= 00

•CO

CO

UNIV. OF
TORONTO
LIBRARY

!

SYSTEM OF LOGIC

RATIOCINATIVE AND INDUCTIVE

VOL. I.

SYSTEM OF LOGIC

RATIOCINATIVE AND INDUCTIVE

BEING A CONNECTED VIEW OF THE
PRINCIPLES OF EVIDENCE

AND THE
METHODS OF SCIENTIFIC INVESTIGATION

BY

IN TWO VOLUMES
VOL. I.

f
SEVENTH EDITION

LONDON :
LONGMANS, GREEN, READER, AND DYER

MDCCCLXVIII

6

i

PEEFACE TO THE FIEST EDITION.

THIS book makes no pretence of giving to the
world 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 systematize, the best ideas which have
been either promulgated on its subject by speculative
writers, or conformed to by accurate thinkers in their
scientific inquiries.

To cement together the detached fragments of a
subject, never yet treated as a whole ; to harmonize
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 considerable amount of original
speculation. To other originality than this, the pre
sent 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 effected a revolution in the
theory of the investigation of truth, or added any
fundamentally new process to the practice of it.
The improvement which remains to be effected in
the methods of philosophizing (and the author be
lieves that they have much need of improvement)
can only consist in performing, more systematically

b 3

VI

PREFACE.

and accurately, operations witli 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 Katio-
cination, 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 contempt
entertained by many modern philosophers for the
syllogistic art, it will be seen that he by no means
participates; though the scientific theory on which
its defence is usually rested appears to him erro
neous : and the view which he has suggested of the
nature and functions of the Syllogism may, perhaps,
afford the means of conciliating 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 Proposi
tions; because many useful principles and distinc
tions 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 rationalize the philosophical
foundation on which they stood. The earlier chap
ters of this preliminary Book will consequently
appear, to some readers, needlessly elementary and
scholastic. But those who know in what darkness
the nature of our knowledge, and of the processes by
which it is obtained, is often involved by a confused
apprehension of the import of the different classes of
Words and Assertions, will not regard these discus
sions as either frivolous, or irrelevant to the topics
considered in the later Books.

PREFACE. Vll

On the subject of Induction, the task to be per
formed was that of generalizing the modes of investi
gating 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 Archbishop Whately,
and the author of a celebrated article on Bacon in
the Edinburgh Review] have not scrupled to pro
nounce it impossible.* The author has endeavoured
to combat their theory in the manner in which
Diogenes confuted the sceptical reasonings against
the possibility of motion; remembering that Dio
genes' argument would have been equally conclusive,
though his individual perambulations might not have
extended beyond the circuit of his own tub.

Whatever may be the value of what the author
has succeeded in effecting on this branch of his sub
ject, it is a duty to acknowledge that for much of it

* 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 down, or that they may
not be " of eminent service," but that they " must always be com
paratively 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 scien
tific who expects." (Book iv. ch. ii. § 4.) To effect this, however,
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 Archbishop Whately and me on
the subject.

Vlll PREFACE.

he has been indebted to several important treatises,
partly historical and partly philosophical, on the
generalities and processes of physical science, which
have been published within the last few years. To
these treatises, and to their authors, he has endea
voured to do justice in the body of the work. But
as with one of these writers, Dr. Whewell, he has
occasion frequently to express differences 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 solution of a question, which the decay
of old opinions, and the agitation that disturbs Euro
pean society to its inmost depths, render as impor
tant in the present day to the practical interests of
human life, as it must at all times be to the com
pleteness of our speculative knowledge : 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 forma
tion of a similar body of received doctrine in moral
and political science.

PEEFACE TO THE THIED AND FODETH
EDITIONS,

SEVERAL criticisms, of a more or less controversial
character, on this work, have appeared since the pub
lication 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.*

I have carefully reconsidered all the points on
which my conclusions 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 objec
tions 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 discussion
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 from any taste

* Now forming a chapter in his volume on The Philosophy
of Discovery.

PREFACE.

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 subjects, 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.

In the subsequent editions, the attempt to improve
the work lay additions and corrections, suggested by
criticism or by thought, has been continued. In the
present (seventh) edition, a few further corrections
have been made, but no material additions.

CONTENTS

OP
THE FIRST VOLUME.

INTRODUCTION.

PAGB

§ 1. A definition at the commencement of a subject must be

provisional ...... 1

2. Is logic the art and science of reasoning ? . . .2

3. Or the art and science of the pursuit of truth ? .3

4. Logic is concerned with inferences, not with intuitive truths 5

5. Eelation of logic to the other sciences . . .8

6. Its utility, how shown . . . . .10

7. Definition of logic stated and illustrated . . .11

BOOK I.

OF NAMES AND PROPOSITIONS.

CHAPTEB I. Of the Necessity of commencing with an Analysis of
Language.

§ 1. Theory of names, why a necessary part of logic . . 17

2. First step in the analysis of Propositions . . .18

3. Names must be studied before Things . . .21

CHAPTER II. Of Names.

§ 1. Names are names of things, not of our ideas . . 23

2. Words which are not names, but parts of names . . 24

3. General and Singular names . . . .26

4. Concrete and Abstract . . . . .29

5. Connotative and Non-connotative . . . .31

6. Positive and Negative . . . . .42

7. Relative and Absolute . . . . .44

8. Univocal and ^Equivocal . . . .47

CONTENTS.

CHAPTER III. Of the Things denoted ly Names.

PAGE

§ 1. Necessity of an enumeration of Nameable Things. The

Categories of Aristotle . • • • .49

2. Ambiguity of the most general names

3. Peelings, or states of consciousness • • 54

4. Feelings must be distinguished from their physical antece

dents. Perceptions, what . • • .56

5. Volitions, and Actions, what ....

6. Substance and Attribute . . • « .59

7. Body 61

8. Mind . ... 67

9. Qualities . . •

10. Relations . . .... 72

11. Resemblance .....

12. Quantity . . .... 78

13. All attributes of bodies are grounded on states of con-

7Q
sciousness ....••

14. So also all attributes of mind . . • .80

15. Recapitulation . . • • • .81

CHAPTER IV. Of Propositions.

§ 1. Nature and office of the copula

2. Affirmative and Negative propositions . . .87

3. Simple and Complex ....

4. Universal, Particular, and Singular • 93

CHAPTER V. Of the Import of Propositions.

§ 1. Doctrine that a proposition is the expression of a relation

between two ideas . ... 96

2. Doctrine that it is the expression of a relation between the

meanings of two names . . • • .99

3. Doctrine that it consists in referring something to, or ex

cluding something from, a class . • • 103

4. What it really is . . . • » . 107

5. It asserts (or denies) a sequence, a coexistence, a simple

existence, a causation .

6. — or a resemblance . ^"

7. Propositions of which the terms are abstract . • 115

CONTENTS. xiil

CHAPTEE VI. Of Propositions merely Verb a I.

PAGE

§ 1. Essential and Accidental propositions . . . 119

2. All essential propositions are identical propositions . 120

3. Individuals have no essences .... 124

4. Seal propositions, how distinguished from verbal . 126

5. Two modes of representing the import of a Heal proposition 127

CHAPTER VII. Of the Nature of Classification, and the
Five Predicdbles.

§ 1. Classification, how connected with Naming . . 129

2. The Predicables, what . . . . .131

3. Genus and Species ...... 131

4. Kinds have a real existence in nature . . . 134

5. Differentia ....... 139

6. Differentiae for general purposes, and differentiae for special

or technical purposes ..... 141

7. Proprium . . . . . . 144

8. Accidens ....... 145

CHAPTEB VIII. Of Definition.

§ 1. A definition, what ...... 148

2. Every name can be defined, whose meaning is susceptible

of analysis ...... 150

3. Complete, how distinguished from incomplete definitions . 152
3. — and from descriptions . . . . ' . 154

5. What are called definitions of Things, are definitions of

Names with an implied assumption of the existence of

Things corresponding to them .... 157

6. — even when such things do not in reality exist . . 165

7. Definitions, though of names only, must be grounded on

knowledge of the corresponding Things

XIV CONTENTS.

BOOK II.

OF REASONING.
CHAPTEE I. Of Inference, or Seasoning, in general.

PAGE

§ 1. Eetrospect of the preceding book .... 175

2. Inferences improperly so called .... 177

3. Inferences proper, distinguished into inductions and ratio

cinations ....... 181

CHAPTER II. Of Ratiocination, or Syllogism.

§ 1. Analysis of the Syllogism ..... 184

2. The dictum de omni not the foundation of reasoning, but

a mere identical proposition .... 191

3. What is the really fundamental axiom of Ratiocination . 196

4. The other form of the axiom .... 199

CHAPTEE III. Of the Functions, and Logical Value, of the

Syllogism.
^»»

§ 1. Is the syllogism a petitio principii ? . . . 202

2. Insufficiency of the common theory . . . 203

3. All inference is from particulars to particulars . . 205

4. General propositions are a record of such inferences, and

the rules of the syllogism are rules for the interpretation

of the record ...... 214

5. The syllogism not the type of reasoning, but a test of it . 218

6. The true type, what . . . . .222

7. Relation between Induction and Deduction . . 226

8. Objections answered ..... 227

9. Of Formal Logic, and its relation to the Logic of Truth . 231

CHAPTEE IV. Of Trains of Reasoning, and Deductive
Sciences,

1. For what purpose trains of reasoning exist . . 234

2. A train of reasoning is a series of inductive inferences . 234

3. — from particulars to particulars through marks of marks 237

4. Why there are deductive sciences .... 240

5. Why other sciences still remain experimental . . 244

6. Experimental sciences may become deductive by the pro

gress of experiment ..... 246

7. In what manner this usually takes place . . . 247

CONTENTS. XV

CHAPTER V. Of Demonstration, and Necessary Truths.

Tftf~*+>** PA&E

§ 1. The Theorems of geometry are necessary truths only in

the sense of necessarily following from hypotheses . 251

2. Those hypotheses are real facts with some of their circum

stances exaggerated or omitted .... 255

3. Some of the first principles of geometry are axioms, and

these are not hypothetical .... 256

4. — but are experimental truths .... 258

5. An objection answered ..... 261

6. Dr. WhewelTs opinions on axioms examined . . 264

CHAPTER VI. The same Subject continued.

§ 1. All deductive sciences are inductive . . . 281

2. The propositions of the science of number are not verbal,

but generalizations from experience . . . 284

3. In what sense hypothetical ..... 289

4. The characteristic property of demonstrative science is to

be hypothetical ...... 290

5. Definition of demonstrative evidence . . . 292

CHAPTER VII. ^Examination of some Opinions opposed to
the preceding doctrines.

§ 1. Doctrine of the Universal Postulate . . . 294

2. The test of inconceivability does not represent the aggre

gate of past experience ..... 296

3. — nor is implied in every process of thought . . 299

4. Sir W. Hamilton's opinion on the Principles of Contra

diction and Excluded Middle .... 306 \

BOOK III.

OF INDUCTION.

CHAPTER I. Preliminary Observations on Induction in general.

§ 1. Importance of an Inductive Logic .... 313
2. The logic of science is also that of business and life . 314

CHAPTER II. Of Inductions improperly so called.

§ 1. Inductions distinguished from verbal transformations . 319

2. — from inductions, falsely so called, in mathematics . 321

3. — and from descriptions ..... 323

4. Examination of Dr. Whewell's theory of Induction . 326

5. Further illustration of the preceding remarks . . 336

XVI

* A*

i/ 2

dnj

CONTENTS.

IHAPTER III. On the Ground of Induction.

PAGE

341

§1

3.

MM9'

Axiom of the uniformity of the course of nature .

Not true in every sense. Induction per enumeration*™

.. . 346

stmplicem . •

The question of Inductive Logic stated .

CHAPTER IV. Of Laws of Nature.
The general regularity in nature is a tissue of partial re
gularities, called laws .
Scientific induction must be grounded on previous spon-

. -, ,• o55

taneous inductions . ^ •

Are there any inductions fitted to be a test of all others P
CHAPTER V. Of the Law of Universal Causation.

The universal law of successive phenomena is the Law of
Causation . • • • • * .

— i. e. the law that every consequent has an invariable
antecedent ...

The cause of a phenomenon is the assemblage of its con
ditions .

The distinction of agent and patient illusory

The cause is not the invariable antecedent, but the uncon
ditional invariable antecedent .

Can a cause be simultaneous with its effect P

Idea of a Permanent Cause, or original natural agent .

Uniformities of coexistence between effects of different
permanent causes, are not laws .

Doctrine that volition is an efficient cause, examined

360
363

365
373

375

380
383

386
387

CHAPTER VI. Of the Composition of Causes.

8 1. Two modes of the conjunct action of causes, the mechani-

-i 4iOo

cal and the chemical .

2. The composition of causes the general rule ; the other case

exceptional . •

3. Are effects proportional to their causes? . . .. *»

CHAPTER VII. Of Observation and Experiment.
§ 1. The first step of inductive inquiry is a mental analysis of

complex phenomena into their elements . . • 414

2. The next is an actual separation of those elements . 416

3. Advantages of experiment over observation . • 417

4. Advantages of observation over experiment . • 420

CONTENTS.

CHAPTEE VIII. Of the Four Methods of Experimental
Inquiry.

PAGE

§ 1. Method of Agreement ..... 425

2. Method of Difference .... 428

3. Mutual relation of these two methods . . . 429

4. Joint Method of Agreement and Difference . . 433

5. Method of Residues ..... 436

6. Method of Concomitant Variations . . . 437

7. Limitations of this last method .... 443

CHAPTEE IX. Miscellaneous Examples of the Four Methods.

§ 1. Liebig's theory of metallic poisons . . 449

2. Theory of induced electricity . . . 453

3. Dr. Wells' theory of dew .... 457

4. Dr. Brown-Sequard's theory of cadaveric rigidity . 465

5. Examples of the Method of Residues . . 471

6. Dr. Whewell's objections to the Four Methods . . 475

CHAPTEB X. Of Plurality of Causes ; and of the Intermixture
of Effects.

§ 1. One effect may have several causes . . . 482

2. — which is the source of a characteristic imperfection of

the Method of Agreement ... 483

3. Plurality of Causes, how ascertained . . . 487

4. Concurrence of Causes which do not compound their effects 489

5. Difficulties of the investigation, when causes compound

their effects ...... 494

6. Three modes of investigating the laws of complex effects 499

7. The method of simple observation inapplicable . . 500

8. The purely experimental method inapplicable . . 501

CHAPTEE XI. Of the Deductive Method.

§ 1. First stage ; ascertainment of the laws of the separate

causes by direct induction . . . 507

2. Second stage ; ratiocination from the simple laws of the

complex cases ...... 512

3. Third stage; verification by specific experience . . 514

CONTENTS.

CHAPTER XII. Of the Explanation of Laws of Nature.

PAGE

§ 1. Explanation defined • • 518

2. First mode of explanation, by resolving the law of a com

plex effect into the laws of the concurrent causes and

the fact of their coexistence . . ' . . ' 518

3. Second mode ; by the detection of an intermediate link in

the sequence .

4. Laws are always resolved into laws more general than

themselves . ... 520

5. Third mode ; the subsumption of less general laws under

a more general one . "**

6. What the explanation of a law of nature amounts to . 526

CHAPTER XIII. Miscellaneous Examples of the Explanation of
Laws of Nature.

§ 1. The general theories of the sciences . • .529

2. Examples from chemical speculations

3. Example from Dr. Brown- Sequard's researches on the

nervous system . . • • '

4. Examples of following newly-discovered laws into their

complex manifestations .

5. Examples of empirical generalizations, afterwards con

firmed and explained deductively

6. Example from mental science . . . 538
7. Tendency of all the sciences to become deductive . 539

INTBODUCTION.

§ 1. 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 them
selves of the same language as a means of delivering 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 inevitable 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 determine which of them are
fittest to be chosen for this purpose. Accordingly, in the case
of so complex an aggregation of particulars as are compre
hended in anything which can be called a science, the defini
tion 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 themselves, we cannot fix upon
the most correct and compact mode of circumscribing them by
a general description. It was not until after an extensive and
accurate acquaintance with the details of chemical phenomena,

VOL. I. 1

2 INTRODUCTION.

that it was found possible to frame a rational definition of
chemistry ; and the definition of the science of life and orga
nization is still a matter of dispute. So long as the sciences
are imperfect, the definitions must partake of their imperfec
tion ; and if the former are progressive, the latter ought to he
so too. As much, therefore, as is to he expected from a defi
nition placed at the commencement 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 statement 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 definition
of logic ; but it is at all events a correct definition of the sub
ject of these volumes.

§ 2. Logic has often been called the Art of Seasoning.
A writer* who has done more than any other person to restore
this study to the rank from which it had fallen in the esti
mation of the cultivated class in our own country, has adopted
the 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 process cor
rectly. There can be no doubt as to the propriety of the
emendation. A right understanding of the mental process
itself, of the conditions 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 possibly be founded. Art
necessarily presupposes knowledge ; art, in any but its infant
state, presupposes scientific 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 groundwork of a single
art. So complicated are the conditions which govern our prac
tical agency, that to enable one thing to be done, it is often
requisite to know the nature and properties of many things.

* Archbishop Whately.

DEFINITION AND PROVINCE OF LOGIC. 3

Logic, then, comprises the science of reasoning, as well as
an art, founded on that science. But the word Reasoning,
again, like most other scientific terms in popular use, abounds
in ambiguities. In one of its acceptations, 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 demonstrations of geometry.

Writers on logic have generally preferred the former accep
tation of the term : the latter, and more extensive significa
tion 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 provi
sional definition he pleases of his own subject. But sufficient
reasons will, I believe, unfold 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 lan
guage, 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 comprehend 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 argu
mentation, 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
subject only of the third part: the two former treated of
Terms, and of Propositions ; under one or other of which heads
were also included Definition and Division. By some, indeed,
these previous topics were professedly introduced only on
account of their connexion with reasoning, and as a prepara
tion 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

1—2

* INTRODUCTION.

writers on logic have generally understood the term as it was
employed by the able author of the Port Koyal 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 precision of language, and accuracy of classification :
and we perhaps oftener hear persons speak of a logical arrange
ment, 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 the accu
racy of his deductions, but for the extent of his command
over premises ; because the general propositions required for
explaining a difficulty or refuting a sophism, copiously and
promptly occur to him : because, in short, his knowledge,
besides being ample, is well under his command for argumen
tative use. Whether, therefore, we conform to the practice of
those who have made the subject their particular study, or to
that of popular writers and common discourse, the province
of logic will include several operations of the intellect not
usually considered to fall within the meaning of the terms
Reasoning and Argumentation.

These various operations might be brought within the com
pass of the science, and the additional advantage be obtained
of a very simple definition, 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 under
standing 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 sub
sidiary. 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 purposes, indeed, are also served by these operations ;
for instance, that of imparting our knowledge to others. But,
viewed with regard to this purpose, they have never been con
sidered as within the province of the logician. The sole object
of Logic is the guidance of one's own thoughts : the com
munication of those thoughts to others falls under the con-

DEFINITION AND PROVINCE OF LOGIC. 5

sideration of Khetoric, in the large sense in which that art
was conceived hy the ancients ; or of the still more extensive
art of Education. Logic takes cognizance of our intellectual
operations, only as they conduce to our own knowledge, and
to our command over that knowledge for our own uses. If
there were hut 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 we formerly examined
included too little, that which is now suggested has the oppo
site 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 reasoning, unless something could be known antecedently
to all reasoning.

Examples of truths known to us by immediate conscious
ness, are our own bodily sensations and mental feelings. I
know directly, and of my own knowledge, that I was vexed
yesterday, or that I am hungry to-day. Examples 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 testimony adduced, or from the traces of those
past occurrences which still exist ; the latter, from the pre
mises laid down in books of geometry, under the title of defi
nitions and axioms. Whatever we are capable of knowing

* I use these terms indiscriminately, because, for the purpose in view, there
is no need for making any distinction between them. But metaphysicians
usually restrict the name Intuition to the direct knowledge we are supposed to
have of things external to our minds, and Consciousness to our knowledge of
our own mental phenomena.

6 INTRODUCTION.

must belong to the one class or to the other ; must be in the
number of the primitive data, or of the conclusions which can
be drawn from these.

With the original data, or ultimate premises of our know
ledge ; with their number or nature, the mode in which they
J 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 con
ceive the science, nothing to do. These questions are partly
not a subject of science at all, partly that of a very different
science.

Whatever is known to us by consciousness, is known be
yond possibility of question. What one sees or feels, whether
bodily or mentally, one cannot 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 inference, may seem to be apprehended intui
tively. It has long been agreed by thinkers of the most oppo
site 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 degrees of faintness of colour; that our estimate of the
object's distance from us is the result partly of a rapid inference
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 making 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 appeared
when close at hand, or when their degree of remoteness was
known by other evidence. The perception of distance by the

DEFINITION AND PROVINCE OF LOGIC. 7

eye, which seems so like intuition, is thus, in reality, an infe
rence grounded on experience; an inference, too, which we
learn to make ; and which we make with more and more cor
rectness as our experience 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 per
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 those 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 apper
tain 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 on
these topics, it is almost universally allowed that the existence
of matter or of spirit, of space or of time, is in its nature un
susceptible of being proved j and that if anything is known of
them, it must be by immediate intuition. To the same science
belong the inquiries into the nature of Conception, Perception,
Memory, and Belief; all of which are operations of the under
standing 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

* 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 ; reprinted in Dissertations and Discussions, vol. ii.)

8 INTRODUCTION.

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
<i priori 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 restricted to that portion of
our knowledge which consists of inferences from truths pre
viously 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 Evi
dence. 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 consciousness, that
is, without evidence in the 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 inferences has been said to be the great business of life.
Every one has daily, hourly, and momentary need of ascertain
ing facts which he has not directly observed ; not from any
general purpose of adding to his stock of knowledge, but
because the facts themselves are of importance to his interests
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 accord
ingly. 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

DEFINITION AND PROVINCE OF LOGIC. 9

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 know
ledge. Logic is the common judge and arbiter of all parti
cular 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 inform 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 expe
rience 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 any
other, but points out to what conditions all facts must con
form, 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 ex
clusively to the particular art or science, or to our knowledge
of the particular subject.

It is in this sense that logic is, what Bacon so expressively
called it, ars artium ; the science of science itself. All science
consists of data and conclusions from those data, of proofs and
what they prove : now logic points out what relations must
subsist between 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 realities of things. Whatever has at any
time been concluded justly, whatever knowledge has been
acquired otherwise than by immediate intuition, depended on

10 INTRODUCTION.

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 heen observed.

§ 6. We need not, therefore, seek any farther for a solu
tion 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 instance in
which it infers rightly, there seems little necessity for dis
cussing whether a person is more likely to observe those rules,
when he knows the rules, than when he is unacquainted with
them.

A science may undoubtedly be brought to a certain, not
inconsiderable, stage of advancement, without the application
of any other logic to it than what all persons, who are said to
have a. sound understanding, 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
before 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 extraordinary genius, or by the
accidental acquisition of a good set of intellectual habits, may
work without principles 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 mankind 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 neces
sary condition, 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 defective a state ; if not only so little is proved, but
disputation has not terminated even about the little which

DEFINITION AND PROVINCE OF LOGIC. 11

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 estimation 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 estimation of
evidence : both the process itself of advancing from known
truths to unknown, and all other intellectual operations in so
far as auxiliary to this. It includes, therefore, the operation
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 conclu
sions from them permanent and readily accessible in the
memory, but for so marshalling the facts which we may at
any time be engaged in investigating, 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 instrumental 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

12

INTRODUCTION.

far as it goes is correct, and if it goes far enough for the
practical purposes of logic considered as an art. The separa
tion of a complicated phenomenon 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
compounds. All other things are at any rate compounded of
those elements : whether the elements themselves admit of
decomposition, is an important inquiry, but does not affect the
certainty 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 ascertaining 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 know
ledge of their anatomy might be very necessary 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 beyond the point at which
any inaccuracy 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 necessary 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 mental processes with which Logic is concerned. Logic
has no interest in carrying the analysis beyond the point at
which it becomes apparent whether the operations have in any
individual case been rightly or wrongly performed : in the
same manner as the science of music teaches us to discriminate

DEFINITION AND PROVINCE OF LOGIC. 13

between musical notes, and to know the combinations of which
they are susceptible, but not what number of vibrations in a
second correspond to each ; which, though useful 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 general ; the science which deals
with the constitution of the human faculties ; and to which, in
the part of our mental 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 this work
have no necessary connexion with any particular views re
specting the ulterior analysis. Logic is common 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 occasionally 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 altogether irrelevant to those more abstruse discussions ;
nor is it possible but that the view we are led to take of the
problem which logic proposes, must have a tendency favour
able to the adoption of some one opinion, on these controverted
subjects, rather than another. For metaphysics, in endeavour
ing to solve its own peculiar problem, must employ means, the
validity of which falls under the cognizance of logic. It pro
ceeds, no doubt, as far as possible, merely by a closer and more
attentive interrogation of our consciousness, or more properly
speaking, of our memory ; and so far is not amenable to logic.
But wherever this method is insufficient to attain the end of
its inquiries, it must proceed, like other sciences, by means of
evidence. Now, the moment this science begins to draw in
ferences from evidence, logic becomes the sovereign judge
whether its inferences are well grounded, or what other in
ferences would be so.

14

INTRODUCTION.

This, however, constitutes no nearer or other relation be
tween 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 definition and purpose of Logic, stands
in marked opposition to that of the school of philosophy which, in this country,
is represented 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 irre
levant to Logic, whatever relates to Belief and Disbelief, or to the pursuit of
truth as such, and restricting the science to that very limited portion of its
total province, which has reference to the conditions, not of Truth, but of Con
sistency. What I have thought it useful to say in opposition to this limitation
of the field of Logic, has been said at some length in a separate work, first
published in 1865, and entitled An Examination of Sir William Hamilton's
Philosophy, and of the Principal Philosophical Questions discussed in his
Writings. For the purposes of the present Treatise, I am content that the
justification of the larger extension which I give 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
which that particular part occupies in the whole to which it belongs, will be
found in the present volume (Book II. chap. iii. § 9).

BOOK I,

OF NAMES AND PEOPOSITIONS.

'La scolastique, qui produisit dans la logique, comme dans la morale, et
dans une partie de la me"taphysique, une subtilite", une precision d'ide"es, dont
1'habitude inconnue aux anciens, a contribue" plus qu'on ne croit au progres
de la bonne philosophie.' — CoNDOKCET, Vie de Turgot.

* To the schoolmen the vulgar languages are principally indebted for what
precision and analytic subtlety they possess.' — SIR W. HAMILTON, Discussions
in Philosophy.

CHAPTER I.

OF THE NECESSITY OF COMMENCING WITH AN
ANALYSIS OF LANGUAGE.

§ 1. IT is so much the established practice of writers on
logic to commence 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 following the common usage, to be as particular in
assigning my reasons, as it is usually expected that those
should be who deviate from it.

The practice, indeed, is recommended by considerations
far too obvious to require a formal justification. Logic is a
portion of the Art of Thinking: Language is evidently, and
by the admission of all philosophers, one of the principal in
struments or helps of thought ; and any imperfection 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 and
right use of the various kinds of words, to attempt the study
of methods of philosophizing, 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 Keasoning, or Inference, the principal subject of
logic, is an operation 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 significa
tion and purposes of words, will be under chances, amounting
almost to certainty, of reasoning or inferring incorrectly. And
logicians have generally felt that unless, in the very first stage,
they removed this source of error; unless they taught their
VOL. i. 2

18 NAMES AND PROPOSITIONS.

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 perplex, his vision ; he would not be in a con
dition to practise the remaining part of their discipline with
any prospect 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
preliminary 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 consideration : because without it he cannot
examine into the import of Propositions. 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 ascertain 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 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 receive an answer from direct consciousness, 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 conceiv
able ; 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 Assertion.
Whatever can be an object_of belief, or even of disbelief, must,
when put into words, assume the form of a proposition. _A1L.
truth and all error lie in propositions. What, by a convenient
misapplication of an abstract term, we call a Truth, means
simply a True Proposition ; and errors are false propositions.

NECESSITY OF AN ANALYSIS OF NAMES. 19

To know the import of all possible propositions, would be to
kjQow_a]]Ljjuestions which can be raised, all matters which are
susceptible of being either believed or disbelieved. How many
kinds of inquiries can be propounded ; how many kinds of
judgments can be made; and how many kinds of propositions
it is possible to frame with a meaning ; are but different forms
of one and the same question. Since, then, the objects of all
Belief and of all Inquiry express themselves in propositions ;
a sufficient scrutiny of Propositions and of their varieties will
apjmze 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 proposition shows that it is
formed by putting together two names. A proposition, ac
cording to the common simple definition, which is sufficient
for our purpose, is, discourse, in ivhich something is affirmed
or denied of something. Thus, in the proposition, Gold is
yellow, the quality yellow is affirmed of the substance gold.
In the proposition, Franklin was not born in England, the
fact expressed by the words born in England is denied of the
man Franklin.

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

2—2

20 NAMES AND PROPOSITIONS.

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 some
thing to do with, two objects: two names, to say the least;
; and (since the names must be names of something) two name-
.' able 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, and the idea of yellow ; and that what
takes place (or part of what takes place) in the act of belief,
consists in bringing (as it is often expressed) one of these
ideas under the other. But this we are not yet in a condition
to say : whether such be the correct mode of describing the
phenomenon, is an after consideration. The result with which
for the present we must be contented, is, that in every act
nf bftliftf turn objects are in some manner taken cognizance,
of. ; that there can be no belief claimecj, or question pro
pounded, which does not embrace two distinct (either material
or intellectual) subjects of thought ; each of them capable, or
not, of being conceived by itself, but incapable of being be
lieved by 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, in
stead 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.
" The 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

NECESSITY OF AN ANALYSIS OF NAMES. 21

square" does not include the meaning of " a round square
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 instances, meet with it ;
in the second, with belief or disbelief, as the case might be ; in
the third, with disbelief.

§ 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 with
out a preliminary survey of language. If we attempt to pro
ceed further in the same path, that is, to analyse any further
the import of Propositions ; we. find forced upon UST as a sub
ject of previous consideration, the import of Names, For
every proposition 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 meaning 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 ascertain 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 exhortation to
discard the whole fruits of the labours of his predecessors, and
conduct himself as if he were the first person who had ever
turned an inquiring eye upon nature. What does any one's

22 NAMES AND PROPOSITIONS.

personal knowledge of Things amount to, after subtracting
all which he has acquired hy 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 con
tained in his individual mind afford as sufficient a hasis for a
catalogue raisonn/ as the notions which are in the minds of all
mankind ?

In any enumeration and classification of Things, which
does not set out from their names, no varieties of things will
of course be comprehended but those recognised by the par
ticular inquirer ; and it will still remain to be established, by
a subsequent examination 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 mankind have multiplied the varieties unnecessarily, and
have imagined distinctions among things, where there were
only distinctions in the manner of naming them. But we are
not entitled to assume this in the commencement. We must
begin by recognising the distinctions made by ordinary lan
guage. 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 sub
sequent stage, is not a course which a logician can reasonably
adopt.

CHAPTER II.

OF NAMES.

§ 1. "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
pronounced to others, may be to them a sign of what thought
the speaker hadf before in his mind." This simple definition
of a name, as a word (or set of words) serving the double pur-]
pose of a mark to recall to ourselves the likeness of a forme
thought, and a sign to make it known to others, appears un
exceptionable. Names, indeed, do much more than this ; bu
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 expression in com
mon use ; the last is that of some metaphysicians, who con
ceived that in adopting it they were introducing a highly
important distinction. The eminent thinker, just quoted,
seems to countenance the latter opinion. " But seeing." he
continues, " names ordered in speech (a.s is definejl) are signs.
of our conceptions, it is manifest J^ey are not signg_of_the
thj^g^_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 conception alone, and notf
the thing itself, is recalled by the name, or imparted to the\
hearer, this of course cannot be denied. Nevertheless, there N\
seems good reason for adhering to the common usagef and

* Computation or Logic, chap. ii.

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

24 NAMES AND PROPOSITIONS.

calling the word sun the name of the sun, 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 in-
form him what we believe. Now, when I use a name for the
purpose of expressing 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 necessary 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, truly, often ; the inflected cases of nouns
substantive, as me, him, John's ; and even adjectives, as large,
heavy. These words do not express things of which anything
can be affirmed 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 complete
names, viz. names of those particular sounds, or of those
particular collections of written characters. This employment
of a word to denote the mere letters and syllables of which it

NAMES. 25

is composed, was termed by the schoolmen the suppositio
materialis of the word. In any other sense we cannot intro
duce 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^howjever, is capable of standing by itself as
the predicate of a proposition ; as when we say, Snow is white ;
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 grammatical ellipsis : Snow is white, instead 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
speaking, 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 adjec
tives as names, whether in their own right, or as representative
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.

Words which are not capable of being used PS names, but
only as parts of names, were called by some of the schoolmen
Syncategorematic terms : from avv, with, and Karr/yopta*, 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 Categorematic term. A combination of one or more Gate-

26

NAMES AND PROPOSITIONS.

gorematic, and one or more Syncategorematic words, as A
heavy body, or A court of justice, they sometimes called a
mixed term; but this seems a needless multiplication 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.

For, 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 determining whether any set of words makes only one
name, or more than one, is by predicating something of it,
and observing whether, by this predication, we make only one
assertion or several. Thus, when we say, John Nokes, who
was the mayor of the town, died yesterday — by this predica
tion 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 assertion that John Nokes died yesterday, there is included
another assertion, 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 the 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 yesterday, we make two assertions fone, 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 according to
the words they are composed of, but according to their
signification.

§ 3. All names are names of something, real or imagi
nary ; but all things have not names appropriated to them

NAMES. 27

individually. For some individual objects we require, and
consequently have, separate distinguishing names ; there is a
name for every person, and for every remarkable place. Other
objects, of which we have not occasion to speak so frequently,
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 number 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 particular 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 employed ; if they
only served, by mutually limiting each other, to afford a
designation for such individual objects 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 I
enabled 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 singular names, is fundamental ; and may be consicTered as:
the first grand" division of names.

A general name is familiarly defined, 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. For though
there are many persons who bear that name, it is not conferred

S

28

NAMES AND PROPOSITIONS.

upon them to indicate any qualities, or anything which be
longs to them in common ; and cannot be said to be affirmed
of them in any sense at all, consequently not in the same
sense. " The king who succeeded William the Conqueror," is
also an individual name. For, that there cannot be more than
one person of whom it can be truly affirmed, is implied in the
meaning of the words. Even " the 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 explaining what is meant by
a genera] name, to say that it is the name of a class. But
this, though a convenient mode of expression for some pur
poses, 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 proposition, and turn it into a definition
of the word class: " A class is the indefinite 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 collective 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 collective 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 individual soldiers of whom any regiment is
composed.

NAMES. 29

§ 4. The second general division of names is into con
crete and abstract. A concrete name is a name which stands
for a thing; an abstract name is a name which stands for an
attribute of a thing. Thus John, the sea, this table, are names
of things. White, also, is a name of a thing, or rather of
things. Whiteness, again, is the name of a quality or attri
bute 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, notwithstanding the
imperfections of their philosophy, 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 modern
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
generalization, and consequently to all general names, instead
of confining it to the names of attributes. The metaphysicians
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 language,
until there is now some difficulty in restoring the word to its
original signification. A more wanton alteration in the mean
ing 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 misappropriated, while the
misappropriation leaves that important class of words, the
names of attributes, without any compact distinctive appella
tion. The old acceptation, however, has not gone so com
pletely out of use, as to deprive those who still adhere to it of
all chance of being understood. By abstract, then, I shall I
always, in Logic, mean the opposite of concrete : by an ab- '

30 NAMES AND PROPOSITIONS.

stract 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 name common to whiteness, redness, &c. Such is
even the word whiteness, in respect of the different shades of
whiteness to which it is applied in common ; the word magni
tude, in respect of the various degrees of magnitude 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 attributes. But
when only one attribute, neither variable in degree nor in
kind, is designated by the name ; as visibleness ; tangibleness ;
equality ; squareness ; milkwhiteness ; then the name can
hardly be considered general ; for though it denotes an attri
bute of many different objects, the attribute itself is always
conceived as one, not many.* To avoid needless logomachies,
the best course would probably 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 be
whiteness is not snow, but the colour of snow. Whiteness,
therefore, is the name of the colour exclusively : white is a

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

NAMES. 31

name of all things whatever having the colour ; a name, not of
the quality whiteness, but of every white object. It is true,
this name was given to all those various objects on account of
the quality ; and we may therefore say, without impropriety,
that the quality forms part of its signification; but a name
can only be said to stand for, or to be a name of, ttie 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 occa
sion to 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^jtherefore, are connotative._ But white,
long, virtuous, are connotative. The word white, denotes all
white things, as snow, paper, the foam of the sea, &c., and
implies, or as it was termed by the schoolmen, connotes* the
attribute whiteness. The word white is not predicated of the
attribute, but of the subjects, snow, &c. ; but when we predi
cate it of them, we imply, or connote, that the attribute white
ness 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 Man of Boss, and

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

32 NAMES AND PROPOSITIONS.

an ^indefinable number of otber individuals, past, present, and
to come. These individuals, 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 received the name of virtue. It is applied to all
beings that are considered to possess this attribute ; and to
none which are not so considered.

All concrete general names are connotative. The word
man, for example, denotes Peter, Jane, John, and an indefinite
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 possessing
reason equal to that of human beings, but with the form of an
elephant, they would not be called men. Swift's Howyhnhnms
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 constituted. The name, therefore, is said to signify the
subjects directly, the attributes indirectly; it denotes the
subjects, and implies, or involves, or indicates, or as we shall
say henceforth connotes, the attributes. It is a connotative
name.

Connotative names have hence been also called denominative,

NAMES. 33

because the subject wbich they denote is denominated by, or
receives a name from, the attribute which they connote. Snow,
and other objects, receive the name white, because they possess
the attribute which is called whiteness ; Peter, James, and
others receive the name man, because they possess the attri
butes which are considered 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 couno-
tative. Even abstract names, though the names only of attri
butes, may in some instances be justly considered as connota-
tive ; 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 bad or hurtful quality.
This word is a name common to many attributes, and connotes
hurtfulness, an attribute of those various attributes. When,
for example, we say that slowness, in a horse, is a fault, we
do not mean that the slow movement, 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 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 indi
viduals 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 Paul, or a dog by the name
Ceesar, these names are simply marks used to enable those
individuals to be made subjects of discourse. It may be said,
indeed, that we must have had some reason for giving them

* Archbishop Whately, who, in the later editions of his Elements of Logic,
aided in reviving the important distinction treated of in the text, proposes the
term "Attributive" as a substitute for "Connotative" (p. 22, 9th ed.) The
expression is, in itself, appropriate ; but as it has not the advantage of being
connected with any verb, of so markedly distinctive a character as "to connote,"
it is not, I think, fitted to supply the place of the word Connota+ive in scienti
fic use.

VOL. I. 3

34 NAMES AND PROPOSITIONS.

those names rather than any others ; and this is true ; but
the name, once given, is independent of the reason. A man
may have heen 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 other
wise, when the fact confessedly 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 in
dividual a name utterly unmeaning, which we call a proper
name, — a word which answers the purpose of showing what
thing it is we are talking about, but not of telling anything
about it ; yet a name peculiar to an individual is not neces
sarily 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 illus
trate, being, in strictness of language, general, not individual
names : for, however they may be in fact predicable 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 mankind 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 the meaning of the connotative name itself,

NAMES. 35

that there can exist but one individual possessing the attribute
which it connotes : as, for instance, " the only son of John
Stiles;" "the first emperor of Home." Or the attribute
connoted may be a connexion with some determinate event,
and the connexion may be of such a kind as only one individual
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 employment
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, " Cesar's army " is an individual name, if
it appears from the context that the army meant is that which
Cffisar commanded in a particular battle. The still more
general expressions, "the Roman army," or "the Christian
army," may be individualized in a similar manner. Another
case of frequent occurrence has already been noticed ; it is the
following. 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, consis
tently with the meaning of the general term. This is exem
plified in such an instance as the following : " the present
prime minister of England." Prime Minister of England is a
general name ; the attributes which it connotes may be pos
sessed by an indefinite number of persons : in succession
however, not simultaneously; 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
attributes at one indivisible point of time, it becomes applicable
only to one individual. And as this appears from the mean-

3—2

36 NAMES AND PROPOSITIONS.

ing 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 in
formation, that is, whenever they have properly any meaning,
the meaning resides not in what they denote, but in what they
connote. The only names of objects which connote nothing
are proper names ; and these have, strictly speaking, no signi
fication.*

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 dis
tinction. 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 dis
tinguish that which I am now looking at, from any of the
others; I must therefore contrive to make the appearance 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 difference 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

* A writer who entitles his book Philosophy ; or, the Science of Truth,
charges me in his very first page (referring at the foot of it to this passage)
with asserting that general names have properly no signification. And he
repeats this statement many times in the course of his volume, with comments,
not at all flattering, thereon. It is well to be now and then reminded to how
great a length perverse misquotation (for, strange as it appears, I do not believe
that the writer is dishonest) can sometimes go. It is a warning to readers,
when they see an author accused, with volume and page referred to, and the
apparent guarantee of inverted commas, of maintaining something more than
commonly absurd, not to give implicit credence to the assertion without veri
fying the reference.

