises of their theory as including
all that is required for explaining
social phenomena, or for determining
the choice of forms of government and
measures of legislation and adminis-
tration. They were too highly in-
structed, of too comprehensive intel-
lect, and some of them of too sober
and practical a character, for such an
error. They would have applied, and
did apply, their principles with in-
numerable allowances. But it is not
allowances that are wanted. There
is little chance of making due amends
in the superstructure of a theory for
the want of sufficient breadth in its
foundations. It is unphilosophical to
construct a science out of a few of the
agencies by which the phenomena are
determined, and leave the rest to the
routine of practice or the sagacity of
conjecture. We either ought not to
pretend to scientific forms, or we ought
to study all the determining agencies
equally, and endeavour, so far as it
can be done, to include all of them
within the pale of the science ; else
we shall infallibly bestow a dispropor-
tionate attention upon those which
our theory takes into account, while
we misestimate the rest, and probably
underrate their importance. That the
deductions should be from the whole
and not from a part only of the laws
of nature that are concerned, would
be desirable even if those omitted were
so insignificant in comparison with the
others, that they might, for most pur-
poses and on most occasions, be left
out of the account. But this is far
indeed from being true in the social
science. The phenomena of society
do not depend, in essentials, on some
one agency or law of human nature,
with only inconsiderable modifications
from others. The whole of the quali-
ties of human nature influence those
phenomena, and there is not one which

influences them in a small degree.
There is not one, the removal or any
great alteration of which would not ma-
terially affect the whole aspect of so-
ciety, and change more or less the se-
quences of socialphenomena generally.
The theory which has been the
subject of these remarks is, in this
country at least, the principal cotem-
porary example of what I have styled
the geometrical method of philosophis-
ing in the social science ; and our exa-
mination of it has, for this reason,
been more detailed than would other-
wise have been suitable to a work
like the present. Having now suffi-
ciently illustrated the two erroneous
methods, we shall pass without further
preliminary to the true method ; that
which proceeds (conformably to the
practice of the more complex phyBical
sciences) deductively indeed, but by
deduction from many, not from one
or a very few, original premises; con-
sidering each effect as (what it really
is) an aggregate result of many causes,
operating sometimes through the same,
sometimes through different mental
agencies, or laws of human nature.

CHAPTER IX.

OF THE PHYSICAL, OR CONCRETR
DEDUCTIVE METHOD.

§ I. After what has been said to
illustrate the nature of the inquiry
into social phenomena, the general
character of the method proper to
that inquiry is sufficiently evident,
and needs only to be recapitulated,
not proved. However complex the
phenomena, all their sequences and
co-existences result from the laws of
the separate elements. The effect
produced, in social phenomena, by
any complex set of circumstances,
amounts precisely to the sum of the
effects of the circumstances taken
singly ; and the complexity does not
arise from the number of the laws
themselves, which is not remarkably
great, but from the extraordinary

5^4

LOGIC OF THE MORAL SCIENCES.

number and variety of the data or
elements — of the agents which, in
obedience to that small number of
laws, co-operate towards the effect.
The Social Science, therefore, (which,
by a convenient barbarism, has been
termed Sociology,) is a deductive
science ; not, indeed, after the model
of geometry, but after that of the
more complex physical sciences. It
infers the law of each effect from the
laws of causation on which that effect
depends ; not, however, from the law
merely of one cause, as in the geome-
trical method ; but by considering all
the causes which conjunctly influence
the effect, and compounding their laws
with one another. Its method, in
short, is the Concrete Deductive Me-
thod; that of which astronomy fur-
nishes the most perfect, natural philo-
sophy a somewhat less perfect example,
and the employment of which, with
the adaptations and precautions re-
quired by the subject, is beginning to
regenerate physiology.

Nor does it admit of doubt that
similar adaptations and precautions
are indispensable in sociology. In
applying to that most complex of all
studies what is demonstrably the sole
method capable of throwing the light
of science even upon phenomena of a
far inferior degree of complication,
we ought to be aware that the same
superior complexity which renders the
instrument of deduction more neces-
sary, renders it also more precarious ;
and we must be prepared to meet, by
appropriate contrivances, this increase
of difficulty.

The actions and feelings of human
beings in the social state are, no
doubt, entirely governed by psycho-
logical and ethological laws ; what-
ever influence any cause exercises
upon the social phenomena, it exer-
cises through those laws. Supposing,
therefore, the laws of human actions
and feelings to be sufficiently known,
there is no extraordinary difficulty in
determining from those laws the na-
ture of the social effects which any
given cause tends to produce. But

when the question is that of com-
pounding several tendencies together,
and computing the aggregate result
of many co-existent causes ; and espe-
cially when, by attempting to predict
what will actually occur in a given
case, we incur the obligation of esti-
mating and compounding the influ-
ences of all the causes which happen
to exist in that case ; we attempt a
task to proceed far in which surpasses
the compass of the human faculties.

If all the resources of science are
not sufficient to enable us to calculate
a priori, with complete precision, the
mutual action of three bodies gravi-
tating towards one another ; it may
be judged with what prospect of suc-
cess we should endeavour to calculate
the result of the conflicting tendencies
which are acting in a thousand diffe-
rent directions and promoting a thou-
sand different changes at a given in-
stant in a given society : although
we might and ought to be able, from
the laws of human nature, to distin-
guish correctly enough the tendencies
themselves, so far as they depend on
causes accessible to our observation ;
and to determine the direction which
each of them, if acting alone, would
impress upon society, as well as, in a
general way at least, to pronounce
that some of these tendencies are
more powerful than others.

But, without dissembling the ne-
cessary imperfections of the a priori
method when applied to such a sub-
ject, neither ought we, on the other
hand, to exaggerate them. The same
objections which apply to the Method
of Deduction in this its most difficult
employment, apply to it, as we for-
merly showed,* in its easiest ; and
would even there have been insuper-
able, if there had not existed, as was
then fully explained, an appropriate
remedy. This remedy consists in the
process which, under the name of
Verification, we have characterised
as the third essential constituent part
of the Deductive Method ; that of

* Supra, p. 295.

THE PHYSICAL MfiTHOC.

58s

collating the conclusions of the ratio-
cination either with the concrete phe-
nomena themselves, or, when such
are obtainable, with their empirical
laws The ground of confidence in
any concrete deductive science is not
the a priori reasoning itself, but the
accordance between its results and
those of observation a posteriori.
Either of these processes, apart from
the other, diminishes in value as the
subject increases in complication, and
this in so rapid a ratio as soon to be-
come entirely worthless ; but the re-
liance to be placed in the concurrence
of the two sorts of evidence not only
does not diminish in anything like
the same proportion, but is not neces-
sarily much diminished at all. No-
thing more results than a disturbance
in the order of precedency of the two
processes, sometimes amounting to its
actual inversion : insomuch that, in-
stead of deducing our conclusions by
reasoning, and verifying them by ob-
servation, we in some cases begin by
obtaining them provisionally from
specific experience, and afterwards
connect them with the principles of
human nature by d priori reasonings,
which reasonings are thus a real Veri-
fication.

The only thinker who, with a com-
petent knowledge of scientific me-
thods in general, has attempted to
characterise the Method of Sociology,
M. Comte, considers this inverse
order as inseparably inherent in the
nature of sociological speculation.
He looks upon the social science as
essentially consisting of generalisa-
tions from history, verified, not origi-
nally suggested, by deduction from
the laws of human nature. Though
there is a truth contained in this
opinion, of which I shall presently
endeavour to show the importance, I
cannot but think that this truth is
enunciated in too unlimited a manner,
and that there is considerable scope
in sociological inquiry for the direct,
as well as for the inverse, Deductive
Method.

It will, in fact, be shown in the

next chapter, that there is a kind of
sociological inquiries to which, from
their prodigioiis complication, the
method of direct deduction is alto-
gether inapplicable, while by a happy
compensation it is precisely in these
cases that we are able to obtain the
best empirical laws : to these inquiries,
therefore, the Inverse Method is ex-
clusively adapted. But there are also,
as will presently appear, other cases
in which it is impossible to obtain
from direct observation anything
worthy the name of an empirical
law ; and it fortunately happens that
these are the very cases in which the
Direct Method is least affected by
the objection, which undoubtedly must
always affect it in a certain degree.

We shall begin, then, by looking
at the Social Science as a science of
direct Deduction, and considering
what can be accomplished in it, and
under what limitations, by that mode
of investigation. We shall, then, in
a separate chapter, examine and en-
deavour to characterise the inverse
process.

§ 2. It is evident, in the first place,
that Sociology, considered as a system
of deductions a priori, cannot be a
science of positive predictions, but
only of tendencies. We may be able
to conclude, from the laws of human
nature applied to the circumstances
of a given state of society, that a
particular cause will operate in a
certain manner unless counteracted ;
but we can never be assured to what
extent or amount it will so operate,
or aflBrm with certainty that it wilt
not be counteracted ; because we can
seldom know, even approximately,
all the agencies which may co-exist
with it, and still less calculate the
collective result of so many combined
elements. The remark, however, must
here be once more repeated, that
knowledge insuflacient for prediction
may be most valuable for guidance.
It is not necessary for the wise con-
duct of the affairs of society, no more
than of any one's private concerns,

586

LOGIC OF THii MORAL SCIENCES.

that we should be able to foresee
infallibly the results of what we do.
We must seek our objects by means
which may perhaps be defeated, and
take precautions against dangers which
possibly may never be realised. The
aim of practical politics is to surround
any given society with the greatest
possible number of circumstances of
which the tendencies are beneficial,
and to remove or counteract, as far
as practicable, those of which the
tendencies are injurious. A know-
ledge of the tendencies only, though
without the power of accurately pre-
dicting their conjunct result, gives us
to a considerable extent this power.

It would, however, be an error to
suppose that, even with respect to
tendencies, we could arrive in this
manner at any great number of pro-
positions which will be true in all
societies without exception. Such a
supposition would be inconsistent with
the eminently modifiable nature of the
social phenomena, and the multitude
and variety of the circumstances by
which they are modified ; circum-
stances never the same, or even
nearly the same, in two different
societies, or in two different periods
of the same society. This would not
be so serious an obstacle if, though
the causes acting upon society in
general are numerous, those which
influence any one feature of society
were limited in number ; for we
might then insulate any particular
social phenomenon, and investigate
its laws without disturbance from
the rest. But the truth is the very
opposite of this. Whatever affects,
in an appreciable degree, any one
element of the social state, affects
through it all the other elements.
The mode of production of all social
phenomena is one great case of Inter-
mixture of Laws. We can never
either understand in theory or com-
mand in practice the condition of a
society in any one respect, without
taking into consideration its condi-
tion in all other respects. There is
no social phenomenon which is not

more or less influenced by every
other part of the condition of the
same society, and therefore by every
cause which is influencing any other
of the contemporaneous social pheno-
mena. There is, in short, what phy-
siologists term a consensus, similar to
that existing among the various organs
and functions of the physical frame
of man and the more perfect animals,
and constituting one of the many ana-
logies which have rendered universal
such expressions as the " body politic "
and " body natural." It follows from
this consensus, that unless two societies
could be alike in all the circumstances
which surround and influence them,
(which would imply their being alike
in their previous history,) no portion
whatever of the phenomena will, un-
less by accident, precisely correspond ;
no one cause will produce exactly the
same effects in both. Every cause,
as its effect spreads through society,
comes somewhere in contact with
different sets of agencies, and thus
has its effects on some of the social
phenomena differently modified ; and
these differences, by their reaction,
produce a difference even in those of
the effects which would otherwise
have been the same. We can never,
therefore, affirm with certainty that
a cause whiph has a particular ten-
dency in one people or in one age will
have exactly the same tendency in
another, without referring back to our
premises, and performing over again
for the second age or nation that
analysis of the whole of its influ-
encing circumstances which we had
already performed for the first. The
deductive science of society will not
lay down a theorem, asserting in an
universal manner the effect of any
cause ; but will rather teach us how
to frame the proper theorem for the
circumstances of any given case. It
will not give the laws of society in
general, but the means of determin-
ing the phenomena of any given
society from the particular elements
or data of that society.

All the general propositions which

tHE f HYslCAL MEtltOU.

587

Pan be framed by the deductive science
are, therefore, in the strictest sense of
the word, hypothetical. They are
grounded on some supposititious set
of circumstances, and declare how
some given cause w^ould operate in
those circumstances, supposing that
no others were combined with them.
If the set of circumstances supposed
have been copied from those of any
existing society, the conclusions will
be true of that society, provided, and
in as far as, the effect of those circum-
stances shall not be modified by others
which have not been taken into the ac-
count. If we desire a nearer approach
to concrete truth, we can only aim at
it by taking, or endeavouring to take,
a greater number of individualising
circumstances into the computation.

Considering, however, in how ac-
celerating a ratio the uncertainty of
our conclusions increase as we at-
tempt to take the effect of a greater
number of concurrent causes into our
calculations, the hypothetical combi-
nations of circumstances on which we
construct the general theorems of the
science cannot be made very complex
without so rapidly accumulating a lia-
bility to error as must soon deprive our
conclusionsof all value. Thismodeof in-
quiry, considered as a means of obtain-
ing general propositions, must there-
fore, on pain of frivolity, be limited
to those classes of social facts which,
though influenced like the rest by all
sociological agents, are under the im-
mediate influence, principally at least,
of a few only.

§ 3. Notwithstanding the universal
consensus of the social phenomena,
whereby nothing which takes place in
any part of the operations of society is
without its share of influence on every
other part ; and notwithstanding the
paramount ascendancy which the gen-
eral state of civilisation and social pro-
gress in any given society must hence
exercise over all the partial and sub-
ordinate phenomena ; it is not the
less true that different species of social
facts are in the main dependent, im-

mediately and in the first resort, on
different kinds of causes ; and there-
fore not only may with advantage,
but must, be studied apart : just as in
the natural body we study separately
the physiology and pathology of each
of the principal organs and tissues,
though every one is acted upon by
the state of all the others ; and though
the peculiar constitution and general
state of health of the organism co-ope-
rates with, and often preponderates
over, the local causes, in determining
the state of any particular organ.

On these considerations is grounded
the existence of distinct and separate,
though not indepen den t, branches or de -
partmentsof sociological speculation.

There is, for example, one large
class of social phenomena in which the
immediately determining causes are
principally those which act through
the desire of wealth, and in which
the psychological law mainly con-
cerned is the familiar one that a
greater gain is preferred to a smaller.
I mean, of course, that portion of the
phenomena of society which emanates
from the industrial or productive ope-
rations of mankind, and from those
of their acts through which the distri-
bution of the products of those indus-
trial operations take place, in so far
as not effected by force or modified
by volvmtary gift. By reasoning from
that one law of human nature, and
from the principal outward circum-
stances (whether universal or confined
to particular states of society) which
operate upon the human mind through
that law, we may be enabled to ex-
plain and predict this portion of the
phenomena of society, so far as they
depend on that class of circumstances
only, overlooking the influence of any
other of the circumstances of society,
and therefore neither tracing back
the circumstances which we do take
into account to their possible origin
in some other facts in the social state,
nor making allowance for the manner
in which any of those other circum-
stances may interfere with and coun-
teract or modify the effect of the for*

sss

Logic of tsij moral sciences.

mer. A department of science may
thus be constructed, which has re-
ceived the name of Political Economy.