NAMES. 37

in some degree analogous to what the rohber intended in chalk
ing the house. We put a mark, not indeed upon the object
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 the chalk, enable us 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 ex
perience, or in the discourse 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 point
ing to a city, that it is York, we do not, merely by so doing,
convey to the hearer any information about them, except that
those are their names. By enabling him to identify the in
dividuals, we may connect them with information previously
possessed by him ; by saying, This is York, we may tell him
that it contains the Minster. But this is in virtue of what
he has previously heard concerning 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 in
formation, and this merely by the signification of the many-
worded connotative name, " built of marble." Such names
are not signs of the mere objects, invented because we have
occasion to think and speak of those objects individually;
but signs which accompany an attribute : a kind of livery in
which the attribute clothes all objects which are recognised as
possessing 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 indi
vidual which it is predicated of, so (as well from the importance
of adhering to analogy, as for the other reasons formerly as-

38 NAMES AND PROPOSITIONS.

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
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 individual, but their meaning is altogether dif
ferent ; they are applied to that individual for two different
purposes ; the one, merely to distinguish him from other per
sons who are spoken of; the other to indicate a fact relating
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 Sophroniscus, 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 meaning is apprised of a distinct fact or number of facts
concerning him ; but those who knew nothing about the names
except that they were applicable to Sophroniscus, would be al
together 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 dif
ference 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 ordinarily found in the
beings whom we are accustomed to call men, would suffice in

NAMES. 39

a newly-discovered race to make us refuse them the name of
man. Bationality, also, being a quality which admits of de
grees, it has never been settled what is the lowest degree of
that quality which would entitle any creature to be con
sidered 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 complete
precision ; in order that, in natural history for instance, indi
viduals or species of no very marked character may be ranged
with those more strongly characterized individuals 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 precau
tions. One of the chief sources, indeed, of lax habits of thought,
is the custom of using connotative terms without a distinctly
ascertained connotation, 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 different objects have in common. In the case of
these two words the process is so easy as to require no as
sistance from culture; the objects called 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 possess, it is not immediately apparent
what are the particular attributes, upon the possession of which

40 NAMES AND PROPOSITIONS.

in common by them all, their general resemblance depends.
When this is the case, people use the name without any re
cognised connotation, that is, without any precise meaning ;
they talk, and consequently think, vaguely, and remain con
tented 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 presenting themselves to men,
women, and children, which they are called upon to class pro-
prio motu. They, accordingly, do this on no other principle
than that of superficial similarity, 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 independently 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 technical, to attempt to make the
original stock of names serve with but little augmentation to
express a constantly increasing number of objects and distinc
tions, and, consequently, to express them in a manner pro
gressively more and more imperfect.

To what a degree this loose mode of classing and denomi
nating objects has rendered the vocabulary of mental and moral
philosophy unfit for the purposes of accurate thinking, is best
known to whoever has most meditated on the present condi-

NAMES. 41

tion 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 dis
cussion, is extremely difficult 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 retaining the existing phraseology, how best to alleviate
its imperfections. This can only be accomplished by giving to
every general concrete name which there is frequent occasion
to predicate, a definite and fixed connotation ; 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 subtraction, of
the group of objects which, in however imperfect a manner, it
serves to circumscribe and hold together; and with the least
vitiation of the truth of any propositions which are commonly
received as true.

This desirable purpose, of giving a fixed connotation where
it is wanting, 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 leading expressions, is a
proof how great an extent the evil to which we have adverted
has attained.

Names with indeterminate connotation are not to be con
founded 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 paucity of
existing names, in comparison with the demand for them, may
often render it advisable and even necessary to retain a name

42 NAMES AND PROPOSITIONS.

in this multiplicity of acceptations, distinguishing these so
clearly as to prevent their being confounded with one another.
Such a word may he considered as two or more names, acci
dentally written and spoken alike.*

§ 6. The fourth principal division of names, is into posi
tive and negative. Positive, as man, tree, good ; negative, as
not-man, not-tree, not-good. To every positive concrete name,
a corresponding negative one might he 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 whatever, 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 connotative, the
corresponding negative name is connotative likewise ; but in
a peculiar way, connoting not the presence but the absence of
an attribute. Thus, not-white denotes all things whatever
except white things ; and connotes the attribute of not possess-

* Before quitting the subject of connotative names, it is proper to observe,
that the first writer who, in our times, has adopted from the schoolmen the
word to connote, Mr. James Mill, in his Analysis of the Phenomena of tlie
Human Mind, employs it in a signification different from that in which it is
here used. He uses the word in a sense coextensive with its etymology, apply
ing it to every case in which a name, while pointing directly to one thing,
(which is consequently termed its signification,) includes also a tacit reference
to some other thing. In the case considered in the text, that of concrete gene
ral names, his language and mine are the converse of one another. Considering
(very justly) the signification of the name to lie in the attribute, he speaks of
the word as noting the attribute, and connoting the things possessing the attri
bute. And he describes abstract 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 deli
berately sanctioned, I have been influenced by the urgent necessity for a term
exclusively appropriated to express the manner in which a concrete general
name serves to mark the attributes which are involved in its signification. This
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 philo
sophy of language without such a word. It is hardly an exaggeration to say,

NAMES. 43

ing whiteness. For the non-possession 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.

Names which are positive in form are often negative in
reality, and others are really positive though their form is
negative. The word inconvenient, for example, does not
express the mere absence of convenience ; it expresses a posi
tive attribute, that of being the cause of discomfort or annoy
ance. 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 painful, 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 equivalent in its signification to a positive and a nega-

that some of the most prevalent of the errors with which logic has been infected,
and a large part of the cloudiness and confusion of ideas which have enveloped
it, would, in all probability, have been avoided, if a term had been in common
use to express exactly what I have signified by the term to connote. And the
schoolmen, 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 technical term, and to fix its meaning as such, with that admir
able precision which always characterizes their definitions, they clearly explained
that nothing was said to be connoted except forms, which word may generally,
in their writings, be understood as synonymous with attributes.

Now, if the word to connote, so well 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 em
ploying these, I should fail of attaining the object for which alone the name is
needed, namely, to distinguish this particular kind of involving and implying
from all other kinds, and to assure to it the degree of habitual attention which
its importance demands.

44 NAMES AND PROPOSITIONS.

tive 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 par
ticular 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
supposed 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.

§ 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 me
taphysics, not to be willingly spared 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; unlike; unequal; longer, shorter; cause, effect.
Their characteristic property is, that they are always given in
pairs. Every relative name which is predicated 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.

NAMES. 45

When we say of any object that it is like, we mean that it is
like some other ohject, which is also said to be like the first.
In this last case both objects receive the same name ; the rela
tive term is its own correlative.

It is evident that these words, when concrete, are, like
other concrete general names, connotative ; they denote a sub
ject, and connote an attribute; and each of them has or might
have a corresponding abstract 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, paternity, 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 ? Wherein consists the peculiarity in
the connotation of a relative name ?

The attribute signified by a relative name, say some, is a
relation ; and this they give, if not as a sufficient explanation,
at least as the only one attainable. If they are asked, What
then is a relation ? they do not profess to be able to tell. It
is generally regarded as something peculiarly recondite 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 con
note, 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 de
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 propositions are exactly equivalent: neither of them

46 NAMES AND PROPOSITIONS.

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 concerned, 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 intended to convey. The series of events may
be said to constitute the relation ; the schoolmen called it the
foundation of the relation, fundamentum relationis.

In this manner any fact, or series of facts, in which two
different objects are implicated, and which is therefore pre-
dicable of both of them, may be either considered as consti
tuting an attribute of the one, or an attribute of the other.
According as we consider it in the former, or in the latter
aspect, it is connoted by the one or the other of the two cor
relative names. Father connotes the fact, regarded as consti
tuting an attribute of A : son connotes the same fact, as con
stituting an attribute of B. It may evidently be regarded
with equal propriety in either light. And all that appears
necessary to account for the existence of relative names, is,
that whenever there is a fact in which two individuals are con
cerned, 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 object 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 rela
tive, 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 under
stood. These definitions are all, at bottom, equivalent, being
modes of variously expressing this one distinctive circum
stance — that every other attribute of an object might, without
any contradiction, be conceived still to exist if no object be-

NAMES. 47

sides that one had ever existed ;* but those of its attributes
which are expressed by relative names, would on that supposi
tion be swept away.

§ 8. Names have been further distinguished into unlvocal
and (equivocal : these, however, are not two kinds of names,
but two different modes of employing names. A name is
nnivocal, or applied univocally, with respect to all things of
which it can be predicated in the same sense : it is equivocal,
or applied equivocally, as respects those things of which it is
predicated in different senses. It is scarcely necessary to give
instances of a fact so familiar as the double meaning of a word.
In reality, as has been already observed, an equivocal or am
biguous 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 con
sidered one word, because written alike, than grease and Greece
have, because they are pronounced alike. They are one sound,
appropriated to form two different words.

An intermediate case is that of a name used analogically
or metaphorically ; that is, a name which is predicated of two
things, not univocally, or exactly in the same signification,
but in significations somewhat similar, and which being de
rived 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 achievement. 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 transferred
to the achievement in a derivative signification, supposed to
be somewhat like the primitive one. The word, however, is

* Or rather, all objects except itself and the percipient mind ; for, as we
shall see hereafter, to ascribe any attribute to an object, necessarily implies a
mind to perceive it.

The simple and clear explanation given in the text, of relation and relative
names, a subject so long the opprobrium of metaphysics, was given (as far as I
know) for the first time, by Mr. James Mill, in his Analysis of the Phenomena
of the Human Mind.

48 NAMES AND PROPOSITIONS.

just as properly two names instead of one, in this case, as in
that of the most perfect ambiguity. And one of the com
monest forms of fallacious reasoning arising from ambiguity,
is that of arguing from a metaphorical expression 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.

OF THE THINGS DENOTED BY NAMES.

§ 1. LOOKING back now to the commencement of our
inquiry, let us attempt to measure how far it has advanced.
Logic. \vf found, is the; Theory of .Proof. P>ut proof supposes
something provable, which must be a Proposition or Assertion ;
since nothing 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 concerned 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 existing state of human knowledge, is capable 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 preceding 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 which are capable of being made predi
cates, or of having anything predicated of them : after which
to determine the import of Predication, that is, of Proposi
tions, can be no arduous task.

The necessity of an enumeration of Existences, as the basis
of Logic, did not escape the attention of the schoolmen, and
of their master Aristotle, the most comprehensive, if not also
the most sagacious, of the ancient philosophers. The Cate
gories, or Predicaments — the former a Greek word, the latter
its literal translation in the Latin language — were intended by
him and his followers as an enumeration of all things capable
VOL. i. 4

50 NAMES AND PROPOSITIONS.

of being named ; an enumeration by the summa genera, i.e.
the most extensive classes into, which things could be distri
buted ; which, therefore, were so many highest Predicates,
o"ue or other of which was supposed capable of being affirmed
with truth of every nameable thing whatsoever. The follow
ing are the classes into which, according to this school of
philosophy, Things in general might be reduced :—

Ovffia, Substantia.

Hoabv, Quantitas.

Hoiov, Qualitas.

ITpoc TI, Relatio.

Houtv, Actio.

Hd<rx"v> Passio.

Ho?-, Ubi.

HOTI, Quando.
KelaOai, Situs.

Habitus.

The imperfections of this classification 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 penetrate, by philosophic analysis, to the rationale
even of those common distinctions. Such an analysis, how
ever superficially conducted, would have shown the enumera
tion to be both redundant and defective. Some objects are
omitted, and others repeated several times under different
heads. It is like a division of animals into men, quadrupeds,
horses, asses, and ponies. That, for instance, could not be a
very comprehensive view of the nature of Kelation which could
exclude action, passivity, and local situation from that cate
gory. The same observation applies to the categories Quando
(or position in time), and Ubi (or position in space) ; while
the distinction between the latter and Situs is merely verbal.
The incongruity 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 feelings and states of mind ; as hope,
joy, fear; sound, smell, taste; pain, pleasure; thought, judg-

THINGS DENOTED BY NAMES. 51

ment, conception, and the like? Probably all these would
have been placed by the Aristotelian scbool in the categories
of actio and pas.sio ; and the relation of such of them as are
active, to tbeir objects, and of such of them as are passive, to
their causes, would rightly be so placed; but tbe things
themselves, the feelings or states of mind, wrongly. Feelings,
or states of consciousness, are assuredly to be counted among
realities, but they cannot be reckoned either among substances
or attributes.

§ 2. Before recommencing, under better auspices, the
attempt made with such imperfect success by the great founder
of the science of logic, 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 sup
posed to mean a substance. There seems a kind of contra
diction in using such an expression as that one thing is merely
an attribute of another thing. And the announcement of a
Classification of Things would, I believe, prepare most readers
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 existence. But this

4—2

52 NAMES AND PROPOSITIONS.

word, strange as the fact may appear, is still more completely
spoiled for the purpose which it seemed expressly made for,
than the word Thing. Being is, by custom, exactly synony
mous 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 originally and in strict
ness applicable to both, is apt to suggest in preference the idea
of matter Attributes are never called Beings ; nor are feel
ings. A Being is that which excites feelings, and which pos
sesses attributes. The soul is called a Being; God and angels
are called Beings ; but if we were to say, extension, colour,
wisdom, 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 fol
lowers of Epicurus that of Sensible Forms, which detach
themselves in every direction from bodies, and by coming in
contact with our organs, cause our perceptions. We should
be supposed, in short, to believe that Attributes are Substances.
In consequence of this perversion of the word Being, phi
losophers 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, born at the same time and of the
same parents, scarcely underwent a more complete transforma
tion when,, from being the abstract of the verb to be, 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 impaired than any of the names before men
tioned. 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 suspected of believing it to be a sub
stance than if you called it a being ; but you are by no means

THINGS DENOTED BY NAMES. 53

free from the suspicion. Every word which was originally in
tended to connote mere existence, seems, after a long time, to
enlarge its connotation to separate existence, or existence freed
from the condition of belonging to a substance ; which con
dition 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 tools, the next best
thing is to understand 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 meaning doubtful or obscure. No
one of the above terms being altogether unambiguous, 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 improper 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

54 NAMES AND PROPOSITIONS.

which must be made to use vague word's so as to convey a pre-
nise meaning, is not wholly a matter of regret. It is not un
fitting 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 lan
guage 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 enumera
tion. 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 CONSCIOUSNESS.

§ 3. A Feeling and a State of Consciousness 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
existence. In popular language Feeling is not always synony
mous 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 emotional
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 language ; just as, by a
popular perversion 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 sensa
tions, but to the sensations of a single sense, that of touch,
needs not be more particularly adverted to.

Feeling, in the proper sense of the term, is a genus, of
which Sensation, Emotion, and Thought, are subordinate
species. Under the word Thought is here to be included what-

THINGS DENOTED BY NAMES. 55

ever we are internally conscious of when we are said to think ;
from the consciousness 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 remembered, how
ever, 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 think
ing of the sun, or of 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 yester
day, 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. Unfortunately foi
clearness and due discrimination in considering these subjects,
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 circumlocution, and say, The

56 NAMES AND PROPOSITION'S.

sensation of white, or The sensation of whiteness ; we must
denominate the sensation 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 any
thing 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 universe with nothing in it except
sounds, and ourselves hearing them : and what is easily con
ceived separately, easily obtains a separate name. But in general
our names of sensations denote indiscriminately the sensation
arid 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 sensationsr another distinction has also
to be kept in view, which is often confounded, and never with
out mischievous consequences. This is, the distinction between
the sensation itself, 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 con
fusion on this subject is the division commonly made of feelings
into Bodily and Mental. Philosophically speaking, there is no
foundation at all for this distinction : even sensations are states
of the sentient mind, not states of the body, as distinguished
from it. What I am conscious of when I see the colour blue,
is a feeling of blue colour, which is one thing ; the picture on
my retina, or the phenomenon of hitherto mysterious 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
investigation alone could have apprised me of. These are
states of my body ; but the sensation of blue, which is the con-

THINGS DENOTED BY NAMES. 57

sequence of these states of body, is not a state of body : that
which perceives and is conscious is called Mind. When sen
sations are called bodily feelings, it is only as being the class
of feelings which are immediately occasioned by bodily states ;
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 sensation 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 ex
ternal object as the exciting cause of the sensation. This per
ception, they say, is an act of the mind, proceeding from its
own spontaneous activity ; while in a sensation the mind is
passive, 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 sen
sation, that the existence of God, the soul, and other hyper-
physical objects is recognised.

These acts of what is termed perception, whatever be the
conclusion ultimately 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
intention of declaring or insinuating any theory as to the law
of mind in which these mental processes may be supposed to
originate, or the conditions under which they may be legiti
mate or the reverse. Far less do I mean (as Dr. Whewell
seems to suppose must be meant in an analogous case*) to in
dicate that as they are "merely states of mind," it is super
fluous to inquire into their distinguishing peculiarities. 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 ex-

* Philosophy of the Inductive Sciences, vol. i. p. 40.

58 NAMES AND PROPOSITIONS.

ternal to itself, I can see only cases of belief; but of belief
which claims to be intuitive, or independent of external evi
dence. 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, belongs not to 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 metaphy
sicians 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 im
portance. For us, they all are states of mind, 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 care
fully 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 connotation 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

THINGS DENOTED BY NAMES. 59

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,
obligor 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 correla
tive ; as the word brother. From these instances, it may be
seen how large a portion of the connotation 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 consequence of the
intention, is another thing; the two together constitute the
action. I form the purpose of instantly moving my 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,
consequent on a state of mind. The intention, 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 ; Sensations, Thoughts, and Emotions.
The first two of these we have illustrated at considerable
length ; the third, Emotions, not being perplexed by similar
ambiguities, does not require similar exemplification. And,
finally, we have found it necessary to add to these three a
fourth species, commonly known by the name Volitions.
Without seeking to prejudge the metaphysical question
whether any mental state or phenomenon can be found which
is not included in one or other of these four species, it appears

60

NAMES AND PROPOSITIONS.

to me that the amount of illustration bestowed upon these may,
so far as we are concerned, suffice for the whole genus. We
shall, therefore, proceed to the two remaining classes of name-
able things ; all things which are external to the mind being
considered as belonging either to the class of Substances or to
that of Attributes.

II. SUBSTANCES.

Logicians have endeavoured to define Substance and Attri
bute ; 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 sub
stances or of attributes. Such definitions are rather lessons of
English, or of Greek, Latin, or German, than of mental phi
losophy. An attribute, say the school logicians, must be the
attribute of something; colour, for example, must 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 attribute, the existence of the attribute
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 substance be a re
lative name ; if so, it must be followed either by of, or by some
other particle, implying, as that preposition does, a reference
to something else : but then the other characteristic 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 referred 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 before there was a child : and there would
be no contradiction in supposing him to exist, though the

THINGS DENOTED BY NAMES. 61

whole universe 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 conceived to exist without any
other substance, but so also may an attribute without any
other attribute : and we can no more imagine a substance
without attributes than we can imagine attributes without a
substance.

Metaphysicians, however, have probed the question deeper,
and given an account of Substance considerably more satis
factory than this. Substances are usually distinguished as
Bodies or Minds. Of each of these, philosophers have at
length provided us with a definition which seems unexcep
tionable.

§ 7. A Body, according to the received doctrine of
modern metaphysicians, may be defined, the external cause to
which we ascribe our sensations. When I see and touch a
piece of gold, I am conscious of a sensation of yellow colour,
and sensations of hardness 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 conscious ; but I consider them as pro
duced by something not only existing independently of my
will, but external 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 theiv sufficient ground for so
ascribing them ? It is known, that there are metaphysicians

62 NAMES AND PROPOSITIONS.

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 maintain 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 com
pounded of its visible form and size, which are complex sensa
tions of sight ; its tangible form and size, which are complex
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 sensation of sight ; its hardness, which is
a sensation of the muscles ; its composition, 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, expe
rienced 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 conceive 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 what
ever ; 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, intangible,
imperceptible not only by all our senses, but by the senses of
all other sentient beings, real or possible ; nothing, say these

THINGS DENOTED BY NAMES. 63

thinkers, would remain. For of what nature, they ask, could
be the residuum ? and by what token could it manifest its pre
sence ? To the unreflecting its existence seems to rest on the
evidence of the senses. But to the senses nothing is apparent
except the sensations. We know, indeed, that these sensations
are bound together by some law ; they do not come together
at random, but according to a systematic order, which is part
of the order established in the universe. When we experience
one of these sensations, we usually experience the others also,
or know that we have it in our power to experience them.
But a fixed law of connexion, 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 connexion presents itself to our imagination ; a mode of,
as it were, realizing the idea. If there be such a substratum,
suppose it this instant miraculously annihilated, and let the
sensations continue to occur in the same order, and how would
the substratum be missed ? By what signs 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 warranted in believing it,
how can we be so now ? A body, therefore, according to these
metaphysicians, is not anything 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 sen
sation, joined together according to a fixed law.

The controversies to which these speculations have given
rise, and the doctrines which have been developed in the
attempt to find a conclusive answer to them, have been fruitful
of important consequences to the Science of Mind. The sensa
tions (it was answered) which we are conscious of, and which
we receive, not at random, but joined together in a certain
uniform manner, imply not only a law or laws of connexion,
but a cause external to our mind, which cause, by its own
laws, determines the laws according to which the sensations
are connected and experienced. The schoolmen used to call
this external cause by the name we have already employed, a

64 NAMES AND PROPOSITIONS.

substratum ; and its attributes (as they expressed themselves)
inhered, literally stuck, in it. To this substratum the name
Matter is usually given in philosophical discussions. It was
soon, however, acknowledged by all who reflected on the sub
ject, that the existence of matter cannot be proved by extrinsic
evidence. The answer, therefore, now usually made to Berkeley
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, acknowledge their sensations to be the effects
of something external to them : this knowledge, therefore, it
is affirmed, is as evidently intuitive as our knowledge 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 meta
physicians, that objects are nothing but our sensations and
the laws which connect them, has not been generally adopted
by subsequent 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 know
of 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 universe of " Things in them
selves," totally distinct from the universe of phenomena, or of
things as they appear to our senses; and even when bringing
into use a technical expression (Noumenori) to denote what
the thing is in itself, as contrasted with the representation of
it in our minds ; he allows that this representation (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

THINGS DENOTED BY NAMES. 65

Hamilton,* "be they external, be they internal, we know
nothing, or know them only as incognisable ; and become
aware of their incomprehensible existence, only as this is in
directly and accidentally revealed to us, through certain quali
ties related to our faculties of knowledge, and which qualities,
again, we cannot think as unconditioned, irrelative, existent
in and of themselves. All that we know is therefore pheno
menal, — phenomenal of the unknown."f The same doctrine
is laid down in the clearest and strongest terms by M. Cousin,
whose observations on the subject are the more worthy of
attention, as, in consequence of the ultra-German and ontolo-
gical character of his philosophy in other respects, they may
be regarded as the admissions of an opponent.!

There is not the slightest reason for believing that what
we call the sensible qualities of the object are a type of any-

* Discussions on Philosophy, &c. Appendix I. pp. 643-4.
t It is to be regretted that Sir William Hamilton, though he often strenu
ously insists on this doctrine, and though, in the passage quoted, he states it
with a comprehensiveness 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
An Examination of Sir William Hamilton's Philosophy.

J " Nous savons qu'il existe quelque chose hors de nous, parceque nous ne
pouvons expliquer nos perceptions sans les rattacher a des causes distinctes de
nous-memes ; nous savons de plus que ces causes, dont nous ne connaissons pas
d'ailleurs 1'essence, produisent les effets les plus variables, les plus divers, et
ineme les plus contraires, selon qu'elles rencontrent telle nature ou telle dis
position du sujet. Mais savons-nous quelque chose de plus? et m§me, vu le
caractere inde'termine' des causes que nous concevons dans les corps, y a-t-il
quelque chose de plus a savoir ? Y a-t-il lieu de nous enqueYir si nous per-

cevons les choses telles qu'elles sont ? Non eVidemmerit Je ne dis

pas que le piobleme est insoluble, je dis qu'il est absurde et enferme une contra
diction. Nous ne savons pas ce que ces causes sonl en elles-mtmes, et la raison
nous defend de chercher k le connaitre : mais il est bien evident apriori, Belles
ne sont pas en elles-mSmes ce qu'elles sont par rapport a nous, puisque la presence
du sujet modifie ne"cessairement leur action. Supprimez tout sujet sen tan t, il
est certain que ces causes agiraieut encore puisqu'elles continueraient d'exister •
raais elles af iraient autrement ; elles seraient encore des qualites et des pro-'
price's, mais qui ne ressembleraient a rien de ce que nous connaissons. Le feu
ne manifesterait plus aucune des proprietes qutf-nous lui connaissons : que
serait-il ? (Test ce que nous ne saurons jamais. Vest d'ailleurs peut-etre un
proUeme qui ne repuyne pas seulement a la nature de notre esprit, mais a I' essence
meme des choses. Quand meme en effet on supprimerait par la pense'e tous les
VOL. I. 5

66 NAMES AND PROPOSITIONS.

thing 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 boil
ing water. Why then should matter resemble our sensations ?
Why should the inmost nature of fire or water resemble the
impressions made by those objects upon our senses ?* Or on
what principle are we authorized to deduce from the effects,
anything concerning the cause, except that it is a cause ade
quate to produce those effects ? It may, therefore, 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 sensations which we experience from it.f

sujets sentants, il faudrait encore admettre que nul corps ne manifesterait ses
proprie'tes autrement qu'en relation avec un sujet quelconque, et dans ce cas
ses proprietes ne seraient encore que relatives: en sorte qu'il me parait fort
raisonuable d' admettre que les proprie'te's de'termine'es des corps n'existent pas
independamment d'un sujet quelconque, et que quand on demande si les pro
prie'te's de la matiere sont telles que nous les percevons, il faudrait voir aupara-
vant si elles sont en tant que de"termin<Ses, et dans quel sens il est vrai de dire
qu'elles sont." — Cours d'Histoire de la Philosophic Morale au 18me siecle, 8me

169011.

* Au 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 sensa
tions, 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 ana
lysis than had previously been applied to the notions of extension and figure,
pointed out that the sensations from which those notions are derived, are sen
sations 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, which was adopted and followed up by James Mill, has been further
and greatly improved upon in Professor Bain's profound work, The Senses and
the Intellect, and in the chapters on " Perception" of a work of eminent ana
lytic power, Mr. Herbert Spencer's Principles of Psychology.

On this point M. Cousin may again be cited in favour of the better doctrine.
M. Cousin recognises, in opposition to Reid, the essential subjectivity of our
conceptions of what are called the primary qualities of matter, as extension,
solidity, &c., equally with those of colour, heat, and the remainder of the so-
called secondary qualities. — Cours, ut supra, 9me lecon.

f This doctrine, which is the most complete form of the philosophical theory
known as the Relativity of Human Knowledge, has, since the recent revival in

THINGS DENOTED BY NAMES. 67

§ 8. Body having now been defined the external cause,
and (according to the more reasonable opinion) the unknown
external cause, to which we refer our sensations ; it remains
to frame a definition of Mind. Nor, after the preceding ob
servations, 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 understood to be the mysterious
something which excites the mind to feel, so mind is the
mysterious something which feels and thinks. It is unnecessary
to give in the case of mind, as we gave in the case of matter,

this country of an active interest in metaphysical speculation, been the subject
of a greatly increased amount of discussion and controversy ; and dissentients
have manifested themselves in considerably greater 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
Terrier, in his Institutes of Metaphysic, and Professor John Grote in his Explo-
ratio 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 ia Professor
Grote's case at least, the denial of Noumena is only apparent, and that he does
not essentially differ from the other class of objectors, including Mr. Bailey in
his valuable Letters on the Philosophy of the Human Mind, and (in spice of
the striking passage quoted in the text) also Sir William Hamilton, who con
tend for a direct knowledge by the human mind of more than the sensations—
of certain attributes or properties as they exist not in us, but in the Things
themselves.

With the first of these opinions, that which denies Noumena, I have, as a
metaphysician, no quarrel ; but, whether it be true or false, it is irrelevant to
Logic. And since all the forms of language are in contradiction to it, nothing
but confusion could result from its unnecessary introduction into a treatise,
every essential doctrine 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, considered as distinct
from the sensations we receive from it, is of far greater practical moment. But
even this question, depending on the nature and laws of Intuitive Knowledge, is
not within the province of Logic. For the grounds of my own opinion con-
cerning 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.

0 — 2

68 NAMES AND PROPOSITIONS.

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 Mr. James
Mill) a certain " thread of consciousness ;" a series of feelings,
that is, of sensations, thoughts, emotions, and volitions, more
or less numerous and complicated. There is a 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 conceive 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 sensa
tions 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 feelings 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 anything 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 capa
cities, as yet unknown to me, of feeling, thinking, or willing.

Thus, then, as body is the unsentient cause to which we
are naturally prompted to refer a certain portion of our feel
ings, 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 experiences, we do not, according to the best existing
doctrine, know anything ; 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

THINGS DENOTED BY NAMES. 69

our subject, and pass to the third and only remaining class or
division of Nameable Things.

III. ATTRIBUTES: AND, FIRST, QOALITIES.

§ 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 pro
perties 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 ourselves
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 white
ness. When we ascribe whiteness to any substance, as, for
instance, snow ; when we say that snow has the quality white
ness, what do we really assert ? Simply, that when snow is
present to our organs, we have a particular sensation, which
we are accustomed to call the sensation of white. But how do
I know that snow is present ? Obviously 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 com
posing 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 sen
sations they excite in us ; that the fact of our receiving from
snow the particular sensation which is called a sensation of

70 NAMES AND PROPOSITIONS.

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 exist
ence of another thing, it does not follow that the two are one
and the same. The attribute whiteness (it may be said) is not

j the fact of receiving the sensation, but something in the
object itself; a poiver inherent in it; something in ikrfole of

I 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 produces 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 discussion of the
subject belongs to the other department of scientific inquiry,
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 disposition, wherever we meet
with two names which are not precisely synonymous, to sup
pose that they must be the names of two different things;
whereas in reality they may be names of the same thing viewed
in two different lights, or under different suppositions as to
surrounding circumstances. 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 impression 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 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 scholastic doctrine of occult

THINGS DENOTED BY NAMES. 71

causes ; the very absurdity which Moliere so happily ridiculed
when he made one of his pedantic physicians account for the
fact that " 1'opium endormit," by the maxim " parcequ'il a une
vertu soporifique."

It is evident that when the physician stated that opium
had " une vertu soporifique," he did not account for, but merely
asserted over again, the fact that it endormit. 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 sen
sation 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 constitution of things. And to this we must at last
come, even after interpolating the imaginary entity. Whatever
number of links the chain of causes and effects may consist of,
how any one link produces the one which is next to it, remains
equally inexplicable to us. It is as easy to comprehend that
the object should produce the sensation directly and at once,
as that it should produce the same sensation by the aid of
something else called the power of producing 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 quali
ties. 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

NAMES AND FMOPOS . 7 ; N -

- ±-;: -:: v.

thejhamUfiiMi of the quality whiteness. For logical
s the sensation is the only essential part of what is

y the word ; the only part which we ever can be con-

n proving. When that is proved, the quality is proved ;

.•:•! excites a sensation, it has, of course, the ower of

F\". RELATTOXS.

JO. Tbe qvatitif* of a body, we bave said, are the

« grounded on tbe sensations which tbe presence of
" : '. '. r :•. : : j : - :—•..::.: . ".? T :

whesn we ascribe to any object tbe kind of attribute called a
: - :bf : : : : : : . -; itir.: ..:: :. ..-: :•: ?. •„-.:'.-. j

in wbich other objects are concerned besides itself and the

As there may with propriety be said to be a relation be

tween any two things t.o which two correlative names are or
may be riven, we may expect to discover what constirut<es a
relation in general, if we enumerate the principal cases in which
mankind bave imposed correlative names, and observe what
these cases have in common.

What, then, is tbe character whk-h is possessed in common
bv states of circumstances so heterogeneous and discordant as

after, along mrth another : one tl
than another: one thin? the c.av*c o:

i -. 1 : : : v

THINGS DE.VOTED BY NAMES. 73

related to each other, both enter as parties concerned. This
fact, or phenomenon, is what the Aristotelian logicians called
the fundamtntum relatitmii. Thus in the relation of greater
and less between two magnitudes, the fundamtntum relatvmig
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 relaticmi* 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 indefinitely multiplied; but it is already obvious
that whenever two things axe said to be related, there is some
fact, or series of facts, into which they both enter ; and that
whenerer any two things are involved in some one fact, or
series of facts, we may ascribe to those two things a mutual
relation grounded OB the fact. Even if they have nothing in
common but what is common to all things, that thev are
members of the universe, we call that a relation, and deno
minate them fellow-creatures, fellow-beings, or fellow-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 relation grounded
upon it. And there are as many conceivable relations as there
are conceivable kinds of fact in which two things can bejointlv
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 relation 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 «n4
creditor, principal and agent, guardian and ward, the funda-
mentum relations consists entirely of thoughts, feelings, and
volitions (actual or contingent), either of the persons them
selves or of other persons concerned in the same series of trans
actions ; as, for instance, the intentions which would be formed

74 NAMES AND PROPOSITIONS.

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, occa
sioned 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 consciousness ; 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.
Cases 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 preceded 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
phenomenon at all. Unless, indeed, we choose to call the suc
cession of the two objects a third thing ; but their succession
is not something added to the things themselves ; it is some
thing involved in them. Dawn and sunrise announce them
selves to our consciousness by two successive sensations. Our
consciousness of the succession of these sensations is not a third
sensation 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 having them either successively, or else
simultaneously. Sensations, or other feelings, being given,
succession and simultaneousness are the two conditions, 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.

§ 11. In a somewhat similar position are two other sorts
of relations, Likeness and Unlikeuess. I have two sensations ;

THINGS DENOTED BY NAMES. 75

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 constituting the fundamentum of this
relation ? The two sensations first, and then what we call a
feeling of resemblance, or of want of resemblance. Let us
confine ourselves to the former case. Kesemblance is evidently
a feeling ; a state of the consciousness of the observer. Whether
the feeling of the resemblance of the two colours be a third
state of consciousness, which I have after having the two sen
sations of colour, or whether (like the feeling of their succes
sion) it is involved in the sensations themselves, may be a
matter of discussion. But in either case, these feelings of
resemblance, and of its opposite dissimilarity, 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 unlikeness, 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 conscious
ness, but on states which are peculiar, unresolvable, and
inexplicable.

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 compounded of like
nesses between the various parts respectively, and of likeness
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 likenesses must the general or complex likeness be
compounded : likeness in a succession of bodily postures ;
likeness 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.

76

NAMES AND PROPOSITIONS.

All likeness and unlikeness of which we have any cogni
zance, resolve themselves into likeness and unlikeness between
states of our own, or some other, mind. When we say that
one hody is like another, (since we know nothing of bodies but
the sensations 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 feeling
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, resem
bles the relation in which Philip stood to Alexander ; resembles
it so closely that they are called the same relation. The rela
tion in which Cromwell stood to England resembles the rela
tion 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 fundamentum 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 produces 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 relation of a fertile soil to a seed
contained in it, there exists a resemblance : the real resem
blance being in the two fundamenta relationis, in each
of which there occurs a germ, producing by its develop
ment a multitude of other things similar to itself. And
as, whenever two objects are jointly concerned in a pheno
menon, this constitutes a relation between those objects,
so, if we suppose a second pair of objects concerned in a
second phenomenon, the slightest resemblance between the

THINGS DENOTED BY NAMES. 77

two phenomena is sufficient 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 resemblance, 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 undis-
tinguishableness, 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
instance, are the same, because they are so much alike that
one might be mistaken for the other : but we constantly use
this mode of expression when speaking of feelings ; 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
application 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 ambiguity we say, that two persons are ill of the
same disease ; that two persons hold the same office ; 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 under
standings, by not being sufficiently alive to the fact (in itself
not always to be avoided), that they use the same name to
express ideas so different as those of identity and undis-
tinguishable resemblance. Among modern writers, Arch
bishop Whately stands almost alone in having drawn atten
tion to this distinction, and to- the ambiguity connected
with it.

Several relations, generally called by other names, are really

78 NAMES AND PROPOSITIONS.

cases of resemblance. As, for example, equality ; which is
but another word for the exact resemblance commonly called
identity, considered as subsisting between 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. QUANTITY.

§ 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 presence known to us by a set of sensations
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
different 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 sensations
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 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 sensations I receive from the gallon of
water, and those I receive from the gallon of wine, are not
the same, that is, not precisely alike ; neither are they alto
gether unlike: they are partly similar, partly dissimilar;
and that in which they resemble is precisely 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

THINGS DENOTED BY NAMES. 79

likeness and unlikeness 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 sensa
tions 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. Everybody
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 difference, 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.

VI. ATTRIBUTES CONCLUDED.

§ J 3. Thus, then, all the attributes of bodies which are
classed under Quality or Quantity, are grounded on the
sensations which we receive from those bodies, and may be
defined, the powers which the bodies have of exciting those
sensations. And the same general explanation has been found
to apply to most of the attributes usually classed under the
head of Kelation. 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 con
sciousness by which it makes itself known; and the relation
being simply the power or capacity which the object possesses
of taking part along with the correlated object in the produc
tion of that series of sensations or states of consciousness.
We have been obliged, indeed, to recognise a somewhat
different character in certain peculiar relations, those of sue-

80 NAMES AND PROPOSITIONS.

cession and simultaneity, of likeness and unlikeness. 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 rela
tions, grounded on states of consciousness, are themselves
states of consciousness : resemblance is nothing but our feeling
of resemblance ; succession is nothing but our feeling of suc
cession. 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 confined to those which subsist between
sensations, or other states of consciousness ; for, though we
ascribe resemblance, or succession, or simultaneity, to objects
and to attributes, it is always in virtue of resemblance or suc
cession or simultaneity in the sensations or states of con
sciousness 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 mind,, we have to consider its own states, as
well as those which it produces in other minds. Every attri
bute of a mind consists either in being itself affected in a
certain way, or affecting other minds in a certain way. Con
sidered 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 attributes 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

THINGS DENOTED BY NAMES. 81

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 ex
pressive 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 contemplation 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 sem
blance of a single attribute, two are really predicated : one of
them, a state of the mind itself; the other, a state with which
other minds are affected by thinking of it. As when we sav
of any one that he is generous. The word generosity 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 following purport : Certain feelings form
habitually a part of this person's sentient existence ; and the
idea of those feelings of his, excites the sentiment of approba
tion 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.

VII. GENERAL RESULTS.

§ 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 themselves made the subject of predications — is now con
cluded.

Our enumeration commenced with Feelings. These we
scrupulously distinguished from the objects which excite them,
and from the organs by which they are, or may be supposed
VOL. i. 6

82 NAMES AND PROPOSITION'S.

to be, conveyed. Feelings are of four sorts: Sensations,
Thoughts, Emotions, and Volitions,. What are called Per
ceptions are merely a particular case of Belief, and belief is a
kind of thought. Actions are merely volitions followed by an
effect. If there be any other kind of mental state not included
under these subdivisions, we did not think it necessary or
proper in this place to discuss its existence, or the rank which
ought to be assigned to it.

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 concerning
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 recipient.

The only remaining class of Nameable Things is Attributes;
and these are of three kinds, Quality, Kelation, and Quantity.
Qualities, like substances, are known to us no otherwise than
by the sensations or other states of consciousness which they
excite : and while, in compliance with common 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
anything 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. Kelations, 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 manifestly 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

THINGS DENOTED BY NAMES. 83

inextricably 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 he classed among states of con
sciousness, 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.

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

Jst. Feelings, or States of Consciousness.
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 last 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 philosophy.

4th, and last. The Successions and Co-existences, the
Likenesses and Unlikenesses, between feelings or states of
consciousness. Those relations, when considered as sub
sisting between 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 suggested, may serve as a sub
stitute for the abortive Classification of Existences, termed
the Categories of Aristotle. The practical application of it
will appear when we commence the inquiry into the Import of
Propositions; in other words, when we inquire 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 cor
rect, 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.

6— 2

84 NAMES AND PROPOSITIONS.

For distinction's sake, every fact which is solely composed
of feelings 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
different 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 corresponding subjective one ;
and has no meaning to us, (apart from the subjective fact
which corresponds to it,) except as a name for the unknown
and inscrutable process by which that subjective or psycho
logical fact is brought to pass.

CHAPTER IV.

OF PROPOSITIONS.

§ 1. 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 tbat analysis of tbe 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 affirmed or denied of a subject. A
predicate and a subject are all that is necessarily required to
make up a proposition : but as we cannot conclude from merely
seeing two names put together, that they are a predicate 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 dis
course. This is sometimes done by a slight alteration of one
of the words, called an inflection ; as when we say, Fire
burns ; the change of the second word from burn to burns
showing that we mean to affirm the predicate burn of the sub
ject fire. But this function is more commonly 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 predication 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 respect
ing 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

86 NAMES AND PROPOSITIONS.

than a mere sign of predication; that it also signifies existence.
In the proposition, 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, how
ever, only shows that there is an ambiguity in the word is ; a
word which not only performs the function of the copula in
affirmations, but has also a meaning of its own, in virtue of
which it may itself be made the predicate of a proposition.
That the employment of it as a copula does not necessarily
include the affirmation of existence, appears from such a pro
position 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 specula
tions concerning the nature of Being, (TO ov, ovcria, Ens, Enti-
tas, Essentia, and the like) which have arisen from overlook
ing this double meaning of the word to be ; from supposing
that when it signifies to exist, and when it signifies to be some
specified thing, as to be a- man, to be Socrates, to be seen or
spoken of, to be a phantom, even to be 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
which 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 Ari
stotle 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 exertions
far greater effects than Milo of Crotona could, but he is not
therefore 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 ambi
guities of words, by finding that the same word in one laD-

PROPOSITIONS. 87

guage corresponds, on different 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 unpro-
fitably (as was frequently done by the two philosophers 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 ambi
guity, and pointed out how many errors in the received systems
of philosophy it has had to answer for. It has indeed misled
the moderns scarcely less than the ancients, though their
mistakes, because our understandings are not yet so com
pletely 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 express those distinctions.

§ 2. A proposition being a portion of discourse in which
something is affirmed or denied of something, the first divi
sion of propositions is into affirmative and negative. An
affirmative proposition is that in which the predicate is
affirmed of the subject ; as, Csesar is dead. A negative pro
position is that in which the predicate is.denied of the subject ;
as, Ceesar 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 affirmation.

Some logicians, among whom may be mentioned Hobbes,

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

88 NAMES AND PROPOSITIONS.

state this distinction differently ; they recognise only one form
of copula, is, and attach the negative sign to the predicate.
" Ca&sar is dead," and " Caesar is not dead," according to these
writers, are propositions agreeing not in the suhject and pre
dicate, but in the subject only. They do not consider " dead,"
but " not dead," to be the predicate of the second proposi
tion, and they accordingly define a negative proposition to
be one in which the predicate is a negative name. The point,
though not of much practical moment, deserves notice as
an example (not unfrequent 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 distinc
tion 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 attribute. So that when we affirm a negative
name, what we are really predicating 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 distinc
tion is between a fact and the non-existence of that fact ;
between seeing something and not seeing it, between Cesar'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 simplifi
cation : 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
together, and to put them or keep them asunder, will
remain different operations, whatever tricks we may play with
language.