The motive which suggests the
separation of this portion of the social
phenomena from the rest, and the
creation of a distinct branch of science
relating to them, is, that they do
mainly depend, at least in the first
resort, on one class of circumstances
only ; and that even when other cir-
cumstances interfere, the ascertain-
ment of the effect due to the one class
of circumstances alone is a sufficiently
intricate and difficult business to make
it expedient to perform it once for all,
and then allow for the effect of the
modifying circumstances ; especially
as certain fixed combinations of the
former are apt to recur often, in con-
junction with ever-varying circum-
stances of the latter class.

Political Economy, as I have said
on another occasion, concerns itself
only with " such of the phenomena of
the social state as take place in con-
sequence of the pursuit of wealth.
It makes entire abstraction of every
other human passion or motive, ex-
cept those which may be regarded as
perpetually antagonising principles to
the desire of wealth, namely, aversion
to labour, and desire of the present en-
joyment of costly indulgences. These
it takes, to a certain extent, into its
calculations, because these do not
merely, like our other desires, occa-
sionally conflict with the pursuit of
wealth, but accompany it always as a
drag or impediment, and are therefore
inseparably mixed up in the considera-
tion of it. Political Economy con-
siders mankind as occupied solely in
acquiring and consuming wealth, and
aims at showing what is the course of
action into which mankind, living in
a state of society, would be impelled
if that motive, except in the degree
in which it is checked by the two
perpetual counter- motives above ad-
verted to, were absolute ruler of all
their actions. Under the influence of
this desire, it shows mankind accu-
mulating wealth, and employing that

wealth in the production of other
wealth ; sanctioning by mutual agree-
ment the institution of property; esta-
blishing laws to prevent individuals
from encroaching upon the property
of others by force or fraud ; adopting
various contrivances for increasing
the productiveness of their labour ;
settling the division of the produce
by agreement, under the influence of
competition, (competition itself being
governed by certain laws, which laws
are therefore the ultimate regulators
of the division of the produce ;) and em-
ploying certain expedients (as money,
credit, &c.) to facilitate the distri-
bution. All these operations, though
many of them are really the result of
a plurality of motives, are considered
by political economy as flowing solely
from the desire of wealth. The science
then proceeds to investigate the laws
which govern these several operations,
under the supposition that man is a
being who is determined, by the neces-
sity of his nature, to prefer a greater
portion of wealth to a smaller in all
cases, without any other exception
than that constituted by the two
counter-motives already specified ; not
that any political economist was ever
so absurd as to suppose that mankind
are really thus constituted, but be-
cause this is the mode in which science
must necessarily proceed. When an
effect depends on a concurrence of
causes, these causes must be studied
one at a time, and their laws separately
investigated, if we wish, through the
causes, to obtain the power of either
predicting or controlling the effect ;
since the law of the effect is com-
pounded of the laws of all the causes
which determine it. The law of the
centripetal and that of the projectile
force must have been known before
the motions of the earth and planets
could be explained or many of them
predicted. The same is the case with
the conduct of man in society. In
order to judge how he will act under
the variety of desires and aversions
which are concurrently operating upon
him, we must know how he would act

11

THE PHYSICAL METHOD.

.under the exclusive influence of each
one in particular. There is, perhaps,
no action of a man's life in which he
is neither under the immediate nor
under the remote influence of any im-
pulse but the mere desire of wealth.
With respect to those parts of human
conduct of which wealth is not even
the principal object, to these political
economy does not pretend that its
conclusions are applicable. But there
are also certain departments of human
affairs in which the acquisition of
wealth is the main and acknowledged
end. It is only of these that political
economy takes notice. The manner
in which it necessarilj' proceeds is
that of treating the main and ac-
knowledged end as if it were the sole
end ; which, of all hypotheses equally
simple, is the nearest to the truth.
The political economist inquires, what
are the actions which would be pro-
duced by this desire, if within the
departments in question it were un-
impeded by any other. In this way
a nearer approximation is obtained
than would otherwise be practicable
to the real order of human affairs in
those departments. This approxima-
tion has then to be corrected by mak-
ing proper allowance for the effects of
any impulses of a different descrip-
tion which can be shown to interfere
with the result in any particular case.
Only in a few of the most striking
cases (such as the important one of
the principle of population) are these
corrections interpolated into the ex-
positions of political economy itself ;
the strictness of purely scientific ar-
rangement being thereby somewhat
departed from, for the sake of prac-
tical utility. So far as it is known,
or may be presumed, that the conduct
of mankind in the pursuit of wealth
is under the collateral influence of
any other of the properties of our
nature than the desire of obtaining
the greatest quantity of wealth with
the least labour and self-denial, the
conclusions of political economy will
so far fail of being applicable to the ex-
planation or prediction of real events,

589

until they are modified by a correct
allowance for the degree of influence
exercised by the other cause." *

Extensive and important practical
guidance may be derived, in any given
state of society, from general proposi-
tions such as those above indicated ;
even though the modifying influence
of the miscellaneous causes which the
theory does not take into account, as
well as the effect of the general social
changes in progress, be provisionally
overlooked. And though it has been
a very common error of political eco-
nomists to draw conclusions from the
elements of one state of society, and
apply them to other states in which
many of the elements are not the
same, it is even then not difficult,
by tracing back the demonstrations,
and introducing the new premises in
their proper places, to make the same
general course of argument which
served for the one case serve for the
others too.

For example, it has been greatly
the custom of English political econo-
mists to discuss the laws of the distri-
bution of the produce of industry, on
a supposition which is scarcely realised
anywhere out of England and Scot-
land, namely, that the produce is
"shared among three classes, alto-
gether distinct from one another,
labourers, capitalists, and landlords ;
and that all these are free agents,
permitted in law and in fact to set
upon their labour, their capital, and
their land, whatever price they are
able to get for it. The conclusions
of the science, being all adapted to
a society thus constituted, require to
be revised whenever they are applied
to any other. They are inapplicable
where the only capitalists are the
landlords, and the labourers are their
property, as in slave countries. They
are inapplicable where the almost uni-
versal landlord is the state, as in
India. They are inapplicable where
the agricultural labourer is generally
the owner both of the land itself and

* Essays on tomt Unsettled Qu€ftions of
Political Economy, p. 137-140.

590

LOGIC OF THE MORAL SCIENCES.

of the capital, as frequently in France,
or of the capital only, as in Ireland."
But though it may often be very justly
objected to the existing race of politi-
cal economists "'that they attempt to
construct a permanent fabric out of
transitory materials ; that they take
for granted the immutability of ar-
rangements of society, many of which
are in their nature fluctuating or pro-
gressive, and enunciate, with as little
qualification as if they were univer-
sal and absolute truths, propositions
which are perhaps applicable to no
state of society except the particular
one in which the writer happened to
live ; " this does not take away the
value of the propositions, considered
with reference to the state of society
from which they were drawn. And
even as applicable to other states of
Bociety, " it must not be supposed that
the science is so incomplete and un-
satisfactory as this might seem to
prove. Though many of its conclu-
sions are only locally true, its method
of investigation is applicable univer-
sally ; and as whoever has solved a
certain number of algebraic equations
can without difficulty solve all others
of the same kind, so whoever knows
the political economy of England, or
even of Yorkshire, knows that of all
nations, actual or possible, provided
he have good sense enough not to
expect the same conclusion to issue
from varying premises." Whoever
has mastered with the degree of pre-
cision which is attainable the laws
which, under free competition, deter-
mine the rent, profits, and wages,
received by landlords, capitalists, and
labourers, in a state of society in which
the three classes are completely sepa-
rate, will have no difficulty in deter-
mining the very different laws which
regulate the distribution of the pro-
duce among the classes interested in
it in any of the states of cultivation
and landed property set forth in the
foregoing extract.*

* The quotations in this paragraph are
from a paper written by the author, and
puljlished i» a periodipal in 1834,

§ 4. I would not here undertake to
decide what other hypothetical or
abstract sciences similar to Political
Economy may admit of being carved
Qut of the general body of the social
science ; what other portions of the
social phenomena are in a sufficiently
close and complete dependence, in the
first resort, on a peculiar class of
causes, to maKC it convenient to
create a preliminary science of those
causes : postponing the consideration
of the causes which act through them,
or in concurrence with them, to a
later period of the inquiry. There is,
however, among these separate depart-
ments one which cannot be passed
over in silence, being of a more com-
prehensive and commanding character
than any of the other branches into
which the social science may admit
of being divided. Like them, it is
directly conversant with the causes
of only one class of social facts, but a
class which exercises, immediately or
remotely, a paramount influence over
the rest. I allude to what may be
termed Political Ethology, or the
theory of the causes which determine
the type of character belonging to a
people or to an age. Of all the sub-
ordinate branches of the social science,
this is the most completely in its in-
fancy. The causes of national char-
acter are scarcely at all understood,
and the effect of institutions or social
arrangements upon the character of
the people is generally that portion of
their effects which is least attended
to, and least comprehended. Nor is
this wonderful when we consider the
infant state of the Science of Ethology
itself, from whence the laws must be
drawn, of which the truths of political
ethology can be but results and ex-
emplifications.

Yet to whoever well considers the
matter, it must appear that the laws
of national (or collective) character
are by far the most important class of
sociological laws. In the first place,
the character which is formed by any
state of social circumstances is in
itself the roost interesting pheno'

THE PHYSICAL METHOD.

591

hienon which that state of society can
possibly present. Secondly, it is also
a fact which enters largely into the
production of all the other phenomena.
And above all, the character, that is,
the opinions, feelings, and habits of
the people, though greatly the results
of the state of society which precedes
them, are also greatly the causes of
the state of society which follows
them ; and are the power by which
all those of the circumstances of
society which are artificial — laws and
customs, for instance — are altogether
moulded : customs evidently, laws no
less really, either by the direct influ-
ence of public sentiment upon the
ruling powers, or by the effect which
the state of national opinion and feel-
ing has in determining the form of
government, and shaping the char-
acter of the governors.

As might be expected, the most
imperfect part of those branches of
social inquiry which have been culti-
vated as separate sciences is the
theory of the manner in which their
conclusions are affected by ethological
considerations. The omission is no
defect in them as abstract or hypo-
thetical sciences, but it vitiates them
in their practical application as
branches of a comprehensive social
science. In political economy, for
instance, empirical laws of human
nature are tacitly assmned by English
thinkers, which are calculated only
for Great Britain and the United
States. Among other things, an in-
tensity of competition is constantly
supposed, which, as a general mercan-
tile fact, exists in no country in the
world except these two. An English
political economist, like his country-
men in general, has seldom learned
that it is possible that men, in con-
ducting the business of selling their
goods over a counter, should care more
about their ease or their vanity than
about their pecuniary gain. Yet those
who know the habits of the Continent
of Europe are aware how apparently
small a motive often outweighs the
desire of money-gettin3, even in the

operations which have money-getting
for their direct object. The more
highly the science of ethology is culti-
vated, and the better the diversities
of individual and national character
are understood, the smaller, probably,
will the number of propositions be-
come which it will be considered safe
to build on as universal principles of
human nature.

These considerations show that the
process of dividingoff the social science
into compartments, in order that each
may be studied separately, and its
conclusions afterwards corrected for
practice by the modifications supplied
by the others, must be subject to at
least one important limitation. Those
portions alone of the social phenomena
can with advantage be made the sub-
jects, even provisionally, of distinct
branches of science, into which the
diversities of character between dif-
ferent nations or different times enter
as influencing causes only in a secon-
dary degree. Those phenomena, on
the contrary, with which the influences
of the ethological state of the people
are mixed up at every step (so that
the connection of effects and causes
cannot be even rudely marked out
without taking those influences into
consideration) could not with any
advantage, nor without great dis-
advantage, be treated independently
of political ethology, nor, therefore, of
all the circumstances by which the
qualities of a people are influenced.
For this reason (as well as for others
which will hereafter appear) there can
be no separate Science of Govern-
ment ; that being the fact which, of
all others, is most mixed up, both as
cause and effect, with the qualities of
the particular people or of the par-
ticular age. All questions respecting
the tendencies of forms of government
must stand part of the general science
of society, not of any separate branch
of it.

This general Science of Society, as
distinguished from the separate de-
partments of the science (each of which
asserts its conclusions only condi-

592

LOGIC OF THE MORAL SCIENCES.

tionally, subject to the paramount
control of the laws of the general
science) now remains to be charac-
terised. And, as will be shown pre-
sently, nothing of a really scientific
character is here possible, except by
the inverse deductive method. But
before we quit the subject of those
sociological speculations which pro-
ceed by way of direct deduction, we
must examine in what relation they
stand to that indispensable element
in all deductive sciences, Verification
by Specific Experience — comparison
between the conclusions of reasoning
and the results of observation.

§ 5. We have seen that, in most
deductive sciences, and among the
rest in Ethology itself, which is the
immediate foundation of the Social
Science, a preliminary work of pre-
paration is performed on the observed
facts, to fit them for being rapidly
and accurately collated (sometimes
even for being collated at all) with
the conclusions of theory. This pre-
paratory treatment consists in finding
general propositions which express con-
cisely what is common to large classes
of observed facts ; and these are called
the empirical laws of the pheno-
mena. We have, therefore, to inquire,
whether any similar preparatory pro-
cess can be performed on the facts of
the social science ; whether there are
any empirical laws in history or sta-
tistics.

In statistics it is evident that em-
pirical laws may sometimes be traced,
and the tracing them forms an im-
portant part of that system of in-
direct observation on which we must
often rely for the data of the Deduc-
tive Science. The process of the
science consists in inferring effects
from their causes ; but we have often
no means of observing the causes ex-
cept through the medium of their
effects. In such cases the deductive
science is unable to predict the effects,
for want of the necessary data ; it
can determine what causes are cap-
able of producing any given effect,

but not with what frequency and in
what quantities those causes exist.
An instance in point is afforded by
a newspaper now lying before me.
A statement was furnished by one of
the official assignees in bankruptcy,
showing, among the various bank-
ruptcies which it had been his duty
to investigate, in how many cases the
losses had been caused by miscon-
duct of different kinds, and in how
many by unavoidable misfortunes.
The result was, that the number of
failures caused by misconduct greatly
preponderated over those arising from
all other causes whatever. Nothing but
specific experience could have given
sufficient ground for a conclusion to
this purport. To collect, therefore,
such empirical laws (which are never
more than approximate generalisa-
tions) from direct observation, is an
important part of the process of socio-
logical inquiry.

The eioerimental process is not
here to be regarded as a distinct road
to the truth, but as a means (hap-
pening accidentally to be the only,
or the best, available) for obtaining
the necessary data for the deductive
science. When the immediate causes
of social facts are not open to direct
observation, the empirical law of the
effects gives us the empirical law
(which in that case is all that we can
obtain) of the causes likewise. But
those immediate causes depend on
remote causes ; and the empirical
law, obtained by this indirect mode
of observation can only be relied onj
as applicable to unobserved cases, so
long as there is reason to think that '
no change has taken place in any of
the remote causes on which the im-
mediate causes depend. In making ,
use, therefore, of even the best statis-
tical generalisations for the purpose]
of inferring (though it be only con-|
jecturally) that the same empirical!
laws will hold in any new case, it isi
necessary that we be well acquainted]
with the remoter causes, in order that |
we may avoid applying the empirical
law to cases which differ in any of the

THE PHYSICAL METHOD.