A remark of a similar nature may be applied to most of
those distinctions among propositions which are said to have
reference to their modality ; as, difference of tense or time ;
the sun did rise, the sun is rising, the sun ivill rise. These

PROPOSITIONS. 89

differences, like that between affirmation and negation, might
be glossed over by considering 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 hereafter. But the simplification would be merely
verbal. Past, present, and future, do not constitute so many
different kinds of rising; they are designations belonging 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. That which we affirm to be past, present,
or future, is not what the subject signifies, nor what the pre
dicate signifies, but specifically and expressly what the pre
dication signifies ; what is expressed only by the proposition
as such, and not by either or both of the terms. Therefore
the circumstance of time is properly considered 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 ; Csesar is perhaps dead ; it is
possible that Csesar is dead ; it is only because these fall alto
gether 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 " Csesar may be dead" means " I am not sure that Csesar
is alive."

§ 3. The next division of propositions is into Simple
and Complex. A simple proposition is that in which one
predicate is affirmed or denied of one subject. A complex
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 distinction 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 propo
sition is often not a proposition at all, but several proposi
tions, held together by a conjunction. Such, for example, is
this : Csesar is dead, and Brutus is alive : or even this, Csesar
is dead, but Brutus is alive. There are here two distinct

90 NAMES AND PROPOSITIONS,

assertions ; and we might as well call a street a complex
house, as these two propositions a complex proposition. It
is true that the syncategorematic words and and but have 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 abbreviations, and generally abbreviations of
propositions ; a kind of short-hand, whereby something which,
to be expressed fully, would have required a proposition or
a series of propositions, is suggested to the mind at once.
Thus the words, Caesar is dead and Brutus is alive, are
equivalent to these : Cffisar is dead ; Brutus is alive ; it is
desired that the two preceding propositions should be thought
of together. If the words were, Csesar is dead but Brutus is
alive, the sense would be equivalent to the same three pro
positions together with a fourth ; " between the two preceding
propositions there exists a contrast :" viz. either between the
two facts themselves, or between the feelings with which it is
desired that they should be regarded.

In the instances cited the two propositions are kept visibly
distinct, each subject having its separate predicate, and each
predicate its separate subject. For brevity, however, and to
avoid repetition, the propositions are often blended together :
as in this, " Peter and James preached at Jerusalem 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 proposition at all, but a plurality of propositions ; since
what it expresses is not a single assertion, but several asser
tions, which, if true when joined, are true also when separated.
But there is a kind of proposition which, though it contains
a plurality of subjects and of predicates, and may be said in
one sense of the word to consist of several propositions, con
tains but one assertion; and its truth does not at all imply
that of the simple propositions which compose it. An
example of this is, when the simple propositions are con-

PROPOSITIONS. 91

nected 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 hypothetical was originally common to both. As has
been well remarked by Archbishop Whately and others, the
disjunctive form is resolvable into the conditional; every dis
junctive proposition being equivalent to two or more con
ditional 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." All hypothetical
propositions, therefore, though disjunctive in form, are con
ditional in meaning; and the words hypothetical and condi
tional may be, as indeed they generally are, used synony
mously. Propositions in which the assertion is not dependent
on a condition, are said, in the language of logicians, to be
categorical.

An hypothetical proposition is not, like the pretended com
plex propositions which we previously considered, a mere
aggregation of simple propositions. 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 intend 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
hypothetical 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 proposi
tion ? "The Koran" is not the subject of it, nor is "Maho
met:" 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 proposition are names
of propositions. The subject 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

NAMES AND PROPOSITIONS.

is here afforded of the remark, that particles are abbrevia
tions ; since " If A. is B, C is D," is found to be an abbre
viation of the following : " The proposition C is D, is a legiti
mate inference from the proposition A is B."

The distinction, therefore, between hypothetical and cate
gorical propositions, is not so great as it at first appears. In
the conditional, as well as in the categorical form, one predi
cate is affirmed of one subject, and no more : but a conditional
proposition is a proposition concerning a proposition ; the
subject of the assertion is itself an assertion. Nor is this a
property peculiar to hypothetical propositions. 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 pro
position, 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 Kevolution : 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 different predicates are affirmed of, is the
proposition, "the whole is greater than its part;" the proposi
tion, "the Holy Ghost proceeds from the Father alone;" the
proposition, " kings have a 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 we did not remember
that what they predicate of a proposition, namely, its being
an inference from something else, is precisely that one of its
attributes with which most of all a logician is concerned.

PROPOSITIONS. 93

§ 4. The next of the common divisions of Propositions is
into Universal, Particular, Indefinite, and Singular : a distinc
tion 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 :

All men are mortal — Universal.

Some men are mortal — Particular.

Man is mortal — Indefinite.

Julius Caesar is mortal — Singular.

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

When the name which is the subject 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 subject, 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 proposition, since the predicate, immortal, is denied
of each and every individual denoted by the term man ; the
negative proposition being exactly equivalent to the following,
Every man is not-immortal. But " some men are wise,"
" some men are not wise," are particular propositions ; the
predicate wise 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
individuals, without specifying what portion ; for if this were
specified, the proposition would be changed either into a sin
gular proposition, or into an universal proposition with a dif
ferent subject; as, for instance, " all properly instructed men
are wise." There are other forms of particular propositions ;
as, " Most men are imperfectly educated :" it being immaterial
how large a portion of the subject the predicate is asserted of,
as long as it is left uncertain how that portion is to be distin
guished from the rest.

NAMES AND PROPOSITIONS.

When the form of the expression does not clearly show
whether the general name which is the subject of the proposi
tion is meant to stand for all the individuals denoted hy 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 gender. The speaker must mean to assert the propo
sition either as an universal or as a particular proposition,
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 indicative of universality is commonly
omitted, only because the meaning is evident without it. In
the proposition, " Wine is good," it is understood with equal
readiness, though for somewhat different reasons, that the
assertion is not intended to be universal, but particular.*

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 distributed, or taken distributively.
Thus, in the proposition, All men are mortal, the subject, Man,
is distributed, because mortality is affirmed of each and every
man. The predicate, Mortal, is not distributed, because the
only mortals who are spoken of in the proposition are those
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 predicate and the subject are undistributed.
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.

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

PROPOSITIONS. 95

This phraseology, which is of great service in stating and
demonstrating the rules of the syllogism, enables us to express
very concisely the definitions of an universal and a particular
proposition. An universal proposition is that of which the
suhject is distributed ; a particular proposition is that of which
the subject is undistributed.

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

CHAPTER V.

OF THE IMPORT OF PROPOSITIONS.

§ 1. 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 recog
nises 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. 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 im
portant 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, German, 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 indis
criminately, 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:

IMPORT OF PROPOSITIONS. 97

and the whole doctrine of Propositions, together with the
theory of Reasoning, (always necessarily founded on the theory
of Propositions,) was stated as if Ideas, or Conceptions, or
whatever other terra the writer preferred as a name for mental
representations generally, constituted essentially the subject
matter and suhstance 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 together 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 apostle 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 intricate of
metaphysical problems. But whatever the solution may be,
we may venture to assert that it can have nothing whatever
to do with the import of propositions; for this reason, that
propositions (except sometimes when the mind itself is the
subject treated of) are not assertions respecting 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 re
ference 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 believe, is a fact relating to the outward
thing, gold, and to the impression 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
VOL. i. 7

98 NAMES AND PROPOSITIONS.

ground unless I have the idea of the ground, and of a spade,
and of all the other things I am operating upon, and unless I
put those ideas together.* But it would be a 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 manner, believing is an act which has for its subject
the facts 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 enter
tained 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 proposition, 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 intro
duced into the philosophy of Logic ; and the principal cause
why the theory of the science has made such 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 extraor
dinary abilities and attainments, almost always tacitly imply a
theory that the investigation of truth consists in contemplating

* Dr. Whewell (Philosophy 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 apprehen
sion may or may not accompany his instinctive actions. But 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.

IMPORT OP PROPOSITION'S. 99

and handling our ideas, or conceptions of things, instead of
the things themselves : a doctrine tantamount to the assertion,
that the only mode of acquiring knowledge of nature is to
study it at second hand, as represented in our own minds.
Meanwhile, inquiries into every kind of natural phenomena
were incessantly establishing great and fruitful truths on most
important subjects, by processes upon which these views of the
nature of Judgment and Seasoning threw no light, and in
which they afforded no assistance whatever. No wonder that
those who knew by practical experience how truths are
arrived at, should deem a science futile, which consisted chiefly
of such speculations. What has been done for the advance
ment of Logic since these doctrines came into vogue, has
been done not by professed logicians, but by discoverers in
the other sciences; in whose methods of investigation many
principles of logic, not previously thought of, have suc
cessively come forth into light, but who have generally com
mitted the error of supposing that nothing whatever was known
of the .art of philosophizing by the old logicians, because
their modern 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 Pro
position, and the conformity of which to fact constitutes the
truth of the proposition ?

§ 2. One of the clearest and most consecutive thinkers
whom this country or the world has produced, I mean Hobbes,
has given the following answer to this question. In every
proposition (says he) wjiat is signified is, the belief of the
speaker that the predicate is a name of the same thing of which
the_sjibjec^j^jijianie ; ancTiFit really is so7 the proposition is
true. Thus the proposition, All men are living beings (he

7—2

TOO NAMES AND PROPOSITIONS.

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 not 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 he 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 significa
tion, 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 pro
position : and his analysis has consequently one of the requi
sites 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 th» meaning of propo
sitions, is part of the meaning of all propositions, and the whole
meaning of some. This, however, only shows what an ex
tremely minute fragment of meaning it is quite possible to
include within the logical formula of a proposition. It does
not show that no proposition means more. To warrant 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 mean
ing necessarily implied in the form of discourse called a Pro
position, why do I object to it as the scientific definition of
what a proposition means ? Because, though the mere collo
cation which makes the proposition a proposition, conveys no
more than this scanty amount of meaning, that same collo-

IMPORT OF PROPOSITIONS. 101

cation combined with other circumstances, that form combined
with other matter, does convey more, and much more.

The only propositions of which Hobbes' principle is a suffi
cient account, are that limited and unimportant class in which
both the predicate 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 proper name is predicated of another proper name, all
the signification conveyed is, that both the names are marks
for the same object. But this is precisely what Hobbes pro
duces as a theory of predication in general. His doctrine is a
full explanation of such predications as these: Hyde was
Clarendon, or, Tully is Cicero. It exhausts the meaning of
those propositions. 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 indi
viduals ; 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 class of abstract
names which are not connotative, resides in the connotation.
\\ hen, therefore, we are analysing the meaning of any pro
position in which the predicate and the subject, or either
of them, are counotative 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 remarkable that
so powerful a thinker should not have asked himself the ques-

102 NAMES AND PROPOSITIONS.

tion, But how came they to he 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 happen 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
connotes a certain attribute or attributes ; and when we say,
All men are mortal, the meaning of the proposition 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 consequence, 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 attri
butes 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. Conuotative
names do not precede, but follow, the attributes which they
connote. If one attribute happens to be always found in con
junction 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 concur
rent application of the two names, is a mere consequence 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

IMPORT OF PROPOSITIONS. 103

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 attribute of com
bustibility existed in the diamonds upon which the experi
ment 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 connotes. 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 signifi
cation of names, but of laws of nature ; the order existing
among phenomena.

§ 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 iden
tical 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 generally received notion of Predication
decidedly is that it consists in referring 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 included in the class mortal. " Plato is a philosopher,"
asserts that the individual Plato is one of those who compose
the class philosopher. 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 propo
sition, 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 Predication and
the theory of Hobbes. For a class is absolutely nothing but
an indefinite number of individuals denoted by a general

104 NAMES AND PROPOSITIONS.

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 he 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 predication have prevailed, is
evident from this, that they are the basis of .th.e._ce]ebrated
dictum de omni et nullo. 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 class ;
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 logi
cians, 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
class.

This theory appears to me a signal example of a logical
error very often committed in logic, that of vartpov Trporlpov,
or explaining a thing by something which presupposes it.
When I say that snow is white, I may and ought to be think
ing 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 judg
ments, 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 classifi
cation.

There is a sort of language very generally prevalent in
these discussions, which seems to suppose that classification
is an arrangement and grouping of definite and known indi-

IMPORT OF PROPOSITIONS. 105

viduals : that when names were imposed, mankind took into
consideration all the individual objects in the universe, distri
buted 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 lan
guage consists ; which having been once done, if a question
subsequently 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 explanations 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 composed ; 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 meaning, is by being
a name of an indefinite variety of things; namely, of all
things, known or unknown, past, present, or future, which
possess certain definite attributes. When, by studying not
the meaning of words, but the phenomena of nature, we dis
cover that these attributes are possessed 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

106 NAMES AND PROPOSITIONS.

place the individual in the class because the proposition is
true; the proposition is not true because the object is 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 understanding which have truth for their object, to pro
cesses of mere classification 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 revolution
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, accord
ing to the well-known remark of Leibnitz, and the avowal of
Hobbes himself,* renders truth and falsity completely arbi
trary, 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
distinction 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 unacquaintance with their other specula
tions. But this shows how little hold their doctrine possessed
over their own minds. No person, at bottom, ever imagined
that there was nothing more in truth than propriety of expres
sion; than using language in conformity to a previous conven
tion. 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 ignorance of the meaning of

* "From hence also this may be deduced, that the first truths were arbi
trarily 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, that it pleased men to impose both these
names on the same thing." — Computation or Logic, ch. iii. sect. 8.

IMPORT OF PROPOSITIONS. 107

words, but that in others the source of the error is a misappre
hension of things ; that a person who has not the use of lan
guage 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, b,ut only
error. And he has himself laid down, in other places, 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 attributes. " 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 acci
dents."^ 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

" Men are subject to err not only in affirming and denying, but also in
perception, and in silent cogitation. . . Tacit errors, or the errors -of sense and
cogitation, are made by passing from one imagination to the imagination of
another different 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 the sun itself to be there ; or by seeing swords, that there has been,
or shall be, fighting, because 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 common to all things that have sense." — Computa
tion or Logic, ch. v. sect. 1.

f Ch. iii. sect. 3.

NAMES AND PROPOSITIONS.

word white connotes an attribute which is possessed by the
individual object designated by the words "summit of Chim-
borazo ;" which attribute consists in the physical fact, of its
exciting in human beings the sensation which we call a sensa
tion of white. It will be admitted that, by asserting the pro
position, we wish to communicate information of that physical
fact, and are not thinking of the names, except as the neces
sary means of making that communication. The meaning of /
I the proposition, therefore, is, that the individual thing denoted/
by the subject, has the attributes connoted by the predicate. V,

If we now suppose the subject also to be a connotative
name, the meaning expressed by the proposition has advanced
a step farther in complication. 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 belief of) is, of course, that the objects
denoted by the subject (man) possess the attributes connoted
by the predicate (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 proposition 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 number 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 subject, has also
those connoted by the predicate ; that the latter set of attri
butes constantly 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, (connotation) : and that conse-

IMPORT OF PROPOSITIONS. 109

If it be remembered tbat 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 forming part of, the fact or
phenomenon upon which the attribute is grounded; we may
add one more step to complete the analysis. The proposition
which asserts that one attribute always accompanies another \
attribute, really asserts thereby no other thing than this, that
one phenomenon always accompanies another phenomenon ;
insomuch that where we find the one, we have assurance of
the existence of the other. 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 exhibit, and which are partly
physical phenomena, namely the impressions made on our
senses by their bodily form and structure, and partly mental
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 physical 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 precise time
undecided.

quently coexistence of attributes does not, any more than the opposite theory
of equation of groups, correspond with the living processes of thought and
language." I acknowledge the distinction here drawn, which, indeed, I had
myself laid down and exemplified a few pages back (p. 104). But though it is
true that we naturally "construe the subject of a proposition in its extension,"
this extension, or in other words, the extent of the class denoted by the name,
is not apprehended or indicated directly. It is both apprehended and indi
cated solely through the attributes. In the " living processes of thought and
language " the extension, though in this case really thought of (which in the
case of the predicate it is not), is thought of only through the medium of what
my acute and courteous critic terms the "intension."

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

110 NAMES AND PROPOSITIONS.

§ 5. We have already proceeded far enough, not only to
demonstrate the error of Hobhes, hut to ascertain the real
import of hy 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 commencement 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 Phenomena, in other words, two
states of consciousness ; and what it is which the proposition
affirms (or denies) to subsist between them, namely either suc
cession 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 par
ticulars of his conduct : both are phenomena : the former are
facts of internal consciousness ; the latter, so far as distinct
from the former, are physical 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 occasion 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 consciousness, accompanied or followed by physical
facts. When we say, A generous person is worthy of honour,
we affirm co-existence between the two complicated pheno
mena connoted by the two terms respectively. We atfirm,
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 feeling,
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

IMPORT OF PROPOSITIONS. 1H

of propositions. When there is any obscurity, or difficulty,
it does not lie in the meaning of the proposition, but in the
meaning of the names which compose it ; in the extremely com
plicated connotation of many words ; the immense multitude
and prolonged series of facts which often constitute the
phenomenon connoted by a name. But where it is seen
what the phenomenon 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 phenomenon to another: their con
junction, in short, so that where the one is found, we may
calculate on finding both.

This, however, though the most common, is not the only
meaning which propositions are ever intended to convey. la
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 conscious of, phenomena ; and the same being true,
mutatis mutandis, of attributes ; no assertion can be made, at
least with a meaning, concerning these unknown and un
knowable entities, except in virtue of the Phenomena by
which alone they manifest themselves to our faculties. When
we say, Socrates was cotemporary with the Peloponuesian war,
the foundation of this assertion, as of all assertions concern
ing substances, is an assertion concerning the phenomena
which they exhibit, — namely, that the series of facts by which
Socrates manifested himself to mankind, and the series of
mental states which constituted his sentient existence, went
on simultaneously with the series of facts known by the name
of the Peloponnesian war. Still, the proposition does not
assert that alone; it asserts that the Thing in itself, the
noumenon 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 be
tween phenomena, but between noumena, or between a noume
non and phenomena. And both of uoumena and of phenomena

112 NAMES AND PROPOSITIONS.

we may affirm simple existence. But what is a noumenon ?
An unknown cause. In affirming, therefore, the existence of a
noumepon, we affirm causation. Here, therefore, are two addi
tional kinds of fact, capable of being asserted in a proposition.
"Besides the propositions which assert Sequence or Coexistence,
there are some which assert simple Existence ; and others assert
Causation, which, subject to the explanations which will follow
in the Third Book, must be considered provisionally as a dis
tinct and peculiar kind of assertion.

§ 6. To these four kinds of matter-of-fact or assertion,
must be added a fifth, Kesemblance. 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 affirmation 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 encumbering ourselves,
especially in this place, with a generalization which may be
looked upon as strained. Logic does not undertake to analyse
mental facts into their ultimate elements. Resemblance be
tween 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 propositions whatever, of which
the predicate is a general name, do, in point of fact, affirm or
deny resemblance. All such propositions affirm that a thing
belongs to a class ; but things being classed together accord
ing to their resemblance, everything is of course classed with
the tbings which it is supposed to resemble most ; and thence,
it may be said, when we affirm that Gold is a metal, or that

IMPORT OF PROPOSITIONS. 113

Socrates is a man, the affirmation intended is, that gold re
sembles 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 man, is
grounded indeed on a resemblance among the things which
are placed in the same class, but not on a mere general resem
blance: the resemblance it is grounded on consists in the
possession by all those things, of certain common peculiari
ties ; and those peculiarities it is which the terms connote, and
which the propositions consequently assert; not the resem
blance : for though when I say, Gold is a metal, I say by im
plication 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 implied 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 pos
sess the attributes constituting the class, are so far from assert
ing nothing but resemblance, that they do not, properly speak
ing, assert resemblance at all.

But we remarked some time ago (and the reasons of the
remark will be more fully entered into in a subsequent Book*)
that there is sometimes 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 characteristic
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 animals

* Book iv. ch. vii.
VOL. I. tf

114 NAMES AND PROPOSITIONS.

has a few anomalous genera or species 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 affirm, 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 differ
ence 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 significant.

There is still another exceptional case, in which, though
the predicate is the name of a class, yet in predicating it we
affirm nothing but resemblance, the class being founded not
on resemblance in any given particular, but on general unana
lysable resemblance. The classes in question are those into
which our simple sensations, or other simple feelings, are
divided. Sensations of white, for instance, are classed toge
ther, 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, therefore, 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 affirm 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 con
crete general names, are connotative ; but they connote a
mere resemblance. When predicated of any individual feeling,

IMPORT OF PROPOSITIONS. 115

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, Coexistence, Sequence, Causation, Resemblance :
one or other of these is asserted (or denied) in every proposi
tion which is not merely verbal. This five-fold division is an
exhaustive classification of matters-of-fact ; of all things that
can be believed, or tendered for belief; of all questions that
can be propounded, and all answers that can be returned to
them. Instead of Coexistence and Sequence, we shall some
times say, for greater particularity, Order in Place, and Order
in Time: Order in Place being the specific mode of coex
istence, not necessary to be more particularly analysed here ;
while the mere fact of coexistence, or simultaneousness, may
be classed, together with Sequence, under the head of Order
in Time.

§ 7. %In the foregoing inquiry into the import of Propo
sitions, we have thought it necessary to analyse directly those
alone, in which the terms of the proposition (or the predicate
at least) are concrete terms. But, in doing so, we have indi
rectly analysed those in which the terms are abstract. The
distinction between an abstract term and its corresponding
concrete, does not turn upon any difference in what they are
appointed to signify ; for the real signification of a concrete

1 general name is, as we have so often said, its connotation;
and what the concrete term connotes, forms the entire mean
ing of the abstract name. Since there is nothing in the
import of an abstract name which is not in the import of the
corresponding 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 be framed of concrete terms.

And this presumption a closer examination will confirm.
An abstract name is the name of an attribute, or combination
of attributes. The corresponding concrete is a name given to

8—2

116 NAMES AND PROPOSITIONS.

things, because of, and in order to express, their possessing
that attribute, or that combination of attributes. When,
therefore, we predicate of anything 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 predi
cate is a concrete name, what is really predicated is one of
five things : Existence, Coexistence, Causation, Sequence, or
Resemblance. An attribute, therefore, is necessarily either
an existence, a coexistence, a causation, a sequence, or a
resemblance. When a proposition consists of a subject and
predicate which are abstract terms, it consists of terms which
must necessarily signify one or other of these things. When
we predicate of anything 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 Coexistence, or of Causation, or of
Sequence, or of Resemblance.

It is impossible to imagine any proposition 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 connote the attri
butes themselves, or the names of the fundamenta of those
attributes ; the facts or phenomena on which they are
grounded. To illustrate 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 sensations, the equivalent pro
positions 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 Resem
blance. In the following examples, the concrete terms are
those which directly correspond to the abstract names; con-

IMPORT OF PROPOSITIONS. 117

noting 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 equiva
lent to this — "All courageous persons deserve 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 sub
ject one of the examples given above to a minuter analysis.
The proposition we shall select is the following : — " Prudence
is a virtue." Let us substitute for the word virtue an equiva
lent but more definite expression, 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 consequent on, and caused by, prudence. Here is a
sequence ; but between what ? We understand the consequent
of the sequence, but we have yet to analyse the antecedent.
Prudence is an attribute; and, in connexion with it, two
things besides itself are to be considered ; prudent persons,
who are the subjects of the attribute, and prudential conduct,
which may 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 prudent per
sons? No; except in so far as they are prudent; for prudent
persons who are scoundrels can seldom on the whole be bene
ficial 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 pru
dence 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 prudential it is beneficial to society,
may yet, by reason of some other of its qualities, be productive
of an injury outweighing the benefit, and deserve a displeasure

118 NAMES AND PROPOSITION'S.

exceeding the approbation which would be due to the pru
dence. Neither the substance, therefore, (viz. the person,) nor
the phenomenon, (the conduct,) is an antecedent on which the
other terra of the sequence is universally consequent. But the
proposition, " Prudence is a virtue," is an universal proposi
tion. What is it, then, upon which the proposition affirms the
effects in question to be universally consequent ? Upon that
in the person, and in the conduct, which causes them to be
called prudent, 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 deliberate 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 attri
bute Prudence ; since wherever these states of mind exist we
may predicate prudence, even before we know whether any
conduct has followed. And in this manner every assertion
respecting an attribute, may be transformed into an assertion
exactly equivalent respecting the fact or phenomenon which
is the ground of the attribute. And no case "can be assigned,
where that which is predicated of the fact or phenomenon, does
not belong to one or other of the five species formerly enume
rated : it is either simple Existence, or it is some Sequence,
Coexistence, 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 necessary to apply the same
analysis to Particular affirmations and negations. " Some
birds are web-footed," affirms that, with the attributes con
noted by bird, the phenomenon web-feet is sometimes co-exis
tent : " Some birds are not web-footed," asserts that there are
other instances in which this coexistence does not have place.
Any further explanation of a thing which, if the previous ex
position has been assented to, is so obvious, may here be spared.

CHAPTER VI.

OF PROPOSITIONS MERELY VERBAL.

§ 1. As a preparation for the inquiry which is the proper
object of Logic, namely, in what manner propositions 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 investigation into the import of Propositions, we
examined the opinion of the Conceptualists, that a proposition
is the expression of a relation between two ideas; and the
doctrine of the Nominalists, that it is the expression of an
agreement or disagreement between 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 examined the different kinds of Proposi
tions, 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, Causation,
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 unknown source of a fact or phenomenon.

In distinguishing, however, the different kinds of matters
of fact asserted in propositions, we reserved one class of pro
positions, which do not relate to any matter of fact, in the
proper sense of the term, at all, but to the meaning 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

120 NAMES AND PROPOSITIONS.

the acceptation in which the 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 examining 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 conventionally assigned to the same individual,
there would be little to attract to such propositions the atten
tion of philosophers. But the class of merely verbal proposi
tions embraces not only much more than these, but much more
than any propositions which at first sight present themselves
as verbal ; comprehending a kind of assertions which have
been regarded not only as relating to things, but as having
actually a more intimate relation with them than any other
propositions whatever. The student in philosophy will per
ceive that I allude to the distinction 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 essential,
and what were called accidental, propositions, and between
essential and accidental properties or attributes.

§ 2. Almost all metaphysicians prior to Locke, as well as
many since his time, have made a great mystery of Essential
Predication, and of predicates 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 con
ceived to be. Thus, rationality was of the essence of man,
because without rationality, man could not be conceived to
exist. The different attributes which made up the essence of
the thing were called its essential properties ; and a proposition
in which any of these were predicated of it was called an
Essential Proposition, and was considered to go deeper into the
nature of the thing, and to convey more important information

VERBAL AND REAL PROPOSITIONS. 121

respecting it, than any other proposition could do. All pro
perties, 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 Pro
positions. A connexion may be traced between this distinc
tion, which originated with the schoolmen, and the well-known
dogmas of substantice secunda or general substances, and sub
stantial forms, doctrines which under varieties of language per
vaded alike the Aristotelian and the Platonic schools, and of
which more of the spirit has come down to modern times than
might be conjectured from the disuse of the phraseology.
The false views of the nature of classification and generaliza
tion which prevailed among the schoolmen, and of which these
dogmas were the technical expression, afford the only explana
tion which can be given of their having misunderstood the real
nature of those Essences which held so conspicuous a place in
their philosophy. They said, truly, that man cannot be con
ceived without 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 con
sequences of it. All therefore which is really true in the asser
tion that man cannot be conceived without rationality, is only,
that if he had not rationality, he would not be reputed a man.
There is no impossibility in conceiving the thing, nor, for
aught we know, in its existing : the impossibility is in the con
ventions of language, which will not allow the thing, even if
it exist, to be called by the name which is reserved for rational
beings. Rationality, in short, is involved in the meaning of the
word man : is one of the attributes connoted by the naoie. The
essence of man, simply means the whole of the attributes con
noted by 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 pro
perties to which mankind have chosen to attach that name, but

NAMES AND PROPOSITIONS.

by participation 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 attached to all general names, but only to some, they
thought that an object borrowed only a part of its properties
from an universal 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 phi
losophers that the supposed essences of classes were merely the
signification of their names ; nor, among the signal services
which his writings rendered to philosophy, was there one more
needful or more valuable.

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 object, 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 attributes, another name which
connotes only one of these attributes, or some smaller number
of them than all. In such cases, the universal affirmative pro
position will be true ; since whatever 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

* The doctrines which prevented the real meaning of Essences from being
understood, 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. Aristotle himself (in his Treatise on the Categories) ex
pressly denies that the dtvnpai ovffiat, or Substantial Secundse, inhere in a
subject. They are only, he says, predicated of it.

VERBAL AND REAL PROPOSITIONS. 123

includes all this : and that every man has the attributes con
noted hy 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 possessing the attributes con
noted by it ; and this implied assertion may convey informa
tion, even to those who understood the meaning of the name.
But 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 ex
istence is, after all, the result of an imperfection 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 word connoting
existence. The actual existence of the subject of the proposi
tion is therefore only apparently, not really, implied in the
predication, if an essential one : we may say, A ghost is a dis
embodied spirit, without believing in ghosts. But an accidental,
or non-essential, affirmation, does imply the real existence of
the subject, because in the case of a non-existent subject
there is nothing for the proposition to assert. Such a propo
sition as, The ghost of a murdered person haunts the couch of
the murderer, can only have a meaning if understood as im
plying 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 conse
quences 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
assumption of the real existence of the objects so named.
Apart from this assumption of real existence, the class of pro
positions in which the predicate is of the essence of the subject

124

NAMES AND PROPOSITIONS.

(that is, in which the predicate connotes the whole or part of
what the subject connotes, 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 useful, 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 connotative
word,) the whole of what it connotes. In defining a name,
however, 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 involved in the meaning of
the name, answers this purpose equally well. The various
kinds of definition which these distinctions give rise to, and
the purposes to which they are respectively subservient, will be
minutely considered in the proper place.

§ 3. According to the above view of essential propositions,
no proposition can be reckoned such which relates to an indi
vidual 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. Thus, because the pro
position Man is a rational being, was an essential proposition,
they affirmed the same thing of the proposition, Julius Cassar
is a rational being. This followed very naturally if genera and
species were to be considered as entities, distinct from, but
inhering in, the individuals composing them. If man was a
substance inhering in each individual man, the essence of man
(whatever that might mean) was naturally supposed to accom
pany it ; to inhere in John Thompson, and to form the common
essence of Thompson and Julius Ceesar. It might then be

VERBAL AND REAL PROPOSITIONS. 125

fairly said, that rationality, being of the essence of Man, was
of the essence also of Thompson. But if Man altogether be
only the individual men and a name bestowed upon them in
consequence of certain common properties, what becomes of
John Thompson's essence ?

A fundamental error is seldom expelled from philosophy
by a single victory. It retreats slowly, defends every inch
of ground, and often, after it has been driven from the open
country, retains a footing in some remote fastness. The
essences of individuals were an unmeaning figment arising
from a misapprehension of the essences of classes, 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, Eeal and Nominal. 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 unfor
tunately 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 comparatively innocuous ;) but if we
did, we could, from them alone, demonstrate the sensible pro
perties of the object, as the properties of the triangle are

* The always acute and often profound author of An Outline of Sematology
(Mr. B. H. Smart) justly says, " Locke will be much more intelligible if, in
the majority of places, we substitute ' the knowledge of for what he calls ' the
Idea of" (p. 10). 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 point of
difference respecting the import of Propositions, between my view and what I
have spoken of as the 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) cur Knowledge, or Belief, concerning the
thing itself.

126 NAMES AND PROPOSITIONS.

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
admits of being demonstrated from another property. It is
enough here to remark that, according to this definition, the
real essence of an object has, in the progress of physics, come
to be conceived as nearly equivalent, in the case of bodies, to
their corpuscular structure : 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 the 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 acci
dental propositions, on the contrary, may be called Real Pro
positions, in opposition to Verbal. They predicate of a thing
some fact not involved in the signification of the name by
which the proposition speaks of it; some attribute not con
noted by that name. Such are all propositions concerning
things individually designated, and all general or particular
propositions in which the predicate connotes any attribute not
connoted by the subject. All these, if true, add to our know
ledge : they convey information, 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
metaphysicians between what they term analytic, and synthetic, judgments ; the
former being those which can be evolved from the meaning of the terms used.

VERBAL AND REAL PROPOSITIONS. 127

Nothing has probahly contributed more to the opinion
so ]ong prevalent of the futility of the school logic, than the
circumstance that almost all the examples used in the common
school hooks to illustrate the doctrine of predication and that
of the syllogism, consist of essential propositions. They were
usually taken either from the branches or from the main trunk
of the Predicamental Tree, \vhich included nothing but what
was of the essence of the species : Omne corpus est substantia,
Omne animal est corpus, Oinnis homo est corpus, Omnis homo
est animal, Omnis homo est rationalis, and so forth. It is
far from wonderful 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 pro
fessed 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 evidence, 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 specifically
required them.

§ 5. With respect to propositions which do convey in
formation — which assert something of a Thing, under a
name that does not already 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. According as we
consider propositions in one or the other of these lights, their
import may be conveniently expressed 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 pro
position 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

128 NAMES AND PROPOSITIONS.

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 expressing the same meaning better adapted to in
dicate the office which the proposition performs. The prac
tical use of a proposition is, to apprise or remind us what
we have to expect, in any individual case which comes within
the assertion contained in the proposition. 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 attri
bute is made manifest. No men are gods, means that the
attributes of man are a mark or evidence that some or all
of the attributes 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 pro
position means, the latter to the manner in which it is to be
used.

Now it is to be observed that Seasoning (the subject to
which we are next to proceed) is a process into which propo
sitions enter not as ultimate results, but as means to the
establishment of other propositions. We may expect, there
fore, that the mode of exhibiting the import of a general pro
position which shows it in its application to practical use, will
best express the function which propositions perform in Rea
soning. And accordingly, in the theory of Reasoning, the
mode of viewing the subject which considers a Proposition
as asserting that one fact or phenomenon is a mark or
evidence of another fact or phenomenon, will be found almost
indispensable. 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 pro
positions.

CHAPTEE VII.

OF THE NATURE OF CLASSIFICATION, AND THE FIVE
PREDICABLES.

§ 1. IN examining into the nature of general proposi
tions, we have adverted 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 philoso
phical theory of general terms and general propositions. We
have considered general names as having a meaning, quite in
dependently of their being the names of classes. That cir
cumstance is in truth accidental, 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, mermaid, ghost, are as much so as if real objects
existed, corresponding to those names. Every name the sig
nification 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 attri
butes, the things, be they more or fewer, which happen to
possess those attributes, are constituted ipso facto a class.
But in predicating the name we predicate only the attributes ;
and the fact of belonging to a class does not, in many cases,
come into view at all.

Although, however, Predication does not presuppose Classi
fication, 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 a close connexion
between Classification and the employment of General Names.

VOL. I. 9

130 NAMES AND PROPOSITIONS.

By every general came 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 signification of the name.
Classes, therefore, mostly owe their existence to general lan
guage. 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 con-
notative 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, Digitigrades, &c., are as much the expression 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 convenience of classification was here the
primary motive for introducing the names; while in other
cases the name is introduced as a means of predication, and
the formation of a class denoted by it is only an indirect con
sequence.

The principles which ought to regulate 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 language, we cannot forbear
to treat here, without leaving the theory of general names

CLASSIFICATION AND THE PRED1CABLES. 131

and of their employment 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 Predicables ;
a set of distinctions handed down from Aristotle, and his fol
lower Porphyry, many of which have taken a firm root in
scientific, and some of them even in popular, phraseology. The
predicables are a five-fold 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 genus of the thing (y^oe).

A species • (ilSos).

A differentia (Siatpopa).

A proprium (ISiov).

An accidens

It is to be remarked of these distinctions, that they ex
press, not what the predicate is in its own meaning, but what
relation it bears to the subject of which it happens on the
particular 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 re
ferred to one or another predicable, according to the 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 Differentise of a geometrical 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 relation
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 Snecies, are
9—2

132 NAMES AND PROPOSITIONS.

not only used by naturalists in a technical acceptation 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 Mathematician. 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
j sub-classes or species included in it, may be itself a species
with reference to a more comprehensive, 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 Mathe
matician. Animal is a genus, divided into two species, man
and brute; but animal is also a species, which, with another
species, vegetable, makes up the genus, organized being.
Biped is a genus with reference to man and bird, but a
species with respect to the superior genus, animal. Taste is
a genus divided into species, but also a species of the genus
sensation. Virtue, a genus with reference to justice, tem
perance, &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 designated 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 im
portance which of the two modes of speaking we adopt, pro-

CLASSIFICATION AND THE PREDICABLES. 133

vided the rest of our language is consistent with it; but, if we
the class itself the genus, we must not talk of predicating
the genus. We predicate of man the name mortal; and by
predicating the name, we may be said, in an intelligible sense,
o predicate what the name expresses, the attribute mortality;
but in no allowable sense of the word predication do we predi
cate of man the class mortal. We predicate of him the fact
of belonging to the class.

By the Aristotelian logicians, the terms genus and species
3 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 considered a genus ; man
and brute co-ordinate species under that genus : biped, however
would not have been admitted to be a genus with reference to'
man, but a proprium or accidens only. It was requisite, ac
cording 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 classification they considered
some one class as the lowest or infima species. Man, for in
stance, 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 distinction between the essence of a class, and the attri
butes 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 connexion with the ex
ploded tenets of the Realists; and what the schoolmen chose
to call the essence of an individual, was simply the essence
of the class to which that individual was most familiarly
referred.

134 NAMES AND PROPOSITIONS.

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 differences which exist among
objects as differences in kind (genere or specie], 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 considering others as
secondary divisions, grounded on differences of a comparatively
superficial nature ? Examination will show that the Aristo
telians did mean something by this distinction, and some
thing important ; but which, being but indistinctly conceived,
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 negative

gether.

But if we contemplate any one of the classes so i<
such as the class animal or plant, or the class sulphur or phos
phorus or the class white or red, and consider in what parti
culars the individuals included in the class differ from those
which do not come within it, we find a very remarkable diver
sity in this respect between some classes and others,
are some classes, the things contained in which differ from
other things only in certain particulars which may be num
bered, while others differ in more than can be numbered, mor
even than we need ever expect to know. Some classes have
little or nothing in common to characterize them by, except

CLASSIFICATION AND THE PREDICABLES. 135

precisely what is connoted by the name : white things, for ex
ample, are not distinguished by any common properties, except
whiteness ; or if they are, it is only by such as are in some way
dependent on, or connected with, whiteness. But a hundred
generations have not exhausted the common properties of
animals or of plants, of sulphur or of phosphorus ; nor do we
suppose them to be exhaustible, but proceed to new obser
vations 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 in
vestigation the common properties of ail 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 be
lieve 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, there
fore, that the properties, on which we ground our classes, some
times exhaust all that the class has in common, or contain it
all by some mode of implication ; but in other instances we
make a selection of a few properties from among not only a
greater number, but a number inexhaustible by us, and to
which as we know no bounds, they may, so far as we are con
cerned, be regarded as infinite.

There is no impropriety in saying that, of these two classi
fications, 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 classification 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 perhaps 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, differences 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

136 NAMES AND PROPOSITIONS.

to those particular properties. The differences, however, are
made by nature, in both cases ; 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 neces
sity of taking notice of it depends on the importance or unim
portance of the particular qualities in which the difference
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 one of 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
itself, but continue to express it in their language. According
to that language, the proximate (or lowest) Kind to which any
individual is referable, is called its species. Conformably to
this, Sir 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, dis
tinct Kinds of men. A Christian, for example, 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 connected with it through some law of cause and effect. We

CLASSIFICATION AND THE PREDICABLES. 137

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, physiologists are perpetually carrying on such an
inquiry; nor is the answer ever likely to he completed. Man,
therefore, 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 temperaments, the two sexes, and even
the various ages, may be differences of kind, within our mean
ing 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 primary 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 beings, 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, organized
beings are not usually said to be of different species, if it is sup
posed that they could possibly have descended from the same
stock. That, however, is a sense artificially given to- the
word, for the technical purposes of a particular 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 they are
descended from common ancestors or not. But if their dif
ferences can all be traced to climate and habits, or to some

138 NAMES AND PROPOSITIONS.

one or a few special differences in structure, they are not, in the
logician's view, specially distinct.

When the infima species, or proximate Kind, to which an
individual belongs, has been ascertained, the properties com
mon to that Kind include necessarily the whole of the common
properties of every other real Kind to which the individual can
be referable. Let the individual, for example, be Socrates, and
the proximate Kind, man. Animal, or living creature, is also
a real Kind, and includes 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 common
properties of the sub-class, man. And if there be any class
which includes Socrates without including 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 addi
tion to whatever is implied in their flat noses, any common
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 peculiarities, not deducible
from the former by an ascertainable 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
proximate Kind. Therefore, the properties of the proximate
Kind do comprehend those (whether known or unknown) of
all other Kinds to which the individual belongs ; which was
the point we undertook to prove. And hence, every other
Kind which is predicable of the individual, will be to the
proximate Kind in the relation of a genus, according to even
the popular acceptation of the terms genus and species ; that
is, it will be a larger class, including 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 distin
guished from all other classes by an indeterminate multitude
of properties not derivable from one another, is either a genus
or a species. A Kind which is not divisible into other Kinds,

CLASSIFICATION AND THE PREDICABLES.

139

cannot be a genus, because it has no species under it ; but it
is itself a species, both with reference to the individuals below
and to the genera above (Species Praedicabilis and Species
Subjicibilis.) But every Kind which admits of division into
real Kinds (as animal into mammal, 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 discussion, and pass
to the three remaining predicables, Differentia, Proprium, and
Accidens.

§ 5. To begin with Differentia. This word is correlative
with the words genus and species, and as all admit, it signifies r
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 attributes it signi
fies. 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 animal : Rational (or rationality, for it
is of no consequence here whether we use the concrete or the
abstract form) is generally assigned by logicians as the Diffe
rentia ; and doubtless this attribute serves the purpose of
distinction : but it has also been remarked of man, that he
is a cooking animal ; the only animal that dresses its food.
This, therefore, is another of the attributes by which the
species man is distinguished from other species of the same
genus : would this attribute serve equally well for a diffe
rentia? The Aristotelians say No; having laid it down that j
the differentia must, like the genus and species, be of the
essence of the subject.