593

circumstances on which the truth of
the law ultimately depends. And thus,
even where conclusions derived from
specific observation are available for
practical inferences in new cases, it is
necessary that the deductive science
should stand sentinel over the whole
process ; that it should be constantly
referred to, and its sanction obtained
to every inference.

The same thing holds true of all
generalisations which can be grounded
on history. Not only are there such
generalisations, but it will presently
be shown that the general science of
society, which inquires into the laws
of succession and co-existence of the
great facts constituting the state of
society and civilisation at any time,
can proceed in no other manner than
by making such generalisations —
afterwards to be confirmed by con-
necting them with the psychological
and ethological laws on which they
must really depend.

§ 6. But (reserving this question
for its proper place) in those more
special inquiries which form the sub-
ject of the separate branches of the
social science, this twofold logical pro-
cess and reciprocal verification is not
possible : specific experience affoi'ds
nothing amoimting to empirical laws.
This is particularly the case where
the object is to determine the effect
of any one social cause among a great
number acting simultaneously ; the
effect, for example, of corn laws, or
of a prohibitive commercial system
generally. Though it may be per-
fectly certain, from theory, what kind
of effects corn laws must produce,
and in what general direction their
influence must tell upon industrial
prosperity, their effect is yet of neces-
sity so much disgiaised by the similar
or contrary effects of other influen-
cing agents, that specific experience
can at most only show that on the
average of some great number of in-
stances, the cases where there were
corn laws exhibited the effect in a
greater degree than those where there

were not. Now the number of in-
stances necessary to exhaust the whole
round of combinations of the various,
influential circumstances, and thus
afford a fair average, never can be
obtained. Not only we can never
learn with sufficient authenticity the
facts of so many instances, but the
world itself does not afford them in
sufficient numbers, within the limits
of the given state of society and civi-
lisation which such inquiries always
presuppose. Having thus no pre-
vious empirical generalisations with
which to collate the conclusions of
theory, the only mode of direct verifica-
tion which remains is to compare those
conclusions with the result of an in-
dividual experiment or instance. But
here the difficulty is equally great.
For in order to verify a theory by an
experiment, the circumstances of the
experiment must be exactly the same
with those contemplated in the theory.
But in social phenomena the circum-
stances of no two cases are exactly
alike. A trial of corn laws in another
country or in a former generation
would go a very little way towards
verifying a conclusion drawn respect-
ing their effect in this generation and
in this country. It thus happens, in
most cases, that the only individual
instance really fitted to verify the
predictions of theory is the very in-
stance for which the predictions were
made ; and the verification comes too
late to be of any avail for practical
guidance.

Although, however, direct verifica-
tion is impossible, there is an indirect
verification, which is scarcely of less
value, and which is always practicable.
The conclusion drawn as to the indi-
vidual case can only be directly veri-
fied in that case ; but it is verified
indirectly by the verification of other
conclusions, drawn in other individual
cases from the same laws. The ex-
perience which comes too late to verify
the particular proposition to which it
refers is not too late to help towards
verifying the general sufficiency of the
theory. The test of the degree in

2 P

594

LOGIC OF THE MORAL SCIENCES.

which the science affords safe ground
for predicting (and consequently for
practically dealing with) what has
not yet happened, is the degree in
which it would have enabled us to
predict what has actually occurred.
Before our theory of the influence
of a particular cause, in a given state
of circumstances, can be entirely
trusted, we must be able to explain
and account for the existing state of
all that portion of the social pheno-
mena which that cause has a tendency
to influence. If, for instance, we would
apply our speculations in political eco-
nomy to the prediction or guidance of
the phenomenaof anycountry, we must
be able to explain all the mercantile
or industrial facts of a general char-
acter appertaining to the present state
of that country : to point out causes
sufficient to account for all of them,
and prove, or show good ground for
supposing, that these causes have
really existed. If we cannot do this,
it is a proof either that the facts
which ought to be taken into account
are not yet completely known to us,
or that although we know the facts,
we are not masters of a sufiiciently
perfect theory to enable us to assign
their consequences. In either case
we are not, in the present state of our
knowledge, fully competent to draw
conclusions, speculative or practical,
for that country. In like manner, if
we would attempt to judge of the
efi"ect which any political institution
would have, supposing that it could
be introduced into any given country,
we must be able to show that the ex-
isting state of the practical govern-
ment of that country, and of whatever
else depends thereon, together with
the particular character and tenden-
cies of the people, and their state in
respect to the various elements of
social well being, are such as the in-
stitutions they have lived und-r, in
conjunction with the other circum-
stances of their nature or of their
position, were calculated to produce.

To prove (in short) that our science,
and our knowledge of the particular

case, render us competent to predict
the future, we must show that they
would have enabled us to predict the
present and the past. If there be
anything which we could not have
predicted, this constitutes a residual
phenomenon, requiring further study
for the purpose of explanation ; and
we must either search among the cir-
cumstances of the particular case un-
til we find one which, on the principles
of our existing theory, accounts for the
unexplained phenomenon, or we must
turn back, and seek the explanation
by an extension and improvement of
the theory itself.

CHAPTER X.

OP THE INVERSE DEDUCTIVE, OR
HISTORICAL METHOD.

§ I. There are two kinds of socio-
logical inquiry. In the first kind, the
question proposed is, what effet;t will
follow from a given cause, a certain
general condition of social circum-
stances being presupposed. As, for
example, what would be the effect of
imposing or of repealing corn laws, of
abolishing monarchy or introducing
universal suffrage, in the present con-
dition of society and civilisation in
any European country, or under any
other given supposition with regard to
the circumstances of society in gene-
ral, without reference to the changes
which might take place, or which
may already be in progress, in those
circumstances. But there is also a
second inquiry, namely, what are the
laws which determine those general
circumstances themselves. In this
last the question is, not what will be
the effect of a given cause in a certain
state of society, but what are the
causes which produce, and the pheno-
mena which characterise, States of
Society generally. In the solution
of this question consists the general
Science of Society, by which the
conclusions of the other and more

THE HISTORICAL METHOD.

special kind of inquiry must be limited
and controlled.

§ 2. In order to conceive correctly
the scope of this general science, and
distinguish it from the subordinate
departments of sociological specula-
tion, it is necessary to fix the ideas
attached to the phrase "a State of
Society. " What is called a state of
society is the simultaneous state of
all the greater social facts or pheno-
mena. Such are the degree of know-
ledge, and of intellectual and moral
culture, existing in the community,
and of every class of it ; the state of
industry, of wealth and its distribu-
tion ; the habitual occupations of the
community ; their division into classes,
and the relations of those classes
to one another ; the common beliefs
which they entertain on all the sub-
jects most important to mankind, and
the degree of assurance with which
those beliefs are held ; their tastes,
and the character and degree of their
aesthetic development ; their form of
government, and the more important
of their laws and customs. The con-
dition of all these things, and of many
more which will readily suggest them-
selves, constitute the state of society
or the state of civilisation at any given
time.

When states of society, and the
causes which produce them, are spoken
of as a subject of science, it is implied
that there exists a natural correlation
among these different elements ; that
not every variety of combination of
these general social facts is possible,
but only certain combinations ; that,
in short, there exist Uniformities of
Co-existence between the states of the
various social phenomena. And such
is the truth ; as is indeed a neces.sary
consequence of the influence exercised
by every one of those phenomena over
every other. It is a fact implied in
the consensvis of the various parts of
the social body.

States of society are like different
constitutions or different ages in the
physical frame ; they are conditions

595

not of one or a few organs or func-
tions, but of the whole organism.
Accordingly, the information which
we possess respecting past ages, and
respecting the various states of society
now existing in different regions of
the earth, does, when duly analysed,
exhibit uniformities. It is f< -und that
when one of the features of society is
in a particular state, a state of many
other features, more or less precisely
determinate, always or usually co-
exists with it.

But the uniformities of co-existence
obtaining among phenomena which
are effects of causes must (as we have
so often observed) be corollaries from
the laws of causation by which these
phenomena are really determined.
The mutual correlation between the
different elements of each state of
society is therefore a derivative law,
resulting from the laws which regu-
late the succession between one state
of society and another ; for the proxi-
mate cause of every state of society is
the state of society immediately pre-
ceding it. The fundamental problem,
therefore, of the social science, is to
find the laws according to which any
state of society produces the state
which succeeds it and takes its place.
This opens the great and vexed ques-
tion of the progressiveness of man and
society ; an idea involved in every
just conception of social phenomena
as the subject of a science.

§ 3. It is one of the characters, not
absolutely peculiar to the sciences of
human nature and society, but be-
longing to them in a peculiar degree,
to be conversant with a subject-matter
whose properties are changeable. I
do not mean changeable from day to
day, but from age to age ; so that not
only the qualities of individuals vary,
but those of the majority are not the
same in one age as in another.

The principal cause of this peculi-
arity is the extensive and constant re-
action of the effects upon their causes.
The circumstances in which mankind
are placed, operating according to

596

LOGIC OF THE MORAL SCIENCES.

their own laws and to the laws of
human nature, form the characters of
the human beings ; but the human
beings, in their turn, mould and shape
the circumstances for themselves and
for those who come after them. From
this reciprocal action there must neces-
sarily result either a cycle or a pro-
gress. In astronomy also, every fact is
at once effect and cause ; the succes-
sive positions of the various heavenly
bodies produce changes both in the
direction and in the intensity of the
forces by which those positions are
determined. But in the case of the
solar system, these mutual actions
bring round again, after a certain
number of changes, the former state
of circumstances ; which of course
leads to the perpetual recurrence of
the same series in an unvarying order.
Those bodies, in short, revolve in or-
bits : but there are (or, conformably
to the laws of astronomy, there might
be) others which, instead of an orbit,
describe a trajectory — a course not
returning into itself. One or other
of these must be the type to which
human affairs must conform.

One of the thinkers who earliest
conceived the succession of historical
events as subject to fixed laws, and
endeavoured to discover these laws
by an analytical survey of history,
Vico, the celebrated author of Scienza
Nuova, adopted the former of these
opinions. He conceived the pheno-
mena of human society as revolving
in an orbit ; as going through perio-
dically the same series of changes.
Though there were not wanting cir-
cumstances tending to give some plau-
sibility to this view, it would not bear
a close scrutiny ; and those who have
succeeded Vico in this kind of specu-
lations have universally adopted the
idea of a trajectory or progress, in lieu
of an orbit or cycle.

The words Progress and Progres-
siveness are not here to be understood
as synonymous with improvement and
tendency to improvement. It is con-
ceivable that the laws of human nature
might determine, and even necessitate,

a certain series of changes in man and
society, which might not in every case,
or which might not on the whole, be
improvements. It is my belief indeed
that the general tendency is, and will
continue to be, saving occasional and
temporary exceptions, one of improve-
ment— a tendency towards a better
and happier state. This, however, is
not a question of the method of the
social science, but a theorem of the
science itself. For our purpose it is
sufficient that there is a progressive
change, both in the character of the
human race and in their outward cir-
cumstances so far as moulded by them-
selves; that in each successive age
the principal phenomena of society are
different from what they were in the
age preceding, and still more different
from any previous age : the periods
which most distinctly mark these suc-
cessive changes being intervals of one
generation, during which a new set
of human beings have been educated,
have grown up from childhood, and
taken possession of society.

The progressiveness of the human
race is the foundation on which a
method of philosophising in the social
science has been of late years erected,
far superior to either of the two modes
which had previously been prevalent,
the chemical or experimental, and the
geometrical modes. This method,
which is now generally adopted by i
the most advanced thinkers on thej
Continent, consists in attempting, by|
a study and analysis of the geners
facts of history, to discover (what thes
philosophers term) the law of progress j
which law, once ascertained, must ac-
cording to them enable us to predict fu-
ture events, just as after a few terms of
an infinite series in algebra we are able
to detect the principle of regularity ii
their formation, and to predict the res
of the series to any number of tert
we please. The principal aim of hisi^
torical speculation in France, of lat
years, has been to ascertain this law.^
But while I gladly acknowledge the
great services which have been ren-
dered to historical knowledge by this

THE HISTORICAL METHOD.

597

school, I cannot but deem them to be
mostly chargeable with a fundamental
misconception of the true method of
social philosophy. The misconception
consists in supposing that the order of
succession which we may be able to
trace among the different states of
society and civilisation which history
presents to us, even if that order were
more rigidly imiform than it has yet
been proved to be, could ever amount
to a law of nature. It can only be
an empirical law. The succession of
states of the human mind and of
human society cannot have an inde-
pendent law of its own ; it must de-
pend on the psychological and etho-
logical laws which govern the action
of circumstances on men and of men
on circumstances. It is conceivable
that those laws might be such, and
the general circumstances of the
human race such, as to determine the
successive transformations of man
and society to one given and unvary-
ing order. But even if the case were
so, it cannot be the ultimate aim of
science to discover an empirical law.
Until that law could be connected
with the psychological and ethologi-
cal laws on which it must depend,
and, by the consilience of deduction d
priori with historical evidence, could
be converted from an empirical law
into a scientific one, it could not be
relied on for the prediction of future
events, beyond, at most, strictly ad-
jacent cases. M. Comte alone, among
the new historical school, has seen
the necessity of thus connecting all
our generalisations from history with
the laws of human nature.

§ 4. But while it is an imperative
rule never to introduce any generali-
sation from history into the social
science unless sufficient grounds can
be pointed out for it inhuman nature, I
do not think any one will contend that
it would have been possible, setting
out from the principles of human na-
ture and from the general circum-
stances of the position of our species,
to determine ^ priori the order in

which human development must take
place, and to predict, consequently,
the general facts of history up to the
present time. After the first few
terms of the series, the influence exer-
cised over each generation by the
generations which preceded it be-
comes (as is well observed by the
writer last referred to) more and more
preponderantover all other influences ;
until at length what we now are and
do is in a very small degree the re-
sult of the universal circumstances of
the human race, or even of our own
circumstances acting through the ori-
ginal qualities of our species, but
mainly of the qualities produced in us
by the whole previous history of hu-
manity. So long a series of actions
and reactions between Circumstances
and Man, each successive term being
composed of an ever greater number
and variety of parts, could not pos-
sibly be computed by human faculties
from the elementary laws which pro-
duce it. The mere length of the series
would be a sufficient obstacle, since a
slight error in any one of the terms
would augment in rapid progression
at every subsequent step.

If, therefore, the series of the effects
themselves did not, when examined
as a whole, manifest any regularity,
we should in vain attempt to construct
a general science of society. We must
in that case have contented ourselves
with that subordinate order of socio-
logical speculation formerly noticed,
namely, with endeavouring to ascer-
tain what would be the effect of the
introduction of any new cause, in a
state of society supposed to be fixed ;
a knowledge sufficient for the more
common exigencies of daily political
practice, but liable to fail in all cases
in which the progressive movement of
society is one of the influencing ele-
ments ; and therefore more precarious
in proportion as the case is more im-
portant. But since both the natural
varieties of mankind, and the original
diversities of local circumstances are
much less considerable than the points
of agreement, there will naturally Ikj

LOGIC OF THE MORAL SCIENCES.

59S

a certain degree of uniformity in the
progressive development o the species
and of its works. And this uniformity
tends to become greater, not less, as
society advances ; since the evolution
of each people, which is at first deter-
mined exclusively by the nature and
circumstances of that people, is gra-
dually brought under the influence
(which becomes stronger as civilisa-
tion advances) of the other nations of
the earth, and of the circumstances
by which they have been influenced.
History accordingly does, when judi-
ciously examined, afford Empirical
Laws of Society. And the problem
of general sociology is to ascertain
these, and connect them with the laws
of human nature, by deductions show-
ing that such were the derivative laws
naturally to be expected as the conse-
quences of those ultimate ones.

It is, indeed, hardly ever possible,
even after history has suggested the
derivative law, to demonstrate dpjnoH
that such was the only order of suc-
cession or of co-existence in which the
effects could, consistently with the
laws of human nature, have been pro-
duced. We can at most make out
that there were strong d priori reasons
for expecting it, and that no other
order of succession or co-existence
would have been so likely to result
from the nature of man and the gene-
ral circumstances of his position.
Often we cannot do even this ; we
cannot even show that what did take
place was probable d priori, but only
that it was possible. This, however,
— which, in the Inverse Deductive
Method that we are now characteris-
ing, is a real process of verification, —
is as indispensable as verification by
specific experience has been shown to
be, where the conclusion is originally
obtained by the direct way of deduc-
tion. The empirical laws must be the
result of but a few instances, since
few nations have ever attained at all,
and still fewer by their own indepen-
dent development, a high stage of
social progress. If, therefore, even
one or two of these few instances be

insufficiently known, or imperfectly
analysed into their elements, and
therefore not adequately compared
with other instances, nothing is more
probable than that a wrong empirical
law will emerge instead of the right
one. Accordingly, the most errone-
ous generalisations are continually
made from the course of history : not
only in this country, where history
cannot yet be said to be at all culti-
vated as a science, but in other coun-
tries where it is so cultivated, and by
persons well versed in it. The only
check or corrective is constant verifi-
cation by psychological and ethological
laws. We may add to this, that no
one but a person competently skilled
in those laws is capable of preparing
the materials for historical generalisa-
tion by analysing the facts of history,
or even by observing the social pheno-
mena of his own time. No other will
be aware of the comparative import-
ance of different facts, nor conse-
quently know what facts to look fori
or to observe ; still less will he be]
capable of estimating the evidence of ^
facts which, as is the case with most,]
cannot be ascertained by direct ob-
servation or learnt from testimony,
but must be inferred from marks.

§ 5. The Empirical Laws of Society]
are of two kinds ; some are unifor-
mities of co-existence, some of succes-
sion. According as the science is]
occupied in ascertaining and verify-
ing the former sort of uniformities orj
the latter, M. Comte gives it th«
title of Social Statics or of Socia
Dynamics, conformably to the dis-
tinction in mechanics between the!
conditions of equilibrium and thosej
of movement, or in biology betweei
the laws of organisation and those
life. The first branch of the science'
ascertains the conditions of stability
in the social union ; the second, the
laws of progress. Social Dynamics!
is the theory of society considered]
in a state of progressive movement
while Social Statics is the theory of
the consensus already spoken of

THE HISTORICAL METHOD.

599

existing among the different parts of
the social organism ; in other words,
the theory of the mutual actions and
reactions of contemporaneous social
phenomena ; "making* provisionally,
as far as possible, abstraction, for
scientific purposes, of the fundamen-
tal movement which is at all times
gradually modifying the whole of
them.

"In this first point of view, the
provisions of sociology will enable us
to infer one from another (subject to
ulterior verification by direct observa-
tion) the various characteristic marks
of each distinct mode of social exist-
ence ; in a manner essentially analo-
gous to what is now habitually prac-
tised in the anatomy of the physical
body. This preliminary aspect, there-
fore, of political science, of necessity
supposes that (contrary to the exist-
ing habits of philosophers) each of the
numerous elements of the stxjial state,
ceasing to be looked at independently
and absolutely, shall be always and
exclusively considered relatively to all
the other elements, with the whole of
which it is united by mutual inter-
dependence. It would be superfluous
to insist here upon the great and con-
stant utility of this branch of stxiio-
logical speculation. It is, in the first
place, the indispensable basis of the
theory of social progress. It may,
moreover, be employed, immediately
and of itself, to supply the place, pro-
visionally at least, of direct observa-
tion, which in many cases is not always
practicable for some of the elements
of society, the real condition of which
may, however, be sufficiently judged
of by means of the relations which
connect them with others previously
known. The history of the sciences
may give us some notion of the ha-
bitual importance of this auxiliary
resource, by reminding us, for ex-
ample, how the vulgar errors of mere
erudition concerning the pretended
acquirements of the ancient Egyp-
tians in the higher astronomy, were

* Court de Philosophic Fositive, iv. 325-329.

irrevocably dissipated (even before
sentence had been passed on them by
a sounder erudition) from the single
consideration of the inevitable con-
nection between the general state of
astronomy and that of abstract geo-
metry, then evidently in its infancy.
It would be easy to cite a multitude
of analogous cases, the character of
which could admit of no dispute. In
order to avoid exaggeration, however,
it should be remarked that these ne-
cessary relations among the different
aspects of society cannot, from their
very nature, be to simple and precise
that the results observed could only
have arisen from some one mode of
mutual co-ordination. Such a notion,
already too narrow in the science of
life, would be completely at variance
with the still more complex nature
of sociological speculations. But the
exact estimation of these limits of
variation, both in the healthy and in
the morbid state, constitutes, at least
as much as in the anatomy of the
natural body, an indispensable com-
plement to every theory of Sociolo-
gical Statics, without which the in-
direct exploration above spoken of
would often lead into error.

" This is not the place for methodi-
cally demonstrating the existence of a
necessary relation among all the pos-
sible aspects of the same social orga-
nism ; a point on which, in principle
at least, there is now little difference
of opinion among sound thinkers.
From whichever of the social ele-
ments we choose to set out, we may
easily recognise that it has always a
connection, more or less immediate,
with all the other elements, even
with those which at first sight appear
the most independent of it. The
dynamical consideration of the pro-
gressive development of civilised hu-
manity, affords, no doubt, a still more
efficacious means of effecting this in-
teresting verification of the consensus
of the social phenomena, by displaying
the manner in which every change in
any one part operates immediately,
or very speedily, upon all the rest,

6oo

LOGIC OF THE MORAL SCIENCES.

But this indication may be preceded,
or at all events followed, by a confir-
mation of a purely statical kind ; for,
in politics as in mechanics, the com-
munication of motion from one object
to another proves a connection be-
tw^een them. Without descending to
the minute interdependence of the dif-
ferent branches of any one science or
art, is it not evident that among the
different sciences, as well as among
most of the arts, there exists such a
connection, that if the state of any
one well-marked division of them is
sufficiently known to us, we can with
real scientific assurance infer, from
their necessary correlation, the con-
temporaneous state of every one of
the others ? By a further extension
of this consideration, we may conceive
the necessary relation which exists
between the condition of the sciences
in general and that of the arts in
general, except that the mutual de-
pendence is less intense in proportion
as it is more indirect. The same is
the case when, instead of consider-
ing the aggregate of the social pheno-
mena in some one people, we examine
it simultaneously in different contem-
poraneous nations, between which
the perpetual reciprocity of influence,
especially in modern times, cannot be
contested, though the consensus must
in this case be ordinarily of a less de-
cided character, and must decrease
gradually with the affinity of the cases
and the miiltiplicity of the points of
contact, so as at last, in some cases,
to disappear almost entirely ; as, for
example, between "Western Europe
and Eastern Asia, of which the vari-
ous general states of society appear to
have been hitherto almost indepen-
dent of one another."

These remarks are followed by illus-
trations of one of the most important,
and, until lately, most neglected, of
the general principles which, in this
division of the social science, may be
considered as established ; namely,
the necessary correlation between the
form of government existing in any
society and the contemporaneous state

of civilisation: a natural law which
stamps the endless discussions and in-
numerable theories I'especting forms
of government in the abstract as
fruitless and worthless for any other
purpose than as a preparatory treat-
ment of materials to be afterwards
used for the construction of a better
philosophy.

As already remarked, one of the
main results of the science of social
statics would be to ascertain the re-
quisites of stable political union.
There are some circumstances which,
being found in all societies without
exception, and in the greatest degree
where the social union is most com-
plete, may be considered (when psy-
chological and ethological laws con-
firm the indication) as conditions of
the existence of the complex pheno-
menon called a State. For example,
no numerous society has ever been
held together without laws, or usages
equivalent to them ; without tribu-
nals, and an organised force of some
sort to execute their decisions. There
have always been public authorities
whom, with more or less strictness,
and in cases more or less accurately
defined, the rest of the community
obeyed, or according to general opin-
ion were bound to obey. By follow-
ing out this course of inquiry we shall
find a number of requisites which have
been present in every society that has
maintained a collective existence, and
on the cessation of which it has either
merged in some other society, or re
constructed itself on some new basis,
in which the conditions were cou
formed to. Although these results,
obtained by comparing different forms
and states of society, amount in them-
selves only to empirical laws, some
of them, when once suggested, are
found to follow with so much proba-
bility from general laws of human
nature, that the consilience of the two
processes raises the evidence to proof,
and the generalisations to the rank of
scientific truths.

This seems to be affirmable (for in-
stance) of the conclusions arrived at

1

The filSTORICAL METHOD.

6ol

in the following passage, extracted,
with some alterations, from a criticism
on the negative philosophy of the
eighteenth century,* and which I
quote, though (as in some former in-
stances! from myself, because I have
no better way of illustrating the con-
ception I have formed of the kind of
theorems of which sociological statics
would consist : —

" The very first element of the social
union, obedience to a government of
some sort, has not been found so easy
a thing to establish in the world.
Among a timid and spiritless race
like the inhabitants of the vast plains
of tropical countries, passive obedience
may be of natural growth ; though
even there we doubt whether it has
ever been found among any people
with whom fatalism, or, in other words,
submission to the pressure of circum-
stances as a divine decree, did not
prevail as a religious doctrine. But
the difficulty of inducing a brave and
warlike race to submit their individual
arbitrium to any common umpire has
always been felt to be so great, that
nothing short of supernatuial power
has been deemed adequate to over-
come it ; and such tribes have always
assigned to the first institution of civil
society a divine origin. So differently
did those judge who knew savage men
by actual experience, from those who
had no acquaintance with them ex-
cept in the civilised state. In modem
Europe itself, after the fall of the
Roman Empire, to subdue the feudal
anarchy and bring the whole people
of any European nation into subjec-
tion to government (though Christi-
anity in the most concentrated form
of its influence was co-operating in
the work) required thrice as many
centuries as have elapsed since that
time.

"Now if these philosophers had
known human nature under any other
type than that of their own age, and
of the particular classes of society

* Since reprinted entire in Dissertations
and Discussions, as the concluding paper of
the first volume.

among whom they lived, it would
have occurred to them, that wherever
this habitual submission to law and
government has been firmly and dur-
ably established, and yet the vigour
and manliness of character which re-
sisted its establishment have been in
any degree preserved, certain requi-
sites have existed, certain conditions
have been fulfilled, of which the fol-
lowing may be regarded as the prin-
cipal : —

"First, there has existed, for all
who were accounted citizens, — for all
who were not slaves, kept down by
brute force, — a system of education,
beginning with infancy and continued
through life, of which, whatever else it
might include, one main and incessant
ingredient was redrainirKj discipline.
To train the human being in the habit,
and thence the power, of subordinat-
ing his personal impulses and ain\^
to what were considered the ends
of society ; of adhering, against all
temptation, to the course of conduct
which those ends prescribed ; of con-
trolling in himself all feelings which
were liable to militate against those
ends, and encouraging all such as
tended towards them ; this was the
purpose to which every outward mo-
tive that the authority directing the
system could command, and eveiy in-
ward power or principle which its
knowledge of human nature enabled
it to evoke, were endeavoured to be
rendered instrumental. The entire
civil and military policy of the ancient
commonwealths was such a system of
training ; in modem nations its place
has been attempted to be supplied,
principally, by religious teaching.
And whenever and in proportion as
the strictness of the restraining dis-
cipline was relaxed, the natural ten-
dency of mankind to anarchy reas-
serted itself ; the state became dis-
organised from within ; mutual con-
flict for selfish ends neutralised the
energies which were required to keep
up the contest against natural causes
of evil ; and the nation, after a longer
or briefer interval of progressive de-

6o2

LOGIC OF THE MORAL SCIENCES.

cline, became either the slave of a
despotism, or the prey of a foreign
invader.

"The second condition of perma-
nent political society has been found
to be the existence, in some form or
other, of the feeling of allegiance or
loyalty. This feeling may vary in its
objects, and is not confined to any
particular form of government ; but
whether in a democracy or in a mon-
archy, its essence is always the same,
viz. that there be in the constitution
of the state something which is settled,
something permanent, and not to be
called in question ; something which,
by general agreement, has a right to
be where rt is, and to be secure
against disturbance, whatever else
may change. This feeling may attach
itself, as among the Jews, (and in most
of the commonwealths of antiquity, )
to a common God or gods, the protec-
tors and guardians of their state. Or
it may attach itself to certain persons,
who are deemed to be, whether by
divine appointment, by long prescrip-
tion, or by the general recognition of
their superior capacity and worthiness,
the rightful guides and guardians of
the rest Or it may connect itself
with laws ; with ancient liberties or
ordinances. Or, finally, (and this is
the only shape in which the feel-
ing is likely to exist hereafter,) it
may attach itself to the principles
of individual freedom and political
and social equality, as realised in in-
stitutions which as yet exist nowhere,
or exist only in a rudimentary state.
But in all political societies which
have had a durable existence there
has been some fixed point, something
which people agree in holding sacred ;
which, wherever freedom of discus-
sion was a recognised principle, it was
of course lawful to contest in theory,
but which no one could either fear or
hope to see shaken in practice ; which,
in short (except perhaps during some
temporary crisis) was in the common
estimation placed beyond discussion.
And the necessity of this may easily
be made evident. A state never is,

nor, until mankind are vastly im-
proved, can hope to be, for any long
time exempt from internal dissension ;
for there neither is nor ever has been
any state of society in which collisions
did not occur between the immediate
interests and passions of powerful sec-
tions of the people. What, then, en-
ables nations to weather these storms,
and pass through turbulent times with-
out any permanent weakening of the
securities for peaceable existence ?
Precisely this — that however impor-
tant the interests about which men fell
out, the conflict did not affect the
fundamental principle of the system of
social union which happened to exist,
nor threaten large portions of the com-
munity with the subversion of that on
which they had built their calcula-
tions, and with which their hopes and
aims had become identified. But when
the qtiestioning of these fundamental
principles is (not the occasional dis-
ease or salutary medicine, but) the
habitual condition of the body politic,
and when all the violent animosities
are called forth which spring natu-
rally from such a situation, the state is
virtually in a position of civil war,
and can never long remain free from
it in act and fact.

•'The third essential condition of
stability in political society is a strong
and active principle of cohesion among
the members of the same community
or state. We need scarcely say that
we <'^ not mean nationality, in the
vulgar sense of the term ; a senseless
antipathy to foreigners ; indifference
to the general welfare of the human
race, or an unjust preference of the
supposed interest of our own country ;
a cherishing of bad peculiarities be-
cause they are national, or a refusal
to adopt what has been found good by
other countries. We mean a principle
of sympathy, not of hostility ; of union,
not of separation. We mean a feeling
of common interest among those who
live under the same government, and
are contained within the same natural
or historical boundaries. We mean,
that one part of the community do

I

THE HISTORICAL METHOD.