And here we lose even that vestige of a meaning grounded
in the nature of the things themselves, which may be sup
posed 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,

140

NAMES AND PROPOSITIONS.

and the differences which are not of kind ; they meant to inti
mate 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 he 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 innu
merable properties, known and unknown, that are common to
the class man, a portion only, and 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 infima species, to be the essence of the individual
too ; for it was their maxim, that the species contained the
" whole essence" of the thing. Metaphysics, 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 differentia of the class ; but the peculiarity of cooking
their food, not being connoted, was relegated to the class of
accidental properties.

The distinction, therefore, between Differentia, Proprium,
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 includes the species, in other
words denotes more than the species, or is predicable of a
greater number of individuals, it follows that the species must
connote more than the genus. It must connote all the attri
butes which the genus connotes, or there would be nothing

CLASSIFICATION AND THE PREDICABLES. 141

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 denotes all the indi
viduals denoted by man, and many more. Man, therefore,
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_£urplus of connotation — this which the species
connotes over and above the connotation of the genus — is the
Differentia, or specific difference ; or, to state the same propo
sition in other words, the Differentia is that which must be
added to the connotation of the genus, to complete the conno
tation of the species.

The word man, for instance, exclusively of what it con
notes in common 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. Tlie^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
outward 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 notion of differentia from
being restricted within too narrow limits, it is necessary to
remark, that a species, even as referred to the same genus,
will not always have the same differentia, but a different one,
according to the principle and purpose which preside over the
particular classification. For example, a naturalist surveys
the various kinds of animals, and looks out for the classifica
tion of them most in accordance with the order in which, for

NAMES AND PROPOSITIONS.

zoological purposes, he considers it desirable that we should
think of them. With this view he finds it advisable that
one of his fundamental 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 car
nivorous, 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 familiarly and spontaneously referred ;
nor should we ever think of assigning to them so prominent
a position in our arrangement of the animal kingdom, unless
for a preconceived purpose 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 characterizes : 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 derivative properties were of primary importance for the
purposes of the naturalist, 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 arrangement of
objects run in lines not coinciding 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, a fortiori must we be warranted, when our genera
and species are real genera and species, in marking the dis
tinction between them by those of their properties which con
siderations of practical convenience most strongly recommend.
I 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

CLASSIFICATION AND THE PREDICABLES. 143

man. Suppose, however, that 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 rationality, 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 diffe
rentia ; 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 number or character of the teeth ; in the
Linnaean system it connotes the number 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 Linnasus's three cha
racteristics 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 be, who adhere to the Linnsean
classification ; and the question would arise, whether the word
should continue to be used in two senses, or the classification
be given up, and the technical sense of the term be abandoned
along with it.

Words not otherwise connotative may, in the mode just
adverted to, acquire a special or technical connotation. Thus
the word whiteness, as we have so often remarked, connotes

144 ' NAMES AND PROPOSITIONS.

nothing ; it merely denotes the attribute corresponding to a
certain sensation : but if we are making a classification of
colours, and desire to justify, or even merely to point out, the
particular place assigned to whiteness in our arrangement, we
may define it " the colour 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
the 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 distin
guishes the species in question from all other species of the
genus to which on the particular occasion we are refer
ring it.

§ 7. Having disposed of Genus, Species, and Differentia,
we shall not find much difficulty in attaining a clear con
ception of the distinction between the other two predicates,
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 con
notation of the name denoting the species. Pjojrium and
Accidens, on the other hand, form no part of the essence, but
are predicated 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 Predicables, Accidens is used for one sort of accident
I only, Proprium being another sort. Proprium, continue the
• schoolmen, is predicated accidentally, indeed, but necessarily ;

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

ri AC.
v^^ooxxx^^w- ~*,~ --

or, as they further explain it, signifies an attribute which is
not indeed part of the essence, but which flows from, or is a
consequence 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 neces
sarily be possessed by whatever conies under that definition.
Accidens, on the contrary, has no connexion whatever with
the essence, but may come and go, and the species still re
main 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 Accidens, 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 supposing any of the essential properties of
the species to be altered, since with them an Accidens has no
connexion.

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 another in two ways; and
there are consequently two kinds of Proprium. It may
follow as a conclusion follows premises, 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, nevertheless follows from those con
noted by it, namely, from having the opposite sides straight
lines and parallel, and the number of sides four. The attri
bute, therefore, of having the opposite sides equal, is a Pro
prium of the class parallelogram ; and a Proprium of the
first kind, which follows from the connoted attributes by way
of demonstration. The attribute of being capable of under
standing language, is a Proprium of the species man, since
VOL. i. 10

NAMES AND PROPOSITIONS.

without being connoted by the word, it follows from an attri
bute which the word does connote, viz. from the attribute
of rationality. But this is a Proprium of the second kind,
which follows by way of eausation. How it is that one pro
perty of a thing follows, or can be inferred, from another;
under what conditions this is possible, and what is the exact
meaning of the phrase ; are among the questions which will
occupy us in the two succeeding Books. At present it needs 1
only be said, that whether a Proprium follows by demonstra- •*
tion or by causation, it follows necessarily ; that is to say, its
not following would be inconsistent with some law which we
regard as a part of the constitution either of our thinking
faculty or of the universe.

§ 8. Under the remaining predicable, Accidens, are in
cluded all attributes of a thing which are neither involved in
the signification of the name (whether ordinarily or as a term
of art), nor have, so far as we know, any necessary connexion
.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 connexion
between them and the attributes constitutive of the species,
and although, therefore, so far as we are aware, they might be
absent without making the name inapplicable and the species
a different species — are yet never in fact known to be absent.
A concise mode of expressing the same meaning is, that in
separable accidents are properties which are universal to the
species, but not necessary to it. Thus, blackness is an attri
bute of a crow, and, as far as we know, an universal one. But
if we were to discover a race of white birds, in other respects
resembling 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 popular use or as a term
of art, could blackness be inferred. Not only, therefore, 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 present state of our

CLASSIFICATION AND THE PREDICABLES. 147

knowledge, ranks as an accident, but an inseparable accident,
of the species crow.

Separable Accidents are tbose which are found, in point of
fact, to be sometimes 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 born, 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 attributes 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.

10-2

CHAPTER VIII.

OF DEFINITION.

§ 1. ONE necessary part of the theory of Names and of
Propositions remains to be treated of in this place : the theory
of Definitions. As being the most important of the class of
propositions which we have characterized as purely verbal,
they have already received some notice in the chapter pre
ceding the last. But their fuller treatment was at that time
postponed, because definition is so closely connected with clas
sification, that, until the nature of the latter process is in some
measure understood, the former cannot be discussed to much
purpose.

The simplest and most correct notion of a Definition is, a
proposition 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 discourse, intends to annex to it.

The definition of a word being the proposition which
enunciates its meaning, 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 de
clared ; 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 Thomson "
to say he is " the son of General Thomson ;" for the name
John Thomson does not express this. Neither is it any
definition of " John Thomson " to say he is " the man now
crossing the street." These propositions may serve to make
known who is the particular man to whom the name belongs,
but that may be done still more unambiguously by pointing to

DEFINITION.

149

him, which, however, has not been esteemed one of the modes
of definition.

In the case of connotative names, the meaning, as has been
so often observed, is the connotation ; and the definition of a
connotative name, is the proposition which declares its conno
tation. 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 connoting 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 attributes : Man is everything which possesses
corporeity, organization, life, rationality, and certain pecu
liarities of external form.

This form of definition is the most precise and least equi
vocal of any ; but it is not brief enough, and is besides too
technical for common discourse. The more usual mode of
declaring the connotation of a name, is to predicate of it
another name or names of known signification, which connote
the same aggregation of attributes. 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 this 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 corporeal, organized, 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

150

NAMES AND PROPOSITIONS.

without the aid of any other premises ; whether the definition
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 he an analysis. To resolve
any complex whole into the elements of which it is com
pounded, is the meaning of analysis : and this we do when we
replace one word which connotes a set of attributes collectively,
by two or more which connote the same attributes singly, or
in smaller groups.

§ 2. From this, however, the question naturally arises, in
what manner are we to define a name which connotes only a
single attribute : for instance, "white," which connotes nothing
but whiteness ; " rational," which connotes nothing but the
possession 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 question as to the word white,
it is obvious that in the case of rational some further explana
tion may be given of its meaning than is contained in the pro
position, "Rational is that which possesses the attribute of
reason ;" since the attribute reason itself admits of being de
fined. 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 attributes as are connotative,
and express attributes of those attributes, there is no diffi
culty : like other connotative names they are defined by
declaring their connotation. Thus, the word fault may be
defined, " a quality productive of evil or inconvenience."
Sometimes, again, the attribute to be defined is not one
attribute, but an union of several : we have only, therefore,
to put together the names of all the attributes taken sepa
rately, and we obtain the definition of the name which belongs

DEFINITION.

151

to them all taken together ; a definition which will correspond
exactly to that of the corresponding concrete name. For, as
we define a concrete name by enumerating the attributes which
it connotes, and as the attributes connoted by a concrete name
form the entire signification 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 definition
of humanity will be corporeity and animal life, combined
with rationality, and with such and such a shape.

When, on the other hand, the abstract name does not
express a complication 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 different parts, either coexistent or in suc
cession. To obtain a definition of the attribute, we must
analyse the phenomenon into these parts. Eloquence, 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 ascribed the attribute ; and
by resolving this phenomenon of causation into its two parts,
the cause and the effect, we obtain a definition of eloquence,
viz. the power of influencing the feelings by speech or writing.
A name, therefore, whether concrete or abstract, admits of
definition, provided 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
abstract : if a set of attributes, by enumerating them ; if a
single attribute, by dissecting the fact or phenomenon (whether
of perception or of internal consciousness) which is the foun
dation of the attribute. But, further, 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,

152 NAMES AND PROPOSITIONS.

would do so if all our simple feelings had names. Whiteness
may he defined, the property or power of exciting the sensa
tion of white. A white object maybe defined, an object which
excites the sensation of white. The only names which are un
susceptible 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 re
sembles 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 recal those former sensations, except the very
word which we seek to define, or some other which, being
exactly synonymous with it, requires definition as much, words
cannot unfold the signification 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, we proceed to examine some opinions of philo
sophers, and some popular conceptions 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 con
vention. Anything, therefore, is to them a sufficient definition
of a term, which will serve as a correct 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 unscientific definition ;
Essential but incomplete Definitions, and Accidental Defi
nitions, 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.

DEFINITION. 153

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 complete definition of the word Man, since
(as before remarked) if we adhered 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. Though 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 enume
rated attributes, possess also those which are omitted ; so that
the field of predication which the word covers, and the employ
ment of it which is conformable to usage, are as well indicated
by the inadequate definition as by an adequate one. Such
definitions, however, are always liable to be overthrown 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 being
seldom taken to mean the whole of the peculiarities constitu
tive of the species, but some one of those peculiarities only,
a complete definition would be per genus et differentias, rather
than differentiam. It would include, with the name of the
superior genus, not merely some attribute which distinguishes
the species intended to be defined from all other species of the
same genus, but all the attributes implied in the name of the
species, which the name of the superior genus has not already
implied. The assertion, however, that a definition must of
necessity consist of a genus and differentiae, is not tenable. It
was early remarked by logicians, that the summum genus in
any classification, 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 ultimately composed.

154

NAMES AND PROPOSITIONS.

§ 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 defi
nition ; it has always been deemed necessary that the attri
butes 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 been the case if it had
been in any degree made up of attributes not connoted 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. connota
tion, — 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 willingness
to accept as a definition anything which, whether it expounds
the meaning of the name or not, enables us to discriminate the
things denoted by the name from all other things, and conse
quently 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
combination of attributes which happens to be peculiar to it,
though separately each of those attributes may be common to
it with some other things. It is only necessary that the defi
nition (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 pre
dicable ; though the attributes specified may have no con
nexion with those which mankind had in view when they
formed or recognised the class, and gave it a name. The fol
lowing 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

DEFINITION. 155

other animal does) : Man is an animal who cooks his food :
Man is a featherless biped.

What would otherwise he 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
description, becomes on the particular occasion and for the
particular purpose a complete and genuine definition. This
actually occurs with respect 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 distribution of the animal kingdom.

In cases of this sort, though the definition is still a decla
ration of the meaning which in the particular instance the
name is appointed to convey, it cannot be said that to state
the meaning of the word is the purpose 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 certain 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
scientific convenience, he had resolved to found his division of
animated nature.

Scientific definitions, whether they are definitions of scien
tific terms, or of common terms used in a scientific sense, are

156 NAMES AND PROPOSITIONS.

almost always of the kind last spoken of: their main purpose
is to serve as the landmarks of scientific classification. And
since the classifications in any science are continually modified
as scientific knowledge advances, the definitions in the sciences
are also constantly varying. A striking 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 con
sequence the attributes connoted by the word have receded and
become fewer. At first it connoted the attributes, of combin
ing with an alkali to form a neutral substance (called a salt) ;
being compounded 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 attention 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 con
notation of the word. But carbonic acid, silica, sulphurous
acid, have no hydrogen in their composition ; that property
cannot therefore be connoted by the term, unless those sub
stances are no longer to be considered acids. Causticity and
fluidity have long since been excluded from the characteristics
of the class, by the inclusion of silica and many other sub
stances in it; and the formation of neutral bodies by com
bination with alkalis, together with such electro-chemical
peculiarities as this is supposed to imply, are now the only
differentia; which form the fixed connotation 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 accord
ingly, (as observed in the Introductory Chapter of this work,)
the definition of a science must necessarily be progressive and
provisional. Any extension of knowledge or alteration in the
current opinions respecting the subject matter, may lead to a

DEFINITION. 157

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 defining its name.

In the same manner in which a special or technical defini
tion 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 defini
tion to expound the ordinary, and what they deemed the
natural, 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 entiam, and would also
explain why a single differentia was deemed sufficient. But
to expound, or express in words, a distinction of Kind, has
already been shown to be an impossibility : the very meaning
of a Kind is, that the properties which distinguish 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, therefore, 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 connotation of the names
will do this : for the name of each class must necessarily con
note enough of its properties to fix the boundaries of the class.
If the definition, therefore, be a full statement of the connota
tion, it is all that a definition can be required to be.

§ 5. Of the two incomplete and popular modes of defini
tion, and in what they differ from the complete or philoso
phical mode, enough has now been said. We shall next examine
an ancient doctrine, once generally 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 important
processes of the understanding in the pursuit of truth.
According to this, the definitions of which we have now

158 NAMES AND PROPOSITIONS.

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 heing incomparably
the most important.

This opinion was held by the ancient philosophers, and by
their followers, with the exception of the Nominalists ; but as
the spirit of modern metaphysics, until a recent period, has
been on the whole a Nominalist spirit, the notion of defini
tions of things has been to a certain extent in abeyance, still
continuing, however, to breed confusion in logic, by its conse
quences 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 Logic.* In a
review of that work published by me in the Westminster

* In the fuller discussion which Archbishop Whately has given to this
subject in his later editions, he almost ceases to regard the definitions of names
and those of things as, in any important sense, distinct. He seems (9th ed.
p. 145) to limit the notion of a Real Definition to one which " explains any
thing more of the nature of the thing than is implied in the name ;" (including
under the word "implied," not only what the name connotes, but everything
which can be deduced by reasoning from the attributes connoted). Even this,
as he adds, is usually called, not a Definition, but a Description ; and (as it
seems to me) rightly so called. A Description, I conceive, can only be ranked
among Definitions, when taken (as in the case of the zoological definition of
man) to fulfil the true office of a Definition, by declaring the connotation given
to a word in some special use, as a term of science or art : which special conno
tation of course would not be expressed by the proper definition of the word in
its ordinary employment.

Mr. De Morgan, exactly reversing the doctrine of Archbishop Whately, un
derstands by a Real Definition one which contains less than the Nominal Defi
nition, provided only that what it contains is sufficient 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 separate 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 example are at variance ; for the
peculiar mode of drinking of the elephant certainly forms no part of the mean
ing 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.

DEFINITION. 159

Review for January 1828, and containing some opinions which
I no longer entertain, I find the following observations on the
question now before us ; observations with which my present
view of that question is still sufficiently in accordance.

"The distinction between nominal and real definitions,
between definitions of words and what are called definitions
of things, though conformable to the ideas of most of the
Aristotelian logicians, cannot, as it appears to us, be main
tained. We apprehend that no definition is ever intended to
* explain and unfold the nature of a thing.' It is some confir
mation 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 proposition
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 whatever
is predicated of the thing, unfolds 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 implied that
there exists a thing, corresponding 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 rectilineal figure with three sides,'
are, in form, expressions precisely similar; although in the
former it is not implied that any thing, conformable to the
term, really exists, while in the latter it is ; as may be seen by
substituting, 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 geometry
from a proposition expressive only of the manner in which we
intend to employ a particular sign.

160 NAMES AND PROPOSITIONS.

" 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 definition.
Its difference from the other kind consists 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 distinguishable. 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 explanation 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
disconformity 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 iden
tical proposition, which gives information only about the use
of language, and from which no conclusions affecting matters
of fact can possibly be drawn. The accompanying postulate,
on the other hand, affirms a fact, which may lead to conse
quences of every degree of importance. 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 philosophy, numerous proposi
tions 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

DEFINITION. 161

science of Geometry is deduced from definitions. This, so
long as a definition was considered to be a proposition " un
folding the nature of the thing," did well enough. But
Hobhes followed, and rejected utterly the notion that a defi
nition 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 predecessors, that the ap^al, principia,
or original premises of mathematics, and even of all science,
are definitions ; producing the singular paradox, 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 nature ;
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 aban
doning 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, pro
vided the name has corresponding to it an existing thing.
But if this proviso be necessary, from which of the two is
the inference really drawn ? From the existence of a thing
having the properties, or from the existence of a name meaning
them?

Take, for instance, any of the definitions laid down as
premises in Euclid's Elements ; the definition, let us say, of a
circle. This, being analysed, consists of two propositions ;
the one an assumption with respect to a matter of fact, the
other a genuine definition. "A figure may exist, having all
the points in the line which bounds it equally distant from a
single point within it :" " Any figure possessing this property
is called a circle." Let us look at one of the demonstrations
which are said to depend on this definition, and observe to
which of the two propositions contained in it the demonstra
tion really appeals. " About the centre A, describe the circle
VOL. i. 11

162 NAMES AND PROPOSITIONS.

B C D." Here is an assumption that a figure, such as 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 into 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 need
less ; but not the postulate implied in it ; without that the
demonstration could not stand. The circle being now described,
let us proceed to the consequence. " Since B 0 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 D 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 adrnissibility 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 theorems 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 defined, 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 pur
pose of rendering 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 reasonings, except such
as relate to words only. If this supposition were true, we
might argue correctly from true premises, and arrive at a false
conclusion. We should only have to assume as a premise the
definition of a nonentity; or rather of a name which has
no entity corresponding to it. Let this, for instance, be our
definition :

A dragon is a serpent breathing flame.

DEFINITION. 163

This proposition, considered only as a definition, is indis
putably correct. A dragon is 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 definition, would, in the
present instance, be false. Out of this definition we may carve
the premises of the following 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 unexceptionable 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
conclusion being false and the syllogism correct, the premises
cannot be true. But the premises, considered as parts of a
definition, are true. Therefore, the premises considered as
parts of a definition cannot be the real ones. The real pre
mises 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 conclu
sion presents no absurdity.

If we would determine what conclusion follows from the
same ostensible premises when the tacit assumption 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 which breathes flame :

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

Some word or words 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 proposition relating to the meaning of
words.

There is still another shape into which we may transform
this syllogism. We may suppose the middle term to be the

11—2

164 NAMES AND PROPOSITIONS.

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 propositions affirming
that an idea existing in the mind, includes certain ideal ele
ments. The truth of the conclusion 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 propo-

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

A dragon is a thing which breathes flame,

A dragon is a serpent,

Therefore some serpent or serpents breathe flame,

"there is just as much truth in the conclusion as there is in the premises, or
rather, no more in the latter than in the former. If the general name serpent
includes 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 cannot 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. The conclusion must run thus,
" Some serpent or serpents either do or are imagined to breathe flame." And
to prove this conclusion by the instance of dragons, the premises must be, A
dragon is imagined as breathing flame, A dragon is a (real or imaginary) ser
pent : from which it undoubtedly follows, that there are serpents which are
imagined to breathe flame ; but tlie 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 ,'issertion — 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 statement 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 conclusion being so,) the real
emise cannot be the definition, which is true, but the statement of fact,
which is false.

DEFINITION. 165

sition 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 postu
late involved in the definition which stands as the apparent
premise, is the existence of a thing conformable to the defini
tion, and not merely of an idea conformable to it. This as
sumption of real existence will always convey the impression
that we intend to make, when we profess to define any name
which is already known to bo 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 postulates 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 realized by art. People had a difficulty,
therefore, in conceiving that the most certain of all con
clusions could rest on premises which, iDstead of being cer
tainly true, are certainly not true to the full extent 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 conclusion. 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 accu
rately 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
definition is a statement and analysis not of the mere mean
ing 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

166 NAMES AND PROPOSITION'S.

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
definition 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 geometry are accurately true.

Allowing this doctrine respecting the nature of demonstra
tive truth to be correct (which, in a subsequent place, I
shall endeavour to prove that it is not ;) even on that suppo
sition, 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 cannot
conceive length without breadth ; it can only, in con
templating objects, attend to their length, exclusively of
their other sensible qualities, and so determine what pro
perties may be predicated of them in virtue of their length
alone. If this be true, the postulate involved in the geome
trical definition of a line, is the real existence, not of length
without breadth, but merely of length, that is, of long objects.
This is quite enough to support all the truths of geometry,
since every property of a geometrical line is really a property

DEFINITION. 167

of all physical objects in so far as possessing length. But
even what I hold to he the false doctrine on the subject,
leaves the conclusion that our reasonings are grounded on the
matters of fact postulated in definitions, and not on the de
finitions themselves, entirely unaffected ; and accordingly this
conclusion is one which I have in common with Dr. Whew ell,
in his Philosophy of the Inductive 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 emi
nently serviceable in clearing from confusion the initial steps
in the analysis of the mental processes, even where his views
respecting the ultimate analysis are such as (though with un
feigned 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 considerations 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 Dialogues; 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 fun
damental question with speculative moralists in all ages,
" What is virtue ?"

It would be a mistake to represent these difficult ami
noble inquiries as having nothing in view beyond ascertaining
the conventional meaning of a name. They are inquiries not
so much to determine what is, as what should be, the meaning
of a name ; which, like other practical questions of terminology,
requires for its solution that we should enter, and sometimes
enter very deeply, into the properties 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 objects w£re

168 NAMES AND PROPOSITIONS.

named before the attributes ; as appears from the fact that in
all languages, abstract names are mostly compounds or other
derivatives 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 sig
nified by the name.

But where the resemblances and differences on which
our classifications are founded are not of this palpable and
easily determinable kind; especially 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 discri
minated, 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 resem
blance between the new object and all or some of the old
familiar objects which they have been accustomed 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 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, habit
ually employs his general 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 tri
bunal of the outward senses to be identified and discrimi
nated, connote little more than a vague gross resemblance

DEFINITION. 169

to the things which they were earliest, or have been most,
accustomed to call hy those names. When, for instance,
ordinary persons predicate the words just or unjust of any
action, noble or mean of any sentiment, expression, or
demeanour, statesman 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 deno
minated by those appellations.

Language, as Sir James Mackintosh used to say of govern
ments, " 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 Stewart in his Philosophical
Essays) a name not unfrequently passes by successive links of
resemblance from one object to another, until it becomes ap
plied to things having nothing in common with the first things
to which the name was given ; which, however, do not, for
that reason, drop the name ; so that it at last denotes a con
fused huddle of objects, having nothing whatever in common;
and connotes nothing, not even a vague and general resem
blance. 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 multi
farious denotation, and confining it to objects possessed of
some attributes in common, which it may be made to connote.
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 compared to a road which is not made but has
made itself: it requires continual mending in order to be
passable.

From this it is already evident, why the question respect-

170 NAMES AND PROPOSITIONS.

ing 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 agreement on the point, they do
not mean to predicate distinctly any attribute at all. Never
theless, 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
corsipon 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 inquiry, 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 inquiries
into matters of fact. And if the second question (whether the
actions form a class at all) has been 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
denote.

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 logically remodel them. The classifica
tions rudely made by established language, when retouched, as
they almost all require to be, by the hands of the logician, are
often in themselves excellently suited to his purposes. As
compared with the classifications of a philosopher, they are
like the customary law of a country, which has grown up as
it were spontaneously, compared with laws methodized and
digested into a code : the former are a far less perfect instru
ment than the latter ; but being the result of a long, though
unscientific, course of experience, they contain a mass of mate
rials which may be made very usefully available in the forma
tion 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 resem
blance, is evidence, in the first place, that the resemblance is

DEFINITION. 171

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 resemblance com
mon to them all, still at every step in its progress we shall
find such a resemblance. And these transitions of the mean
ing of words are often an index to real connexions between
the things denoted by them, which might otherwise escane
the notice of thinkers ; of those at least who, from usinj, 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 oversights, committed for want of per
ceiving the hidden link that connected together the seemingly
disparate meanings 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 predicated. 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

* "Few people" (I have said in another place) " have reflected how great
a knowledge of Things is required to enable a man to affirm 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 these ideas a sagacious and penetrating mind will discern, as it were intui
tively, an unobvious link of connexion, 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
turning on the double meaning of a term. And the greater the genius of him
who thus safely leaps over the chasm, the greater will probably be the crowing
and vain- glory 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."

172 NAMES AND PROPOSITIONS.

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 resemblance which has led to their being
classed together. When these common attributes have been
ascertained and specified, the name which belongs in common
to the resembling objects acquires a distinct instead of a vague
connotation ; and by possessing this distinct connotation, be
comes 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 consequences to which they lead.
He will select, as far as possible, such differentiae 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 character and aspect to a set of
objects, which determine the groups into which they naturally
fall. But to penetrate to the more hidden agreement 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 im
portant. And since upon the result of this inquiry respecting
the causes of the properties of a class of things, there inci
dentally depends the question what shall be the meaning of a
word ; some of the most profound and most valuable investi
gations which philosophy presents to us, have been introduced
by, and have offered themselves under the guise of, inquiries
into the definition of a name.

m

BOOK II.

OF REASONING.

SE rovrwv Xt-yw^utv rjSrj, Sia TIVWV, KOI TTOTZ,
KOI 7rd»e yivtrai Trag <rv\\oji(rfji6^' vartpov c\ XEKTEOV Trept
aTroSet^Etuf . n/oortpov yap TTfjOt o'uXXo'ytff/iov XtKreov, 77 Trt/ot
aTroSet^ewc, ^ta TO ica^oXov juaXXov eivat TOV (rwXXoyta/uov.
'H JUEV Y«/° aTroSft^fCj ffyXXoYto-juo? 7"t?' o ervXXoytcrjuoe oe ou

ABIST. Analyt. Prior. 1. i. cap. 4.

CHAPTER I.

OF INFERENCE, OB REASONING, IN GENERAL.

§ 1 . IN the preceding Book, we have been occupied not
with the nature of Proof, but with the nature of Assertion :
the import conveyed by a Proposition, whether that Proposi
tion be true or false ; not the means by which to discriminate
true from false Propositions. The proper subject, however, 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. Assertion, 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 definitions are the most important, hold 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 respecting 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 propo
sition, and whatever its nominal subject or predicate, the real
subject of every proposition is some one or more facts or phe
nomena of consciousness, 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

176 REASONING.

negative, of those phenomena or those powers, is always
either Existence, Order in Place, Order in Time, Causation,
or Resemblance. 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 suffi
ciently scientific for many of the purposes for which such a
general expression is required. This expression recognises
the commonly received distinction between Subject and Attri
bute, and gives the following as the analysis of the meaning
of propositions : — 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 consciousness
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 affirmative 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 propositions; to
give credence to it, or claim credence for it, as a conclusion
from something else ; is to reason, in 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 syllogism 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 addi
tional motives will be suggested by the considerations on
which we are now about to enter.

INFERENCE IN GENERAL. 177

§ 2. In proceeding to take into consideration the cases
in which inferences 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,
appears on analysis to be merely a repetition 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
ffiquipollency or equivalence of propositions, are of this nature.
Thus, if we were to argue, No man is incapable 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 appealing 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 par
ticular : 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 some
thing which had been asserted 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 antecedent having affirmed a
predicate of a given subject, the consequent affirms of the
same subject something already connoted by the former pre
dicate : as, Socrates is a man, therefore Socrates is a living
creature ; where all 'that is connoted by living creature was
affirmed 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 includes it,
is already denied by implication. 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
VOL. i, 12

178 REASONING.

illustrated, are often of 'this ill-chosen kind ; formal demon
strations of conclusions 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 predicate, and framing out of the same terms
thus reversed, another proposition, which must be true if the
former is true. Thus, from the particular affirmative proposi
tion, 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 pro
position, All A is B, is legitimately convertible into Some
B is A. This process, which converts an universal propo
sition into a particular, is termed conversion per accidens.
From the proposition, 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 Englishmen are not men. The
only mode usually recognised of converting a particular nega
tive proposition, is in the form, Some A is not B, therefore,
something which is not B is A ; and this is termed conver
sion by contraposition. 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 B], and [A]. The
original proposition, Some A is not B, is first changed into
a proposition sequipollent with it. Some A is "a thing which
is not B ;" and tbe 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 con
version.*

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

INFERENCE IN GENERAL. 181

apprehended in any particular case which can occur. In this
respect, however, these axioms of logic are on a level with
those of mathematics. That things which are equal to the
same thing are equal to one another, is as obvious in any par
ticular case as it is in the general statement : and if no such
general maxim had ever heen laid down, the demonstrations in
Euclid would never have halted for any difficulty in stepping
across the 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 generalizations 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 appre
hending a general truth. And the student of logic, in the dis
cussion 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 any considerable
mental attainment, and which it is one of the primary objects
of logical discipline to cultivate.

§ 3. Having noticed, in order to exclude from the pro
vince of Reasoning or Inference properly so called, the cases
in which the progression from one truth to another is only ap
parent, 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 dis
tinct from them.

Reasoning, in the extended sense in which I use the term,
and in which it is synonymous with Inference, is popularly
said to be of two kinds : reasoning 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 rea
soning, which falls under neither of these descriptions, and
which, nevertheless, is not only valid, but is the foundation of
both the others.

It is necessary to observe, that the expressions, reasoning

REASONING.

for the other; for, to say that when the attributes of a quad
ruped are present, those of a warm-blooded creature are pre
sent, 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 sequipollency 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 important
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 important
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 con
siderations as these, that contrary propositions may both be
false, but cannot both be true ; that subcontrary propositions
may both be true, but cannot both be false ; that of two con
tradictory propositions one must be true and the other false ;
that of two subalternate propositions the truth of the uni
versal proves the truth of the particular, and the falsity of the
particular proves the falsity of the universal, but not vice
versa ;* 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 necessary to make the principles intel
ligible, would enable the truths which they convey to be

* All A is B \
No A is B / °

Some A. is B ) ,

> subcontraries.
Some A is not B )

All A is B )

5 contradictories.
Some A is not B )

No A is B ) , r . .

I also contradictories.
Some A is B )

All A is B ) , No A is B )

[ and J respectively subalternate.

borne A is B) Some A is not B )

INFERENCE IN GENERAL. 181

apprehended in any particular case which can occur. In this
respect, however, these axioms of logic are on a level with
those of mathematics. That things which are equal to the
same thing are equal to one another, is as obvious in any par
ticular case as it is in the general statement : and if no such
general maxim had ever heen laid down, the demonstrations in
Euclid would never have halted for any difficulty in stepping
across the 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 generalizations 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 appre
hending a general truth. And the student of logic, in the dis
cussion 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 any considerable
mental attainment, and which it is one of the primary objects
of logical discipline to cultivate.

§ 3. Having noticed, in order to exclude from the pro
vince of Reasoning or Inference properly so called, the cases
in which the progression from one truth to another is only ap
parent, 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 dis
tinct from them.

Reasoning, in the extended sense in which I use the term,
and in which it is synonymous with Inference, is popularly
said to be of two kinds : reasoning 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 rea
soning, which falls under neither of these descriptions, and
which, nevertheless, is not only valid, but is the foundation of
both the others.

It is necessary to observe, that the expressions, reasoning

182 REASONING.

from particulars to generals, and reasoning from generals to
particulars, are recommended by brevity rather than by pre
cision, and do not adequately mark, without the aid of a
commentary, the distinction between Induction (in the sense
now adverted to) and Ratiocination. The meaning intended
by these expressions is, that Induction is inferring a propo
sition from propositions less general than itself, and Ratioci
nation is inferring a proposition from propositions equally or
more general. When, from the observation of a number of
individual instances, we ascend to a general proposition, or
when, by combining a number of general propositions, we
conclude from them another proposition still more general,
the process, 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 combining 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 Ratiocination.
When, 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 Ratio
cination.

As all experience begins with individual cases, and pro
ceeds from them to generals, it might seem most conformable
to the natural order of thought that Induction should be
treated of before we touch upon Ratiocination. It will, how
ever, 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 constructing our knowledge ; and should trace
derivative 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 advantages of this order of
proceeding in the present instance will manifest themselves as
we advance, in a manner superseding the necessity of any
further justification or explanation.

INFERENCE IN GENERAL. 183

Of Induction, therefore, we shall say no more at present,
than that it at least is, without doubt, a process of real infer
ence. The conclusion in an induction embraces more than is
contained in the premises. The principle or law collected
from particular instances, the general proposition in which we
embody the result of our experience, covers a much larger
extent 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 gene
ralization grounded on those cases, and expressive 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 in
duction we proceed 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 observed ; future facts, for example ; but which we
do not hesitate to believe on the sole evidence of the induction
itself.

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

CHAPTEE II.

OF RATIOCINATION, OR SYLLOGISM.

§ 1. THE analysis of the Syllogism has been so accurately
and fully performed in the common manuals of Logic, that in
the present work, which is not designed as a manual, it is suf
ficient to recapitulate, memoriae, causa, the leading results of
that analysis, as a foundation for the remarks to be afterwards
made on the functions of the syllogism, and th;s 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 con
clusion, or proposition to be proved, and two other propositions
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 middleterm, 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 con
clusion 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 middleterm
which is in them both. The premise which contains the mid
dleterm and the major term is called the major premise ; that
which contains the middleterm 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
predicate 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

RATIOCINATION, OR SYLLOGISM.

185

the minor. This is reckoned as the first figure. When the
middleterm 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 middleterm 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.

Each figure is divided into moods, according to what are
called the quantity and quality of the propositions, that is, ac
cording as they are universal or particular, affirmative or nega
tive. The following are examples of all the legitimate moods,
that is, all those in which the conclusion correctly follows from
the premises. A is the minor term, C the major, B the middle-

No B is C
Some A is B

therefore
Some A is not C

All C is B
Some A is not B
therefore

term.

FIRST FIGURE.

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

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

SECOND FIGURE.

No C is B All C is B No G 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 Some A is not C

THIRD FIGURE.

All B is C No B is C Some B is C All B is C Some B is not C No B is C

All B is A All B is 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.

AllCisB AllCisB 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

SomeAisC Some A is not C Some A is C SomeAisnotC SomeAisnotC

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
because, their predicate being affirmed or denied of the
whole of the subject, they are ranked, for the purposes of the
syllogism, with universal propositions. Thus, these two syllo
gisms —

186

REASONING.

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 hoth ranked in the first
mood of the first figure.

The reasons why syllogisms in any of the above forms are
legitimate, that is, why, if the premises are true, the conclu
sion 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 particular, affirmative and negative propositions,)
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 himself.
The reader may, however, be referred, for every needful expla
nation, to Archbishop Whately's Elements of Logic, where he
will find stated with philosophical precision, and explained with
remarkable perspicuity, the whole of the common doctrine of
the syllogism.

All valid ratiocination ; all reasoning by which, from gene
ral propositions previously admitted, other propositions equally
or less general are inferred ; may be exhibited in some of the
above forms. The whole of Euclid, for example, might be
thrown without difficulty into a series of syllogisms, regular in
mood and figure.

Though a syllogism framed according to any of these for
mulas is a valid argument, all correct ratiocination admits of
being stated in syllogisms 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 conversion 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 proposition, No C is B,

RATIOCINATION, OR SYLLOGISM. 187

being an universal negative, admits of simple conversion, and
may be changed into No B is C, which, as \ve showed, is the
very same assertion in other words — the same fact differently
expressed. This transformation 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
figure must resemble the following : —

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 affirma
tives, 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 propo
sition 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 syllo
gism 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 conclu
sion 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 alteration in the mere manner of expressing

188

REASONING.

them. Every valid ratiocination, therefore, may be stated in
the first figure, that is, in one of the following forms : —

Every B is C No B is C

AHA ) • TJ AHA )

isB, isB,

Borne A ) Some A j

therefore therefore

All A is C> No A is

>
Some A j Some A is not

Or if more significant symbols are preferred : —

To prove an affirmative, the argument must admit of being
stated in this form : —

All animals are mortal ;

All men \

Some men j- are animals ;

Socrates )

therefore
All men \

Some men i- 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

are capable of self-control;

Mr. A's negro

therefore

No negroes are \

Some negroes are not J- necessarily vicious.

Mr. A's negro is not )

Though all ratiocination admits of being thrown into one
or the other of these forms, and sometimes gains consider
ably 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 conclusiveness is more

RATIOCINATION, OR SYLLOGISM. 189

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 was virtuous,
would be a more natural mode of stating the argument, and

O O 7

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 1704) contains among other things
one of the most elaborate and complete expositions which had
ever been made of the syllogistic doctrine, has expressly ex
amined what sort of arguments fall most naturally and suitably
into each of the four figures ; and his investigation is charac
terized 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 he reduced,
are the same premises in everything except language, or, at
least, as much of them as contributes to" the proof of the con-

* His conclusions are, " The first figure is suited to the discovery or proof
of the properties of a thing ; the second to the discovery or proof of the dis
tinctions between 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 reference of syllogisms in the last three figures to the dictum
de omni et nullo is, in Lambert'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
diverse for the second figure, dictum de excmplo for the third, and dictum de
reciproco for the fourth. See part i. or Uianoiologie, chap. iv. § 229 et seqq.
Mr. Bailey, (Theory of Reasoning, 2nd ed. pp. 70-74) takes a similar view of the
subject.

190

REASONING.

elusion is the same. We are therefore at liberty, in con
formity with the general opinion of logicians, to consider
the two elementary forms of the first figure as the universal
types of all correct ratiocination ; the one, when the conclusion
to he proved is affirmative, the other, when it is negative ;
even though certain arguments may have a tendency to clothe
themselves in the forms of the second, third, and fourth
figures ; which, however, cannot possibly happen with the
only class of arguments which are of first-rate scientific im
portance, those in which the conclusion is an universal affirma
tive, 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 Morgan's " Formal Lo^ic ;
or, the Calculus of Inference, Necessary and Probable;" and the "New
Analytic of Logical Forms," attached as an Appendix to Sir William Hamil
ton's Discussions on Philosophy, and at greater length, to his posthumous Lec
tures on Loyic.

In Mr. De Morgan's volume — abounding, in its more popular parts, with
valuable observations felicitously expressed— the principal feature of originality
is an attempt to bring within strict technical rules the cases in which a conclusion
can be drawn from premises of a form usually classed as particular. Mr. De
Morgan observes, very justly, that from the premises Most Bs 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 neces
sarily in part consist of the same individuals. 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 be at 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 examin
ing what inferences ad.nit of being drawn from the various combinations which
may be made of premises of this description, Mr. De Morgan establishes uni
versal formula? 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 the cases examined by Mr. De
Morgan, can legitimately be drawn, and that the ordinary theory takes no

RATIOCINATION, OR SYLLOGISM. 191

§ 2. On examining, then, these two general formulae, we
find that in both of them, one premise, the major, is an uni
versal proposition; and according as this is affirmative or
negative, the conclusion is so too. All ratiocination, therefore,
starts from a general proposition, principle, or assumption : a

account of them, I will not say that it was not worth while to show in detail
how these also could be reduced to formulae 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 forN any practical purpose. The practical use of technical forms of rea
soning is to bar out fallacies : but the fallacies which require to be guarded
against in ratiocination properly so called, arise from the incautious use of the
common forms of language ; and the logician must track the fallacy into that
territory, instead of waiting for it on a territory of his own. While he remains
among propositions which have acquired the numerical precision of the Calculus
of Probabilities, the enemy is left in possession of the only ground on which he
can be formidable. And since the propositions (short of universal) on which
a thinker has to depend, either for purposes of speculation or of practice, do
not, except in a few peculiar cases, admit of any numerical precision ; common
reasoning cannot be translated into Mr. De Morgan's forms, which therefore
cannot serve any purpose as a test of it.

Sir William Hamilton's theory of the "quantification of the predicate" (con
cerning the originality of which in his case there can be no doubt, however Mr.
De Morgan may have also, and independently, originated an equivalent doc
trine) may be briefly described as follows : — •

" Logically" (I quote his own words) " we ought to take into account the
quantity, always understood in thought, but usually, for manifest reasons,
elided in its expression, 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 tantamount 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 coextensive with the subject, they all admit 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 coextensive. The last three forms, though
conveying real assertions, have no place in the ordinary classification of Pro
positions. All propositions, then, being supposed to be translated into this
language, and written each in that one of the preceding forms which answers
to its signification, there emerges a new set of syllogistic rules, materially dif
ferent from the common ones. A general view of the points of difference may
be given in the words of Sir W. Hamilton (Discussions, 2nd ed. p. 651) :

"The revocation of the two terms of a Proposition to their true relation ; a
proposition being always an equation of its subject and its predicate.

"The consequent reduction of the Conversion of Propositions from three
species to one — that of Simple Conversion.

192 REASONING.

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

The other premise is always affirmative, and asserts that
something (which may be either an individual, a class, or part

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

Canon.

"The evolution fiom that one canon of all the Species and varieties of Syl
logisms.

" The abrogation of all the Special Laws of Syllogism.

" A demonstration of the exclusive possibility of Three syllogistic Figures ;
and (on new grounds) the scientific and final abolition of the Fourth.

" A manifestation that Figure is an unessential variation in syllogistic form ;
and the consequent absurdity of Keducing the syllogisms of the other figures to

the first.

" An enouncement of one Organic Principle 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, throughout every schematic

difference.

« That, in the second and third figures, the extremes holding both the same
relation to the middle term, there is not, as in the first, an opposition and sub-
ordination between a term major and a term minor, mutually containing and
contained, in the counter wholes of Extension and Comprehension.

"Consequently, in the second and third figures, there is no determinate
major and minor premise, and there are two indifferent conclusions : whereas
in the first the premises are determinate, and there is a single proximate con
clusion."

This doctrine, like that of Mr. De Morgan previously noticed, is
addition to the syllogistic theory ; and has moreover this advantage over Mr.
De Morgan's "numerically definite Syllogism," that the forms it supplies are
really available as a test of the correctness of ratiocination ; since propositions
in the common form may always have their predicates quantified, and so be
made amenable to Sir W. Hamilton's rules. Considered however as a con
tribution to the Science of Logic, that is, to the analysis of the mental pro
cesses concerned in reasoning, the new doctrine appears to me, I confess, not
merely superfluous, but erroneous ; since the form in which it clothes propos
tions does not, like the ordinary form, express what is in the mind <
speaker when he enunciates the proposition. I cannot think Sir William
Hamilton ri^ht in maintaining that the quantity of the predicate is
understood in thought." It is implied, but is not present to the mmd c
person who asserts the proposition. The quantification of the predicate, instead

RATIOCINATION, OR SYLLOGISM. 193

of a class) belongs to, or is included in, the class respecting
which something was affirmed or denied in the major premise.
It follows that the attribute affirmed or denied of the entire
class may (if that affirmation or denial was correct) be
affirmed or denied of the object or objects alleged to be in
cluded 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 generalized, and erected into a logical maxim, on which
all ratiocination 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 everything included
in the class. This axiom, supposed to be the basis of the
syllogistic theory, is termed by logicians the dictum de omni et
nullo.

This maxim, however, when considered as a principle of
reasoning, appears suited to a system of metaphysics once
indeed generally received, but which for the last two centuries
has been considered as finally abandoned, though there have
not been wanting in our own day attempts at its revival.
So long as what are 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
expressed the intercommunity of nature, which it was neces-

of being a means of bringing out more clearly the meaning of the proposition,
actually leads the mind out of the proposition, into another order of ideas. For
when we say, All men are mortal, we simply mean to affirm the attribute mor
tality of all men ; without thinking at all of the class mortal in the concrete, or
troubling ourselves about whether it contains any other beings or not. It is
only for some artificial purpose that we ever look at the proposition in the aspect
in which the predicate also is thought of as a class-name, either including the
subject only, or the subject and something more. (See above, p. 104.)

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 Philo
sophy. "

VOL. I. 13

194- REASONING.

sary on that theory that we should suppose to exist between
those general substances and the particular substances which
were subordinated to them. That everything predicable of
the universal was predicable of the various individuals con
tained under it, was then no identical proposition, but a
statement of what was conceived as a fundamental 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 substances called by the same
name ; that the properties of Man, for example, were proper
ties 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 known that a class, an universal, a genus or species, is
not an entity per se, but neither more nor less than the indi
vidual substances 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 common attri
butes indicated by the name ; what, I should be glad to know,
do we learn by being told, that whatever 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 applica
tion 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 defi
nition ; we must look upon it as intended to explain, in a
circuitous and paraphrastic manner, the meaning of the word,
class..

An error \\hich seemed finally refuted 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

RATIOCINATION, OR SYLLOGISM. 195

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 comprehended under
them are in a perpetual flux, knowledge, which necessarily
imports stability, can only have relation to those general sub
stances or universals, and not to the facts or particulars in
cluded 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 ontology of the later Kantians, has never ceased to poison
philosophy. Once accustomed to consider scientific investiga
tion 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 investiga
tion of truth consisted entirely or partly in some kind of con
juration 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 reasoning, two such premises fairlv
put together were likely, if he was a consistent 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 derive irresistible confirma
tion from the example of algebra. If 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 Hen faite ;
in other words, that the one sufficient rule for discovering 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

13—2

196 REASONING.

them properly except in proportion as we are already acquainted
with their nature and properties. 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 con
ceivable manipulation of mere names, as such ; and that what
can be learned from names, is only what somebody who used
the names knew before ? Philosophical analysis confirms the
indication of common sense, that the function of names is but
that of enabling us to remember and to communicate our
thoughts. That they also strengthen, even to an incalculable
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 considered 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 consider
able 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 dictum de omni as the
foundation of the syllogism, looked upon arguments in a
manner corresponding to the erroneous view which Hobbes
took of propositions. Because there are some propositions
which are merely verbal, Hobbes, in order apparently that his
definition might be rigorously universal, 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 syllogism. 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

RATIOCINATION, OR SYLLOGISM. 197

that what was included in the lower class is included in the
higher, and the result, therefore, nothing except that the classi
fication is consistent with itself. But we have seen that it
is no sufficient account of the meaning of a proposition, to say
that it refers something to, or excludes something 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 (constantly
or occasionally) coexist. Since such is the purport of all
propositions which convey any real knowledge, and since
ratiocination is a mode of acquiring real knowledge, any
theory of ratiocination 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 premises of
a syllogism, we obtain the following results. The major pre
mise, which, as already remarked, 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, denoting objects and connoting attributes. The asser
tion in the major premise is, that along with one of the two
sets of attributes, we always find the other : that the attri
butes connoted by "man" never exist unless conjoined with
the attribute called mortality. The assertion in the minor
premise is that the individual named Socrates possesses the
former attributes ; and it is concluded that he possesses also the

198 REASONING.

attribute mortality. Or if both tbe premises are general pro
positions, as

All men are mortal,
All kings are men,

therefore

All kings are mortal,

the minor premise asserts that the attributes denoted by king
ship only exist in conjunction with those signified by the word
man. The major asserts as before, that the last-mentioned
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 omni
potent, it would assert, not that the attributes connoted by
"man" never exist without, but that they never exist with,
those connoted by " omnipotent :" from which, together with
the minor premise, it is concluded, that the same incompati
bility exists between the attribute omnipotence and those con
stituting a king. In a similar manner we might analyse
any other example of the syllogism.

If we generalize this process, and look out for the prin
ciple or law involved 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 nullo, but a fundamental principle, or rather two
principles, strikingly resembling the axioms of mathematics.
The first, which is the principle of affirmative syllogisms,
is, that things which coexist with the same thing, coexist
with one another. The second is the principle of negative
syllogisms, and is to this effect : that a thing which coexists
with another thing, with which other a third thing does not
coexist, is not coexistent 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 argu
ment in which facts and not conventions are the matter
treated of.*

* Mr. Herbert Spencer (Principles of Psychology, pp. 125-7), though his
theory of the syllogism coincides with all that is essential of mine, thinks it a,

RATIOCINATION, OR SYLLOGISM. 199

§ 4. It remains to translate this exposition of the syllo
gism from the one into the other of the two languages in

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 out by Arch
bishop Whately and myself, of confounding exact likeness with literal identity ;
and maintains, that we ought not to say that Socrates possesses the same attri
butes which are connoted by the word Man, but only that he possesses attri
butes exactly like them : according to which phraseology, Socrates, and the at
tribute mortality, are not two things coexisting with the same thing, as the
axiom asserts, but two things coexisting with two different things.

The question between Mr. Spencer and me is merely one of language ; for
neither of us (if I understand Mr. Spencer's opinions rightly) believes an attri
bute to be a real thing, possessed of objective existence ; we believe it to be a
particular mode of naming 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 comparative appropriateness, for philosophical
purposes, of two different modes of using a name. Considered in this point of
view, the phraseology I have employed, which is that commonly used by philo
sophers, seems to me to be the best. Mr. Spencer is of opinion that because
Socrates and Alcibiades 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 sensations 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 which it will then
manifest itself 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 general conception, instead of 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 thing as general language.
A name would have no general meaning if man connoted one thing when pre
dicated of John, and another, though closely resembling, thing when predicated
of William. Accordingly a recent pamphlet asserts the impossibility of general
knowledge on this precise ground.

The meaning of any general name is some outward or inward phenomenon,
consisting, 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 indi
vidual 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 rejoin, the attribute is precisely that similarity. The names of
attributes are in their ultimate analysis names for the resemblances of our sen
sations (or other feelings). Every general name, whether abstract or concrete,
denotes or connotes one or more of those resemblances. It will not, probably,

200 REASONING.

which we formerly remarked* that all propositions, and of
course therefore all comhinations of propositions, might be
expressed. We observed that a proposition might be con
sidered in two different lights ; as a portion of our knowledge
of nature, or as a memorandum for our guidance. Under the
former, or speculative aspect, an affirmative general proposi
tion is an assertion 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 know
ledge, but as an aid for our practical exigencies, by enabling
us, when we see or learn that an object possesses one of the
two attributes, to infer that it possesses the other; thus em
ploying the first attribute as a mark or evidence of the second.
Thus regarded, every syllogism comes within the following
general 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 arguments which we have lately

be denied, that if a hundred sensations are undistinguishably alike, their resem
blance ought to be spoken of as one resemblance, and not a hundreu resem
blances which merely resemble one another. The things compared are many,
but the something common to all of them must be conceived as one, just as the
name is conceived as one, though corresponding to numerically different sensa
tions of sound each time it is pronounced. The general term man does not
connote the sensations derived once from one man, which, once gone, can no
more occur again than the same flash of lightning. It connotes the general type
of the sensations derived always from all men, and the power (always thought
of as one) of producing sensations of that type. And the axiom might be thus
worded : Two types of sensation each of which coexists with a third type,
coexist with another ; or Two powers each of which coexists with a third power
coexist with one another.

Mr. Spencer has misunderstood me in another particular. He supposes that
the coexistence spoken of in the axiom, of two things with the same third
thing, means simultaneousness in time. The coexistence meant is that of being
jointly attributes of the same subject. The attribute of being born without
teeth, and the attribute of having thirty-two teeth in mature age, are in this
sensf coexistent, both being attributes of man, though ex vi termini never of
the same man at the same time.

* Supra, p. 128.

RATIOCINATION, OR SYLLOGISM. 201

cited as specimens of the syllogism, will express themselves in
the following manner : —

The attrihutes 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 omnipotence,
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 in the form of the
syllogisms, the axioms on which the syllogistic process is
founded must undergo a corresponding transformation. In
this altered phraseology, both those axioms may be brought
under one general expression ; 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 acquainted
with, to express with precision and force what is aimed at, and
actually accomplished, in every case of the ascertainment of
a truth by ratiocination.

CHAPTER III.

OF THE FUNCTIONS AND LOGICAL VALUE OF THE
SYLLOGISM.

§ 1. WE have shown what is the real nature of the truths
with which the Syllogism is conversant, in contradistinction
to the more superficial manner in which their import is con
ceived in the common theory; and what are the fundamental
axioms on which its probative force or conclusiveness depends.
We have now to inquire, whether the syllogistic process, that
of reasoning from generals to particulars, is, or is not, a pro
cess of inference ; a progress 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 allowed that a
syllogism is vicious if there be anything more in the conclu
sion than was assumed in the premises. But this is, in fact,
to say, that nothing ever was, or can be, 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
represented 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 syllogism 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 repre
sent the syllogism as the correct analysis of what the mind
actually performs in discovering 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

FUNCTIONS AND VALUE OF THE SYLLOGISM. 203

of the syllogism 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 attention
of the reader to certain considerations, without which any just
appreciation of the true character of the syllogism, and the
functions it performs in philosophy, appears to me impossible ;
but which seem to have been either overlooked, or insufficiently
adverted to, both by the defenders of the syllogistic theory and
by its assailants.

§ 2. It must be granted that in every syllogism, con
sidered 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 adversaries 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 certain of the mortality of every individual man : that
if it be still doubtful whether Socrates, or any other individual
we choose to name, be mortal or not, the same degree of un
certainty must hang over the assertion, 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 evidence aliunde ; and
then what remains for the syllogism to prove? That, in
short, no reasoning from generals to particulars can, as such,
prove anything : since from a general principle we cannot
infer any particulars, but those which the principle itself
assumes as known.

This doctrine appears to me irrefragable ; and if logicians,

204- REASONING.

though unable to dispute it, have usually exhibited a strong
disposition to explain it away, this was not because they could
discover any flaw in the argument itself, but because the
contrary opinion seemed to rest on arguments equally indis
putable. In the syllogism last referred to, for example, 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 ?
3s 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 reason
ing? We believe that the Duke of Wellington is mortal.
We do not know this by direct observation, 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 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 pre
mises, the argument is vicious. For it is impossible to attach
any serious scientific value to such a mere salvt, as the dis
tinction drawn between being involved by implication in the
premises, and being directly asserted in them. When Arch
bishop 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

* Logic, p. 239 (9th ed.).

FUNCTIONS AND VALUE OF THE SYLLOGISM. 205

to perceive and acknowledge the full force of that which he
has admitted," he does not, I think, meet the real difficulty re
quiring to be explained, namely, how it happens that a science,
like geometry, can be 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 considered and
understood its full force. When you admitted the major
premise, you asserted the conclusion ; but, says Archbishop
Whately, you asserted it by implication merely : this, how
ever, 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 pro
position 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 holding you
fast in it ?*

§ 3. From this difficulty there appears to be but one
issue. The proposition that the Duke of Wellington is
mortal, is evidently an inference ; it is got at as a conclusion

* It is hardly necessary to say, that I am not contending for any such
absurdity as that we actually "ought to have 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 observations. There is no difference between me and Archbishop
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, be
fore the Duke of Wellington was born, that all men are mortal, knew that the
Duke of Wellington was mortal ; 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 Wellington's mortality, a general statement which presupposes it.
Finding no sufficient resolution of this difficulty in any of the writers on Logic,
I have attempted to supply one.

206 REASONING.

from something else ; but do we, in reality, conclude it from
the proposition, All men are mortal ? I answer, no.

The error committed is, I conceive, that of overlooking
the distinction between two parts of the process of philo
sophizing, 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 unable 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 note-book : unless the book was written,
like the Koran, with a quill from the wing of the angel
Gabriel.

.Assuming that the proposition, The Duke of Wellington
is mortal, is immediately an inference from the proposition,
All men are mortal ; whence do we derive our knowledge of
that general truth ? Of course from observation. Now, all
which man can observe 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 com
pendious form for recording and preserving in the memory
a number of particular facts, all of which have been observed.
Generalization is not a process of mere naming, it is also a
process of inference. From instances which we have ob
served, we feel warranted 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 contrivance 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 expression; and have thus only
one proposition, instead of an endless number, to remember
or to communicate. The results of manv observations and

FUNCTIONS AND VALUE OF THE SYLLOGISM. 207

inferences, and instructions for making innumerable infe
rences 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 generalization, All men are mortal, as an inter
mediate 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 resides. The inference is finished when we
have asserted that all men are mortal. What remains to
be performed afterwards is merely decyphering our own
notes.

Archbishop Whately has contended that syllogizing, or
reasoning from generals to particulars, is not, agreeably 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 incon
sequence have concluded at once from those instances,
that the Duke of Wellington is mortal. The mortality of
•John, Thomas, and company 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 general pro
position. Since the individual cases are all the evidence we
can possess, evidence which no logical 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 sufficient for the other ; I am
unable to see why we should be forbidden to take the shortest
cut from these sufficient premises to the conclusion, and con
strained to travel the " high priori road," by the arbitral-)'
fiat of logicians. I cannot perceive why it should be impos-

208 REASONING.

sible to journey from one place to another unless we "march
up a hill, and then march down again." It may he the safest
road, and there may be a resting-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 reason from particulars to particulars
without passing through generals, but we perpetually do so
reason. All our earliest inferences are of this nature. From
the first dawn of intelligence we draw inferences, 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 generalizing ;
he is inferring a particular 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 animals
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 tradition, 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

FUNCTIONS AND VALUE OF THE SYLLOGISM. 209

judge from an enlarged consideration of the manner in which
human heings in general, or persons of some particular cha
racter, are accustomed to feel and act ; hut 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, who, when called to a consultation upon the case of
a neighbour's child, pronounces on the evil and its remedy
simply on the recollection and authority 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 judgment, which we may be
utterly incapable 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, 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 theoretical 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 between ground and array. But his
experience of encampments, in circumstances more or less
similar, has left a number of vivid, unexpressed, ungeneral-
ized analogies in his mind, the most appropriate of which,
instantly suggesting itself, determines him to a judicious
arrangement.

The skill of an uneducated person in the use of weapons,
VOL. i. U

210 REASONING.

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 necessarily involved,
the weight and form of the weapon, the direction and distance
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 extraor
dinary 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 work
man came ; but his mode of proportioning the ingredients,
in which lay the secret of the effects he produced, was by
taking them up in handfuls, while the common method was to
weigh them. The manufacturer sought to make him turn his
handling system into an equivalent 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 connexion in his mind between fine effects of
colour, and tactual perceptions in handling his dyeing
materials ; and from these perceptions he could, in any par
ticular case, infer the means to be employed, and the effects
which would be produced, but could not put others in pos
session of the grounds on which he proceeded, from having
never generalized them in his own mind, or expressed them
in language.

Almost every one knows Lord Mansfield's advice to a
man of practical good sense, who, being appointed governor
of a colony, had to preside in its court of justice, without
previous judicial practice or legal education. 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 sup-

FUNCTIONS AND VALUE OF THE SYLLOGISM. 211

pose that the bad reason was the source of the good decision.
Lord Mansfield knew that if any reason were assigned it
would he necessarily an afterthought, the judge being in fact
guided by impressions from past experience, without the
circuitous process 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 experience, would have been greatly pre
ferable as a judge, to one, however sagacious, 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 examples of the rudest and
most spontaneous form of the operations of superior minds.
It is a defect in them, and often a source of errors, not to
have generalized as they went on ; but generalization, 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 mankind, 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 mathematics depend entirely on the axioms, it is
by no means necessary to our seeing the conclusiveness of the
proof, that the axioms should be expressly adverted to. When
it is inferred that AB is equal to CD because each of them is
equal to EF, the most uncultivated understanding, as soon as
the propositions were understood, would assent to the in
ference, 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 ratiocina
tion ; 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

14—2

212 REASONING.

its probative 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 composition of forces in dyna
mics, the equal mobility of fluids in hydrostatics, 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
demonstration, 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 generali
zation, 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 demonstrations of geometry, holds
equally true of the definitions. Every demonstration in Euclid
might be carried on without them. This is apparent from the
ordinary process of proving a proposition of geometry by means
of a diagram. What assumption, in fact, do we set out from,
to demonstrate by a diagram any of the properties 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, com
bined with other propositions of a similar kind, some of which
when generalized are called definitions, and others axioms, we
prove that a certain conclusion is true, not of all circles, but

FUNCTIONS AND VALUE OF THE SYLLOGISM. 213

of the particular circle ABC ; or at least would be so, if the
facts precisely accorded with our assumptions. The enuncia
tion, as it is called, that is, the general theorem which stands
at the head of the demonstration, is not the proposition
actually demonstrated. One instance only is demonstrated :
hut 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 con
trivance of general language furnishing us with terms which
connote 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 only
means, that if we can prove an individual conclusion by assum
ing an individual fact, then in whatever case we are warranted
in making an exactly similar assumption, we may draw an
exactly similar conclusion. The definition is a sort of notice
to ourselves and others, what assumptions we think ourselves
entitled 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 short-hand, of the parti
cular facts, which, as occasion arises, we either think we may
proceed on as proved, or intend to assume. In any one de
monstration 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 assumption, but on a similar
assumption confined to the particular case : that case, however,

214 REASONING.

being chosen as a specimen or paradigm of the whole class of
cases included in the theorem, there can he no ground for
making 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 explained presently, so far as explanation is
requisite. But, that unpractised learners, even in making use
of one theorem to demonstrate another, reason rather from
particular to particular than from the general proposition, 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 difficulty which, except in
cases of unusual mental power, long practice can alone
remove, and removes chiefly by rendering us familiar with all
the configurations consistent with the general conditions of the
theorem.

§ 4. From the considerations now adduced, the following
conclusions seem to be established. All inference is from par
ticulars to particulars : General propositions are merely regis
ters of such inferences already made, and short formulae for
making more : The major premise of a syllogism, conse
quently, is a formula of this description : and the conclusion
is not an inference drawn from the formula, but an inference
drawn according to the formula : the real logical antecedent,
or premise, being the particular facts from which the general
proposition was collected by induction. Those facts, and the
individual instances which supplied them, may have been for
gotten ; but a record remains, not indeed descriptive of the
•'acts themselves, but showing how those cases may be distin
guished, respecting which the facts, when known, were consi
dered to warrant a given inference. According to the indica
tions of this record we draw our conclusion ; which is, to all
intents and purposes, a conclusion from the forgotten facts.

FUNCTIONS AND VALUE OF THE SYLLOGISM. 215

l<'or this it is essential that we should read the record correctly :
and the rules of the syllogism are a set of precautions to ensure
our doing so.

This view of the functions of the syllogism is confirmed
hy the consideration of precisely those cases which might be
expected to he least favourable 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 conclusion. There are, how
ever, some peculiar cases in which it is the whole process.
Particulars alone are capable 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 observation. It may present itself as
coming from testimony, which, on the occasion and for the
purpose in hand, is accepted as of an authoritative character :
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 generalization 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 other persons, shall conform our conduct to certain
general instructions. So far as this asserts a fact, namely, a
volition of the legislator, that fact is an 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 subjects should observe, is general
The proposition asserts, not that all men are anything, but
that all men shall do something.

In both these cases the generalities are the original data,
tiud the particulars are elicited from them by a process which
correctly resolves itself into a series of syllogisms. The real
nature, however, of the supposed deductive process, is evident

216

REASONING.

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 pos
sesses the marks by which, as those authorities have signified,
the cases which they meant to certify or to influence may be
known. The object of the inquiry is to make out the wit
ness'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 characterize, more aptly than any other, the
functions of the syllogism in all cases. When the premises
are given by authority, the function of Reasoning is to ascer
tain 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 manner, when
the premises are derived from observation, the function of
Reasoning is to ascertain what we (or our predecessors)
formerly thought might be inferred from the observed facts,
and to do this by interpreting 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 mortality. But when we conclude that
the Duke of Wellington is mortal, we do not infer this from
the memorandum, but from the former experience. All that
we infer from the memorandum is our own previous belief,
(or that of those who transmitted to us the proposition), con
cerning the inferences which that former experience would
warrant,

This view of the nature of the syllogism renders con
sistent and intelligible what otherwise remains obscure and

FUNCTIONS AND VALUE OF THE SYLLOGISM. 217

confused in the theory of Archbishop Whately and other
enlightened 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
reasoning is to prevent inconsistency in our opinions; to pre
vent us from assenting 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 conclu
sion, 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 Wellington 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 premises 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, notwithstand
ing, 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 inferences 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 inferences not conformable to
our former 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 conclu
sions we draw in every particular case, and the previous
general directions for drawing them ; whether those general

218 REASONING.

directions were framed by ourselves as the result of induction,
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 inference; which
is, on the contrary, (when not a mere inference from testi
mony) an inference from particulars to particulars; autho
rized by a previous inference from particulars to generals,
and substantially the same with it ; of the nature, therefore,
of Induction. But while these conclusions appear to me un
deniable, I must yet enter a protest, as strong as that of
Archbishop Whately himself, against the doctrine that the
syllogistic art is useless for the purposes of reasoning. The
reasoning lies in the act of generalization, not in interpreting
the record of that act ; but the syllogistic form is an indis
pensable collateral security for the correctness of the gene
ralization itself.

It has already been seen, that if we have a collection of
particulars sufficient 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 re
marked 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
experience will therefore hold in time to come, it will hold not
merely in some individual case, but in all cases of some given
description. Every induction, therefore, which suffices to
prove one fact, proves an indefinite multitude 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 generality ; and thus to place before our minds, in its

FUNCTIONS AND VALUE OF THE SYLLOGISM. 219

full extent, the whole of what our evidence must prove if it
proves anything.

This throwing of the whole hody 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 presents a larger
object to the imagination than any of the singular proposi
tions which it contains. A process of thought which leads to
a comprehensive 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 observations 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 affect our wishes
or our imagination, and, under that influence, accepting in-
sufficienf 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 legitimately 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 com
prise 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 generalization by a reductio ad impossibile.

Thus if, during the reign of Marcus 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 expect that Commodus
would be a just ruler ; supposing him to stop there, he might
only have been undeceived by sad experience. But if he

220

REASONING.

reflected that this expectation could not be justifiable unless
from the same evidence he was warranted in concluding
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 premises, would have warned him that those premises
could not prove in the instance of Commodus, what they were
inadequate to prove in any collection of cases in which his was
included.

The advantage, in judging whether any controverted in
ference is legitimate, of referring to a parallel case, is univer
sally acknowledged. But by ascending to the general propo
sition, 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 advantageous, to divert our argument into the
circuitous channel of an induction from those known cases to
a general proposition, and a subsequent application of that
general proposition to the unknown case. This second part of
the operation, which, as before observed, is essentially a pro
cess of interpretation, 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, therefore, any fact fairly coming within the
range of one of these general propositions, and consequently
asserted by it, is known or suspected to be other than the
proposition asserts it to be, this mode of stating the argument
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 syllogistic form, and of the

FUNCTIONS AND VALUE OF THE SYLLOGISM. 221

rules for using it correctly, does not consist in their being
the form and the rules according to which our reasonings
are necessarily, or even usually, made ; but in their furnishing
us with a mode in which those reasonings may always be
represented, and which is admirably calculated, if they are
inconclusive, to bring their inconclusiveness to light. An
induction from particulars to generals, followed by a syllo
gistic 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 must reason, but it is
a form in which we may reason, and into which it is indis
pensable to throw our reasoning, when there is any doubt of
its validity : though when the case is familiar and little com
plicated, 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 argument. Its ulterior uses, as respects the general
course of our intellectual operations, hardly require illustra
tion, being in fact the acknowledged uses of general language.
They amount substantially to this, that the inductions may
be made once for all : a single careful interrogation of expe
rience 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
syllogize. The particulars of our experiments may then be
dismissed from the memory, in which it would be impossible
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 forgotten,

* The language of ratiocination would, I think, be brought into closer agree
ment with the real nature of the process, if the general propositions employed
in reasoning, instead of being iu the form All men are mortal, or Every man is
mortal, were expresse I in the form Any man is mortal. This mode of expression,
exhibiting as the type of all reasoning from experience "The men A, B, C &c.
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 par
ticulars to particulars, and that the whole function of general propositions in
reasoning, is to vouch for the legitimacy of such inferences.

222 REASONING.

or as their record became too bulky for reference, is retained
in a commodious and immediately available shape by means
of general language.

Against this advantage is to be set the countervailing
inconvenience, that inferences originally made on insufficient
evidence, become consecrated, aud, 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 pre
sented ; but having forgotten the particulars, it does not
think of revising its own former decision. An inevitable
drawback, which, however considerable in itself, forms evJ-
dently 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 propositions in reasoning. We can reason with
out 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 combination of circum
stances likely to arise. But other minds, and the same minds
where they have not the same pre-eminent advantages of per
sonal experience, are quite helpless without the aid of general
propositions, wherever the case presents the smallest complica
tion ; 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 propositions are necessary to
any considerable progress in reasoning. It is, therefore,
natural and indispensable to separate the process of investiga
tion into two parts ; and obtain general formula? for determin
ing what inferences may be drawn, before the occasion arises
for drawing the inferences. The work of drawing them is
then that of applying the formulas ; and the rules of syllo
gism are a system of securities for the correctness of the
application.

_i § 6. To complete the series of considerations connected

FUNCTIONS AND VALUE OF THE SYLLOGISM. 223

with the philosophical character of the syllogism, it is requi
site 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 pre
mise, and in what manner it contributes to establish the con
clusion : for as to the major, we now fully understand, that
the place which it nominally occupies in our reasonings,
properly 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
security, which it is in a most material degree, for the cor
rectness of the process. The minor, however, being an indis
pensable part of the syllogistic expression of an argument,
without doubt either is, or corresponds to, an equally indis
pensable part of the argument itself, and we have only to
inquire 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 ratio
cination is peculiar. He saw the petitio principii which is
inherent in every syllogism, if we consider the major to be
itself the evidence by which the conclusion is proved, instead of
being, what in fact it is, an assertion of the existence of
evidence sufficient to prove any conclusion of a given descrip
tion. Seeing this, Dr. Brown not only failed to see the
immense advantage, in point of security 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 substituting anything else, and maintained that our
reasonings consist only of the minor premise and the conclu
sion, Socrates is a man, therefore Socrates is mortal : thus
actually suppressing, as an unnecessary step in the argument,

224 REASONING.

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, Socrates 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 entered into on the subject
of propositions, 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 involved in the meaning of "man ;" we might,
undoubtedly, evolve the conclusion from the minor alone,
because the minor would have already asserted it. But 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 corresponds 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 has
not previously perceived this relation, he will not, says Dr.
Brown, infer 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 between the two ideas has
never existed. And in truth it never does exist, except as the
result of experience. Consenting, for the sake of the argu
ment, to discuss the question on a supposition of which we
have recognised the radical incorrectness, namely, that the
meaning of a proposition relates to the ideas of the thing*

FUNCTIONS AND VALUE OF THE SYLLOGISM. 225

spoken of, and not to the things themselves ; I must yet
observe, that the idea of man, as an universal idea, the
common 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
whatever 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 suppose, on the con
trary, that assent to the proposition is produced by evolving,
through an analytic 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 represents, namely,
the various singular propositions expressive of the series of
observations, of which the generalization called the major
premise is the result.

In the argument, then, which proves that Socrates is
mortal, one indispensable part of the premises will be as
follows: "My father, and my father's father, A, B, C, and
an indefinite number of other persons, were mortal ;" which
is only an expression in different words of the observed fact
that they have died. This is the major premise divested of
the petitio principii, 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 pro
position as the following : " Socrates resembles my father, and
my father's father, and the other individuals 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 connoted by the word man.
And we conclude that he further resembles them in the attri
bute mortality.

VOL. i. 15

226 REASONING.

§ 7. We have thus obtained what we were seeking, an
universal type of the reasoning process. We find it resolv
able in all cases into the following elements : Certain indi
viduals have a given attribute ; an individual or individuals
resemble the former in certain other attributes ; therefore
they resemble them also in the given attribute. This type of
ratiocination does not claim, like the syllogism, to be con
clusive, 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 considerations. Whether,
from the attributes in which Socrates resembles those men
who have heretofore died, it is allowable to infer that he
resembles them also in being mortal, is a question of Induc
tion ; 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 inference 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 resembles 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 possession of the
attributes of man as a mark, or satisfactory evidence, of the
attribute of mortality. This we do by laying down the uni
versal proposition, All men are mortal, and interpreting 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 ascer
taining 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

FUNCTIONS AND VALUE OF THE SYLLOGISM. 227

fact taking place, and all reasoning as carried on in the form
into which it must necessarily be thrown to enable us to apply
to it any test of its correct performance.

Although, therefore, all processes of thought in which the
ultimate premises are particulars, whether we conclude 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 Induc
tion as more peculiarly belonging to the process of establish
ing the general proposition, and the remaining operation,
which is substantially that of interpreting the general propo
sition, we shall call by its usual name, Deduction. And we
shall consider every process by which anything is inferred
respecting 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 pre
ceding pages, has obtained, among other important adhesions,
three of peculiar value ; those of Sir John Herschel,* Dr.
Whewell,t and Mr. Bailey ; J Sir John Herschel consider
ing the doctrine, though not strictly " a discovery," § 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 prejudices which it has cast to the winds," there
is no cause for misgiving in the fact that other thinkers, no
less entitled to consideration, have formed a very different esti-

* Review of Quetelet on Probabilities, Essays, p. 367.

f Philosophy of Discovery, p. 289.

t Theory of Reasoning, cb. iv. to which I may refer for an able statement
and enforcement of the grounds of the doctrine.

§ It is very probable that the doctrine is not new, and that it was, as Sir
John Herschel thinks, substantially anticipated by Berkeley. But I certainly
am not aware that it is (as has been affirmed by one of my ablest and most
candid critics) "among the standing marks of what is called the empirical phi
losophy."

15—2

228 REASONING.

mate of it. Their principal objection cannot be better or more
succinctly stated than by borrowing a sentence from Arch
bishop Whately.* " In every case where an 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
judgment that the instance or instances adduced are sufficient
to authorize the conclusion ; that it is allowable to take these
instances as a sample warranting an inference respecting the
whole class ;" and the expression of this judgment in words
(it has been said by several of my critics) is the major
premise.

I quite admit that the major is an affirmation of the suffi
ciency 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 suffi
ciency of the evidence — that is, of the correctness of the induc
tion — 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 generalizing propensity ;
and (until after a considerable amount of practice and mental
discipline) the question of the sufficiency of the evidence is
only raised by a retrospective act, turning back upon our own
footsteps, and examining whether we were warranted in doing
what wTe have already done. To speak of this reflex opera
tion 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 psychology.f
We review our syllogistic as well as our inductive pro
cesses, and recognise that they have been correctly per
formed ; but logicians do not add a third premise to the
syllogism, to express this act of recognition. A careful copyist
verifies his transcript by collating it with the original ; and

* Logic, book iv. ch. i. sect. 1.

t See the important chapter on Belief, in Professor Bain's great treatise,
The Emotions and the Will, pp. 581-4.

FUNCTIONS AND VALUE OF THE SYLLOGISM. 229

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 sufficiency
of the evidence ; as I infer that my friend is walking towards
me because 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 test
ing of the process is not the process itself; and, besides, may
have been omitted altogether, and yet the process be correct.
It is precisely 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 operation a part of the reasoning process
itself. We insist that the inference from particulars to par
ticulars shall pass through a general proposition. But this is a
security for good reasoning, not a condition of all reasoning ;
and in some cases not even a security. Our most familiar
inferences are all made before we learn the use of general pro
positions ; and a person of untutored sagacity will skilfully
apply his acquired experience to adjacent cases, though he
would bungle grievously in fixing the limits of the appropriate
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
Avhat 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 objection, it may be added
that, even when the test has been applied, and the sufficiency
of the evidence recognised, — if it is sufficient to support the
general proposition, it is sufficient also to support an inference
from particulars to particulars without passing through the
general proposition. The inquirer who has logically satisfied
himself that the conditions of legitimate induction were

230 REASONING.

realized in the cases A, B, C, would be as much justified iu
concluding directly to the Duke of Wellington as in conclud
ing to all men. The general conclusion is never legitimate,
unless the particular 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 con
clusion 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 of 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 Quarterly Review" (August 1846), in a review
of this treatise, endeavours to show that there is no petitio principii in the
syllogism, by denying that the proposition, All men are mortal, asserts or
assumes that Socrates is mortal. In support of this denial, he argues that we
may, and in fact do, admit the general proposition that all men are mortal, with
out having particularly examined the case of Socrates, and even without knowing
whether the individual so named is a man or something else. But this of course
was never denied. That we can and do draw conclusions concerning cases
specifically 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 cases, or that it is proved by
a general proposition including both sets of cases, the unknown and the known ?
I contend for the former mode of expression. I hold it 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 he had re
flected very little on the point when he wrote his remarks, is shown by his over
sight respecting the dictum de omni et nullo. He acknowledges that this maxim
as commonly expressed,—" Whatever is true of a class, is true of everything in-

FUNCTIONS AND VALUE OF THE SYLLOGISM. 231

§ 9. The preceding considerations enable us to under
stand the true nature of what is termed, by recent writers,
Formal Logic, and the relation between it and Logic in the
widest sense. Logic, as I conceive it, is the entire theory of

eluded 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 member 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 th'ings 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 con
cerning men does not at all regard him, nor is affected as to its truth or falsity
by anything in which he is concerned.

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 reach,
ing 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 Socrates without knowing it : our own general formula being, to that
extent, for the first time interpreted to us. But according to the reviewer's
theory, the smaller assertion is proved by the larger : while I contend, that both
assertions are proved together, by the same evidence, namely, the grounds of
experience on which the general assertion was made, and by which it must be
justified.

The reviewer says, that if the major premise included the conclusion, " 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 Morgan (Formal Logic, p. 2fi9) : "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 objection
would be well grounded if the assertion 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 supposition, 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 cannot be a necessary part of the argument. It
cannot be a necessary condition of reasoning that we should begin by making

* Mr. De Morgan says " Plato," but to prevent confusion I have kept to my
own exemplum.

232

REASONING.

the ascertainment of reasoned or inferred truth. Formal
Logic, therefore, which Sir William Hamilton from his own
point of view, and Archbishop Whately from his, have re
presented as the whole of Logic properly so called, is really a
very subordinate part of it, not being directly concerned with
the process of Seasoning or Inference in the sense in which
that process is a part of the Investigation of Truth. What,
then, is Formal Logic ? The name seems to be properly
applied to all that portion of doctrine which relates 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 Conver-

an assertion, which is afterwards to be employed 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
lias been ascertained previously : and that the unproved part is bound up in one
formula with the proved part in mere anticipation, and as a memorandum 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 against
erroneous reasoning. The only minor premise necessary to reasoning in the
example under consideration, is, Socrates 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 represented by the minor. Expe
rience, however, of the uncertainty of this loose mode of inference, teaches the
expediency of determining beforehand what kind of likeness to the cases
observed, is necessary to bring an unobserved case within the same predicate ;
and the answer to this question is the major. Thus the syllogistic major and the
syllogistic minor start into existence together, and are called forth by the same
exigency. When we conclude from personal experience without referring to
any record — to any general theorems, either written, or traditional, or mentally
registered 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 substitute a careful one, the revision consists in selecting 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 is well grounded.

FUNCTIONS AND VALUE OF THE SYLLOGISM. 233

sion, ^quipollence, and Opposition ; of those falsely called
Inductions (to be hereafter spoken of*), in which the apparent
generalization is a mere abridged statement of cases known
individually ; and finally, of the syllogism : while the theory
of Naming, and of (what is inseparably connected 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 ob
servance of its precepts, is not truth, but consistency. It has
been seen that this is the only direct purpose of the rules of
the syllogism ; the intention and effect of which is simply to
keep our inferences or conclusions in complete consistency
with our general formulae or directions for drawing them. The
Logic of Consistency 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,
whichj if warrantable at all, admit of being generalized, and,
to test their warrantableness, require to be exhibited in a gene
ralized 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 pre
liminary knowledge 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 a philosophical
justification.

* Infra, book iii. ch. ii.

CHAPTER IV.

OF TRAINS OP REASONING, AND DEDUCTIVE SCIENCES.

§ 1. IN our analysis of the syllogism, 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, 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 resemblance, 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 necessity for trains of reasoning, and De
ductive or Katiocinative Sciences would not exist. Trains of
reasoning exist only for the sake of extending an induction
founded, as all inductions must be, on observed cases, to other
cases in which we not only cannot directly observe what 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 ruminates.
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 expression was correctly performed, the
conclusion respecting the animal now present will be in
stantly drawn ; because, as soon as she is compared with the
formula, she will be identified as being included in it. But
suppose the syllogism to be the following : — All arsenic is

TRAINS OF REASONING. 235

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 evi
dent, but may itself be known only by inference. It may be
the conclusion of another argument, which, thrown into the
syllogistic form, would stand thus : — Whatever when lighted
produces a dark spot on a piece of white porcelain held in the
flame, which spot is soluble in hypochlorite 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 syllogism 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, probably, 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 proper
ties 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 examined various specimens which pos
sessed this metallic and volatile character, whose vapour had
this smell, &c., and have invariably found that they were
poisonous. The first observation we judge that we may ex
tend to all substances whatever which yield that particular
kind of dark spot ; the second, to all metallic and volatile sub
stances 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 sub
stance 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

REASONING.

particulars; but we are now concluding from particulars ob
served, to other particulars which are not, as in the simple
case, seen to resemble them in the material points, but inferred
to do so, because resembling them in something else, which
we have been led by quite a different set of instances to con
sider as a mark of the former resemblance.