603

not consider themselves as foreigners
with regard to another part ; that
they set a value on their connection-
feel that they are one people, that
their lot is cast together, that evil to
any of their fellow-countrymen is evil
to themselves, and do not desire sel-
fishly to free themselves from their
share of any common inconvenience
by severing the connection. How
strong this feeling was in those ancient
commonwealths which attained any
durable greatness every one knows.
How happily Rome, in spite of all her
tyranny, succeeded in establishing the
feeling of a common country among
the provinces of her vast and divided
empire, will appear when any one who
has given due attention to the subject
shall take the trouble to point it out.
In modern times the countries which
have had that feeling in the strongest
degree have been the most powerful
countries; England, France, and, in
proportion to their territory and re-
sources, Holland and Switzerland ;
while England in her connection with
Ireland is one of the most signal ex-
amples of the consequences of its ab-
sence. Every Italian knows why Italy
is under a foreign yoke ; every Ger-
man knows what maintains despotism
in the Austrian empire ;* the evils of
Spain flow as much from the absence
of nationality among the Spaniards
themselves as from the presence of it
in their relations with foreigners :
while the completest illustration of all
is afforded by the republics of South
America, where the parts of one and
the same state adhere so slightly to-
gether, that no sooner does any pro-
vince think itself aggrieved by the
general government than it proclaims
itself a separate nation."

§ 6. While the derivative laws of
social statics are ascertained by ana-
lysing different states of society, and
comparing them with one another,
without regard to the order of their
succession, the consideration of the

* (Written and first published in 1840.)

successiveorder is, on the contrary, pre-
dominant in the study of social dyna-
mics, of which the aim is to observe
and explain the sequences of social
conditions. This branch of the social
science would be as complete as it
can be made if every one of the lead-
ing general circumstances of each
generation were traced to its causes
in the generation immediately pre-
ceding. But the consensus is so com-
plete (especially in modern history)
that, in the filiation of one generation
and another, it is the whole which
produces the whole, rather than any
part a part. Little progress, there-
fore, can be made in establishing the
filiation directly from laws of human
nature, without having first ascer-
tained the immediate or derivative
laws according to which social states
generate one another as society ad-
vances—the axiomata media of Gene-
ral Sociology.

The empirical laws which are most
readily obtained by generalisation
from history do not amount to this.
They are not the " middle principles "
themselves, but only evidence towards
the establishment of such principles.
They consist of certain general ten-
dencies which may be perceived in
society ; a progressive increase of some
social elements and diminution of
others, or a gradual change in the
general character of certain elements.
It is easily seen, for instance, that as
society advances, mental tend more
and more to prevail over bodily quali-
ties, and masses over individuals ;
that the occupation of all that portion
of mankind who are not under ex-
ternal restraint is at first chiefly
military, but society becomes pro-
gressively more and more engrossed
with productive pursuits, and the
military spirit gradually gives way
to the industrial ; to which many
similar truths might be added. And
with generalisations of this descrip-
tion ordinary inquirers, even of the
historical school now predominant on
the Continent, are satisfied. But
these and all such results are still at

6o4

LOGIC OF THE MORAL SCIENCES.

too great a distance from the elemen-
tary laws of human nature on which
they depend, — too many links inter-
vene, and the concurrence of causes
at each link is far too complicated, —
to enable these propositions to be pre-
gented as direct corollaries from those
elementary principles. They have,
therefore, in the minds of most in-
quirers, remained in the state of em-
pirical laws, applicable only within
the bounds of actual observation,
without any means of determining
their real limits, and of judging
whether the changes which have
hitherto been in progress are destined
to continue indefinitely, or to termi-
nate', or even to be reversed.

§ 7. In order to obtain better em-
pirical laws, we must not rest satisfied
with noting the progressive changes
which manifest themselves in the
separate elements of society, and in
which nothing is indicated but the
relation of fragments of the effect to
corresponding fragments of the cause.
It is necessary to combine the statical
view of social phenomena with the
dynamical, considering not only the
progressive changes of the different
elements, but the contemporaneous
condition of each, and thus obtain
empirically the law of correspondence
not only between the simultaneous
states, but between the simultaneous
changes, of those elements. This law
of correspondence it is which, duly
verified d prion, would become the
real scientific derivative law of the
development of humanity and human
affairs.

In the difficult process of observa-
tion and comparison which is here re-
quired, it would evidently be a great
assistance if it should happen to be
the fact that some one element in
the complex existence of social man is
pre-eminent over all others as the
prime agent of the social movement.
For we could then take the progress
of that one element as the central
chain, to each successive link of which
the corresponding links of all the

other progressions being appended,
the succession of the facts would by
this alone be presented in a kind of
spontaneous order, far more nearly
approaching to the real order of their
filiation than could be obtained by
any other merely empirical process.

Now, the evidence of history and
that of human nature combine, by a
striking instance of consilience, to
show that there really is one social
element which is thus predominant,
and almost paramount, among the
agents of the social progression. This
is the state of the speculative faculties
of mankind, including the nature of
the beliefs which by any means they
have arrived at concerning themselves
and the world by which they are sur-
rounded.

It would be a great error, and one
very little likely to be committed, to
assert that speculation, intellectual
activity, the pursuit of truth, is among
the more powerful propensities of
human nature, or hold a predominat-
ing place in the lives of any, save
decidedly exceptional, individuals.
But, notwithstanding the relative
weakness of this principle among
other sociological agents, its influence
is the main determining cause of the
social progress ; all the other disposi-
tions of our nature which contribute
to that progress being dependent on
it for the means of accomplishing their
share of the work. Thus (to take the
most obvious case first) the impelling
force to most of the improvements
effected in the arts of life is the
desire of increased material comfort ;
but as we can only act upon external
objects in proportion to our knowledge
of them, the state of knowledge at any
time is the limit of the industrial im-
provements possible at that time ; and
the progress of industry must follow,
and depend on, the progress of know-
ledge. The same thing may be shown
to be true, though it is not quite so
obvious, of the progress of the fine
arts. Further, as the strongest pro-
pensities of uncultivated or half -culti-
vated human nature (being the purely

i

THE HISTORICAL METHOD.

selfish ones, and those of a sympa-
thetic character which partake most
of the nature of sefishness) evidently
tend in themselves to disunite man-
kind, not to unite them, — to make
them rivals, not confederates ; social
existence is only possible by a discip-
lining of those more powerful pro-
pensities, which consists in subordi-
nating them to a common system of
opinions. The degree of this sub-
ordination is the measure of the com-
pleteness of the social union, and the
nature of the common opinions de-
termines its kind. But in order that
mankind should conform their actions
to any set of opinions, these opinions
must exist, must be believed by them.
And thus the state of the speculative
faculties, the character of the pro-
positions assented to by the intellect,
essentially determines the moral and
political state of the community, as
we have already seen that it deter-
mines the physical.

These conclusions, deduced from
the laws of human nature, are in
entire accordance with the general
facts of history. Every considerable
change historically known to us in
the condition of any portion of man-
kind, when not brought about by ex-
ternal force, has been preceded by a
change of proportional extent in the
state of their knowledge or in their
prevalent beliefs. As between any
given state of speculation and the
correlative state of everything else, it
was almost always the former which
first showed itself ; though the effects,
no doubt, reacted potently upon the
cause. Every considerable advance
in material civilisation has been pre-
ceded by an advance in knowledge ;
and when any great social change has
come to pass, either in the way of
gradual development or of sudden
conflict, it has had for its precursor a
great change in the opinions and
modes of thinking of society. Poly-
theism, Judaism, Christianity, Pro-
testantism, the critical philosophy of
modern Europe, audits positive science
— each of these has been a primary

605

agent in making society what it was
at each successive period, while society
was but secondarily instrumental in
making them, each of them (so far as
causes can he assigned for its ex-
istence) being mainly an emanation
not from the practical life of the
period, but from the previous state of
belief and thought. The weakness of
the speculative propensity in mankind
generally has not, therefore, prevented
the progress of speculation from gov-
erning that of society at large ; it
has only, and too often, prevented
progress altogether, where the intel-
lectual progression has come to an
early stand for want of sufficiently
favourable circumstances.

From this accumulated evidence,
we are justified in concluding that
the order of human progression in all
respects will mainly depend on the
order of progression in the intellectual
convictions of mankind, that is, on
the law of the successive transforma-
tions of human opinions. The ques-
tion remains, whether this law can be
determined, at first from history as
an empirical law, then converted into
a scientific theorem by deducing it
a pHori from the principles of human
nature. As the progress of know-
ledge and the changes in the opinions
of mankind are very slow, and mani-
fest themselves in a well-defined
manner only at long intervals, it
cannot be expected that the general
order of sequence should be discover-
able from the examination of less
than a very considerable part of the
duration of the social progress. It
is necessary to take into considera-
tion the whole of past time, from the
first recorded condition of the human
race, to the memorable phenomena of
the last and present generations.

§ 8. The investigation which I have
thus endeavoured to characterise has
been systematically attempted, up to
the present time, by M. Comte alone.
His work is hitherto the only known
example of the study of social pheno-
mena according to this conception of

6o6

LOGIC OF THE MORAL SCIENCEa

the Historical Method. Without dis-
cussing here the worth of his conclu-
sions, and especially of his predictions
and recommendations with respect to
the Future of society, which appear
to me greatly inferior in value to his
appreciation of the Past, I shall con-
fine myself to mentioning one impor-
tant generalisation, which M. Conite
regards as the fundamental law of the
progress of human knowledge. Specu-
lation he conceives to have, on every
subject of human inquiry, three suc-
cessive stagss ; in the first of which
it tends to explain the phenomena by
supernatural agencies, in the second
by metaphysical abstractions, and in
the third or final state confines itself
to ascertaining their laws of succes-
sion and similitude. This generalisa-
tion appears to me to have that high
degree of scientific evidence which is
derived from the concurrence of the
indications of history with the pro-
babilities derived from the constitu-
tion of the human mind. Nor could
it be easily conceived, from the mere
enunciation of such a proposition,
what a flood of light it lets in upon
the whole course of history, when its
consequences are traced, by connect-
ing with each of the three states
of human intellect which it distin-
guishes, and with each successive
modification of those three states,
the correlative condition of other
social phenomena.*

* This great generalisation is often un-
favourably criticised (as by Dr. Whewell,
for instance) under a misapprehension of
its real import. The doctrine that the
theological explanation of piienomena be-
longs only to tlie infancy of our knowledge
of tliem, ouglit not to be construed as if it
WHS equivalent to tlie assertion thut man-
kind, as their knowledge advances, will
necessarily cease to believe in any kind of
theology. This was M. Comte's o] union ;
but it is by no means implied in his funda-
mental theorem. All that is implied is,
that in an advanced state of human know-
ledge, no other Rtiler of tL<» World will be
acknowledged than one who rules by uni-
▼ersal laws, and does not at all, or does not
unless in very peculiar cases, produce
events by special interpositions. Origi-
nally all natural events were ascribed to
■uch interpositions. At present every

But whatever decision competent
judges may pronounce on the results
arrived at by any individual inquirer,
the method now characterised is that
by which the derivative laws of social
order and of social progress must be
sought. By its aid we may hereafter
succeed not only in looking far for-
ward into the future history of the
human race, but in determining what
artificial means may be used, and to
what extent, to accelerate the natural
progress in so far as it is beneficial ;

educated person rejects tlds explanation
in regard to all classes of phenomena of
which the laws have been fully ascertained ;
though some have not yet reached the
point of referring all phenomena to the
idea of Law, but believe that rain and sun-
shine, famine and pestilence, victory and
defeat, death and life, are issues which the
I reator does not leave to the operation of
his general laws, but reserves to be decided
by express acts of volition. M. Comte's
theory is the neiration of this doctrine.

Dr. Whewell equally misunderstands M.
Comte's doctrine respecting the second or
metaphysical stage of speculation. M.
Comte did not mean that "discussions
concerning ideas" are limited to an early
stage of inquiry, and cease when science
enters into the positive stage (Philosophy
of Discovery, p. 226 et s q.) In all M.
( omte's speculations as much stress is laid
on the process of clearing up our concep-
tions as on the ascertainment of facts.
When M. Comte speaks of the metaphysical
stage of speculaiion, he means tho stage in
which men speak of "Nature" and other
abstractions as if they were active foices,
producing effects ; when Nature is said to
do this, or forbid that ; when Nature's
horror of a vacuum, Nature's non-admis-
sion of a break, Nature's vis medicatrix,
were offered as explanations of pheno-
mena; when the qualities of things were
mistaken for real entities dwelling in ihe
thinf,'s ; when the phenomena of living
bodies were thought to be accounted for
by being referred 1 o a " vital force ; " when,
in short, the abstract names of phenomena
were mi-taken for the causes of their ex-
ist ence. In this sense of the word it can-
not be reasonably denied that the meta-
physical explanation of phenoniena, equally
with the theologicid, gives way before the
advance of leal science.

That the final, or positive stage, as con-
cfiveii by M. Com'e, has been equally
misunderstood, and that, notwithstanding
some expressions open to just criticism, M.
Comte never dream e 1 of denying the legi-
timacy of inquiry into all cau-^es which are
accessible to human investigation, I have
pointed out in a former place.

SCIENCE OF HISTORY.

6o7

to compensate for whatever may be
its inherent inconveniences or disad-
vantages, and to guard against the
dangers or accidents to which our
species is exposed from the necessary
incidents of its progression. Such
practical instnictions, founded on the
highest branch of speculative socio-
logy, will form the noblest and most
beneficial portion of the Political Art.

That of this science and art even
the foundations are but beginning to
be laid is sufficiently evident. But
the superior minds are fairly turning
themselves towards that object. It
has become the aim of really scien-
tific thinkers to connect by theories
the facts of universal history : it is
acknowledged to be one of the requi-
sites of a general system of social
doctrine that it should explain, so
far as the data exist, the main facts
of history ; and a Philosophy of His-
tory is generally admitted to be at
once the verification and the initial
form of the Philosophy of the Pro-
gress of Society.

If the endeavours now making in
all the more cultivated nations, and
beginning to be made even in Eng-
land, (usually the last to enter into
the general movement of the Euro-
pean mind,) for the construction of a
Philosophy of History, shall be di-
rected and controlled by those views
of the nature of sociological evidence
which I have (very briefly and im-
perfectly) attempted to characterise,
they cannot fail to give birth to a
sociological system widely removed
from the vague and conjectural char-
acter of all former attempts, and
worthy to take its place, at last,
among the sciences. When this
time shall come, no important branch
of human affairs will be any longer
abandoned to empiricism and un-
scientific surmise ; the circle of hu-
man knowledge will be complete, and
it can only thereafter receive further
enlargement by perpetual expansion
from within.

CHAPTER XL

ADDITIONAL ELUCIDATIONS OF THE
SCIENCE OF HISTORY.