This first example of a train of reasoning is still extremely
simple, the series consisting of only two syllogisms. The fol
lowing 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, therefore it is not likely to be over
thrown. The major premise in this argument we shall suppose
not to be derived from considerations a priori, but to be a
generalization from history, which, whether correct or errone
ous, must have been founded on observation of governments
concerning whose desire of the good of their subjects there
was no doubt. It hrs been found, or thought to be found,
that these were not easily overthrown, and it has been
deemed that those instances warranted an 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 argu
ments, and must, in any case, be proved by another induc
tion ; for we cannot directly observe the sentiments and
desires of the persons 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 government
acts in that particular manner, therefore it desires the good
of its subjects. But is it true that the government acts in
the manner supposed? This minor also may require proof;
still another induction, as thus : — What is asserted by intel
ligent and disinterested witnesses, may be believed to be
true; that the government acts in this manner, is asserted by
such witnesses, therefore it may be believed to be true. The
argument hence consists of three steps. Having the evidence

TRAINS OF REASONING. 237

of our senses that the case of the government under consi
deration resembles a number of former cases, in the circum
stance of having something asserted respecting it by intelli
gent and disinterested witnesses, 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 question 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 there
upon, by a second induction, inferred that the particular
government spoken of, desires the good of the people. This
brings that government into known resemblance with the
other governments which were thought likely to escape revo
lution, and thence, by a third induction, it is concluded that
this particular government 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 inductively infer that it has the attribute by which it
is assimilated to the next set, and brought within the
corresponding 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, compared with those by which in the preceding
chapter we illustrated the general theory of reasoning, every
doctrine which we then laid down holds equally true in these
more intricate 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 memories, and a sufficient power of maintaining-
order among a huge mass of details, the reasoning could go

REASONING.

on without any general propositions ; they are mere formulae
for inferring particulars from particulars. The principle of
general reasoning is (as before explained), that if from obser
vation 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 determine once for all what are
the distinguishing marks by which such cases may be recog
nised. The subsequent process is merely that of identifying
an object, and ascertaining 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 unobserved one: but in drawing this infe
rence, we conform to a formula which we have adopted for our
guidance 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 ourselves, 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 previous
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 within 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 in-

TRAINS OF REASONING.

ferencewas, that a certain government was not likely to be
overthrown ; this inference was drawn according to a formula

not b dr: of the publio good was set d°™ - • -™

being likely to be overthrown; a mark of this mark was

fin a particular manner; and a mark of acting in that

»nner was, being asserted to do so by intelligent and dis

interested witnesses ; this mark, the government under dlu.

on was recogmsed by the senses as possessing. Hence that

ET^f bin the last mdaction> and b ** -»" i

o one I \ f6 t , The PerCeiTed reS6m Wance °f «"> cLe
one set of observed particular cases, brought it into known

.resemblance w.th another set, and that with a third

In the more complex branches of knowledge, the deduc
ts seldom consist, as in the examples hitherto xhibited of
a su,gle chaJn, a a mark of i, » of c, c of,, therefore « .1?
They cons,st (to carry on the same metaphor) of several
chams umted at the extremity, as thus : a a mark of d, Tof™
c "V, d ef of „, therefore « t c a mark of n. Supp se te
example, the following ^.^^ rf ^^JJ"

ght .mpmgmg on a reflecting surface ; 2nd, that snr
face parabohc; 3rd, those rays parallel to each other and to the
ax,s o the surface. It ,s to be proved that the concourse of
3 three c.rcumstances is a mark that the reacted rays
nil pass through the focus of the parabolic surface. Now
rf the three circumstances is singly a mark of something'
ma enal to the case. Bays of light impinging on a reflect^
surface, are a mark that those rays wiU°be reflected at »
-gle equal to the angle of incidence. The parabolic form of
e surface „ a mark that, from any point of it, a iine drawn
he foeus and a hne parallel to the axis will make equal
angles w.th the surface. And finally, the parallelism ofThe
•ays to the ax.s ,s a mark that their angle of incidence coij

t±h TK fthe8e eqMl angIeS' The three »«k» ^en
together are therefore a mark of all these three things united

But he three united are evidently a mark that the ang of
reflection must coincide with the other of the two equal angles
that formed by a hne drawn to the focus ; and this again by

240 REASONING.

the fundamental axiom concerning straight lines, is a mark
that the reflected rays pass through the focus. Most chains of
physical deduction are of this more complicated type ; and even
in mathematics such are abundant, as in all propositions where
the hypothesis includes numerous conditions : " // a circle be
taken, and if within that circle a point be taken, not the
centre, and if straight lines be drawn from that point to the
circumference, then," &c.

§ 4. The considerations now stated remove a serious diffi-

9

culty 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 exclusively, and that when these were easy, and suscep
tible of no doubt or hesitation, there could be no science, or, at
least, no difficulties in science. The existence, for example, of
an extensive Science of Mathematics, requiring the highest
scientific genius in those who contributed to its creation, 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 considera
tions more recently adduced remove the mystery, by showing,
that even when the inductions themselves are obvious, there
may be much difficulty in finding whether the particular case
which is the subject of inquiry comes within them ; and ample
room for scientific ingenuity in so combining 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
included.

When the more obvious of the inductions 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 applicable ; 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,

TRAINS OF REASONING. 241

which do not obviously come within any formula whereby the
question 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 pre
sent, what we shall endeavour to prove in the next chapter,
that the first principles of geometry are results of induction!
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 triangle equal or unequal ? The first thing to be
considered is, what inductions we have, from which we can
infer equality or inequality. For inferring equality we have
the following formulas :— Things which being applied 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 differences
of equal things are equals. There are no other original for
mula to prove equality. For inferring inequality we have the
following :— A whole and its parts are unequals. The sums of
equal things and unequal things are unequals. The differ
ences of equal things and unequal things are unequals. In
all, eight formulas. 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 inequality,
but the angles cannot be perceived intuitively to have any of
those marks. On examination it appears that they have ; and
we ultimately 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 possessed some of the
marks of equality set down in the various formulas. By an ex
ercise of ingenuity, which, on the part of the first inventor,
deserves to be regarded as considerable, two pairs of angles
were hit upon, which united these requisites. First, it could be
perceived intuitively that their differences were the angles at
the base ; and, secondly, they possessed one of the marks of
VOL. i. 16

24)2 REASONING.

equality, namely, coincidence when applied to one another.
This coincidence, however, was not perceived intuitively, but
inferred, in conformity to another formula.

For greater clearness, I subjoin an analysis of the de
monstration. Euclid, it will be remembered, demonstrates
his fifth proposition by means of the fourth. This it is not
allowable for us to do, because we are undertaking to trace
deductive truths not to prior deductions, but to their original
inductive foundation. We must therefore 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 prolouging the equal sides
AB, AC, to equal distances, and
joining the extremities BE,
DC.)

FIRST FORMULA. The sums of equals are equal.

AD and AE are sums of equals by the supposition. Hav
ing that mark of equality, they are concluded by this formula
to be equal.

SECOND FORMULA. Equal straight lines 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.
Both these pairs of straight lines have the property of equality;
which, according to the second formula, is a mark that, if ap
plied to each other, they will coincide. Coinciding altogether
means coinciding in every pail, and of course at their extremi
ties, D, E, and B, C.

THIRD FORMULA. Straight lines, having their extremities
coincident, coincide.

B E and C D have been brought within this formula by
the preceding induction ; they will, therefore, coincide.

TRAINS OF REASONING. 243

FOURTH FORMULA. Angles, having their sides coincident,
coincide.

The third induction having shown that BE and CD co
incide, and the second that AB, AC, coincide, the angles
ABE and ACD are thereby brought within the fourth for
mula, and accordingly coincide.

FIFTH FORMULA. Things which coincide are equal.

The angles ABE and ACD are brought within this
formula by the induction immediately preceding. This train
of reasoning being also applicable, mutatis mutandis, to the
angles EEC, DCB, these also are brought within the fifth
formula. And, finally,

SIXTH FORMULA. The differences of equals are equal.

The angle ABC being the difference 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
another, while each pair shall be corresponding angles of
triangles which have two sides and the intervening angle
equal. It is by this happy contrivance that so many different
inductions 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 com
bine 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
necessary for bringing the inductions together, even when each
induction may itself be very easy and simple. All the induc
tions involved in all geometry are comprised in those simple
ones, the formulae of which are the Axioms, and a few of the

16—2

244 REASONING.

so-called Definitions. The remainder of the science is made
up of the processes employed for bringing unforeseen cases
within these inductions ; or (in syllogistic language) for prov
ing 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 Deductions, or Trains of Seasoning, forms
the whole difficulty of the science, and with a trifling excep
tion, its whole bulk; and hence Geometry is a Deductive
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 construct the science from the fewest and the simplest
possible inductions, and to make these, by any combinations
however complicated, suffice for proving even such truths,
relating to complex cases, as could be proved, if we chose, by
inductions from specific experience. Every branch of natural
philosophy was originally experimental; each generalization
rested on a special induction, and was derived from its own
distinct set of observations and experiments. From being
sciences of pure experiment, as the phrase is, or, to speak
more correctly, sciences in which the reasonings mostly con
sist 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 induc
tive propositions of a simpler and more universal character.
Thus mechanics, hydrostatics, optics, acoustics, thermo-

* Infra, book iii. ch. iv. § 3, and elsewhere.

TRAINS OF REASONING. 245

logy, have successively been rendered mathematical ; and
astronomy was brought by Newton within the laws of general
mechanics. Why it is that the substitution 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, prepared to examine. But it is necessary 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 Induction. 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 induc
tion. It is deductive, in proportion as it can draw conclusions,
respecting cases of a new kind, by processes which bring those
cases under old inductions ; 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 dis
tinction between sciences which can be made Deductive, and
those which must as yet remain Experimental. The differ
ence consists in our having been able, or not yet able, to dis
cover marks of marks. If by our various inductions we have
been able to proceed no further than to such propositions 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 b with c or d ; we have a science of detached
and mutually independent generalizations, 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, is 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 of d, d of e, &c. In these sciences we can mount

246 REASONING.

the ladder from a to e 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, perhaps, 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 meta
phor, 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.

§ 6. We can now understand how an experimental may
transform itself into a deductive science by the mere progress
of experiment. In an experimental science, the inductions,
as we have said, lie detached, as, a a mark of b, c a mark of
d, e a mark of/, and so on : now, a new set of instances, and
a consequent new induction, may at any time bridge over
the interval between two of these unconnected 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 comprehensive 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 con
nexion has already been traced. As when Newton discovered
that the motions, whether regular or apparently anomalous,
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 varying 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,

TRAINS OF REASONING. 247

continually take place in the less advanced branches of physical
knowledge, without enabling them to throw off the character of
experimental sciences. Thus with regard to the two uncon
nected propositions before cited, namely, Acids redden vege
table blues, Alkalies make them green ; it is remarked by
Liebig, that all blue colouring matters which are reddened by
acids (as well as, reciprocally, all red colouring matters which
are rendered blue by alkalies) contain nitrogen : and it is quite
possible that this circumstance may one day furnish a bond of
connexion between the two propositions in question, by show
ing that the antagonistic action of acids and alkalies in pro
ducing or destroying the colour blue, is the result of some
one, more general, law. Although this connecting of detached
generalizations is so much gain, it tends but little to give a
deductive character to any science as a whole ; because the new
courses of observation and experiment, which thus enable us
to connect together a few general truths, usually make known
to us a still greater number of unconnected new ones. Hence
chemistry, though similar extensions and simplifications of its
generalizations 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 number of the
smaller known inductions together, and change the whole
method of the science at once. Chemistry has already one
great generalization, which, though relating to one of the sub
ordinate 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 enabling 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 de
scription previously obtained by experiment.

§ 7. The discoveries which change the method of a
science from experimental to deductive, mostly consist in

248 REASONING.

establishing, either by deduction or by direct experiment, that
the varieties of a particular phenomenon uniformly accompany
the varieties of some other phenomenon better known. Thus
the science of sound, which previously stood in the lowest
rank of merely experimental science, became deductive when
it was proved by experiment that every variety of sound was
consequent on, and therefore a mark of, a distinct and de
finable variety of oscillatory motion among the particles of the
transmitting medium. When this was ascertained, it followed
that every relation of succession or coexistence which ob
tained between phenomena of the more known class, obtained
also between the phenomena which corresponded to them
in the other class. Every sound, being a mark of a parti
cular oscillatory motion, 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 propa
gation of motion through an elastic medium ; while facts
already empirically known respecting sound, become an indi
cation of corresponding properties of vibrating bodies, pre
viously undiscovered.

But the grand agent for transforming experimental into de
ductive sciences, is the science of number. The properties of
numbers, 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 ascertained 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 discovered that variations of quality in any
class of phenomena, correspond regularly to variations of
quantity either in those same or in some other phenomena ;

TRAINS OF REASONING. 249

every formula of mathematics applicable to quantities which
vary in that particular manner, becomes a mark of a corre
sponding general truth respecting the variations 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 becomes, to this extent, de
ductive likewise.

The most striking instance in point which history affords
(though not an example of an experimental science rendered
deductive, but of an unparalleled extension given to the de
ductive process in a science which was deductive already), is
the revolution in geometry which originated with Descartes,
and was completed by Clairaut. 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 pecu
liar relation of quantity between either two or three rectilineal
co-ordinates ; insomuch that if the law were known according
to which those co-ordinates vary relatively to one another,
every other geometrical property of the line or surface in
question, 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
algebraical one could ; and geometry received an accession
(actual or potential) 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 commonly so called, have
been made algebraical. The varieties of physical 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 pro-

250 REASONING.

positions forming a train of reasoning, viz. that of enabling
us to arrive in an indirect method, by marks of marks, at such
of the properties 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 certain relation
subsists between the quantities of some of the elements con
cerned ; while the fact sought presupposes a certain relation
between the quantities of some other elements : now, if these
last quantities are dependent in some known manner upon the
former, or vice versa, 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.

CHAPTEE V.

OF DEMONSTRATION, AND NECESSARY TRUTHS.

§ 1. IF, as laid down in the two preceding chapters, the
foundation of all sciences, even deductive or demonstrative
sciences, is Induction ; if every step in the ratiocinations even
of geometry is an act of induction ; and if a train of reasoning
is but bringing many inductions to bear upon the same subject
of inquiry, and drawing a case within one induction by means
of another ; wherein lies the peculiar certainty always ascribed
to the sciences which are entirely, or almost entirely, deduc
tive ? 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 assur
ance attainable by reason ? Why are mathematics by almost
all philosophers, and (by some) even those branches of natural
philosophy which, through the medium of mathematics, have
been converted into deductive sciences, considered to be inde
pendent of the evidence of experience and observation, and
characterized as systems of Necessary Truth ?

The answer I conceive to be, that this character of neces
sity, 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 suppose that those truths relate to, and ex
press the properties of, purely imaginary objects. It is
acknowledged that the conclusions of geometry are deduced,
partly at least, from the so-called Definitions, and that those
definitions are assumed to be correct representations, as far as
they go, of the objects with which geometry is conversant.
Now we have pointed out that, from a definition as such, no
proposition, unless it be one concerning the meaning of a
word, can ever follow; and that what apparently follows

REASONING.

from a definition, follows in reality from an implied assump
tion that there exists a real thing conformable thereto. This
assumption, in the case of the definitions of geometry, is false :
there exist no real things exactly conformable to the defini
tions. 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 will perhaps be said that the assumption
does not extend to the actual, but only to the possible, ex
istence of such things. I answer that, according 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 inconsistent with the physical constitution of our planet at
least, if not of the universe. To get rid of this difficulty,
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 geometry, 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
whatever to do with outward experience. By howsoever high
authorities this doctrine may have been sanctioned, it appears
to me psychologically incorrect. 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 visibile, the
smallest portion of surface which we can see. A line, as
defined by geometers, is wholly inconceivable. 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,
instead 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

DEMONSTRATION, AND NECESSARY TRUTHS. 253

experience. I much question if any one who fancies that he
can conceive what is called a mathematical line, thinks so
from the evidence of his consciousness : I suspect it is rather
because he supposes that unless such a conception were possi
ble, 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 ; nothing remains but to consider
geometry 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 generalizations
concerning those natural objects. The correctness of those
generalizations, as generalizations, is without a flaw : the
equality of all the radii of a circle is true of all circles, so far
as it is 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 in
ductions, 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 conclusions, by combining
with them a fresh set of propositions relating to the aberra
tion ; 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 respect to figure and
magnitude, as in the case, for instance, of expansion by heat.
So long, however, as there exists no practical necessity for
attending to any of the properties of the object except its
geometrical properties, or to any of the natural irregularities
in those, it is convenient to neglect the consideration of the
other properties and of the irregularities, and to reason as if
these did not exist: accordingly, we formally announce in the
definitions, that we intend to proceed on this plan. But it is

254 REASONING.

an error to suppose, because we resolve to confine our atten
tion 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 thinking, 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 pro
perties, except those which are material to our purpose, and in
regard to which we design to consider them.

The peculiar accuracy, supposed to be characteristic of the
first principles of geometry, thus appears to be fictitious. The
assertions on which the reasonings of the science are founded,
do not, any more 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 Stewart respecting 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 compelling assent, on condition that those hypotheses
are tme^

When, therefore, it is affirmed that the conciiisinns_of
geometry are necessary 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 pur
posely 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 assumption, which, by the conditions of the inquiry,
is not to be questioned. In this relation, of course, the deri
vative truths of every deductive science must stand to the
inductions, or assumptions, on which the science is founded,
and which, whether true or untrue, certain or doubtful in
themselves, are always supposed certain for the purposes of the

DEMONSTRATION, AND NECESSARY TRUTHS. 255

particular science. And therefore the conclusions of all deduc
tive sciences were said hy the ancients to he necessary propo
sitions. We have observed already 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 endeavoured to enforce, has been contested by Dr.
Whewell, both in the dissertation appended to his excellent
Mechanical Euclid, and in his elaborate work on the Philosophy
of the Inductive Sciences ; in which last he also replies to an
article in the Edinburgh Keview, (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 proving 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 definitions. 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 contained, 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 maintain them to be
hypotheses which have no relation whatever to fact. Since an
hypothesis framed for the purpose of scientific inquiry must

* Mechanical Euclid, pp. 149 et seqy.

256

REASONING.

relate to something which has real existence, (for there can be
no science respecting non-entities,) it follows that any hypo
thesis we make respecting an object, to facilitate our study of
it, must not involve anything which is distinctly false, and re
pugnant to 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 sup
pressing others, under the indispensable obligation of restoring
them whenever, and in as far as, their presence or absence
would make any material difference in the truth of our con
clusions. Of this nature, accordingly, are the first principles
involved 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 corrections, would be true of real
objects : and in fact, when our aim is only to illustrate truths,
and not to investigate them, we are not under any such restriction .
We might suppose an imaginary animal, and work out by de
duction, from the known laws of physiology, its natural history ;
or an imaginary commonwealth, and from the elements com
posing it, might argue what would be its fate. And the con
clusions which we might thus draw from purely arbitrary hypo
theses, 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 constitute any addi
tion 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 liability 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 principles of geometry which are involved in the so-
called definitions, he has, I conceive, greatly the advantage of
Stewart on another important point in the theory of geome
trical reasoning ; the necessity of admitting, among those first

DEMONSTRATION, AND NECESSARY TRUTHS. 257

principles, axioms as well as definitions. Some of the axioms
of Euclid might, no doubt, be exhibited in the form of defini
tions, or might be deduced, by reasoning, from propositions
similar to what are so called. Thus, if instead of the axiom,
Magnitudes which can be made to coincide are equal, we in
troduce a definition, " Equal magnitudes are those which may
be so applied to one another as to coincide ;" the three axioms
which follow (Magnitudes which 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 suscep
tible 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 inclose a space, (or its equivalent, Straight
lines which coincide in two points coincide altogether,) and
some property of parallel lines, other than that which con
stitutes their definition : one of the most suitable for the pur
pose being that selected by Professor Playfair : " Two straight
lines which intersect each other cannot both of them be parallel
to a third straight line."*

The axioms, as well those which are indemonstrable as those
which admit of being demonstrated, differ from that other
class of fundamental principles which are involved in the

* We might, it is true, insert this property into the definition of parallel
lines, framing the definition so as to require, both that when produced indefi
nitely 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 assumption ; we are still obliged to take for granted the
geometrical truth, that all straight lines in the same plane, which have the
former of these properties, have also the latter. For if it were possible that
they should not, that is, if any straight lines other than those which are parallel
according to the definition, had the property of never meeting although indefi
nitely produced, the demonstrations of the subsequent portions of the theory of
parallels could not be maintained.

VOL. I. 17

258 REASONING.

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 imaginary 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 approxi
mations 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 without
qualification or error. The rotation of the earth in twenty-
four hours, of the same length as in our time, has gone on since
the first accurate observations, without the increase or diminu
tion 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 experimental truths ; generalizations from ob
servation. The proposition, Two straight lines cannot inclose
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 probably no pro
position enunciated in this work for which a more unfavourable
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 consider it very fortunate that so emi
nent a champion of the contrary opinion as Dr. Whewell, has

DEMONSTRATION, AND NECESSARY TRUTHS. 259

found occasion for a most elaborate treatment of the whole
theory of axioms, in attempting to construct the philosophy
of the mathematical and physical sciences on the basis of the
doctrine 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 re
presented. 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 conclusive, enough will have
been done, without going further in quest of stronger argu
ments and a more powerful 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 inclose
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 perceived a priori, by the constitution of the mind itself,
from the first moment when the meaning of the proposition is
apprehended ; and without any necessity for verifying it by
repeated trials, as is requisite in the case of truths really
ascertained by observation. A

They cannot, however, but allow that the truth of the
axiom, Two straight lines cannot inclose a space, even if
evident independently of experience, is also evident from
experience. Whether the axiom needs confirmation or not,
it receives confirmation 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 con
tinue 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 experimental truth, than we have for
almost any of the general truths which we confessedly learn
from the evidence of our senses. Independently of a priori
evidence, we should certainly believe it with an intensity of

17—2

260 REASONING.

conviction far greater than \ve 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 know
ledge, and much too early to admit of our retaining any
recollection of the history of our intellectual operations at
that period. Where then is the necessity 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 produce 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 advocates of
the contrary opinion : it is for them to point out some fact,
inconsistent with the supposition that this part of our know
ledge of nature is derived from the same sources as every other
part.*

This, for instance, they would be able to do, if they could
prove chronologically that we had the conviction (at least
practically) so early in infancy as to be anterior to those im
pressions 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.

* Some persons find themselves prevented from believing that the axiom,
tWo straight lines cannot inclose a space, could ever become known to us
through experience, by a difficulty which may be stated as follows. If the
straight lines spoken of are those contemplated in the definition — lines abso
lutely without breadth and absolutely straight ; — that such are incapable of
inclosing a space is not proved by experience, 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 experience, lines straight enough for
practical purposes, but in reality slightly zigzag, and with some, however
trifling, breadth ; as applied to these lines the axiom is not true, for two of
them may, and sometimes do, inclose 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

DEMONSTRATION, AND NECESSARY TRUTHS. 261

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 inclose a space,
were derived from the senses, we could only be convinced of
its truth by actual trial, that is, by seeing or feeling the
straight lines ; 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 mere 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 inclose a space. Intuition is " ima
ginary looking ;"* but experience must be real looking : if we
see a property of straight lines to be true by merely fancying
ourselves to be looking 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 unnecessary, but unattainable. What says the
axiom ? That two straight lines cannot inclose a space ; that
after having once intersected, if they are prolonged to infinity
they do not meet, but continue to diverge from one another.

valid mode of inductive proof ; proof by approximation. Though experience
furnishes us with no lines so uninipeachably straight that two of them are inca
pable of inclosing 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 definition is the ideal limit. And observation shows that
just as much, and as nearly, as the straight lines of experience approximate to
having no breadth or flexure, so much and so nearly does the space-inclosing
power of any two of them approach to zero. The inference that if they had
no breadth or flexure at all, they would inclose no space at all, is a correct in
ductive inference from these facts, conformable to one of the four Inductive
Methods hereinafter characterized, the Method of Concomitant Variations ; of
which the mathematical Doctrine of Limits presents the extreme case.
* Whe well's History of Scientific Ideas, i. 140.

262 . REASONING.

How can this, in any single case, be proved by actual obser
vation ? 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 proof of the im
possibility than observation 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 geome
trical forms — their capacity of being painted in the imagina
tion with a distinctness 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 subjects of
geometrical experimentation as the realities themselves ; inas
much as pictures, if sufficiently accurate, exhibit 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 contemplation) 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 representatives 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 completely fulfilled by an
object existing only in our fancy. Without denying, therefore,
the possibility of satisfying ourselves that two straight lines
cannot inclose a space, by merely thinking of straight lines
without actually looking at them ; I contend, that we do not

DEMONSTRATION, AND NECESSARY TRUTHS. 263

believe this truth on the ground of the imaginary intuition
simply, hut 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, therefore, is
still an induction from observation. And we should not be
authorized 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 properties of the reality are faith
fully represented in the image ; just as we should be scienti
fically warranted in describing 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 precisely equivalent to observation of the
original.

These considerations also remove the objection arising from
the impossibility of ocularly following the lines in their pro
longation 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 begin again to approach, this must take place
not at an infinite, but at a finite distance. Supposing, there
fore, such to be the case, we can transport ourselves thither in
imagination, and can frame a mental image of the appearance
which one or both of the lines must present at that point,
which we may rely on as being precisely similar to the reality.
Now, whether we fix our contemplation upon this imaginary
picture, or call to mind the generalizations we have had occa
sion 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 senses which we describe by the ex
pression, " a bent line," not by the expression, " a straight
line."*

* Dr. Whewell (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 says, " how we can compare our ideas

264 REASONING.

§ C. The first of the two arguments in support of the
theory that axioms are a 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, hut as universally and necessarily true.
Now, experience cannot possibly give to any proposition this

with the realities, since we know the realities only by our ideas." We know
the realities (I conceive) by our senses. Dr. Whewell surely does not hold the
" doctrine of perception by means of ideas," which Reid gave himself so much
trouble to refute.

If Dr. Whewell doubts whether we compare our ideas with the corresponding
sensations, 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 himself.

Dr. Whewell also says, that it does not appear why this resemblance of
ideas to the sensations of which they are copies, should be spoken of as if it
were a peculiarity of 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 sensations, but they do so
with very different degrees of exactness and of reliability. No one, I presume,
can recal in imagination a colour or an odour with the same distinctness and
accuracy with which almost every one can mentally reproduce an image of a
straight line or a triangle. To the extent, however, of their capabilities of
accuracy, our recollections of colours or of odours may serve as subjects of
experimentation, 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 darkest 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 distinct recollection of the
colours ; that is, he might examine his mental pictures, and find there a pro
perty of the outward objects. But in hardly any case except that 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 the 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
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 every
body has a perfectly distinct mental image of a straight line, a circle, or a rec
tangle. And every one concludes confidently from these mental images to the
corresponding outward things. The truth is, that we may, and continually do,
study nature in our recollections, when the objects themselves are absent ; and
in the case of geometrical forms we can perfectly, but in most other cases only
imperfectly, trust our recollections.

DEMONSTRATION, AND NECESSARY TRUTHS. 265

character. I may have seen snow a hundred times, and may
have seen that it was white, but this cannot give me entire
assurance even that all snow is white ; much less that snow
must be white. " However many instances we may have ob
served 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 observations ; and, how
ever numerous these may be, they can show nothing with re
gard 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 record what has happened ; but she cannot find,
in any case, or in any accumulation 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
supplies, in its occurrence, no reason for its recurrence. She
contemplates external objects; but she cannot detect any in
ternal bond, which indissolubly connects the future with the
past, the possible with the real. To learn a proposition by ex
perience, and to see it to be necessarily true, are two altogether
\ different processes of thought."* And Dr. Whewell adds, " If
any one does not clearly comprehend this distinction of neces
sary and contingent truths, he will not be able to go along
with us in our researches into the foundations of human know
ledge ; nor, indeed, to pursue with success any speculation on
the subject."t

In the following passage, we are told what the distinction
is, the non-recognition of which incurs this denunciation.
" Necessary truths are those in which we not only learn that
the proposition is true, but see that it must be true ; in which

* History of Scientific Ideas, i. 65-67. t Ibid. 60.

266 REASONING.

the negation of the truth is not only false, but impossible ; in
which we cannot, even by an effort of imagination, or in a sup
position, 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 to
gether make 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 naturally 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 any
thing more.

This, therefore, is the principle asserted : that propositions,
the negation of which is inconceivable, or in other words, which
we cannot figure to ourselves as being false, must rest on evi
dence of a higher and more cogent description than any which
experience can afford.

Now I cannot but wonder that so much stress should be
laid on the circumstance of inconceivableness, when there is
such ample experience to show, that our capacity or incapacity
of conceiving 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 acknowledged 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

* History of -Scientific Ideas, i. 58, 59.

DEMONSTRATION, AND NECESSARY TRUTHS. 267

separately, there is by the primary law of association an in
creasing difficulty, which may in the end become insuperable,
of conceiving the two things apart. This is most of all con
spicuous in uneducated 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 accus
tomed to exercise their imagination, they have experienced
their sensations and thoughts in more varied combinations, and
have been prevented from forming many of these inseparable
associations. 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
probably 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 impos
sible, because inconceivable, things which their posterity, by
earlier practice and longer perseverance in the attempt, found
it quite easy to conceive, 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 instead of downwards. The
Cartesians long rejected the Newtonian doctrine of the gravi-

b "If all mankind had spoken one language, we cannot doubt that there
would have been a powerful, perhaps a universal, school of philosophers, who
would have believed in the inherent connexion between names and things, who
would have taken the sound man to be the mode of agitating the air which is
essentially communicative of the ideas of reason, cookery, bipedality, &c." — De
Morgan, Formal Logic, p. 246.

268 REASONING.

tation of all bodies towards one another, on the faith of a
general proposition, the reverse of which seemed to them to
be inconceivable — 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.* And they no doubt found it as
impossible to conceive that a body should act upon the earth
at the distance of the sun or moon, as we find it to conceive
an end to space or time, or two straight lines inclosing a space.
Newton himself had not been able to realize the conception,
or we should not have had his hypothesis of a subtle ether, the
occult cause of gravitation ; 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. It would seem that even
now the majority of scientific men have not completely got
over this very difficulty ; for though they have at last learnt
to conceive the sun attracting the earth without any intervening
fluid, they cannot yet conceive the sun illuminating the earth
without some such medium.

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 impossible, what is afterwards not only
found to be conceivable but proved to be true ; what wonder

* It would be difficult to name a man more remarkable at once for the great
ness and the wide range of his mental accomplishments, 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 : — " Toutce qui n'est pas explicable"
says he in a letter to the Abbe" Conti, "par la nature des creatures, est mira-
culeux. II ne suffit pas de dire : Dieu a fait une telle loi de nature ; done la
chose est naturelle. II faut que la loi soit executable par les natures des
creatures. Si Dieu donnait cette loi, par exemple, a un corps libre, de tourner
a 1'entour d'un certain centre, il faudrait ou qu'il y joigntt d'autres corps qui
par leur impulsion Vobligeassent de rester toujours dans son orbite circulaire, ou
qu'il mU un ange d ses trousses, ou enjin il faudrait qu'il y concourut extraordi-
nairement ; car naturellement il s'e'cartera par la tangente." — Works of Leibnitz,
ed. Dutens, iii. 446.

DEMONSTRATION, AND NECESSARY TRUTHS. 269

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 vari
ance with the association, the acquired incapacity should con
tinue, 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 innu
merable familiar analogies to assist the conception ; which,
after all, we should probably 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 con
ceive a slight change in the direction of motion, a circum
stance familiar to our experience. But when experience 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, therefore, we attempt to con
ceive the last point of space, we have the idea irresistibly
raised of other points beyond 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 funda
mental 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 inclose 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 inconceiv
able to us ? What analogy have we, what similar order of
facts in any other branch of our experience, to facilitate to us

270 REASONING.

the conception of two straight lines inclosing a space ? Nor
is even this all. I have already called attention to the pecu
liar property of our impressions of form, that the ideas or
mental images exactly resemhle their prototypes, and ade
quately represent them for the purposes of scientific observa
tion. From this, and from the intuitive character of the
observation, which in this case reduces itself to simple inspec
tion, we cannot so much as call up in our imagination two
straight lines, in order to attempt to conceive them inclosing
a space, without by that very act repeating the scientific
experiment which establishes the contrary. Will it really be
contended that the inconceivableness of the thing, in such cir
cumstances, proves anything against the experimental 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 condi
tion which I can assure him I have conscientiously fulfilled, —
I, in return, with equal confidence, exhort those who agree
with him, to study the general laws of association ; being con
vinced 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 mea
sures the possibility of things in themselves, by the human
capacity of conceiving them.

1 hope to be pardoned for adding, that Dr. Whewell him
self 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 asserts, that propositions
which not only are not self-evident, but which we know to
have been discovered gradually, 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 impos
sible to conceive that they had not been recognised from the

DEMONSTRATION, AND NECESSARY TRUTHS. 271

first by all persons in a sound state of their faculties. " We
now despise those who, in the Copernican controversy, could
not conceive the apparent motion of the sun on the heliocentric
hypothesis ; or those who, in opposition to Galileo, thought
that a uniform force might be that which generated a velocity
proportional to the space ; or those who held there was some
thing absurd in Newton's doctrine of the different refrangi-
bility of differently coloured rays ; or those who imagined that
when elements combine, their sensible qualities must be mani
fest 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 per
suasion 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 prejudiced, 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 manifestly
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 inconceivable."*

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 experience, because their falsity is inconceivable.
But Dr. Whewell himself 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

* Novum Oryanum Renovatum, pp. 32, 33.

272 REASONING.

(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 he right in regarding as inconceivable
what others have conceived, and as self-evident what to others
did not appear evident at all. After so complete an admission
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 to each 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 para
doxes. The first law was especially so. That a body, once
in motion, would continue for ever to move in the same direc
tion with undiminished 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 experience of the most familiar kind, which taught
that it was the nature of motion to abate gradually, and at last
terminate of itself. Yet when once the contrary doctrine was
firmly established, mathematicians, as Dr. Whewell observes,
speedily began to believe that laws, thus contradictory to first
appearances, and which, even after full proof had been ob
tained, 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

* History of Scientific Ideas, i. 264.

DEMONSTRATION, AND NECESSARY TRUTHS. 273

other;" and he himself, though not venturing "absolutely
to pronounce" that all 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,
historically speaking, by means of experiment, we have now
attained a point of view in which we see that it might have
been certainly known to be true, independently of experi
ence.^ Can there be a more striking exemplification than is
here afforded, of the effect of association which we have
described ? Philosophers, for generations, have the most
extraordinary difficulty in putting certain ideas together;
they at last succeed in doing so ; and after a sufficient repeti
tion of the process, they first fancy a natural bond between
the ideas, then experience a growing difficulty, which at last,
by the continuation of the same progress, becomes an impos
sibility, of severing them from one another. If such be the
progress of an experimental conviction of which the date is
of yesterday, 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 suggested even a momentary doubt ?

The other instance4 which I shall quote is a truly asto
nishing one, and may be called the reductio ad absurdum of
the theory of inconceivableness. Speaking of the laws of
chemical composition, Dr. Whewell says :{ " That they could
never have been clearly understood, and therefore never firmly
established, without laborious and exact experiments, is
certain; but yet we may venture to say, that being once
known, they possess an evidence beyond that of mere experi
ment. For how in fact can we conceive combinations, other
wise than as definite in kind and quality ? If we were to
suppose each element ready to combine with any other indif
ferently, and indifferently in any quantity, we should have a

* Hist. Sc. Id., i. 263. f Ibid. 240.

J Hist. Sc. Id., ii. 25, 26.
VOL. I. ] 8

274 REASONING.

world in which all would be confusion 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
consists of bodies distinguishable from each other by definite
differences, capable of being classified and named, and of
having general propositions asserted concerning them. And
as we cannot conceive a world in ivhich this should 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 pro
portions ; 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 combination and that of constant proportions so familiar
and intimate as to be unable to conceive the one fact without
the other; is so signal an instance of the mental law for which
I am contending, that one word more in illustration must be
superfluous.

In the latest and most complete elaboration of his meta
physical system (the Philosophy of Discovery), as well as in
the earlier discourse on the Fundamental Antithesis of Philo
sophy, reprinted as an appendix to that work, Dr. Whewell,
while very candidly admitting that his language was open to
misconception, disclaims having intended to say that mankind
in general can now perceive the law of definite proportions in
chemical combination 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 at
tainment."* And he explains that the inconceivableness

* Phil, of Disc., p. 339.

DEMONSTRATION, AND NECESSARY TRUTHS. 275

which, according to his theory, is the test of axioms, " de
pends entirely upon the clearness of the Ideas which the
axioms involve. So long as those Ideas are vague and indis
tinct, the contrary of an Axiom may he assented to, though
it cannot be distinctly conceived. It may be assented to, not
because it is possible, but because ye do not see clearly what
is possible. To a person who is only beginning to think
geometrically, there may appear nothing absurd in the asser
tion, that two straight lines may inclose 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 processes, Eeaction 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 operations, we should generate new matter,
or destroy matter which already exists."* Necessary truths,
therefore, are not those of which we cannot conceive, but
" those of which we cannot distinctly conceive, the contrary."!
So long as our ideas are indistinct altogether, we do not know
what is or is not capable of being distinctly conceived ; but,
by the ever increasing distinctness with which scientific men
apprehend the general conceptions of science, they in time
come to perceive that there are certain 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
nature has been ascertained, men's minds do not at first acquire
a complete facility of familiarly representing 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 descriptions conformably
to the laws which regulate them — phenomena of all descrip
tions according to the relations which have been ascertained
really to exist between them ; this habit, in the case of newly

* Phil, of Disc., p. 338. f Ib. p. 463.

18—2

276 REASONING.

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 concerned, 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 representing facts which results from the theory, has now
become, to his faculties, the only natural mode of conceiving
them. It is a known truth, that a prolonged habit of arrang-
' ing phenomena in certain groups, and explaining them by
means of certain principles, makes any other arrangement 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
il^*L.them in that mode.

J' But, further, if the theory is true, as we are supposing it to
\fu,s ' /) be, any other mode in which he tries, or in which he was for
merly accustomed, to represent the phenomena, will be seen
by him to be inconsistent with the facts that suggested the new
- — facts which now form a part of his mental picture of
nature. And since a contradiction is always inconceivable, his
imagination rejects these false theories, and declares itself in
capable of conceiving them. Their inconceivableness to him
does not, however, result from anything in the theories them
selves, intrinsically and a priori repugnant to the human
faculties ; it results from the repugnance between them and a

Vr^ Porti°n °f tbe facts ; which facts as long as he did not know,
\ or did not distinctly realize in his mental representations, the
false theory did not appear other than conceivable ; it becomes
•Xl^ inconceivable, merely from the fact that contradictory elements

cannot be combined in the same conception. 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 inconceivable, and that he adopts the true theory because

DEMONSTRATION, AND NECESSARY TRUTHS. 277

it is self-evident, and does not need the evidence of experience
at all.

This I take to be the real and sufficient 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 inconceivable in the suppositions
themselves ; the impossibility is in combining 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 sup
positions 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 ex
ample) to which Dr. Whewell ascribes a more thorough cha
racter of necessity and self-evidence, than that of the indestruc
tibility 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 unassisted senses, takes place every time that water
dries up, or fuel is consumed. Again, the law that bodies
combine chemically in definite proportions is undeniably true ;
but few besides Dr. Whewell have reached the point which he
seems personally to have arrived at, (though he only dares
prophesy similar success to the multitude after the lapse of
generations,) that of being unable to conceive a world in which
the elements are ready to combine with one another " indiffe
rently 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 aeriform, ex
hibit 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

278 REASONING.

the contrary, assumed in the interpretation of experience. Our
inability to " add to or diminish the quantity of matter in the
world," is a truth which " neither is nor can be derived from,
experience ; for the experiments 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 assumed ; but, I apprehend, no otherwise than as
all experimental inquiry assumes provisionally some theory or
hypothesis, which is to be finally held true or not, according as
the experiments decide. The hypothesis chosen for this pur
pose will naturally be one which groups together some consi
derable 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 appearance 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 pro
ceeded to try whether, on more careful examination, the pheno
mena which apparently pointed to a different conclusion, 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
universal 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-evi
dent, 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

ti assumed, for the purpose of connecting them by deductions

I with those facts of experience on which, as evidence, they now

/ confessedly rest.t

\J * Phil, of Disc., pp. 472, 473.

t The Quarterly Review for June 1841, contained an article of great ability

DEMONSTRATION, AND NECESSARY TRUTHS. 279

on Dr. Whewell's two great works (since acknowledged and reprinted in Sir
John Herschel's Essays) which maintains, on the subject of axioms, the doctrine
advanced in the text, that they are generalizations from experience, and sup
ports 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,
(the greater part, indeed, before it was published,) it is not my object to
occupy the reader's attention with a matter so unimportant as the degree
of originality 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 sentiment
between 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 propositions concerning magnitude in the abstract, which are equally true of
space, time, force, number, and every other magnitude susceptible of aggrega
tion and subdivision. Such propositions, where they are not mere definitions,
as some of them are, carry their inductive origin on the face of their enuncia
tion. . . . Those which declare that two straight lines cannot inclose 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 straightness is uniformity of direction, 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., mental experience,
as included in the very idea of uniformity ; nor on that of transfer of the contem
plating being from point to point, and of experience, during such transfer, of
the homogeneity of the interval passed over) we cannot even propose the propo
sition 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 than one path direct to the same object, is matter of
practical experience long before it can by possibility 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 recollection 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 the homogeneity of
the parts of distance, time, force, and measurable aggregates in general, 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 inward 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 sim-

280 REASONING.

plicity of these primary relations, 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 relations."
And again, of the axioms of mechanics : — "As we admit no such propo
sitions, other than as truths inductively collected from observation, even in
geometry itself, it can hardly be expected that, in a science of obviously contin
gent relations, we should acquiesce in a contrary view. Let us take one of these
axioms and examine its evidence : for instance, that equal forces perpendicularly
applied at the opposite ends of equal arms of a straight lever will balance each
other. What but experience, we may ask, in the first place, can possibly inform
us that a force so applied will have any tendency to turn the lever on its centre
at all ? or that force can be so transmitted along a rigid line perpendicular to its
direction, as to act elsewhere in space than 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 molecular 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 a priori
reasoning can possibly assure us that they do act under precisely similar circum
stances? that points which differ in place are similarly circumstanced as regards
the exertion of force ? that universal space may not have relations to universal
force — or, at all events, that the organization of the material universe may not
be such as to place that portion of space occupied by it in such 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
movement in the lever at all ? The case is one of rest, and of quiescent de
struction of force by force. Now how is this destruction effected ? Assuredly
by the counter-pressure which supports the fulcrum. But would not this de
struction equally arise, and by the same amount of counter-acting force, if
each force simply pressed its own half of the lever against the fulcrum ? And
what can assure us that it is not so, except removal of one or other force, and
consequent tilting of the lever ? The other fundamental axiom of statics, that
the pressure on the 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 universal experience, viz. that the weight of a rigid body is
the same, handle it or suspend it in what position or by what point we will,
and that whatever sustains it sustains its total weight. Assuredly, as Mr.
Whewell justly remarks, ' No one probably 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 addi
tional attempt made with scientific accuracy. This would be as if a man
should resolve to decide by experiment whether his eyes were useful forthe purpose
of seeing, by hermetically sealing himself up for half an hour in a metal case."
On the " paradox of universal propositions obtained by experience," the same
writer says : " If there be necessary and universal truths expressible in proposi
tions of axiomatic simplicity and obviousness, and having for their subject-

DEMONSTRATION, AND NECESSARY TRUTHS. 281

matter the elements of all our experience and all our knowledge, surely these are
the truths which, if experience suggest to us any truths at all, it ought to suggest
most readily, clearly, and unceasingly. If it were a truth, universal and neces
sary, that a net is spread over the whole surface of every planetary globe, we
should not travel far on 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 being led by
observation to a recognition of such truths, as general propositions, coextensive
at least with all human experience. That they pervade all the objects of expe
rience, must ensure their continual suggestion by experience ; that they are
true, must ensure that consistency of suggestion, that iteration of uncontra-
dicted assertion, which commands implicit assent, and removes all occasion of
exception ; that they are simple, and admit of no misunderstanding, must
secure their admission by every mind."