§ I. The doctrine which the pre-
ceding chapters were intended to en-
force and elucidate — that the collec-
tive series of social phenomena, in
other words, the course of history, is
subject to general laws, which philo-
sophy may possibly detect — has been
familiar for generations to the scien-
tific thinkers of the Continent, and
has for the last quarter of a century
passed out of their peculiar domain
into that of newspapers and ordinary
political discussion. In our own
country, however, at the time of the
first publication of this Treatise, it
was almost a novelty, and the pre-
vailing habits of thought on historical
subjects were the very reverse of a
preparation for it. Since then a great
change has taken place, and has been
eminently promoted by the important
work of Mr. Buckle, who, with char-
acteristic energy, flung down this
great principle, together with many
striking exemplifications of it, into
the arena of popular discussion, to be
fought over by a sort of combatants
in the presence of a sort of specta-
tors, who would never even have been
aware that there existed such a prin-
ciple if they had been left to learn
its existence from the speculations of
pure science. And hence has arisen
a considerable amount of controversy,
tending not only to make the prin-
ciple rapidly familiar to the majority
of cultivated minds, but also to clear
it from the confusions and misunder-
standings by which it was but natural
that it should for a time be clouded,
and which impair the worth of the
doctrine to those who accept it, and
are the stumbling-block of many who
do not.

Among the impediments to the
general acknowledgment, by thought-
ful minds, of the subjection of his-
torical facts to scientific laws, the
most fundamental continues to be

6o8

LOGIC OF THE MORAL SCIENCES.

that which is grounded on the doc-
trine of Free Will, or, in other words,
on the denial that the law of invari-
able Causation holds true of human
volitions; for if it does not, the
course of history, being the result of
human volitions, cannot be a subject
of scientific laws, since the volitions
on which it depends can neither be
foreseen nor reduced to any canon of
regularity even after they have oc-
curred. I have discussed this ques-
tion, as far as seemed suitable to the
occasion, in a fonner chapter, and
I only think it necessary to repeat
that the doctrine of the Causation of
human actions, improperly called the
doctrine of Necessity, affirms no mys-
terious nexus or overruling fatality :
it asserts only that men's actions are
the joint result of the general laws
and circumstances of human nature,
and of their own particular char-
acters, those characters again being
the consequence of the natural and
artificial circumstances that consti-
tuted their education, among which
circumstances must be reckoned their
own conscious efforts. Any one who
is willing to take (if the expression
may be permitted) the trouble of
thinking himself into the doctrine as
thus stated, will find it, I believe, not
only a faithful interpretation of the uni-
versal experience of human conduct,
but a correct representation of the
mode in which he himself, in every par-
ticular case, spontaneously interprets
his own experience of that conduct.

But if this principle is true of in-
dividual man, it must be true of
collective man. If it is the law of
human life, the law must be realised
in history. The experience of human
affairs when looked at en masse, must
be in accordance with it if true, or
repugnant to it if false. The sup-
port which this A posteriori verifica-
tion affords to the law is the part of
the case which has been most clearly
and triumphantly brought out by Mr.
Buckle.

The facts of statistics, since they
have been made a subject of careful

recordation and study, have yielded
conclusions, some of which have been
very startling to persons not accus-
tomed to regard moral actions as sub-
ject to uniform laws. The very events
which in their own nature appear
most capricious and uncertain, and
which in any individual case no at-
tainable degree of knowledge would
enable us to foresee, occur, when con-
siderable numbers are taken into the
account, with a degree of regularity
approaching to mathematical. What
act is there which all would consider
as more completely dependent on in-
dividual character, and oa the exer-
cise of individual free will, than that
of slaying a fellow-creature? Yet
in any large country, the number of
murders, in proportion to the popula-
tion, varies (it has been found) very
little from one year to another, and
in its variations never deviates widely
from a certain average. What is still
more remarkable, there is a similar
approach to constancy in the propor-
tion of these murders annually com-
mitted with every particular kind of
instrument. There is a like approxi-
mation to identity, as between one
year and another, in the comparative
number of legitimate and of illegiti-
mate births. The same thing is found
true of suicides, accidents, and all other
social phenomena of which the regis-
tration is sufficiently perfect ; one
of the most curiously illustrative ex-
amples being the fact, ascertained by
the registers of the London and Paris
post-offices, that the number of letters
posted which the writers have forgot-
ten to direct is nearly the same, in
proportion to the whole number of
letters posted, in one year as in an-
other. " Year after year," says Mr.
Buckle, " the same proportion of
letter-writers forget this simple act,
so that for each successive period
we can actually foretell the number
of persons whose memory will fail
them in regard to this trifling, and,
as it might appear, accidental occur-
rence." *
* Buckle's History of Civilisation, i. 30.

SCIENCE OF HISTORY.

609

This singular degree of regularity
en masse, combined with the extreme
of irregularity in the cases composing
the mass, is a felicitous verification d
jioderiori of the bw of causation in
its application to human conduct.
Assuming the truth of that law,
every human action, every murder,
for instance, is the concurrent result
of two sets of causes. On the one
part, the general circumstances of
tlie country and its inhabitants ; the
moral, educational, economical, and
other influences operating on the
whole people, and constituting what
we term the state of civilisation. On
the other part, the great variety of
influences special to the individual :
his temperament, and other peculia-
rities of organisation, his parentage,
habitual associates, temptations, and
so forth. If we now take the whole
of the instances which occur within a
sufficiently large field to exhaust all
the combinations of these special in-
fluences, or, in other words, to elimi-
nate chance; and if all these instances
have occurred within such narrow
limits of time that no material change
can have taken place in the general
influences constituting the state of
civilisation of the covmtry, we may
be certain that if human actions are
governed by invariable laws, the ag-
gregate result will be something like
a constant quantity. The number of
murders committed within that space
and time being the effect partly of
general causes which have not varied,
and partly of partial causes the whole
round of whose variations has been
included, will be, practically speak-
ing, invariable.

Literally and mathematically in-
variable it is not, and could not be
expecte.' to be ; because the period
of a y is too short to include all
the possible combinations of partial
causes, while it is, at the same time,
sufficiently long to make it probable
that in some years, at least, of every
series, there will have been intro-
duced new influences of a more or
less general ch^acter; such as a

more vigorous or a more relaxed
police ; some temporary excitement
from political or religious causes ; or
some incident generally notorious, of
a nature to act morbidly on the ima-
gination. That in spite of these un-
avoidable imperfections in the data,
there should be so very trifling a
margin of variation in the annual
results, is a brilliant confirmation of
the general theory.

§ 2. The same considerations which
thus strikingly corroborate the evi-
dence of the doctrine that historical
facts are the invariable effects of
causes, tend equally to clear that
doctrine from various misapprehen-
sions, the existence of which has been
put in evidence by the recent discus-
sions. Some persons, for instance,
seemingly imagine the doctrine to
imply, not merely that the total
number of murders committed in a
given space and time is entirely the
effect of the general circumstances of
society, but that every particular
murder is so too ; that the individual
murderer is, so to speak, a mere in-
strument in the hands of general
causes ; that he himself has no op-
tion, or, if he has. and chose to exer-
cise it, some one else would be ne-
cessitated to take his place ; that if
any one of the actual murderers
had abstained from the crime, some
person who would otherwise have
remained innocent would have com-
mitted an extra murder to make up
the average. Such a corollary would
certainly convict any theory which
necessarily led to it of absurdity. It
is obvious, however, that each parti-
cular murder depends, not on the
•Jfeneral state of society only, but on
that combined with causes special
to the case, which are generally much
more powerful ; and if these special
causes, which have greater influence
than the general ones in causing every
particular murder, have no influence
on the number of murders in a given
period, it is because the field of obser-
vation is go extensive as to include

2q

6io

LOGIC OF THE MORAL SCIENCES.

all passible combinations of the special
causes — all varieties of individual
character and individual temptation
compatible with the general state of
society. The collective experiment,
as it may be termed, exactly separates
the effect of the general from that of
the special causes, and shows the net
result of the former ; but it declares
nothing at all respecting the amount
of influence of the special causes, be
it greater or smaller, since the scale
of the experiment extends to the
number of cases within which the
effects of the special causes balance
one another, and disappear in that
of the general causes.

I will not pretend that all the de-
fenders of the theory have always kept
their language free from this same con-
fusion, and have shown no tendency to
exalt the influence of general causes at
the expense of special. I am of opi-
nion, on the contrary, that they have
done so in a very great degree, and by
so doing have encumbered their theory
with difficulties, and laid it open to ob-
jections which do not necessarily affect
it. Some, for example, (among whom
is Mr. Buckle himself,) have inferred,
or allowed it to be supposed that they
inferred, from the regularity in the re-
currence of events which depend on
moral qualities, that the moral quali-
ties of mankind are little capable of
being improved, or are of little import-
ance in the general progress of society,
compared with intellectual or econo-
mic causes. But to draw this infer-
ence is to forget that the statistical
tables from which the invariable aver-
ages are deduced were compiled from
facts occurring within narrow geogra-
phical limits, and in a small number
of successive years ; that is, from a field
the whole of which was under the ope-
ration of the same general causes, and
during too short a time to allow of
much change therein. All moral causes
but those common to the country gene-
rally have been eliminated by the great
number of instances taken ; and those
which are common to the whole coun-
try have not varied considerably in

the short space of time comprised in
the observations. If we admit the
supposition that they have varied ; if
we compare one age with another, or
one country with another, or even one
part of a country with another, differ-
ing in position and character as to the
moral elements, the crimes committed
within a year give no longer the same,
but a widely different numerical ag-
gregate. And this cannot but be the
case ; for inasmuch as every single
crime committed by an individual
mainly depends on his moral qualities,
the crimes committed by the entire
population of the country must de-
pend in an equal degree on their col-
lective moral qualities. To render
this element inoperative upon the
large scale it would be necessary to
suppose that the general moral aver-
age of mankind does not vary from
country to country, or from age to
age ; which is not true, and even if it
were true, could not possibly be proved
by any existing statistics. I do not on
this account the less agree in the opi-
nion of Mr. Buckle, thattheintellectual
element in mankind, including in that
expression the nature of their beliefs,
the amount of their knowledge, and
the development of their intelligence,
is the predominant circumstance in de- _ .
termining their progress. But I am oiMi
this opinion, not because I regard their*" 1
moral or economical condition either
as less powerful or less variable agen-
cies, but because these are in a great
degree the consequences of the intel-
lectual condition, and are, in all cases,
limited by it, as was observed in the
preceding chapter. The intellectual
changes are the most conspicuous
agents in history, not from their
superior force, considered in them-
selves, but because practically they
work with the united power belong-, jm
ing to all three.* Jl

*I have beer assured byan inHmate friend
of Mr. Buckle that he would not have with-
held his assent from these remarks, and
that he never intended to affirm or imply
that mankind are not progressive in their
moral as well as in their intellectual quali-
ties. "In dealing withhieproblem, he availed

I

SCIENCE OF HISTORY.

6ii

§ 3. There is another distinction
often neglected in the discussion of
this subject, which it is extremely im-
portant to observe. The theory of the
subjection of social progress to in-
variable laws is often held in con-
junction with the doctrine that social
progress cannot be materially influ-
enced by the exertions of individual
persons or by the acts of governments.
But though these opinions are often
held by the same persons, they are
two very different opinions, and the
confusion between them is the eter-
nally recurring error of confounding
Causation with Fatalism. Because
whatever happens will be the effect
of causes, human volitions among the
rest, it does not follow that volitions,
even those of peculiar individuals, are
not of great efiicacy as causes. If any
one in a storm at sea, because about
the same number of persons in every
year perish by shipwreck, should con-
clude that it was useless for him to
attempt to save his own life, we should
call him a Fatalist, and should re-

himself of the artifice resorted to by the
Political Econoiuist, who leave* out of con-
sideration the generous and benevolent
sentiments, and founds his science on the
proposition that mankind are actuated by
ucquisitive propensities alone,"not because
such is the fact, but because it is necessary
to begin by treating the principal influence
as if it was the sole one, and make the due
corrections afterwards. *' He desired to
make abstraction of the intellect as the de-
termining and dynamittil element of the
progression, eliminating the more depen-
dent set of conditions, and treating the
more active one as if it were an entirely
independent variable."

The same friend of Mr. Buckle states that
when he used expressions which seemed to
exaggerate the influence of general at the
expense of .special causes, and especially at
the expense of the influence of individual
minds, Mr. Buckle really intended no more
than to afiirm emphatically that the greatest
men cannot effect great changes in human
affairs unless the general mind has been in
some considerable degiee prepared for them
by the general circumstances of the age ;
a truth wiilch, of coin-se, no one thinks of
denying. And there certixinly are passages
in Mr. Buckle's writings which speak of ihe
influence exercised by great individual in-
tellects in as strong terms as could be de-

mind him that the efforts of ship-
wrecked persons to save their lives are
so far from being immaterial, that the
average amount of those efforts is one
of the causes on which the ascertained
annual number of deaths by shipwi-eck
depend. However universal the laws
of social development may be, they
cannot be more universal or more
rigorous than those of the physical
agencies of nature ; yet human will
can convert these into instruments of
its designs, and the extent to which
it does so makes the chief difference
between savages and the most highly
civilised people. Human and social
facts, from their more complicated
nature, are not less, but more, modi-
fiable than mechanical and chemical
facts ; human agency, therefore, has
still greater power over them. And
accordingly, those who maintain that
the evolution of society depends ex-
clusively, or almost exclusively, on
general causes, always include among
these the collective knowledge and
intellectual development of the race.
But if of the race, why not also of
some powerful monarch or thinker, or
of the ruling portion of some political
society, acting through its govern-
ment ? Though the varieties of char-
acter among ordinary individuals
neutralise one another on any large
scale, exceptional individuals in im-
portant positions do not in any given
age netitralise one another ; there was
not another Themistocles, or Luther,
or Julius Caesar, of equal powers and
contrary dispositions, who exactly
balanced the given Themistocles,
Luther, and Caesar, and prevented
them from having any permanent
effect. Moreover, for aught that ap-
pears, the volitions of exceptional
persons, or the opinions and purposes
of the individuals who at some par-
ticular time compose a government,
may be indispensable links in the
chain of catisation by which even the
general causes produce their effects ;
and I believe this to be the only
tenable form of the theory.

Lord Macaulay, in a celebrated pas-

6l2

LOGIC OF THE MORAL SCIENCES.

sage of one of his early essays, (let me
add that it was one which he did not
himself choose to reprint,) gives ex-
pression to the doctrine of the abso-
lute inoperativeness of great men,
more unqualified, I should think, than
has been given to it by any writer of
equal abilities. He compares them
to persons who merely stand on a
loftier height, and thence receive the
sun's rays a little earlier than the
rest of the human race. "The sun
illuminates the hills while it is still
below the horizon, and truth is dis-
covered by the highest minds a little
before it becomes manifest to the
multitude. This is the extent of their
superiority. They are the first to
catch and reflect a light which, with-
out their assistance, must in a short
time be visible to those who lie far
beneath them."* If this metaphor
is to be carried out, it follows that if
there had been no Newton the world
would not only have had the New-
tonian system, but would have had it
equally soon, as the sun would have
risen just as early to spectators in the
plain if there had been no mountain
at hand to catch still earlier rays.
And so it would be if truths, like the
sun, rose by their own proper motion,
without human effort, but not other-
wise. I believe that if Newton had
not lived, the world must have waited
for the Newtonian philosophy until
there had been another Newton or
his equivalent. No ordinary man,
and no succession of ordinary men,
could have achieved it. I will not
go the length of saying that what
Newton did in a single life might not
have been done in successive steps by
some of those who followed him, each
singly inferior to him in genius. But
even the least of those steps required
a man of great intellectual superiority.
Eminent men do not merely see the
coming light from the hill-top ; they
mount on the hill-top and evoke it ;
and if no one had ever ascended
thither, the light, in many cases,

* Essay on Dryden, in Mitcellaneous
JFritings, i. i86.

might never have risen upon the
plain at all. Philosophy and reli-
gion are abundantly amenable to
general causes ; yet few will doubt
that had there been no Socrates, no
Plato, and no Aristotle, there would
have been no philosophy for the next
two thoxisand years, nor in all pro-
bability then ; and that if there had
been no Christ and no St Paul, there
would have been no Christianity.

The point in which, above all, the
influence of remarkable individuals is
decisive, is in determining the celerity
of the movement. In most states of
s^iety it is the existence of great men
which decides even whether there
shall be any progress. It is conceiv-
able that Greece, or that Christian
Europe, might have been progressive
in certain periods of their history
through general causes only ; but if
there had been no Mahomet, would
Arabia have produced Avicenna or
Averroes, or Caliphs of Bagdad or of
Cordova? In determining, however,
in what manner and order the pro-
gress of mankind shall take place, if
it take place at all, much less depends
on the character of individuals. There
is a sort of necessity established in
this respect by the general laws of
human nature, by the constitution of
the human mind. Certain truths can-
not be discovered or inventions made
unless certain others have been made
first ; certain social improvements,
from the nature of the case, can only
follow, and not precede, others. The
order of human progress, therefore,
may to a certain extent have definite
laws assigned to it ; while as to its
celerity, or even as to its taking place
at all, no generalisation, extending to
the human species generally, can pos-
sibly be made, but only some very
precarious approximate generalisa-
tions, confined to the small portion
of mankind in whom there has been
anything like consecutive progress
within the historical period, and de-
duced from their special position, or
collected from their particular history.
Even looking to the via'^mer of pro*

SCIENCE OF HISTORY.

6n

gtess, the order of succession of social
states, there is need of great flexi-
bility in our generalisations. The
limits of variation in the possible
development of social, as of animal
life, are a subject of which little is
yet understood, and are one of the
great problems in social science. It
is, at all events, a fact that different
portions of mankind, under the in-
fluence of different circumstances,
have developed themselves in a more
or less different manner and into dif-
ferent forms ; and among these de-
termining circumstances, the indivi-
dual character of their great specu-
lative thinkers or practical organisers
may well have been one. Who can
tell how profoundly the whole sub-
sequent history of China may have
been influenced by the individuality
of Confucius ? and of Sparta (and
hence of Greece and the world) by
that of Lycurgus ?

Concerning the nature and extent
of what a great man under favoiu'able
circumstances can do for mankind, as
well as of what a government can do
for a nation, many different opinions
are possible ; and every shade of
opinion on these points is consistent
with the fullest recognition that there
are invariable laws of historical phe-
nomena. Of course the degree of in-
fluence which has to be assigned to
these more special agencies makes a
great difference in the precision which
can be given to the general laws, and
in the confidence with which pre-
dictions can be grounded on them.
Whatever depends on the peculiari-
ties of individuals, combined with the
accident of the positions they hold, is
necessarily incapable of being fore-
seen. Undoubtedly, these casual com-
binations might be elinjinated like any
others by taking a sufficiently large
cycle : the peculiarities of a great his-
torical character make their influence
felt in history sometimes for several
thousand years, but it is highly pro-
bable that they will make no difference
at all at the end of fifty millions.
Since, however, we cannot obtain an

average of the vast length of time
necessary to exhaust all the possible
combinations of great men and cir-
cumstances, as much of the law of
evolution of human affairs as depends
upon this average is and remains in-
accessible to us ; and within the next
thousand years, which are of consider-
ably more importance to us than the
whole remainder of the fifty millions,
the favourable and unfavourable com-
binations which will occur will be to
us purely accidental. We cannot fore-
see the advent of greatmen. Those who
introduce new speculative thoughts or
great practical conceptions into the
world cannot have their epoch fixed
beforehand. What science can do is
this. It can trace through past his-
tory the general causes which had
brought mankind into that prelimi-
nary state, which, when the right sort
of great man appeared, rendered them
accessible to his influence. If this
state continues, experience renders it
tolerably certain that in a longer or
shorter period the great man will be
produced, provided that the general
circumstances of the country and
people are (which very often they are
not) compatible with his existence ;
of which point also science can in
some measure judge. It is in this
manner that the results of progress,
except as to the celerity of their pro-
duction, can be, to a certain extent,
reduced to regularity and law. And
the belief that they can be so is
equally consistent with assigning very
great, or very little efficacy, to the
influence of exceptional men, or of
the acts of governments. And the
same may be said of all other acci-
dents and disturbing causes.

§ 4. It would nevertheless be a great
error to assign only a trifling impor-
tance to the agency of eminent indi-
viduals, or of governments. It must
not be concluded that the influence of
either is small because they cannot
bestow what the general circumstances
of society, and the course of its pre-
vious history, have not prepared it to

6i4

Logic of the moral scii:NOEg.

receive. Xeithei' thinkers nor govern-
ments efifect all that they intend, but
in compensation they often produce
important results which they did not
in the least foresee. Great men and
great actions are seldom wasted :
they send forth a thousand unseen
influences, more effective than those
which are seen ; and though nine out
of every ten things done, with a good
purpose, by those who are in advance
of their age, produce no material effect,
the tenth thing produces effects twenty
times as great as any one would have
dreamed of predicting from it. Even
the men who for want of sufficientl}'
favourable circumstances left no im-
press at all upon their own age have
often been of the greatest value to
posterity. Who could appear to have
lived more entirely in vain than some
of the early heretics? They were
burnt or massacred, their writings ex-
tirpated, their memory anathematised,
and their very names and existence
left for seven or eight centuries in
the obscurity of musty manuscripts —
their history to be gathered, perhaps,
only from the sentences by which they
were condemned. Yet the memory of
these men — men who resisted certain
pretensions or certain dogmas of the
Church in the very age in which
the unanimous assent of Christendom
was afterwards claimed as having been
given to them, and asserted as the
ground of their authority — broke the
chain of tradition, established a series
of precedents for resistance, inspired
later Reformers with the courage, and
armed them with the weapons, which
they needed when mankind were bet-
ter prepared to follow their impulse.
To this example from men let us
add another from governments. The
comparatively enlightened rule of
which Spain had the benefit during a
considerable part of the eighteenth
century did not correct the funda-
mental defects of the Spanish people ;
and in consequence, though it did
great temporary good, so much of that
good perished with it, that it may
plausibly be affirmed to have had no

permanent effect. The case has been
cited as a proof how little govern-
ments can do in opposition to the
causes which have determined the
general character of the nation. It
does show how much there is which
they cannot do ; but not that they
can do nothing. Compare what Spain
was at the beginning of that half cen-
tury of liberal government with what
she had become at its close. That
period fairly let in the light of Euro-
pean thought upon the more educated
classes, and itnever afterwards ceased
to go on spreading. Previous to that
time the change was in an inverse
direction ; culture, light, intellectual,
and even material activity, were be-
coming extinguished. Was it nothing
to arrest this downward and convert
it into an upward course ? How much
that Charles the Third and Aranda
could not do has been the ultimate
conseqiience of what they did ! To
that half century Spain owes tliat she
has got rid of the Inquisition, that she
has got rid of the monks, that she now
has parliaments and (save in excep-
tional intervals) a free press, and the
feelings of freedom and citizenship,
and is acquiring railroads and all the
other constituents of material and
economical progress. In the Spain
which preceded that era, there was
not a single element at work which
could have led to these results in any
length of time, if the country had
continued to be governed as it was
by the last princes of the Austrian
d)masty, or if the Bourbon rulers had
been from the first what, both in
Spain and in Naples, they afterwards
became.

And if a government can do much,
even when it seems to have done
little, in causing positive improve-
ment, still greater are the issues de-
pendent on it in the way of warding
off evils, both internal and external,
which else would stop improvement
altogether. A good or a bad counsel-
lor, in a single cit}' at a particular
crisis, has affected the whole subse-
quent fate of the world. It is as cer-

SCIENCE OF HISTORY.

«>s

tain as any contingent judgment re-
specting historical events can be, that
if there had been no Themistocles
there would have been no victory of
Salamis ; and had there not, where
would have been all our civilisation ?
How different again would have been
the issue if Epaminondas or Timo-
leon, or even Iphicrates, instead of
Chares and Lysicles, had commanded
at Chaeroneia. As is well said in the
second of two essays on the Study of
History* — in my judgment the sound-
est and most philosophical productions
which the recent controversies on
this subject have called forth — his-
torical science authorises not abso-
lute, but only conditional predictions.
General causes count for much, but
individuals also " produce great
changes in history, and colour its
whole complexion long after their
death. . . . No one can doubt that
the Roman republic would have sub-
sided into a military despotism if
Julius Caesar had never lived ; "
(thus much was rendered practically
certain by general causes;) "but is
it at all clear that in that case Gaul
would ever have formed a province of
the empire ? Might not Varus have
lost his three legions on the banks of
the Rhone ? and might not that river
have become the frontier instead of
the Rhine? This might well have
happened if Caesar and Crassus had
changed provinces ; and it is surely
impossible to say that in such an event
the venue (as lawyers say) of Euro-
pean civilisation might not have been
changed. The Norman Conquest in
the same way was as much the act of
a single man as the writing of a
newspaper article ; and knowing as
we do the history of that man and his
family, we can retrospectively predict
with all but infallible certainty that
no other person" (no other in that
age, I presume, is meant) "could
have accomplished the enterprise. If
it had not been accomplished, is there
any ground to suppose that either our

* In the Comhill Magazine for June and
July iS6i.

history or our national character
would have been what they are ? "

As is most truly remarked by the
same writer, the whole stream of
Grecian history, as cleared up by Mr.
Grote, is one series of examples how
often events on which the whole des-
tiny of subsequent civilisation turned
were dependent on the personal char-
acter for good or evil of some one in-
dividual. It must be said, however,
that Greece furnishes the most extreme
example of this nature to be found
in history, and is a very exaggerated
specimen of the general tendency. It
has happened only that once, and will
probably never happen again, that the
fortunes of mankind depended upon
keeping a certain order of things in
existence in a single town, or a country
scarcely larger than Yorkshire ; cap-
able of being ruined or saved by a
hundred causes, of very slight magni-
tude in comparison with the general
tendencies of human affairs. Neither
ordinary accidents nor the characters
of individuals can ever again be so
vitally important as they then were.
The longer our species lasts and the
more civilised it becomes, the more,
as Comte remarks, does the influence
of past generations over the present,
and of mankind en masse over every
individual in it, predominate over other
forces : and though the course of affairs
never ceases to be susceptible of altera-
tion both by accidents and by personal
qualities, the increasing preponderance
of the collective agency of the species
over all minor causes is constantly
bringing the general evolution of the
race into something which deviates
less from a certain and preappointed
track. Historical science, therefore,
is always becoming more possible ;
not solely because it is better studied,
but because, in every generation, it
becomes better adapted for study.

6i6

LOGIC OF THE MOBAL SCIENCES.

CHAPTER XII.

OF THE LOGIC OF PRACTICE, OR ART ;
INCLUDING MORALIXy AND POUOy.

§ I. In the preceding chapters we
have endeavoured to characterise the
present state of those among the
branches of knowledge called Moral
which are sciences in the only proper
sense of the term, that is, inquiries
into the course of nature. It is custo-
mary, however, to include under the
term Moral Knowledge, and even
(though improperly) under that of
Moral Science, an inquiry the results
of which do not express themselves
in the indicative, but in the impera-
tive mood, or in periphrases equiva-
lent to it ; what is called the know-
ledge of duties, practical ethics, or
morality.

Now, the imperative mood is the
characteristic of art, as distinguished
from science. Whatever speaks in
rules or precepts, not in assertions
respecting matters of fact, is art; and
ethics or morality is properly a por-
tion of the art corresponding to the
sciences of human nature and society.*

The Method, therefore, of Ethics,
can be no other than that of Art, or
Practice, in general : and the portion
yet uncompleted, of the task which
we proposed to ourselves in the con-
cluding Book is to characterise the
general Method of Art, as distin-
guished from Science.

§ 2. In all branches of practical
business, there are cases in which in-
dividuals are bound to conform their
practice to a pre-established rule,
while there are others in which it is
part of their task to find or construct
the rule by which they are to govern
their conduct. The first, for example,
is the case of a judge under a definite

* It is almost superfluous to observe, that
there is another mt-aniiig of the word Art,
in which it may b* said to denote the poeti
cal depjirtment or aspect of things in gene-
ral, in contradistinction to the scientific.
In the text, the word is used in its older,
aud, I hope, not yet ob.solete sense.

■\^Titten code. The judge is not called
upon to determine what course would
be intrinsically the most advisable in
the particular case in hand, but only
within what rule of law it falls ; what
the legislature has ordained to be done
in the kind of case, and must there-
fore be presumed to have intended
in the individual case. The method
must here be wholly and exclusively
one of ratiocination or syllogism ; and
the process is obviously what in our
analysis of the syllogism we showed
that all ratiocination is, namely, the
interpretation of a formula.

In order that our illustration of the
opposite case may be taken from the
same class of subjects as the former,
we will suppose, in contrast with the
situation of the judge, the position
of the legislator. As the judge has
laws for his guidance, so the legis-
lator has rules and maxims of policy ;
but it would be a manifest error to
suppose that the legislator is bound
by these maxims in the same manner
as the judge is bound by the laws,
and that all he has to do is to argue
down from them to the particular
case, as the judge does from the laws.
The legislator is bound to take into
consideration the reasons or grounds
of the maxim ; the judge has nothing
to do with those of the law, except so
far as a consideration of them may
throw light upon the intention of the
lawmaker, where his words have left
it doubtful. To the jndge, the rule,
once positively ascertained, is final ;
but the legislator, or other practi-
tioner, who goes by rules rather than
by their reasons, like the old-fa-
shioned German tacticians who were
vanquished by Napoleon, or the phy-
sician who preferred that his patients
should die by rule rather than recover
contrary to it, is rightly judged to be
a mere pedant, and the slave of his
formulas.

Now, the reasons of a maxim of
policy, or of any other rule of art, can
be no other than the theorems of the
corresponding science.

The relation in which rules of art

LOGIC OF PRACTICE OR ART.

617

stand to doctrines of science may be
thus characterised. The art proposes
to itself an end to be attained, defines
the end, and hands it over to the
science. The science receives it, con-
siders it as a phenomenon or effect to
be studied, and having investigated
its causes and conditions, sends it
back to art with a theorem of the
combination of circumstances by which
it could be produced. Art then exa-
mines these combinations of circum-
stances, and according as any of them
are or are not in human power, pro-
nounces the end attainable or not.
The only one of the premises, there-
fore, which Art supplies is the original
major premise, which asserts that the
attainment of the given end is desir-
able. Science then lends to Art the
proposition (obtained by a Wviries of
inductions or of deductions) that the
performance of certain actions will
attain the end. From these premises
Art concludes that the performance
of these actions is desirable, and find-
ing it also practicable, converts the
theorem into a rule or precept.