"A truth, necessary and universal, relative to any object of our knowledge,
must verify itself in every instance where that object is before our contemplation,
and if at the same time it be simple and intelligible, its verification must be
obvious. The sentiment of such, a truth cannot, therefore, but be present to our
minds whenever 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. ' ' Geometry
is thus founded likewise on observation ; but of a kind so familiar and obvious,
that the primary notions which it furnishes might seem intuitive." — Sir John
Leslie, quoted by Sir William Hamilton, Discourses, &c. p. 272.

CHAPTER VI.

THE SAME SUBJECT CONTINUED.

§ 1. IN the examination which formed the subject of
the last chapter, into the nature of the evidence of those
deductive sciences which are commonly represented to he
systems of necessary truth, we have been led to the following
conclusions. The results of those sciences are indeed neces
sary, 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 the word necessity, even in this acceptation of it, means
no more than certainty. But their claim to the character of
necessity in any sense beyond this, as implying an evidence
independent of and superior to observation and experience,
must depend on the previous establishment of such a claim in
favour of the definitions and axioms themselves. With regard
to axioms, we found that, considered as experimental truths,
they rest on superabundant and obvious evidence: - We in
quired, whether, since this is the case, it be imperative to
suppose any other evidence of those truths than experimental
evidence, any other origin for our belief of them than an expe
rimental 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 in
ductions from experience ; the simplest and easiest cases of
generalization from the facts furnished to us by our senses or
by our internal consciousness.

While the axioms of demonstrative sciences thus ap-

DEMONSTRATION, AND NECESSARY TRUTHS. 283

peared to be experimental truths, the definitions, as they are
incorrectly called, in those sciences, were found by us to be
generalizations from experience which are not even, accurately
speaking, truths ; being propositions in which, while we assert
of some kind of object, some property or properties which
observation shows to belong to it, we at the same time deny
that it possesses 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 fiction, or suppo
sition, made for the purpose of excluding the consideration 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 Demonstrative Sciences are all, without exception, Induc
tive 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 according to
which their inductions are made, Hypothetical Sciences. Their
conclusions are only true on certain suppositions, which are,
or ought to be, approximations to the truth, but are seldom,
if ever, exactly true ; and to this hypothetical character is to
be ascribed the peculiar certainty, which is supposed to be
inherent in demonstration.

What we have now asserted, however, 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 doc
trines of this science than of any other, either that they are
not truths a 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
examination apart; and the more so, because on this subject
we have a double set of doctrines to contend with ; that of the
a priori philosophers on one side ; and on the other, a theory
the most opposite to theirs, which was at one time very gene-

284

REASONING.

rally received, and is still far from being altogether exploded,
among metaphysicians.

§ 2. This theory attempts to solve the difficulty appa
rently inherent in the case, by representing the propositions
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 are
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
process in algebra is but a succession of changes in termi
nology, by which equivalent expressions are substituted one
for another ; a series of translations 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 theorem by algebra,) they
have not explained ; 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 ad
vances in philosophy to believe it : men fly to so paradoxical
a belief to avoid, as they think, some even greater difficulty,
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 reconcileable 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 geome
trical demonstration we have a mental diagram, if not one on
paper ; AB, AC, are present to our imagination as lines, in-

DEMONSTRATION, AND NECESSARY TRUTHS. 285

tersecting other lines, forming an angle with one another, and
the like ; but not so a and 6. These may represent lines or
any other magnitudes, but those magnitudes are never thought
of; nothing is realized in our imagination but a and b. The
ideas which, on the particular occasion, they happen to repre
sent, 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 pro
cess has to do with anything more ? We seem to have come
to one of Bacon's Prerogative Instances ; an experimentum
cmcis on the nature of reasoning itself.

Nevertheless, it will appear on consideration, that this
apparently so decisive instance is no instance at all ; that there
is in every step of an arithmetical or algebraical calculation a
real induction, a real inference of facts from facts ; and that
what disguises the induction is simply its comprehensive 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 something, they may be numbers of any
thing. Propositions, therefore, concerning numbers, have the
remarkable peculiarity that they are propositions concerning
all things whatever ; all objects, all existences of every kind,
known to our experience. All things possess quantity ; con
sist 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 conceive 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
generalization still farther : every number represents that par-

286 REASONING.

ticular number of all things without distinction, but every
algebraical symbol does more, it represents all numbers with
out 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 danger of error,
every algebraical formula in the books. The proposition,
2 (a + &) = 2 a + 2 b, is a truth co-extensive with all nature.
Since then algebraical truths are true of all things whatever,
and not, like those of geometry, true of lines only or angles
only, it is no wonder that the symbols should not excite in
our minds ideas of any things in particular. When we de
monstrate 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, b, x, y, z, serve as well for representatives of
Things in general, as any more complex and apparently
more doncrete 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 reason
ing 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 concerning things, not sym
bols ; 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 processes of
thought, when they have been performed often, will do if per
mitted, namely, to become entirely mechanical. Hence the
general language of algebra comes to be used familiarly with-

DEMONSTRATION, AND NECESSARY TRUTHS. 287

out exciting ideas, as all other general language is prone to
do from mere habit, though in no other case than this can it
he done with complete safety. But when we look back to see
from whence the probative 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 sym
bols, the evidence 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 respect
ing Things, they all have the appearance of being identical
propositions. The assertion, Two and one are 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 " ob
jects are themselves" being insignificant, it seems but natural
to consider the proposition, Two and one are 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 de
note the same things, their connotation is different. Three
pebbles in two separate parcels, and three pebbles in one
parcel, do not make the same impression on our senses ; and
the assertion that the very same pebbles may by an alteration
of place and arrangement be made to produce either the one
set of sensations or the other, though a very familiar proposi
tion, 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 Number. The

288 REASONING.

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 separation and re- arrangement 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
proceed 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 senses, in the manner we have
described.

We may, if we please, call the proposition, " 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 aline 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 calculations which
depend on that proposition do not follow from the definition
itself, but from an arithmetical theorem presupposed in it,
namely, that collections of objects exist, which while they
impress the senses thus, °°, may be separated into two parts,
thus, ooo. 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 Number is thus no exception to the conclu
sion we previously arrived at, that the processes even of de
ductive sciences are altogether inductive, and that their first
principles are generalizations from experience. It remains
to be examined whether this science resembles geometry in
the further circumstance, that some of its inductions are not

DEMONSTRATION, AND NECESSARY TRUTHS. 289

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 geome
trical sense of the word Definition; and secondly, the two fol
lowing axioms : The sums of equals are equal, The differences
of equals are equal. These two are sufficient ; for the corre
sponding propositions respecting unequals may be proved from
these, by a reductio ad absurdum.

These axioms, and likewise the so-called definitions, are,
as has already been said, results of induction; true of all ob
jects whatever, and, as it may seem, exactly true, without the
hypothetical assumption of unqualified truth where an approxi
mation to it is all that exists. The conclusions, therefore, it
will naturally be inferred, are exactly true, and the science of
number is an exception to other demonstrative sciences in this,
that the categorical certainty which is predicable of its demon
strations 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 con
dition is implied, without which none of them would be true ;
and that condition is an assumption which maybe 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 always equal to itself,
unless we assume that all horses are of equal strength ? It is
VOL. i. 19

290 REASONING.

certain that 1 is always equal in number to 1 ; 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 arithmetic, so far as they
go to that alone, are true without mixture of hypothesis. There
are a few such cases ; 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 whenever, from equality or inequality of
number, equality or inequality in any other respect is to be
inferred, arithmetic carried into such inquiries becomes as hy
pothetical 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 mathematical certainty, therefore,
which comprises the twofold conception of unconditional truth
and perfect accuracy, is not an attribute of all mathematical
truths, but of those only which relate to pure Number, as dis
tinguished 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
given instance.

§ 4. It appears, therefore, that the method of all Deduc
tive 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

DEMONSTRATION, AND NECESSARY TRUTHS. 291

exactly true, whether they are a sufficiently near approxima
tion 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 numerical 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 observation, 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 concluded if we find, and in proportion as we find, the as
sumptions 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 conclu
sions from facts assumed, as from facts observed; from fic
titious, as from real, inductions. Deduction, as we have seen,
consists of a series of inferences in this form — a, is a mark of b,
b of c, c of d, 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 b, b of c, and
c of d, a would be a mark of d, which last conclusion was not
thought of by those who laid down the premises. A system of
propositions as complicated as geometry might be deduced
from assumptions which are false ; as was done by Ptolemy,
Descartes, and others, in their attempts to explain syntheti
cally the phenomena of the 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. Sometimes the same thing is knowingly

19—2

292 REASONING.

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 follows : a is a mark of b, and b 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 contradiction ; 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 absur
dum ; since the way to enforce assent to it, in case of ob
scurity, 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, would be a contradiction. 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
inadmissible as an explanation of the grounds on which ratio
cination itself rests. If any one denies the conclusion not
withstanding 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 ratiocination :
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 con
tradiction (or rather an infringement) of the fundamental
maxim of ratiocination, namely, that whatever has a mark, has
what it is a mark of; or, (in the case of universal propositions,)
that whatever is a mark of anything, is a mark of whatever
else that thing is a mark of. For in the case of every correct
argument, 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.

DEMONSTRATION, AND NECESSARY TRUTHS. 293

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 heen 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
spontaneously 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 so important a part.

CHAPTER VII.

EXAMINATION OF SOME OPINIONS OPPOSED TO THE
PRECEDING DOCTRINES.

§ 1. POLEMICAL discussion is foreign to the plan of this
work. But an opinion which stands in need of much illus
tration, can often receive it most effectually, and least tedi
ously, 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 preceding
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 proposition is invariably believed ; that is, if I under
stand 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 believed to be true, is our inability to conceive it
as false. " The inconceivability of its negation is the test by
which we ascertain whether a given belief invariably exists

* Principles of Psychology.

THEORIES CONCERNING AXIOMS. 295

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 assignable." 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 inconceivable."
There are numerous other beliefs 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
exists a material world ; that this is the very world which we
directly and immediately 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 negatives. We cannot, he says,
by any effort, conceive these objects of 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 them
selves. The truths which are the subject of direct knowledge,
being, according to this doctrine, known to be truths only
by the inconceivability of their negation; and the truths
which are not the object of direct knowledge, being known
as inferences from those which are ; and those inferences
being believed 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 difference between Mr.
Spencer's doctrine and the ordinary one of philosophers 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 incon
ceivable things, some things which were not inconceivable."
And he himself, in this very book, denies not a few proposi
tions usually regarded as among the most marked examples

296 REASONING.

of truths whose negations are inconceivable. But occasional
failure, he says, is incident to all tests. If such failure viti
ates " the test of inconceivableness," it " must similarly viti
ate all tests whatever. We consider an inference logically
drawn from established 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 con
sider an inference true on no other ground than that it is
logically drawn from established premises ? No : we say that
though men may have taken for logical inferences, inferences
that were not logical, there nevertheless are logical inferences,
and that we are justified 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 inability
to conceive the negation of a thing, may still be our best
warrant for believing 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 conceptive
faculty, into laws of the outward universe.

§ 2. The doctrine, that " a belief which is proved by the
inconceivableness 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 oil the experiences men have had ; and that,
by a widening of their experiences, they may, by and by, be
enabled to conceive things before inconceivable 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
existing experience in support of it, it follows that, at any

THEORIES CONCERNING AXIOMS. 297

time, the inconceivableness of its negation is the deepest test
any belief admits of. ... Objective facts are ever im
pressing themselves upon us ; our experience is a register of
these objective facts; 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 inconceivable ;
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 ... certain absolute uniformities in nature ; if these
uniformities produce, as they must, absolute uniformities in
our experience ; and if ... these absolute uniformities
in our experience disable us from conceiving the negations of
them ; then answering to each absolute uniformity in nature
which we can cognize, there must exist in us a belief of which
the negation is inconceivable, and which is absolutely true.
In this wide range of cases subjective inconceivableness must
correspond to objective impossibility. Further experience will
produce correspondence where it may not yet exist; and we
may expect the correspondence to become ultimately com
plete. 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 : Even if it were true that inconceivableness
represents " the net result" of all past experience, why should we
stop at the representative when we can get at the thing repre
sented ? If our incapacity to conceive the negation of a given
supposition is proof of its truth, because proving that our expe-

298 REASONING.

rience has hitherto been uniform in its favour, the real evidence
for the supposition is not the inconceivahleness, hut the uni
formity 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 uni
formity of experience is evidence 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 potassium in the present cen
tury 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 experience does amount
to the strongest possible proof, as with such propositions as
these, Two straight lines cannot inclose a space, Every event
has a cause, it is not because their negations are inconceivable,
which is not always the fact; but because the experience,
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 uniformity of past experience is
very far from being universally a criterion of truth. But
secondly, inconceivableness is still farther from being a test
even of that test. Uniformity of contrary experience is only
one of many causes of inconceivability. Tradition handed
down from a period of more limited knowledge, is one of the
commonest. The mere familiarity of one mode of production
of a phenomenon, often suffices to make every other mode
appear inconceivable. Whatever connects two ideas by a
strong association may, and continually does, render their
separation in thought impossible ; as Mr. Spencer, in other
parts of his speculations, frequently recognises. It was not
for want of experience that the Cartesians were unable to con-

THEORIES CONCERNING AXIOMS. 299

ceive that one body could produce motion in another without
contact. They had as much experience of other modes of pro
ducing 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 phenomena 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 inconceiv-
ableness, instead of representing their experience, dominated
and overrode their experience. It is needless to dwell farther
on what I have termed the positive argument of Mr. Spencer
in support of his criterion of truth. I pass to his negative
argument, on which he lays more stress.

§ 3. The negative argument is, that, whether inconceiv
ability be good evidence or bad, no stronger evidence is to be
obtained. That what is inconceivable cannot he true, is pos
tulated in every act of thought. It is the foundation of all our
original premises. Still more it is assumed in all conclusions
from those premises. The invariability of belief, tested by the
inconceivableness of its negation, "is our sole warrant for
every demonstration. Logic is simply a systematization of
the process by which we indirectly obtain this warrant for
beliefs that do not directly possess it. To gain the strongest
conviction possible respecting any complex fact, we either
analytically descend from it by successive steps, each of which
we unconsciously test by the inconceivableness of its negation,
until we reach some 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 interme
diate beliefs which invariably exist." The following passage
sums up the whole theory : " When we perceive that the
negation of the belief is inconceivable, 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 con
clusion whatever ultimately rests. We have no other guaraii-

300 REASONING.

tee for the reality of consciousness, of sensations, of personal
existence ; we have no other guarantee for any axiom ; we
have no other guarantee for any step in a demonstration.
Hence, as heing taken for granted in every act of the under
standing, it must be regarded as the Universal Postulate."
But as this postulate which we are under an " inexorable
necessity" of holding true, is sometimes false ; as " beliefs
that once were shown by the inconceivableness of their nega
tions to invariably exist, have since been found untrue," and
as " beliefs that now possess this character 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 in Matter, 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 ex
cept because we cannot conceive the conclusion not to follow
from the premises.

It will be convenient to take the last part of this argu
ment first. In every reasoning, according to Mr. Spencer,
the assumption of the postulate is renewed at every step. At
each inference we judge that the conclusion follows from the
premises, our sole warrant for that judgment being that we
cannot conceive it not to follow. Consequently if the postu
late is fallible, 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 represented
by one syllogism. This argument does rest on an assumption,
and we have seen in the preceding chapters what the assump
tion 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

THEORIES CONCERNING AXIOMS. 301

present ;* let us suppose it (with Mr. Spencer) to be the in-
oonceivableness of its reverse.

Let us now add a second step to the argument : we require,
what ? Another assumption ? No : the same assumption 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, the repeti
tion of the assumption at all weakens the force of the argu
ment. If it were necessary the second time to assume some
other axiom, the argument would no doubt be weakened,
since it would be necessary 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 satisfactory that we are not obliged to suppose the
deductions of pure mathematics to be among the most uncer
tain 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 cha
racter, are taken up by the way.

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. Spencer 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

* Mr. Spencer is mistaken in supposing me to claim any peculiar "neces
sity" for this axiom as compared with others. I have corrected the expression*
which led him into that misapprehension of my meaning.

302 REASONING.

always means an idea, and never a belief. The wrong meaning
of "inconceivable" is,bowever, fully as frequent in philosophical
discussion as the right meaning, and the intuitive school of
metaphysicians could not well do without either. To illustrate
the difference, we will take two contrasted examples. The early
physical speculators considered 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, impos
sible, was to apprehend them as believable. The idea could be
put together, of men sticking on by their feet to the under side
of the earth ; but the belief ivould follow, that they must fall off.
Antipodes were not unimaginable, but they were unbelievable.
On the other hand, when I endeavour 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 can
not help figuring to myself a vast space beyond that last point.
The combination 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 incon-
ceivableness 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 inconceivable ? Until Mr. Spencer ex
pressly stated the contrary, I inferred from the course of his
argument, that he meant unbelievable. He has, however, in
a paper published in the fifth number of the Fortnightly
Review, disclaimed this meaning, and declared that by an in
conceivable proposition he means, now and always, " one of
which the terms cannot, by any effort, be brought before con
sciousness in that relation which the proposition asserts
between them — a proposition of which the subject and predi
cate offer an insurmountable resistance to union in thought."
We now, therefore, know positively that Mr. Spencer always
endeavours to use the word inconceivable in this, its proper,
sense : but it may yet be questioned whether his endeavour is

THEORIES CONCERNING AXIOMS. 308

always successful ; whether 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
cannot conceive that I am not feeling cold, this expression
cannot be translated into, " I cannot conceive myself not feel
ing cold," for it is evident that I can : the word conceive, there
fore, 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
representation, 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 inconceiva
bility, 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 invaria
bility 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 daylight,
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 impossible to conceive," i.e.

* Mr. Spencer makes a distinction between conceiving myself looking into
darkness, and conceiving that I am then and there looking into darkness. To
me it seems that this change of the expression to the form I am, just marks
the transition from conception to belief, and that the phrase " to conceive that
/ ant," or " that anything is," is not consistent with using the word conceive in
its rigorous sense.

304 REASONING.

to believe. So that the statement resolves itself into this : That
I exist, and that I have sensations, I helieve, because I cannot
believe otherwise. And in this case every one will admit that
the necessity is real. Any one's present sensations, or other
states of subjective consciousness, that one person inevitably
believes. They are facts known per se : it is impossible to
ascend beyond them. Their negative is really unbelievable,
and therefore 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 feelings, 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
believe 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 invariable 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 con
sciousness ; that the perception of them irresistibly suggests to
us the idea of something external to ourselves : and I am not
in a condition to say that this is not the fact (though I do not
think any one is entitled 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 ma
terial objects, are mere modifications of consciousness ; com
plex feelings of touch and of muscular action. Mr. Spencer
may think the inference correct from the unimaginable to the
unbelievable, because he holds that belief itself is but the per
sistence of an idea, and that what we can succeed in imagining,
we cannot at the moment help apprehending as believable.
But of what consequence is it what we apprehend at the
moment, if the moment is in contradiction to the permanent
state of our mind ? A person who has been frightened when

THEORIES CONCERNING AXIOMS. 305

an infant by stories of ghosts, though he disbelieves them in
after years (and perhaps disbelieved them at first), may be
unable all his life to be in a dark place, in circumstances stimu
lating 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 tem
porary 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 disbelieve 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. Spencer's 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 disbelievers of the doc
trine. 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 believable, and yet may
not have become conceivable, and that we may habitually
believe one side of an alternative, and conceive only in the
other, is familiarly exemplified in the state of mind of educated
persons respecting 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 sun
rise it is impossible 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
VOL. i. 20

306

REASONING.

this would be an exact parallel to his doctrine about the belief
in matter.

The existence of matter, and other Nouraena, as dis
tinguished 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, stands 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 tribus ; but, being a fact, it calls on antagonists
to show, from what except the real existence of the thing be
lieved, 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. Sir William Hamilton holds as I do, that incon
ceivability is no criterion of impossibility. " There is no ground
for inferring a certain fact to be impossible, merely from our
inability to conceive its possibility." "Things there are which
may, nay must, be true, of which the understanding is wholly
unable to construe to itself the possibility." f 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 experience, 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
faculties debars us from having any knowledge. The axioms
to which he attributes this exceptional emancipation from the
limits which confine all our other possibilities of knowledge ;
the chinks through which, as he represents, one ray of light
finds its way to as from behind the curtain which veils from

* I have myself accepted the contest, and fought it out on this battle
ground, in the eleventh chapter of An Examination of Sir William Hamilton's
Philosophy.

t Discussions, &c., 2nd ed. p. 624.

THEORIES CONCERNING AXIOMS. 307

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 propositions cannot both be true ;
the second, that they cannot both be false. Armed with these
- logical weapons, we may boldly face Things in themselves, and
tender to them the double alternative, sure that they must
absolutely elect one or the other side, 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 ques
tion, those of Contradiction and of Excluded Middle, it is not
unseasonable to consider them here. The former asserts that
an affirmative proposition and the corresponding negative pro
position cannot both be true ; which has generally been held
to be intuitively evident. Sir William Hamilton and the
Germans 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 proposi
tion ; an assertion involved in the meaning of 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 identical 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 fundamental antithesis per
vading nature, and should be enunciated in the simpler form,
that the same proposition 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 generalizations from experience. The original foun-

20—2

308 REASONING.

dation of it I take to be, that Belief and Disbelief are two dif
ferent mental states, excluding one another. This we know by
the simplest observation of our own minds. And if we carry
our observation outwards, we also find that light and darkness,
sound and silence, motion and quiescence, equality and in
equality, preceding and following, succession and simultane-
ousness, any positive phenomenon whatever and its negative,
are distinct phenomena, pointedly contrasted, and the one
always absent where the other is present. I consider the
maxim in question to be a generalization from all these facts.
In like manner as the Principle of Contradiction (that one
of two contradictories must be false) means that an assertion
cannot be loth 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 affir
mative 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, unless with a large qualifi
cation. A proposition 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 infinitely or
finitely divisible.* In the second place, though matter, con
sidered as the occult cause of our sensations, do really exist,

* If it be said that the existence of matter is among the things proved by
the principle of Excluded Middle, that principle must prove also the existence
of dragons and hippogriffs, because they must be either scaly or not scaly,
creeping or not creeping, and so forth.

THEORIES CONCERNING AXIOMS. 309

yet what we call divisibility may be an attribute only of our
sensations of sigbt and touch, and not of their uncognizable
cause. Divisibility may not be predicable at all, in any intel
ligible 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 passage. 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 remembering a certain thing as in a certain place,
the place and the thing are mentally represented together ;
while to think of the non-existence of the thing in that place,
implies a consciousness in which the place is represented, but
not the thing. Similarly, if instead of thinking of an object
as colourless, we think of its having colour, the change con
sists 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 generalization of the
universal experience that some mental states are directly de
structive of other states. It formulates a certain absolutely
constant law, that the appearance of any positive mode of con
sciousness cannot occur without excluding a correlative negative
mode ; and that the negative mode cannot occur without ex
cluding the correlative positive mode : the antithesis of positive
and negative being, indeed, merely an expression of this ex
perience. 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 com
prehensive sense of the term, will form the subject of the Third.

* For further considerations respecting the axioms of Contradiction and
Excluded Middle, see the twenty-first chapter of An Examination of Sir Wil
liam Hamilton'1 s Philosophy.

BOOK III.

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 suc
cessive events, which constitute the order of the universe ; to record the
phenomena which it exhibits to our observations, or which it discloses to
our experiments; and to refer these phenomena to their general laws." —
D. STEWAKT, Elements of the Philosophy of the Human Mind, vol. ii. chap. iv.
sect. 1.

CHAPTER I.

PRELIMINARY OBSERVATIONS ON INDUCTION IN
GENERAL.

§ 1. THE portion of the present inquiry 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 because it relates to a process which has been shown in
the preceding Book to be that in which the investigation of
nature essentially consists. We have found that all Inference,
consequently all Proof, and all discovery of truths not self-
evident, consists of inductions, and the interpretation of induc
tions : that all our knowledge, not intuitive, comes to us ex
clusively from that source. What Induction is, therefore, and
what conditions render it legitimate, cannot but be deemed the
main question of the science of logic — the question which in
cludes all others. It is, however, one which professed writers
on logic have almost entirely passed over. The generalities of
the subject have not been altogether neglected by metaphysi
cians ; but, for want of sufficient acquaintance with the processes
by which science has actually succeeded in establishing general
truths, their analysis of the inductive operation, even when un
exceptionable as to correctness, has not been specific enough
to be made the foundation of practical rules, which might fee
for induction 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 generalize, 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
philosophize on the subject, nor regarded the mode in which

314 INDUCTION.

they arrived at their conclusions as deserving of study, inde
pendently of the conclusions themselves.

§ 2. For the purposes of the present inquiry, Induction
')maybe defined, the operation of discovering and proving general
/propositions. It is true that (as already shown) the process of
indirectly 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, de
finite in kind but indefinite in number ; and on the other hand,
whenever the evidence which we derive from observation 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
observed.

If these remarks are just ; if the principles and rules of in
ference 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 virtually an analysis of all in
duction whatever. Whether we are inquiring into a scientific
principle or into an individual fact, and whether we proceed by
experiment or by ratiocination, every step in the train of in
ferences is essentially inductive, and the legitimacy of the in
duction depends in both cases on the same conditions.

True it is that in the case of the practical inquirer, who is
endeavouring to ascertain facts not for the purposes of science
but for those of business, 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 choosing from

INDUCTION IN GENERAL. 315

among all general propositions ascertained to be true, 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 them
selves, sufficiently trite, and assented to as soon as stated : his
skill lies in bringing his case under those propositions or prin
ciples ; in calling to mind such of the known or received maxims
of probability as admit 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 acquired sagacity, aided
by knowledge of the particular subject, and of subjects allied
with it. Invention, though it can be cultivated, cannot be re
duced 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 something, 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 know
ledge and sagacity in the choice of the inductions out of which
he will construct his argument. But the validity of the argu
ment 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 inductions under which it has been successively
brought ; and finally, the legitimacy of the inductions them
selves must be decided by other rules, and these it is now our
purpose to investigate. If this third part of the operation be, in
many of the questions 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 as to

316 INDUCTION.

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 processes which prove parti
cular facts and those which establish general scientific truths,
required any additional confirmation, it would be sufficient 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 im
portant deductions, 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 inductions founded on other facts which we
can more easily reach. For example, 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 as
certainment of these angular distances ascertained their supple
ments ; and since the angle at the earth's centre subtended by
the distance between the two places of observation was dedu-
cible 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 ascertained, at least
in terms of the earth's radius, from elementary theorems of
geometry. At each step in this demonstration we take in a

INDUCTION' IN GENERAL. 317

new induction, represented, in the aggregate of its results, by
a general proposition.

Not only is the process by which an individual astrono
mical 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 concluded 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 certain 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 circum
stances of the other heavenly bodies, which render them inca
pable of affording such data as the application 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 general truth. Induction,
he says (Philosophy of Discovery, p. 245), "is not the same thing as experience
and observation. Induction is experience or observation consciously looked at
in a general form. This consciousness and generality are necessary parts of
that knowledge which is science." And he objects (p. 241) to the mode in
which 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 "confusion of knowledge with practical tendencies."

I disclaim, as strongly as Dr. Whewell can do, the application of such terms
as induction, inference, or reasoning, to operations performed by mere instinct,
that is, from an animal impulse, without the exertion 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 precautions required by scientific
propriety. To the idea of Science, an express recognition and distinct appre
hension of general laws as such, is essential : but nine-tenths of the conclusions
drawn from experience in the course of practical life, are drawn without any
such recognition : they are direct inferences from known cases, to a case sup
posed to be similar. I have endeavoured to show that this is not only as legi-

318 INDUCTION.

We shall fall into no error, then, if in treating of Induction,
we limit our attention to the establishment of general proposi
tions. 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, applicable to all inquiries in
which man can engage.

timate an operation, but substantially the same operation, as that of ascending
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, because Science wants its conclusions for record, and not for in
stantaneous use. But the inferences drawn for the guidance of practical affairs,
by persons who would often be quite incapable of expressing in unexceptionable
terms the corresponding generalizations, may and frequently do exhibit intel
lectual powers quite equal to any which have ever been displayed in Science :
and if these inferences are not inductive, what are they? The limitation im
posed on the term by Dr. Whewell seems perfectly arbitrary ; neither justified
by any fundamental distinction between what he includes and what he desires
to exclude, nor sanctioned 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.

CHAPTER II.

OF INDUCTIONS IMPROPERLY SO CALLED.

§ 1. INDUCTION, then, is that operation 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 former
in certain assignable respects. In other words, Induction is
the process by which we conclude that what is true of certain
individualsfof ^a_cjass_)is true of the whole class, or that what
is true at certain times will be true in similar circumstances at
all times.

This definition excludes from the meaning of the term In
duction, various 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
conclusion 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 perfect, 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 admits
of being stated in the form, " This and that A are B, there
fore every A is B," — is called an induction, whether any
thing be really concluded or not : and the induction is as
serted not to be perfect, unless every single individual of
the class A is included in the antecedent, or premise : that is,
unless what we affirm of the class has already been ascer
tained to be true of every individual in it, so that the
nominal conclusion is not really a conclusion, but a mere
reassertion of the premises. If we were to say, All the
planets shine by the sun's light, from observation of each

320 INDUCTION.

separate planet, or All the Apostles were Jews, because
this is true of Peter, Paul, John, and every other apostle, —
these, and such as these, would, in the phraseology in ques
tion, he 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 un
known, but a mere short-hand registration of facts known.
The two simulated arguments which we have quoted, are not
generalizations ; the propositions purporting to be conclusions
from them, are not really general propositions. A general
proposition is one in which the predicate 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 the 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 individual falling under a certain general descrip
tion, but only for each of a number of individuals designated
as such, and as it were counted off individually, the proposi
tion, though it may be general in its language, is no general
proposition, but merely that number of singular propositions,
written 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
important part in the preparation of the materials for that
investigation.

As we may sum up a definite number of singular proposi
tions in one proposition, which will be apparently, but 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 induction applied
to every distinct species of animals, it has been established
that each possesses a nervous system, and we affirm thereupon
that all animals have a nervous system; this looks like a
generalization, 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

INDUCTIONS IMPROPERLY SO CALLED. 321

must be made. If in concluding that all animals have a
nervous 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 in
duction. But if our meaning is that the observations 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 pro
position contains more than the sum of the special proposi-
tions from which it is inferred^ The distinction is still more
forcibly brought out when we consider, that if this real gene
ralization be legitimate at all, its legitimacy probably does not
require that we should have examined without exception every
known species. 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 rigorously
verified it in every species. In like manner to (return to a
former example) we might 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
Induction 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 successively proved of the ellipse, the parabola,
and the hyperbola, it may be laid down as an universal pro
perty of the sections of the cone. The distinction drawn in
the two previous examples can have no place here, there being
VOL. i. 21

322

INDUCTION.

no difference between all known sections of the cone and all
sections, since a cone demonstrably cannot be intersected by
a plane except in one of these four lines. It would be diffi
cult, therefore, to refuse to the proposition arrived at, the name
of a generalization, since there is no room for any generaliza
tion 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 somewhat, 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 de
monstration (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 exhibited 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 universal pro
position. 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 Induction, an appropriate
name for it would be, induction by parity of reasoning. But
the term cannot properly belong to it ; the characteristic
quality of Induction is wanting, since the truth obtained,
though really general, is not believed 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 mathematics, some examples of
so-called Induction, in which the conclusion does bear the
appearance of a generalization grounded on some of the par
ticular cases included in it. A mathematician, when he has

* Supra, p. 214.

INDUCTIONS IMPROPERLY SO CALLED. 323

calculated 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 calculations. But I
apprehend he only does so when it is apparent from a priori
considerations (which might be exhibited in the form of
demonstration) that the mode of formation of the subsequent
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 without the sanction
of such general considerations, there are instances on 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 comparing 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 im
probable : but a mathematician like Newton, who seemed to
arrive per saltum at principles 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 priori ground of the law ; since any
one who understands sufficiently the nature of multiplication
to venture upon multiplying several lines of symbols at one
operation, cannot but perceive that in raising a binomial to a
power, the coefficients must depend on the laws of permuta
tion and combination : and as soon as this is recognised, 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 con
siderations which prove it to obtain universally. Even,
therefore, such cases as these, are but examples of what I
have called Induction by parity of reasoning, that is, not
really Induction, because not involving inference of a general
proposition from particular instances.

§ 3. There remains a third improper use of the term
21—2

324 INDUCTION.

Induction, which it is of real importance to clear up, because
the theory of Induction has heen, in no ordinary degree, con
fused hy it, and because the confusion is exemplified in the
most recent and elaborate treatise on the inductive philosophy
which exists in our language. 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 consists 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 (amounting 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
detached fragments together. A navigator 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 completely round it : he then pronounces
it an island. Now there was no particular 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 or three words the
whole of what he so observed. 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 inference from the partial facts which the navigator saw
in the course of his circumnavigation ; it is the facts them
selves ; it is a summary of those facts ; the description of a
complex fact, to which those simpler ones are as the parts of
a whole.

Now there is, I conceive, no difference in kind between this
simple operation, and that by which Kepler ascertained the
nature of the planetary orbits : and Kepler's operation, all
at least that was characteristic in it, was not more an inductive
act than that of our supposed navigator.

INDUCTIONS IMPROPERLY SO CALLED. 325

The object of Kepler was to determine the real path de
scribed by each of the planets, or let us say by the planet
Mars (since it was of that body that he first 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 observation could do was to
ascertain a great number of the successive places of the planet ;
or rather, of its apparent places. That the planet occupied
successively all these positions, or at all events, positions which
produced the same impressions on the eye, and that it passed
from one of these to another insensibly, and without any
apparent breach of continuity ; thus much the senses, with the
aid of the proper instruments, could ascertain. What Kepler
did more than this, was to find what sort of a curve these dif
ferent points would make, supposing them to be all joined
together. He expressed the whole series of the observed
places of Mars by what Dr. Whewell calls the general concep
tion of an ellipse. This operation was far from being as easy
as that of the navigator who expressed the series of his obser
vations on successive points of the coast by the general con
ception 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 cor
rectly 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 obser
vations) that the positions of the planet during the time which
intervened between two observations, must have coincided
with the intermediate points of the curve. For these were
facts which had not been directly observed. They were
inferences from the observations ; facts inferred, as distin
guished 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 born. Astronomers
had long known that the planets periodically returned to the
same places. When this had been ascertained, there was no

326 INDUCTION.

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 ellipse correctly represented the past path,
he knew that it would represent the future path. In finding
a compendious 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 prediction already pos
sessed.

§ 4. The descriptive operation which enables a number
of details to be summed up in a single proposition, Dr.
Whewell, by an aptly chosen expression, has termed the
Colligation of Facts. In most of his observations concerning
that mental process I fully 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 received meaning of the term, is not
induction at all, as the type of induction generally ; and laying
down, throughout his work, as principles of induction, the
principles of mere colligation.

Dr. Whewell maintains that the general proposition which
binds together 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 is a new element added to the combination 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 considered as pro
duced by the motion of one wheel revolving in the inside of
another wheel, these wheels were creations of their minds,
added to the facts which they perceived by sense. And even

* Novum Oryanum Renovatum, pp. 72, 73.

INDUCTIONS IMPROPERLY SO CALLED. 327

if the wheels were no longer supposed to be material, but
were reduced to mere geometrical spheres or circles, they
were not the less products of the mind alone, — something
additional to the facts observed. The same is the case in
all other discoveries. The facts are known, but they are
insulated and unconnected, till the discoverer supplies from
his own store a principle of connexion. The pearls are
there, but they will not hang together till some one provides
the string."

Let me first remark that Dr. Whewell, in this passage,
blends together, indiscriminately, examples of both the pro
cesses which I am endeavouring to distinguish from one
another. When the Greeks abandoned the supposition that
the planetary motions were produced by the revolution 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 de
scription. 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 materiality of the wheels was discarded, and the geome
trical forms alone retained, 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 assertion 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 repre
senting the same observations.

It is true that for these simply descriptive operations, as well
as for the erroneous inductive one, a conception 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

328

INDUCTION.

was something added to the facts. He expresses 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 conception 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 would manifest to our senses, if our senses were able to
take cognizance 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 enable him to see the whole of it at once, he would see
it to be an ellipse ; and if gifted with appropriate instruments
and powers of locomotion, he could prove it to be such by
measuring 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 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 the planet moved
in it. The case would then exactly resemble that of the navi
gator 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 difference 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 condition which has just
been stated, I cannot conceive that the part which concep
tions have in the operation of studying facts, has ever been
overlooked 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 common to those things. But it

INDUCTIONS IMPROPERLY SO CALLED. 329

by no means follows that the conception is necessarily pre-
existent, or constructed 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 themselves something of which
the conception 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 ob
serves, (which he does on several occasions,) how great a
service would be rendered to the science of physiology by the
philosopher " who should establish a precise, tenable, and con
sistent conception of life."* Such a conception can only 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 -attempting 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 hypothetically, 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 description, what will the details be ? and then com
pare these with the details actually observed. If they agreed,
the hypothesis would serve for a description of the pheno
menon : if not, it was necessarily abandoned, and another tried.
It is such a case as this which gives rise to the doctrine that

* Novum Organum Renovatum, p. 32.

330 INDUCTION.

the mind, in framing the descriptions, 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
advantages, but possessing the conception of an ellipse, or
(to express the meaning in less technical language) knowing
what an ellipse was, Kepler tried whether the observed places
of the planet were consistent 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 add to, but found in, the motions of the planet, namely,
that it occupied in succession the various points in the circum
ference of a given ellipse, was the very fact, the separate parts
of which had been separately observed ; it was the sum of the
different observations.

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, suitable 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 hitting upon the " con
ception " of an ellipse, he tried nineteen other imaginary paths,
which, finding them inconsistent with the observations, he was
obliged to reject. But as Dr. Whewell truly says, the suc
cessful 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 particulars, are accidents which rarely occur to any
minds bat those abounding in knowledge and disciplined in
intellectual combinations-
How far this tentative method, so indispensable as a means
to the colligation of facts for purposes of description, admits
of application to Induction itself, and what functions belong
to it in that department, will be considered in the chapter of
the present Book which relates to Hypotheses. On the pre-

INDUCTIONS IMPROPERLY SO CALLED. 331

sent occasion we have chiefly to distinguish this process of
Colligation from Induction properly so called ; and that the
distinction may be made clearer, it is well to advert to a
curious and interesting remark, which is as strikingly true of
the former operation, as it appears to me unequivocally false of
the latter.

In different stages of the progress of knowledge, philoso
phers have employed, for the colligation of the same order of
facts, different conceptions. The early rude observations of
the heavenly bodies, in which minute precision was neither
attained nor sought, presented nothing inconsistent with the
representation of the path of a planet as an exact circle, having
the earth for its centre. As observations increased in accuracy,
and facts were disclosed which were not reconcileable with this
simple supposition ; for the colligation of those additional
facts, the supposition was varied ; and varied again and again
as facts became more numerous 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 contradictory to these representations, other epicycles and
other excentrics were added, producing additional complica
tion; 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 repre
sent to itself with facility, and by a simultaneous glance, the
whole body of facts at the time ascertained : each in its turn
served as a correct description of the phenomena, so far as the
senses had up to that time taken cognizance of them. If a
necessity afterwards arose for discarding one of these general
descriptions of the planet's orbit, and framing a different
imaginary line, by which to express the series of observed posi-

332 INDUCTION.

tions, it was because a number of new facts had now been
added, which it was necessary to combine with the old facts
into one general description. But this did not affect the cor
rectness of the former expression, considered as a general state
ment 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 generalizations, even the rudest and most imperfect of
them, that of uniform movement in a circle, are so far from
being entirely false, that they are even now habitually em
ployed by astronomers when only a rough approximation to
correctness is required. " L'astronomie moderne, en de-
truisant sans retour les hypotheses primitives, envisagees
comme lois reelles du monde, a soigneusement maintenu leur
valeur positive et permanente, la propriete de representer com-
modement les phenomenes quand il s'agit d'une premiere
ebauche. Nos ressources a cet egard sont meme bien plus
etendues, precisement a cause que nous ne nous faisons aucune
illusion sur la realite 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 observed facts, or
in other words, successive 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 purposes : 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 expected 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. 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

* Coura de Philosophic Positive, vol. ii. p. 202.

INDUCTIONS IMPROPERLY SO CALLED. 333

limit, those motions, even as now known to us, might be ex
pressed with any degree of accuracy that might be required.
The elliptical theory, as a mere description, would have a great
advantage 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 explana
tions. The doctrine that the heavenly bodies moved by a
virtue inherent in their celestial nature; the doctrine that
they were moved by impact, (which led to the hypothesis 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, collected 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 are 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 predictions :
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 main
tains, that not only different descriptions, but different explanations of a
phenomenon, may all be true. Of the three theories respecting the motions
of the heavenly bodies, he says (Philosophy of Discovery, p. 231) : " Un
doubtedly all these explanations may be true and consistent with each other,
and would be so if each had been followed out so as to show in 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 with 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

334 INDUCTION.

In every way, therefore, it is evident that to explain in
duction as the colligation of facts by means of appropriate
conceptions, that is, conceptions which will really express

such a centripetal force, and therefore did not contradict the doctrine of a cen
tripetal 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
be false. The attempt to explain gravity by the impulse of streams of particles
flowing through the universe in all directions, which I have mentioned in the
Philosophy, is so far from being inconsistent 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 main
tained 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 ' inherent
virtue' must have coincided in its effect with the Newtonian 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 indi
cates, is found to be untenable, it is of course rejected in the transition to later
and more exact theories, in Inductions of this kind, as well as in what Mr. Mill
calls Descriptions. There is, therefore, still no validity discoverable in the dis
tinction 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 manner 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 Descrip
tion ; it would, no doubt, have been reconcileable 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. Ac
cording 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 New
tonian theory does not absolutely contradict any hypothesis which may be framed
respecting the mode of their production. 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 what does the explanation con
sist ? 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 particle 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 contradiction

INDUCTIONS IMPROPERLY SO CALLED. 335

them, is to confound mere description of the observed facts
with inference from those facts, and ascribe to the latter what
is a characteristic property of the former.

between the assertions, that a man died because somebody killed him, and that
he died a natural death.