§ 3. It deserves particular notice
that the theorem or speculative truth
is not rii>e for being turned into a pre-
cept until the whole, and not a part
merely, of the operation which be-
longs to science has been performed.
Suppose that we have completed the
scientific process only up to a certain
point ; have discovered that a parti-
cular cause will produce the desired
effect, but have not ascertained all
the negative conditions which are
necessary, that is, all the circum-
stances which, if present, would pre-
vent its production. If, in this im-
perfect state of the scientific theory,
we attempt to frame a rule of art, we
perform that operation prematurely.
Whenever any counteracting cause,
overlooked by the theorem, takes
place, the rule will be at fault ; we
shall employ the means, and the end
will not follow. No arguing from or
about the rule itself will then help us
through the difficulty ; there is no-

thing for it but to turn back and
finish the scientific process which
should have preceded the formation
of the rule. We must reopen the
investigation to inquire into the re-
mainder of the conditions (m which
the effect depends ; and only after
we have ascertained the whole of
these are we prepared to transform
the completed law of the effect into a
precept, in which those circumstances
orcombinations of circumstances which
the science exhibits as conditions are
prescribed as means.

It is true that, for the sake of con-
venience, rules must be formed from
something less than this ideally p)er-
fect theory ; in the first place, be-
cause the theory can seldom be made
ideally perfect ; and next, because, if
all the counteracting contingencies,
whether of frequent or of rare oc-
currence, were included, the rules
would be too cumbrous to be appre-
hended and remembered by ordinary
capacities, on the common occasions
of life. The rules of art do not at-
tempt to comprise moi-e conditions
than require to be attended to in
ordinary cases ; and are therefore
always imperfect. In the manual
arts, where the requisite conditions
are not numerous, and where those
which the niles do not specify are
generally either plain to common ob-
servation or speedily learnt from prac-
tice, rules may often be safely acted
on by persons who know nothing more
than the rule. But in the compli-
cated affairs of life, and still more in
those of states and societies, rules
cannot be relied on, without con-
stantly referring back to the scientific
laws on which they are founded. To
know what are the practical contin-
gencies which require a modification
of the rule, or which are altogether
exceptions to it, is to know what com-
binations of circumstances would in-
terfere with, or entirely counteract,
the consequences of those laws : and
this can only be learnt by a reference
to the theoretic grounds of the rule.

By a wis© practitioner, therefore,

6iS

LOGIC OF THE MORAL SCIENCES.

rules of conduct will only be con-
sidered as provisional. Being made
for the most numerous cases, or for
those of most ordinary occurrence,
they point out the manner in which
it will be least perilous to act, where
time or means do not exist for ana-
lysing the actual circumstances of
the case, or where we cannot trust
our judgment in estimating them.
But they do not at all supersede the
propriety of going through (when
circumstances permit) the scientific
process requisite for framing a rule
I from the data of the particular case
before us. At the same time, the
common rule may very properly serve
as an admonition that a certain mode
of action has been found by ourselves
and others to be well adapted to the
cases of most common occurrence ;
so that if it be unsuitable to the case
in hand, the reason of its being so will
be likely to £trise from some unusual
circumstance.

§ 4. The error is therefore appa-
rent of those who would deduce the
line of conduct proper to particular
cases from supposed universal practi-
cal maxims, overlooking the neces-
sity of constantly referring back to the
principles of the speculative science,
in order to be sure of attaining even
the specific end which the rules have
in view. How much greater still,
then, must the error be of setting up
such unbending principles, not merely
as universal rules for attaining a given
end, but as rules of conduct generally ;
without regard to the possibility, not
only that some modifying cause may
prevent the attainment of the given
end by the means which the rule pre-
scribes, but that success itself may
conflict with some other end, which
may possibly chance to be more de-
sirable.

This is the habitual error of many
of the political speculators whom I
have characterised as the geometrical
school ; especially in France, where
ratiocination from rules of practice
forms the staple commodity of jour-

nalism and political oratory ; a mis»
apprehension of the functions of De-
duction which has brought much dis-
credit, in the estimation of other
countries, upon the spirit of genera-
lisation so honourably characteristic
of the French mind. The common-
places of politics, in France, are large
and sweeping practical maxims, from
which, as ultimate premises, men rea-
son downwards to particular appli-
cations, and this they call being logical
and consistent. For instance, they are
perpetually arguing that such and
such a measure ought to be adopted,
because it is a consequence of the
principle on which the form of govern-
ment is founded ; of the principle of
legitimacy, or the principle of the
sovereignty of the people. To which
it may be answered, that if these be
really practical principles, they must
rest on speculative grounds ; the sove-
reignty of the people (for example)
must be a right foundation for govern-
ment, because a government thus
constituted tends to produce certain
beneficial effects. Inasmuch, how-
ever, as no government produces all
possible beneficial effects, but all are
attended with more or fewer incon-
veniences, and since these cannot
usually be combated by means drawn
from the very causes which produce
them, it would be often a much H
stronger recommendation of some H
practical arrangement that it does ^
not follow from what is called the
general principle of the government,
than that it does. Under a govern-
ment of legitimacy, the presumption
is far rather in favour of institutions
of popular origin ; and in a demo-
cracy, in favour of arrangements tend-
ing to check the impetus of popular
will. The line of argumentation so
commonly mistaken in France for
political philosophy tends to the prac-
tical conclusion that we should exert
our utmost efforts to aggravate, in-
stead of alleviating, whatever are the
characteristic imperfections of the
system of institutions which we prefer,
or under which we happen to live,

LOGIC OF PRACTICE OR ART.

619

§ 5. Tlie grounds, then, of every
rule of art are to be found in theorems
of science. An art, or a body of art,
consists of the rules, together with as
much of the speculative propositions
as comprises the justification of those
rules. The complete art of any mat-
ter includes a selection of such a por-
tion from the science as is necessary
to show on what conditions the effects
which the art aims at producing de-
pend. And Art in general consists
of the truths of science, arranged in
the most convenient order for prac-
tice, instead of the order which is the
most convenient for thought. Science
groups and arranges its truths so as
to enable us to take in at one view as
much as possible of the general order
of the universe. Art, though it must
assume the same general laws, follows
them only into such of their detailed
consequences as have led to the for-
mation of rules of conduct, and brings
together from parts of the field of
science most remote from one another
the truths relating to the production
of the different and heterogeneous
conditions necessary to each effect
which the exigencies of practical life
require to be produced.*

Science, therefore, following one
cause to its various effects, while art
traces one effect to its multiplied and
diversified causes and conditions,
there is need of a set of intermediate
scientific truths, derived from the
higher generalities of science, and
destined to serve as the generalia or
first principles of the various arts. The
scientific opei-ation of framing these
intermediate principles, M. Comte
characterises as one of those results
of philosophy which are reserved for
futurity. The only complete example
which he points out as actually rea-
lised, and which can be held up as a
type to be imitated in more important
matters, is the general theory of the

• Professor Bain and others call the se-
lection from tlie truths of science made for
the purposes of an art, a Practical Science ;
and coufiue the name Art to the actual
rules.

art of Descriptive Geometry, as con-
ceived by M. Monge. It is not, how-
ever, difficult to understand what the
nature of these intermediate principles
must generally be. After framing the
most comprehensive possible concep-
tion of the end to be aimed at, that
is, of the effect to be produced, and
determining in the same comprehen-
sive manner the set of conditions on
which that effect depends, there re-
mains to be taken a general survey of
the resources which can be com-
manded for realising this set of con-
ditions ; and when the result of this
survey has been embodied in the few-
est and most extensive propositions
possible, those propositions will ex-
press the general relation between the
available means and the end, and will
constitute the general scientific theory
of the art, from which its practical
methods will follow as corollaries.

§ 6. But though the reasonings
which connect the end or purpose of
every art with its means belong to
the domain of Science, the definition
of the end itself belongs exclusively to
Art, and forms its peculiar province.
Every art has one first principle, or
general major premise, not borrowed
from science ; that which enunciates
the object aimed at, and aflBrms it to
be a desirable object The builder's
art assumes that it is desirable to have
buildings ; architecture, (as one of the
fine arts,) that it is desirable to have
them beautiful or imposing. The hy-
gienic and medical arts assume, the
one that the preservation of health,
the other that the cure of disease,
are fitting and desirable ends. These
are not propositions of science. Pro-
positions of science assert a matter
of fact : an existence, a co-existence,
a succession, or a resemblance. The
propositions now spoken of do not as-
sert that anything is, but enjoin or
recommend that something should be.
They are a class by themselves. A
proposition of which the predicate is
expressed by the words ought or should
he, is genericaDy different from one

620

LOGIC OF THE MORAL SCIENCES,

which is e?<pressed by is or vnll he.
It is true that, in the largest sense
of the words, even these propositions
assert something as a matter of fact.
The fact affirmed in them is, that
the conduct recommended excites in
the speaker's mind the feeling of ap-
probation. This, however, does not
go to the bottom of the matter, for
the speaker's approbation is no suffi-
cient reason why other people should
approve ; nor ought it to be a conclu-
sive reason even with himself. For
the purposes of practice, every one
must be required to justify his appro-
bation ; and for this there is need of
general premises, determining what
are the proper objects of approbation,
and what the proper order of prece-
dence among those objects.

These general premises, together
with the principal conclusions which
may be deduced from them, form (or
rather might form^ a body of doctrine,
which is properly the Art of Life, in
its three departments, Morality, Pru-
dence or Policy, and ^^sthetics ; the
Kight, the Expedient, and the Beauti-
ful or Noble, in human conduct and
works. To this art (which, in the
main, is unfortunately still to be
created) all other arts are subordi-
nate ; since its principles are those
which must determine whether the
special aim of any particidar art is
worthy and desirable, and what is its
place in the scale of desirable things.
Every art is thus a joint result of
laws of nature disclosed by science,
and of the general principles of what
has been called Teleology, or the
Doctrine of Ends ; * which, borrow-
ing the language of the German meta-
physicians, may also be termed, not
improperly, the principles of Practical
Keason.

A scientific observer or reasoner,
merely as such, is not an adviser for
practice. His part is only to show

* The word Teleology is also, but incon-
veniently and improperly, employed by
some writers as a name for the attempt
to explain the phenomena of the iiniverse
troia final causes.

that certain consequences follow fr6m
certain causes, and that to obtain
certain ends, certain means are the
most effectual. Whether the ends
themselves are such as ought to be
pursued, and if so, in what cases and
to how great a length, it is no part of
his business as a cultivator of science
to decide, and science alone will
never qualify him for the decision.
In purely physical science there is
not much temptation to assume this
ulterior office ; but those who treat
of human nature and society invari-
ably claim it ; they always undertake
to say, not merely what is, but what
ought to be. To entitle them to do
this, a complete doctrine of Teleology
is indispensable. A scientific theory,
however perfect, of the subject-mat-
ter, considered merely as part of the
order of nature, can in no degree
serve as a substitute. In this respect
the various subordinate arts afford a
misleading analogy. In them there
is seldom any visible necessity for
justifying the end, since in general
its desirableness is denied by no-
body, and it is only when the
question of precedence is to be de-
cided between that end and some
other, that the general principles of
Teleology have to be called in ; but
a writer on Morals and Politics re-
quires those principles at every step.
The most elaborate and well-digested
exposition of the laws of succession
and co-existence among mental or
social phenomena, and of their rela-
tion to one another as causes and
effects, will be of no avail towards
the art of Life or of Society, if the
ends to be aimed at by that art are
left to the vague suggestions of the
intellectiis sibi permissus, or are taken
for granted without analysis or ques-
tioning.

§ 7. There is, then, a Philosophia
Prima peculiar to Art, as there is one
which belongs to Science. There are
not only first principles of Knowledge,
but first principles of Conduct. There
must be some standard by which to

LOGIC OF PRACTICE OR ART.

621

determine the goodness or badness,
absolute and comparative, of ends
or objects of desire. And whatever
that standard is, there can be but
one : for if there were several ulti-
mate principles of conduct, the same
conduct might be approved by one of
those principles and condemned by
another ; and there would be needed
some more general principle as umpire
between them.

Accordingly, writers on moral philo-
Bophy have mostly felt the necessity
not only of referring all rules of con-
duct, and all judgments of praise and
blame, to principles, but of referring
them to some one principle ; some
rule or standard, with which all other
rules of conduct were required to be
consistent, and from which by ulti-
mate consequence they could all be
deduced. Those who have dispensed
with the assumption of such an uni-
versal standard have only been en-
abled to do so by supposing that a
moral sense, or instinct, inherent in
our constitution, informs us, both
what principles of conduct we are
bound to observe, and also in what
order these should be subordinated to
one another.

The theory of the foundations of
morality is a subject which it would
be out of place, in a work like this, to
discuss at large, and which could not
to any useful purpose be treated in-
cidentally. I ghall content myself
therefore with saying, that the doc-
trine of intuitive moral principles,
even if true, would provide only for
that portion of the field of conduct
which is properly called moral. For
the remainder of the practice of life
some general principle, or standard,
must still be sought ; and if that
principle be rightly cho.«en, it will be
found, I apprehend, to serve quite as
well for the ultimate principle of
Morality, as for that of Prudence,
Policy, or Taste.

Without attempting in this place to
justify my opinion, or even to define
the kind of justification which it ad-
mits of, I merely declare my convic-

tion, that the general principle to
which all rules of practice ought to
conform, and the test by which they
should be tried, is that of conducive-
ness to the happiness of mankind, or
rather, of all sentient beings : in other
words, that the promotion of happi-
ness is the ultimate principle of Teleo-
lo^ry.*

I do not mean to assert that the
promotion of happiness should be
itself the end of all actions, or even
of all rules of action. It is the justi-
fication, and ought to be the con-
troller, of all ends, but is not itself
the sole end. There are many virtu-
ous actions, and even virtuous modes
of action, (though the cases are, I
think, less frequent than is often
supposed,) by which happiness in the
particular instance is sacrificed, more
pain being produced than pleasure.
But conduct of which this can be
truly asserted admits of justification
only because it can be shown that on
the whole more happiness will exist
in the world if feelings are cultivated
which will make people, in certain
cases, regardless of happiness. I fully
admit that this is true : that the
cultivation of an ideal nobleness of
will and conduct should be to in-
dividual human beings an end, to
which the specific pursuit either of
their own happiness or of that of
others (except so far as included in
that idea) should, in any case of con-
flict, give way. But I hold that the
very question, what constitutes this
elevation of character, is itself to be
decided by a reference to happiness
as the standard. The character itself
should be, to the individual, a para-
mount end, simply because the exist-
ence of this ideal nobleness of char-
acter, or of a near approach to it, in
any abundance, would go further than
all things else towards making human
life happy, both in the comparatively
humble sense of p^easure and freedom
from pain, and in the higher meaning

* Fnr an express discnssion nnd vindica-
tion of tills |.iiiiciple, ^ee the little voiuna©
euiitled Utiliiarianifni,

622

LOGIC OF THE MORAL SCIENCES.

of rendering life, not what it now is
almost universally, puerile and insig-
nificant, but such as human beings
with highly developed faculties can
care to have.

§ 8. With these remarks we must
close this summary view of the ap-
plication of the general logic of
scientific inquiry to the moral and
social departments of science. Not-
withstanding the extreme generality
of the principles of method which I
have laid down, (a generality which,
I trust, is not in this instance syno-
nymous with vagueness,) I have

indulged the hope that to some of
those on whom the task will devolve
of bringing those most important of
all sciences into a more satisfactory
state these observations may be use-
ful, both in removing erroneous and
in clearing up the true conceptions of
the means by which, on subjects of so
high a degree of complication, truth
can be attained. Should this hope be
realised, what is probably destined to
be the great intellectual achievement
of the next two or three generations
of European thinkers will have been
in some degree forwarded.

THE ENC.

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