So, again, the theory that the planets move by a virtue inherent in their
stial 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 vjrtue of their celestial nature, which directly contradicts the doctrine that
terrestrial bodies fall by the same law.

If Dr. Whewell is not yet satisfied, any other subject will serve equally well
to test his doctrine. He will hardly say that there is no 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 reconcileable ; or that the
theory that volcanoes are fed from a central fire, and the doctrines which
ascribe them to chemical 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. Whewell quarrels (on what ground it is
not necessary here to consider) with the example I had chosen on this point,
and thinks an objection to an illustration a sufficient answer to a theory!
Examples not liable to his objection are easily found, if the proposition that
conflicting predictions cannot both be true, can be made clearer by any examples.
Suppose the phenomenon to be a newly-discovered comet, and that one astro
nomer predicts its return once in every 300 years— another once in every 400 :
can they both be right ? When Columbus predicted 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 foretold the
wonders of railways and steamships, 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. Whewell sees no distinction between holding contradictory opinions on
a question of fact, and merely employing different analogies to facilitate the
conception of the same fact. The case of different Inductions belongs to the
former class, that of different Descriptions to the latter.

336 INDUCTION.

There is, however, between Colligation and Induction, a
real correlation, 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, accomplishes
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
connexion for those facts ; a new principle for their classifi
cation.

Further, the descriptions which are improperly confounded
with induction, are nevertheless a necessary preparation 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 affirm any predicates at all, of a subject incapable
of being observed otherwise than piecemeal : much less could
we extend those predicates by induction to other similar sub
jects. Induction, therefore, always presupposes, not only that
the necessary observations are made with the necessary accu
racy, but also that the results of these observations are, so far
as practicable, connected together by general descriptions,
enabling the mind to represent to itself as wholes whatever
phenomena are capable of being so represented.

§ 5. Dr. Whewell has replied at some length to the pre
ceding observations, re-stating his opinions, but without (as
far as I can perceive) adding anything material to his former
arguments. 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 diffe-

INDUCTIONS IMPROPERLY SO CALLED. 337

rence of opinion consists, as well as, in some measure, to
account for it.

Nearly all the definitions of induction, by writers of autho
rity, 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 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 will scarcely be contended that Kepler's operation was
an Induction in this sense of the term. The statement, that
Mars moves in an elliptical orbit, was no generalization from
individual cases to a class of cases. Neither was it an exten
sion to all time, of what had been found true at some par
ticular time. The whole amount of generalization which the
case admitted of, was already completed, 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 apparent course of
each planet marked out on the celestial globe in an uninter
rupted line. Kepler did not extend an observed truth to
other cases than those in which it had been observed : 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 successive
places of Mars are points in an ellipse. It is true, this state
ment, as Dr. Whewell says, was not the sum of the observa
tions 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 actually observed, or which could have
been inferred from the observations before the new point of
view presented itself. There was not that transition from

* Phil. ofDiscov.p. 256,
VOL. I. 2£

338 INDUCTION.

known cases to unknown, which constitutes Induction in the
original and acknowledged meaning of the term.

Old definitions, it is true, cannot prevail against new
knowledge : and if the Keplerian operation, as a logical pro
cess, be really identical with what takes place in acknow
ledged induction, 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 employed to designate. Here then it is that I
am at issue with Dr. Whewell. He does think the operations
identical. He allows of no logical process in any case of in
duction, other than what there was in Kepler's case, namely,
guessing until a guess is found which tallies with the facts ;
and accordingly, as we shall see hereafter, he rejects all canons
of induction, because it is not by means of them that we guess.
Dr. Whewell's theory of the logic of science would be very
perfect if it did not pass over altogether the question of
Proof. But in my apprehension 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 unobserved 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.
Whewell's phraseology, connect them by means of a new con
ception ; if the conception does serve to connect the observa
tions, we have all we want. As the proposition in which it
is embodied 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 admits of proof ; though it may serve to prove other
things, inasmuch as, by placing the facts in mental connexion
with other facts, not previously seen to resemble them, it assi
milates the case to another class of phenomena, concerning
which real Inductions have already been made. Thus Kep
ler's so-called law brought the orbit of Mars into the class
ellipse, and by doing so, proved all the properties of an ellipse

INDUCTIONS IMPROPERLY SO CALLED. 339

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 Induc
tions) the major.

Dr. Whewell calls nothing Induction 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 con
ception belongs 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 constituting
induction, that induction does not necessarily stand in need
of it. Most inductions require no conception 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. Whoever knows that any man has died, has all the con
ceptions involved in the inductive generalization. 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 extracts from a number of
detached observations certain general characters in which the
observed phenomena resemble one another, or resemble other
known facts, is what Bacon, Locke, and most subsequent
metaphysicians, have understood by the word Abstraction. A
general expression obtained by abstraction, connecting known
facts by means of common characters, but without concluding
from them to unknown, may, I tliink, with strict logical cor
rectness, be termed a Description ; nor do I know in what
other way things can ever be described. My position, how
ever, does not depend on the employment of that particular
word ; I am quite content to use Dr. Whewell's term Colli
gation, or the more general phrases, " mode of representing,
or of expressing, phenomena :" provided it be clearly seen
that the process is not Induction, but something radically
different.

22—2

340 INDUCTION.

What more may usefully be said 011 the subject of Colliga
tion, or of the correlative expression invented by Dr. Whewell,
the Explication of Conceptions, 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.

CHAPTEE III.

OF THE GROUND OF INDUCTION.

§ 1 . INDUCTION properly so called, as distinguished from
those mental operations^ sometimes though improperly desig
nated by the name, which I have attempted in the preceding
chapter to characterize, may, then, be summarily defined as
-^YpfiHpiIl£fL Tt. nonsist.s in ^nferri^g froni

jsome. individual instances in which a phenomenon is observed

namely, in nil whifth r<tf«wil?l<i tliff former,^ ™hflk 8TJL
as the m alp rial

In what way the material circumstances are to be distin
guished 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 implied in the very statement of what Induction is ;
an assumption with regard to the course of nature and the
order of the universe ; namely, that there are such things in
nature as parallel cases ; that what happens once, will, under
a sufficient degree of similarity of circumstances, happen again,
and not only again, but as often as the same 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 warranted. 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 description.

This universal fact, which is our warrant for all inferences
from experience, has been described by different philosophers
in different forms of language : that the course of nature is
uniform ; that the universe is governed by general laws ; and

342 INDUCTION.

the like. One of the most usual of these modes of expression,
but also one of the most inadequate, is that which has heen
brought into familiar use by the metaphysicians of the school
of Reid and Stewart. The disposition of the human mind to
generalize from experience, — a propensity considered by these
philosophers as an instinct of our nature, — they usually de
scribe under some such name as " our intuitive conviction 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 concern
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
j past and future, that we infer, but from the known to the un-
i known ; from facts observed to facts unobserved ; from what
\we have perceived, or been directly conscious of, to what has
mot 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 funda
mental principle, or general axiom, of Induction. It would yet
be a great error to offer this large generalization as any expla
nation of the inductive process. On the contrary, I hold it to
be itself .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
which are latest in attaining strict philosophical accuracy. 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 opportunities of remarking, have its extent and limits
been always very justly conceived. The truth is, that this
great generalization is itself founded on prior generalizations.

* Essays on the Pursuit of Truth.

GROUND OF INDUCTION. 343

The obscurer laws of nature were discovered by means of it,
but the more obvious ones must have been understood and as
sented to as general truths before it was ever heard of. We
should 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 multitude of phenomena, at some know
ledge of the laws themselves ; which could be done no other
wise 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 Arch
bishop Whately 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 pre
mise of all inductions, and will, therefore, stand to all induc
tions 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 conclu
sion 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 Induction. In a subsequent issue of his Logic, the Archbishop
made a reply to the criticism, which induced me to cancel part of the note,
incorporating the remainder in the text. In a still later edition, the Archbishop
observes in a tone of something like disapprobation, that the objections, " doubt
less 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 Archbishop need give himself no uneasi
ness. His readers, I make bold to say, will fully credit his mere affirmation
that the objections have actually been made.

But as he seems to think that what he terms the suppression of the objec
tions 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

344 INDUCTION.

The statement, that the uniformity of the course of nature
is the ultimate major premise in all cases of induction, may be
thought to require some explanation. The immediate major
premise in every inductive argument, it certainly is not. Of
that, Archbishop 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 syllogism by prefixing as a major premise (what is
at any rate a necessary condition of the validity of the argu
ment) namely, that what is true of John, Peter, &c. is true of
all mankind. But how came we by this major premise ? It is
not self-evident ; nay, in all cases of unwarranted generaliza
tion, 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, there
fore, 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.

which might be regarded as personal criticism on the Archbishop. I had im
puted to him the having omitted to ask himself a particular question. 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 disrespect
ful nor arrogant, I felt, on reconsideration, that I was hardly entitled to make ;
least of al], when the instance which I had regarded as an illustration of them,
failed, as I now saw, to bear them out. The real matter at the bottom of the
whole dispute, the different 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 argu
ments, but answered (though without naming him) those of the Archbishop.

For not having made this statement before, I do not think it needful to
apologize. It would be attaching very great importance to one's smallest say
ings, to think a formal retractation requisite every time that one commits 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.

GROUND OF INDUCTION. 345

Whether there would be this inconsistency or not, may be
a matter of long and delicate inquiry ; but unless there would,
we 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 have for 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 unanimity
among thinkers with respect to the grounds on which it is to
be received as true. I have already stated that I regard it as
itself a generalization from experience. Others hold it to be a
principle which, antecedently to any verification by experience,
we are compelled by the constitution 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 mathe
matics, by arguments which are in a great measure applicable
to the present case, I shall defer the more particular discussion
of this controverted point in regard to the fundamental axiom
of induction, until a more advanced period of our inquiry.f

* But though it is a condition of the validity of every induction that there
be uniformity in the course of nature, it is not a necessary condition that the
uniformity should pervade all nature. It is enough that it pervades the par
ticular class of phenomena to which the induction relates. An induction con
cerning 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 magnetic phenomena are
under the dominion of general laws. Otherwise the early experience of mankind
would have rested on a very weak foundation ; 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 uniformity as foreknown, even in reference
to the kind of phenomena concerned. It implies, either that this general fact
is already known, or 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 amount of confusion and paralogism
respecting the grounds of Induction would be dispelled by keeping in view these
simple considerations.

f Infra, chap. xxi.

346

INDUCTION.

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 suit
able to popular, than the precision requisite in philosophical
language : its terms require to be explained, and a stricter
than their ordinary signification given to them, before the truth
of the assertion can be admitted.

§ 2. Every person's consciousness assures 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 resemble the past. Nobody
believes that the succession of rain and fine weather will be
the same in every future year as in the present. Nobody ex
pects to have the same dreams repeated every night. On the
contrary, everybody mentions it as something extraordinary,
if the course of nature is constant, and resembles itself, in these
particulars. To look for constancy where constancy is not to
be expected, as for instance that a day which has once brought
good 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 combinations in which we met with
them at first ; others seem altogether capricious ; while some,
which we had been accustomed to regard as bound down ex
clusively to a particular set of combinations, we unexpectedly
find detached from some of the elements with which we had
hitherto found them conjoined, and united to others of quite
a contrary description. To an inhabitant of Central Africa,
fifty years ago, no fact probably appeared to rest on more
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 unequivocal 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. During that long time,

GROUND OF INDUCTION.

347

mankind believed in an uniformity of the course of nature
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 induction of the ancients has been well described by
Bacon, under the name of " Inductio per enumerationem sim-
plicem, ubi non reperitur instantia contradictoria." It con
sists in ascribing the character of general truths to all pro
positions which are true in every instance that we happen
to know of. This is the kind of induction 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 known from the unknown, 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 inconclusive,
does not much affect the matter : these are considerations
which occur only on reflection ; the unprompted tendency of
the mind is to generalize its experience, provided this points
all in one direction ; provided no other experience of a con
flicting character comes unsought. The notion of seeking it,
of experimenting for it, of interrogating nature (to use Bacon's
expression) is of much later growth. The observation of \
nature, by uncultivated intellects, is purely passive : they I
accept the facts which present themselves, without taking
the trouble of searching for more : it is a superior mind only j
which asks itself what facts are needed to enable it to come to I
a safe conclusion, and then looks out for these.

But though we have always a propensity to generalize
from unvarying experience, we are not always warranted in
doing so. Before we can be at liberty to conclude that some
thing is universally true because we have never known an

348

INDUCTION.

instance to the contrary, we must have reason to believe 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 assurance, however, can be had, on any of
the ordinary subjects of scientific inquiry. Popular notions
are usually founded on induction by simple enumeration ; 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 accu
rate study of nature, we require a surer and a more potent
instrument.

It was, above all, by pointing out the insufficiency of this
rude and loose conception of Induction, that Bacon merited
the title so generally awarded to him, of Founder of the In
ductive Philosophy. The value of his own contributions to
a more philosophical theory 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 important principles of the Inductive Method,
physical investigation has now far outgrown the Baconian
conception of Induction. Moral and political inquiry, indeed,
are as yet far behind that conception. The current and
approved modes of reasoning on these subjects are still of
the same vicious description against which Bacon protested ;
the method almost exclusively employed by those professing
to treat such matters inductively, is the very inductio per
enumerationem simplicem which he condemns ; and the expe
rience 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 understanding of the problem

* Infra, chap. xxi. xxii.

GROUND OF INDUCTION. 349

which the logician must solve if he would establish a scientific
theory of Induction, let us compare a few cases of incorrect
inductions with others which are acknowledged to he legiti
mate. Some, we know, which were "believed for centuries to
he correct, were nevertheless incorrect. That all swans are
white, cannot have been a good induction, since the conclu
sion has turned out erroneous. The experience, however, on
which the conclusion rested, was genuine. From the earliest
records, the testimony of the inhabitants of the known world
was unanimous on the point. The uniform experience, there
fore, of the inhabitants of the known world, agreeing in a
common result, without one known instance of deviation from
that result, is not always sufficient to establish a general
conclusion.

But let us now turn to an instance apparently not very
dissimilar to this. Mankind were wrong, it seems, in con
cluding that all swans were white : are we also wrong, when
we conclude that all men's heads grow above their shoulders,
and never below, in spite of the conflicting testimony of the
naturalist Pliny? As there were black swans, though civi
lized 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," notwith
standing 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 confidence 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 resemble 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

350

INDUCTION.

a very feeble presumption that the like result will hold in all
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 assured that the conclu
sions 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 experi
ment ; or if we do, it is from a doubt whether the one experi
ment was properly made, not whether if properly made it
would be conclusive. 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 sufficient 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 ex
plored, he had caught and examined a crow, and had found it
to be grey.

I Why is a single instance, in some cases, sufficient for a
complete induction, while in others, myriads of concurring
instances, without a single exception known or presumed, go
such a very little way towards establishing an universal pro
position ? Whoever can answer this question knows more of
the philosophy of logic than the wisest of the ancients, and has
solved the problem of induction.

vy $

v \v

CHAPTER IV.

OF LAWS OF NATURE.

§ 1 . IN the contemplation of that uniformity in the course
of nature, which is assumed in every inference from experi
ence, one of the first observations that present themselves
is, that the uniformity in question is not properly uniformity,
but uniformities. The general regularity results from the
coexistence of partial regularities. The course of nature in
general is constant, because the course of each of the various
phenomena that compose it is so. A certain fact invariably
occurs whenever certain circumstances 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 connexion
between parts of the great whole which we term nature, a
general tissue of connexion unavoidably weaves itself, by which
the whole is held together. If A is always accompanied 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 C by
D E F ; and thus the general character of regularity is pro
duced, 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 uniformities
which exist in respect to single phenomena. These various
uniformities, when ascertained by what is regarded as a suffi
cient induction, we call in common parlance, Laws of Nature.
Scientifically speaking, that title is employed in a more re
stricted sense, to designate the uniformities when reduced to
their most simple expression. Thus in the illustration already
employed, there were seven uniformities ; all of which, if con
sidered sufficiently certain, would in the more lax application

INDUCTION.

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, there
fore, according to the stricter acceptation, are called laws of
nature ; the remainder not ; because they are in truth mere
cases of the three first ; virtually included in them ; said, there
fore, to result from them : whoever affirms those three has
already affirmed all the rest.

To substitute real examples for symbolical ones, the follow
ing are three uniformities, or call them laws of nature : the
law that air has weight, the law that pressure on a fluid is
propagated equally in all directions, and the law that pressure
in one direction, not opposed by equal pressure in the contrary
direction, produces motion, which does not cease until equili
brium is restored. From these three uniformities we should
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 sus
tained 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 pressure on the mercury not being pro
pagated equally in an upward 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 experi
ment, we might deduce its result from those laws. The known
weight of the air, combined with the position of the appa
ratus, 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 characterized in treating of Ratiocination. We should
thus come to know the more complex uniformity, indepen-

LAWS OF NATURE. 353

dently of specific experience, through our knowledge of the
simpler ones from which it results ; though, for reasons which
will appear hereafter, verification by specific experience 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
affirming 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 refer
ence to the original sense of the word law, namely, the ex
pression of the will of a superior. When, therefore, it appeared
that any of the uniformities which were observed in nature,
would result spontaneously from certain other uniformities, no
separate act of creative will being supposed necessary for the
production of the derivative uniformities, these have not usu
ally been spoken of as laws of nature. According to one
mode of expression, the question, What are the laws of nature ?
may be stated thus : — What are the fewest and simplest as
sumptions, which being granted, the whole existing order of
nature would result ? Another mode of stating it would be
thus : What are the fewest general propositions from which
all the uniformities which exist in the universe might be de
ductively 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 proposi
tions called his laws, he, in so doing, pointed out three simple
suppositions which, instead of a much greater number, would
suffice to construct the whole scheme of the heavenly motions,
VOL. i. 23

354 INDUCTION.

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 truths, were dis
covered to be cases of the three laws of motion, as obtaining
among bodies which mutually tend towards one another with
a certain force, and have had a certain instantaneous impulse
originally impressed upon them. After this great discovery,
Kepler's three propositions, though still called laws, would
hardly, by any person accustomed to use language with pre
cision, 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
generalization is either a law of nature, or a result of laws of
nature, capable, if those laws are known, of being predicted
from them. And the problem of Inductive Logic may be
summed up in two questions : how to ascertain the 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 anything but a mere verbal trans
formation 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, some
thing to have advanced 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 entangled with one another, may, to a
certain extent, be studied apart : that (to resume our former
metaphor) the regularity which exists in nature is a web com
posed of distinct threads, and only to be understood by tracing
each of the threads separately ; 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.

LAWS OF NATURE. 355

§ 2. In thus attempting to ascertain the general order of
nature by ascertaining the particular order of the occurrence
of each one of the phenomena 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 according to a stricter and surer
method than that which they had in the first instance spon
taneously adopted, they did not, conformably to the well-
meant but impracticable precept of Descartes, set out from
the supposition that nothing had been already ascertained.
Many of the uniformities existing among phenomena are so
constant, and so open to observation, as to force themselves
upon involuntary recognition. Some facts are so perpetually
and familiarly accompanied by certain others, that mankind
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 existence of a
connexion 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 ulte
rior revision of these spontaneous generalizations themselves,
when the progress of knowledge pointed out limits to them,
or showed their truth to be contingent on some drcumstanoe
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 rigorously impracticable : since it is
impossible to frame any scientific method of induction, or
test of the correctness of inductions, unless on the hypothesis
that some inductions deserving of reliance have been already
made.

Let us revert, for instance, to one of our former illustra-
23—2

356 INDUCTION.

tions, and consider why it is that, with exactly the same
amount of evidence, both negative 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 sort of cases, experience is to be relied on. Expe
rience must be consulted in order to learn from it under what
circumstances arguments from it will be valid. We have no
ulterior test to which we subject experience in general ; 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 in
stances, with a greater degree of assurance, in proportion as
the case belongs to a class in which the uniformities have
hitherto been found more uniform.

This mode of correcting one generalization by means of
another, a narrower generalization 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 essential alteration in its
principle.

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 indispensable foundation,
therefore, of a scientific formula of induction, must be a
survey of the inductions to which mankind have been con
ducted in unscientific practice; with the special purpose of

LAWS OF NATURE. 357

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 circumstances.

§ 3. The necessity of such a survey is confirmed by the
consideration, that the stronger inductions are the touchstone
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 evi
dence of the truth of the better established law in which it is
now found to be included. We may have inferred, from his
torical 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 generalization with much
greater assurance when it is shown to be a corollary from still
better established facts ; the very low degree of elevation 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 selfish propensities. It is at the same
time obvious that even these more general facts derive an acces
sion of evidence from the testimony which history bears to the
effects of despotism. 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 evidence war
rants, the weaker one must give way. The opinion so long
prevalent that a comet, or any other unusual appearance in
the heavenly regions, was the precursor of calamities to
mankind, or to those at least who witnessed it; the belief in
the veracity of the oracles of Delphi or Dodona; the reliance

358 INDUCTION.

on astrology, or on the weather-prophecies in almanacs, were
doubtless inductions supposed to be grounded on experience :*
and faith in such delusions seems quite capabh of holding oat
against a great multitude of failures, provided it be nourished
by a reasonable humber of casual coincidences between the
prediction and the event. What has really put an end to
these insufficient inductions, is their inconsistency with the
stronger inductions subsequently obtained by scientific inquiry,
respecting the causes on which 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 induc
tions, whether strong or weak, whicn can be connected by
•ratiocination, are confirmatory of one another; while any
which lead deductively to consequences that are incompatible,

* Dr. Whewell (Phil, of Discov. p. 246) will not allow these and similar
erroneous judgments to be called inductions ; inasmuch 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, shown
by such deviations from the ordinary course of nature." I conceive the ques
tion 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 assassina
tion of Julius Caesar, 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 themselves ; 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 is, if strength were not lent to it by
an antecedent presumption ; but this is not peculiar to such cases ; preconceived
notions of probability form part of the explanation of many other cases of belief
on insufficient evidence. The d priori prejudice 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 fanners 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.

LAWS OF NATURE. 859

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. Thus the Torricellian experiment, though a mere
oase 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 doubtful gene
ralization into a completely established doctrine.

If, then, a survey of the uniformities which have been
ascertained to exist in rilture, should point out some which,
as far as any human purpose requires certainty, may be con
sidered quite certain and quite universal ; then 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 inference, that either it must be
true, or one of these certain and universal inductions must admit
of an exception ; the former generalization will attain the same
certainty, and indefeasibleness within the bounds assigned 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 will be
a law of nature.

There are such certain and universal inductions ; and it is
because there are such, that a Logic of Induction is possible.

CHAPTER V.

OF THE LAW OF UNIVERSAL CAUSATION.

§ 1. THE phenomena of nature exist in two distinct re
lations to one another ; that of simultaneity, and that of suc
cession. Every phenomenon is related, in an uniform manner,
to some phenomena that coexist with it, and to some that have
preceded and will follow it.

Of the uniformities which exist among synchronous pheno
mena, 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
synchronous 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 years
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, coexist; and the unvarying
laws which are the subject of the science of geometry, are an
expression of the mode of their coexistence.

This is a class of laws, or in other words, of uniformities,
for the comprehension and proof of which it is not necessary
to suppose any lapse of time, any variety of facts or events suc
ceeding one another. If all the objects in the universe were
unchangeably fixed, and had remained in that condition from
eternity, the propositions of geometry would still be true of
those objects. 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 pro
perties which geometry assigns to that figure. If one body be

LAW OF CAUSATION. 861

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 un
erringly 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 re
cognise in the most unqualified manner, the rigorous univer
sality 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 en
deavoured to show) erroneously, to consider their evidence as
lying not in experience, but in the original constitution of the
intellect. 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 uniformi
ties 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 succession. On
a knowledge of these is founded every reasonable anticipation
of future facts, and whatever power we possess of influencing
those facts to oar advantage. Even the laws of geometry are
chiefly of practical importance 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 phenomena are themselves subject Again,
motions, forces or other influences, and times, are numerable
quantities ; and the properties of number are applicable to
them as to all other things. But though the laws of number

362 INDUCTION.

and space are important elements in the ascertainment of
uniformities of succession, they can do nothing towards it
when taken by themselves. They can only be made instru
mental to that purpose when we combine with them additional
premises, expressive of uniformities 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 con
tinuous force move with accelerated 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 quantity 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
another important uniformity of succession, viz., that a body
moving round a centre of force describes areas proportional to
the times. But unless there had been laws of succession 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 prevented 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 therefore 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

LAW OF CAUSATION. 363

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 universal
also in another sense ; it is coextensive 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 every fact which has a beginning has a cause,
is coextensive with human experience.

This generalization may appear to some minds not to
amount to much, 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 generality 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 fundamental truth.

§ 2. The notion of Cause being the root of the whole
theory of Induction, it is indispensable that this idea should,
at the very outset of our inquiry, be, with the utmost prac
ticable degree of precision, fixed and determined. If, indeed,
it were necessary for the purpose of inductive logic that the
strife should be quelled, which has so long raged among the
different 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
considered desperate for a long time to come. But the
science of the Investigation 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 necessity of pushing the analysis of
mental phenomena to that extreme limit which alone ought to
satisfy a metaphysician.

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 dis
tinction familiar in the writings of the Scotch metaphysicians,

364 INDUCTION.

and especially of Reid, the causes with which I concern myself
are not efficient, but physical causes. They are causes in
that sense alone, in which one physical fact is said to be the
cause of another. Of the efficient 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 necessity exists for
the purposes of the present inquiry, nor will any such doctrine
be found in the following pages. The only notion of a cause,
Avhich the theory of induction requires, is such a notion as
Lean be gained from experience. 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
consideration respecting the ultimate mode of production 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 succeeding 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 composed of separate fibres ; this collective order
is made up of particular sequences, 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 con
sequent, the effect. And the universality of the law of causa
tion consists in this, that every consequent is connected in
this manner with some particular antecedent, or set of ante-

LAW OF CAUSATION. 365

cedents. Let the fact be what it may, if it has begun to exist,
it was preceded by some fact or facts, with which it is in
variably connected. For every event there exists some com
bination of objects or events, some given concurrence of cir
cumstances, positive and negative, the occurrence of which
is always followed 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 without having the phenomenon 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 assurance 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 ante
cedents ; 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 common to single out one
only of the antecedents under the denomination of Cause,
calling the others merely Conditions. Thus, if a person eats
of a particular dish, and dies in consequence, 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 connexion between
eating of the dish and death ; but there certainly is, among
the circumstances which took place, some combination or other
on which death is invariably consequent : as, for instance, the
act of eating of the dish, combined with a particular bodily
constitution, a particular state of present health, and perhaps
even a certain state of the atmosphere ; the whole of which
circumstances perhaps constituted in this particular case the
conditions of the phenomenon, or, in other 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

366 INDUCTION.

antecedents ; 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 con
ditions, except the single one of eating the food, were not
events (that is, instantaneous changes, or successions of instan
taneous 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 con
ditions : while as soon as that event, eating the food, occurs,
no other cause is waited for, but the effect begins imme
diately to take place : and hence the appearance is presented
of a more immediate and close connexion between the effect
and that one antecedent, than between the effect and the
remaining conditions. But though we may think proper to
give the name of cause to that one condition, the fulfilment
of which completes the tale, and brings about the effect with
out further delay ; this condition has really no closer relation
to the effect than any of the other conditions has. The pro
duction of the consequent required that they should all exist
immediately previous, though not that they should all begin
to exist immediately previous. The statement of the cause is
incomplete, unless in some shape or other we introduce all the
conditions. A man takes mercury, goes out of doors, and
catches cold. We say, perhaps, that the cause of his taking
cold was exposure to the air. It is clear, however, that his
having taken mercury may have been a necessary condition of
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.

If we do not, when aiming at accuracy, 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 detriment be overlooked.
For example, when we say, the cause of a man's death was

LAW OF CAUSATION. 367

that his foot slipped in climbing a ladder, we omit as a thing
unnecessary to be stated the circumstance 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 conditions are fulfilled, makes up the sum
of the conditions, though no one now regards it as the prin
cipal one. When the decision of a legislative assembly has
been determined by the casting vote of the chairman, we
sometimes say that this one person was the cause of all the
effects which resulted 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 affirma
tive ; but, for the purpose we have in view, which is to insist
on his 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 employ
ment 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 deno
minate the cause. However numerous the conditions may be,
there is hardly any of them which may not, according to
the purpose of our immediate discourse, obtain that nominal
pre-eminence. This will be seen by analysing the conditions
of some one familiar phenomenon. For example, 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
phenomenon itself, to include them also among the conditions
would be a vicious tautology ; and this class of conditions,
therefore, have never received the name of cause from any but
the Aristotelians, by whom they were called the material cause,

368 INDUCTION.

causa materialis. The next condition is, there must be an
earth : and accordingly it is often said, that the fall of a stone
is caused hy 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 that 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 particularity that the motion is towards the earth,
which is not a character of the cause, but of the effect. Let
us now pass to another condition. It is not enough that the
earth should exist ; the body must be within that distance
from it, in which the earth's attraction preponderates over
that of any other body. Accordingly we may say, and the
expression would be confessedly correct, that the cause of the
stone's falling is its being ivithin the sphere of the earth's
attraction. We proceed to a further condition. The stone is
immersed in water : it is therefore a condition of its reaching
the ground, that its specific gravity exceed that of the sur
rounding fluid, or in other words that it surpass in weight
an equal volume of water. Accordingly any one would be
acknowledged 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 condition of the pheno
menon may be taken in its turn, and, with equal propriety in
common parlance, but with equal impropriety in scientific dis
course, may be spoken of as if it were the entire cause. And
in practice, that particular condition is usually styled the cause,
whose share in the matter is superficially the most conspi
cuous, 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 consideration, that it sometimes induces us
to give the name of cause even to one of the negative condi
tions. We say, for example, The army was surprised 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

LAW OF CAUSATION. 369

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 consequences 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 phenome
non 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, sufficiently illus
trates) to associate the idea of causation with the proximate
antecedent 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 indeterminate length of time before
the effect. Thus, rather than say that the earth causes the fall
of bodies, they ascribe it to & force exerted by the earth, or an
attraction by the earth, abstractions which they can represent
to themselves as exhausted by each effort, and therefore con
stituting at each successive instant a fresh fact, simultaneous
with, or only immediately preceding, the effect. Inasmuch as
the coming of the circumstance which completes the assemblage
of conditions, is a change or event, it thence happens that an
event is always the antecedent in closest apparent proximity
to the consequent : and this may account for the illusion 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
VOL. i. 24

370 INDUCTION.

conditions, either positive or negative, is found, on occasion,
completely to accord.*

The cause, then, philosophically speaking, is the sum total
of the conditions, positive and negative taken together ; the
whole of the contingencies of every description, which heing
realized, the consequent invariably follows. The negative

* 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 Prospec
tive Review (the predecessor of the justly esteemed National Review), who main
tains that "we always apply the word cause rather to that element in the ante
cedents 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 expression, that the
cause of a surprise was the sentinel's bein^ off his post, to be incorrect ; 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 wliich would have prevented
the surprise." I cannot think that it would be wrong to say, that the event
took place because the seniinel was absent, and yet right to say that it took
place because he was bribed to be absent. Since the only direct effect of the
bribe was his absence, the bribe could be called the remote cause of the surprise,
only on the supposition that the absence was the proximate 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 person 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 occa
sion could never arise for so speaking of it ; for when in the inaccuracy of com
mon discourse we are led to speak of some one condition of a phenomenon as its
cause, the condition so spoken of is always one which it is at least 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 per
son's death, would not supply the information sought. Once conceive that a
doubt could exist as to his having bodily organs, or that 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 together took poison, it might be said that Faust died because
he was a human being, arid had a body, while Mephistopheles survived 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, though 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, that a man has time for it, wliich is a
necessary condition." These conditions (besides that they are antecedent statet,
and not proximate antecedent events, and are therefore never the conditions in

LAW OF CAUSATION. 371

conditions, 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 coun
teracting 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 retards the upward
motion of a projectile, and deflects it into a parabolic trajectory,
it produces, in so doing, the very same kind of effect, and even

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. Wherever this necessity exi&ts in regard to some one condition, and does
not exist in regard to any other, I conceive that it is consistent with usage, when
scientific accuracy is not aimed at, to apply the name cause to that one condi
tion. If the only condition which can be supposed to be unknown is a nega
tive condition, the negative condition may be spoken of as the 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 constitution, or the 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 Itt me remark, 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 expression, as there would be if it were said that the
cause was his inability to swim ; because, though the one condition is positive
and the other negative, it would be felt that neither of them was sufficient, with
out the other, to produce death.

With regard to the assertion that nothing is termed the cause, except the
element which exerts active force ; I wave the question as to the meaning of
active force, and accepting the phrase in it0 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 in 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 ; l>ut 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 ;

24—2

372

INDUCTION.

(as mathematicians know) the same quantity of effect, as it
does in its ordinary operation of causing the fall of hodies
when simply deprived of their support. If an alkaline solution
mixed with an acid destroys its sourness, and prevents it from
reddening vegetable blues, it is because the specific effect of
the alkali is to combine with the acid, and form a compound
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 according
to which they produce their own,* enables us, by establishing

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 difference. Again, if a person were asked why the army
of Xerxes defeated that of Leonidas, he would probably say, because they were
a thousand times the number ; but I do not think he 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 Powell, 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 passive,
and yet absolutely necessary to physical 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 incongruous 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 instance not of one cause counteracting another 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 de
pends, 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 which includes all the negative conditions of an
effect in the single one of the absence of counteracting causes, is not violated
by such cases as this ; though, if all counteracting agencies were of this descrip
tion, there would be no purpose served by employing the formula, since we
should still have to enumerate specially the negative conditions of each pheno
menon, instead of regarding them as implicitly contained in the positive laws of
the various other agencies in nature.

LAW OF CAUSATION. 373

the general axiom that all causes are 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 phenomenon :
one negative condition invariably 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 phe
nomenon 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 frequently awarded, so there are others to
which it is, in ordinary circumstances, refused. In most cases
of causation a distinction is commonly drawn between some
thing 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 phenomenon ; 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 place, is commonly 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 incongruity woulc'
arise of its being supposed 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 contradiction to the meaning of
the word cause. The stone, therefore, is conceived as the
patient, and the earth (or,' according to the common and
most unphilosophical practice, some occult quality of the
earth) is represented as the agent or cause. But that there is
nothing fundamental in the distinction may be seen from this,
that it is quite possible to conceive the stone as causing its
own fall, provided the language employed be such as to save

374 INDUCTION.

the mere verbal incongruity. We might say that the stone
moves towards the earth hy the properties of the matter com
posing it ; and according 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 be
tween 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 licence 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 philosophers, Brown in particular, for the appa
rent explanation of phenomena,) is simply a sort of logical
fiction, useful sometimes as one among several modes of
expression, but which should never be supposed to be the
enunciation 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
organs, and those of other sentient beings. What we call
states of objects, are always sequences into which the
objects enter, generally as antecedents or causes ; and things
are never more active than in the production of those phe
nomena 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 organization, and even those of our minds, are
as directly operative in determining the effect produced, as the

LAW OF CAUSATION. 375

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
sentient 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 co-operating or counteracting
agencies in relation 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 pro
portion, indeed, of all natural phenomena, 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 con
tribute, 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 phe
nomenon 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- ^UX>U^

\£ § 5. It now remains to advert to a distinction which is of
first-rate importance 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 anything (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 uso
this phrase as exactly synonymous with " the antecedent which
it invariably has followed in our past experience." Such a
mode of conceiving causation would be liable to the objection
very plausibly urged by Dr. Reid, namely, that according to
this doctrine night must be the cause of day, and day the

376 INDUCTION.

cause of night ; since these phenomena have invariably
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 followed by the consequent, but that, as long as the
present constitution of things* endures, it always will be so.
And this would not be true of day and night. "We do not
believe that night will be followed by day under all imagi
nable circumstances, but only that it will be so provided the
sun rises above the horizon. If the sun ceased to rise, which,
for aught we know, may be perfectly compatible with the
general laws of matter, night would be, or might be, eternal.
On the other hand, if the sun is above the horizon, his light
not extinct, and no opaque body between us and him, we
believe firmly that unless a change takes place in the pro
perties of matter, this combination of antecedents will be
followed by the consequent, day ; 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 day, quite independently
of night as a previous condition. Therefore is it 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 linef 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 cause. This
is what writers mean when they say that the notion of cause

* 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 revolution of the earth (for example) is not a part of the constitu
tion of things, because nothing can be so called which might possibly be termi
nated or altered by natural causes.

t I use the words " straight line" for 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
realizing, though but to a limited extent, the coveted desideratum of seeing
round a corner.

LAW OF CAUSATION. 377

.involves the idea of necessity. If there be any meaning
•which confessedly belongs to the term necessity, it is uncon-
ditionalness. 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 conditional on
the occurrence of other antecedents. That which will be
followed by a given consequent when, and only when, some
third circumstance 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, unless the sequence, besides being invariable, is
unconditional. There are sequences, as uniform in past
experience as any others whatever, which yet we do not re
gard 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 antecedents exist ; and where
those antecedents existed, it would follow in any case. No
one, probably, ever called night the cause of day ; mankind
must so soon have arrived at the very obvious generalization,
that the state of general illumination which we call day would
follow from the presence of a sufficiently luminous body,
whether darkness had preceded or not.

We may define, therefore, the cause of a phenomenon, to
be the antecedent, or the concurrence of antecedents, 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 " uncon
ditionally," we must say, " subject to no other than negative
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 experience can give in any case, for
recognising the two phenomena as cause and effect ; and that

378

INDUCTION.

to say that more is necessary — to require a belief that the
succession is unconditional, or in other words that it would
be invariable under all changes of circumstances, is to acknow
ledge 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 con
ditional 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 followed by day. To
say that these beliefs are " not generated by our mere obser
vation of sequence,"* is to forget that twice in every twenty-
four hours, when the sky is clear, we have an experimen-
tum 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 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 antece
dent which is only conditionally invariable, is not the inva
riable 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 antecedent 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 contradict the doctrine which resolves causation into
invariable sequence, but are necessarily implied in that
doctrine. It is evident, that from a limited number of uncon-

* Second Burnett Prize Essay, by Principal Tulloch, p. 25.

LAW OF CAUSATION.

379

ditional sequences, there will result a much greater number of
conditional ones. Certain causes being given, that is, certain
antecedents which are unconditionally followed by certain
consequents ; the mere coexistence of these causes will give
rise to an unlimited number of additional uniformities. It
two causes exist together, the effects of both will exist toge
ther ; and if many causes coexist, these causes (by what we
shall term hereafter the intermixture of their laws) will give
rise to new effects, accompanying or succeeding one another in
some particular order, which order will be invariable while
the causes continue to coexist, 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 antecedents 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 coexist in the same
quantities 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 uncon
ditional.

This distinction between the relations of succession which
so far as we know are unconditional, and those relations,
whether of succession or of coexistence, which, like the earth's
motions, or the succession of day and night, depend on the
existence or on the coexistence of other antecedent facts —
corresponds to the great division which Dr. Whewell and
other writers have made of the field of science, into the in
vestigation of what they term the Laws of Phenomena, and
the investigation of causes ; a phraseology, as I conceive, not
philosophically 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. And 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

380

INDUCTION.

M. Oomte, 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. Comte designates as inac
cessible, are efficient causes. The investigation of physical,
as opposed to efficient, causes (including the study of all the
active forces in Nature, considered as facts of observation) is
as important a part of M. Comte's conception of science as of
Dr. Whewell's. His objection to the word 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 M. Comte, object to
designate events as causes, are objecting without any real
ground to a mere but extremely convenient generalization, to
a very useful common name, the employment of which in
volves, 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 incorrectly 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 forgotten, a
Canon of that description is not one of the many benefits
which the philosophy of Induction has received from M.
Comte's great powers.

§ 6. 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 because its effect has been pro
duced, the two thingj^do very generally coexist ; and there
are some appearances, and some common expressions, seeming
to imply not only that causes may, but that they must, be
contemporaneous with their effects. Cessante causa cessat et

* Letters on the Philosophy of the Human Mind, First Series, p. 219.

LAW OF CAUSATION. 381

effeetus, has been a dogma of the schools : the necessity for
the continued existence of the cause in order to the continu
ance of the effect, seems to have heen 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 produced. Yet
there were at all times many familiar instances of the continu
ance of effects, long after their causes had ceased. A coup de
soleil gives a person a 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 ham
mering, 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 some
times go off as soon as the bandage is removed. The illumina
tion which the sun diffuses over the earth ceases when the sun
goes down.

There is, therefore, a distinction to be drawn. The con
ditions which are necessary for the first production of a phe
nomenon, are occasionally also necessary for its continuance ;
though more commonly its continuance requires 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 phenomena, 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

382

INDUCTION.

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 continuance of the cause is
ever required to maintain the effect. We may say, it is not
required to maintain, but to reproduce, the effect, or else to
counteract some force tending to destroy it. And this may be
a convenient phraseology. But it is only a phraseology. 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 imperceptible to
us that interval may really be filled up. But even granting
that an effect may commence simultaneously with its cause,
the view I have taken of causation is in no way practically
affected. Whether the cause and its effect be necessarily suc
cessive 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 necessity for doing so, to drop the words antecedent
and consequent as applied to cause and effect. I have no
objection 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 immaterial. At all events it does not precede
it ; and when we are in doubt, between two coexistent phe
nomena, which is cause and which effect, we rightly deem the
question solved if we can ascertain which of them preceded
the other.

* Essays, pp. 206-208.

LAW OF CAUSATION. 383

§ 7. It continually happens that several different phe
nomena, which are not in the slightest degree dependent 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 phenomenon is seen to be followed by several
sorts of effects quite heterogeneous, but which go on simul
taneously 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 pheno
mena of the magnetic needle. A crystal of galena causes
the sensations 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 Pro
perties 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 conditions) 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 gravita-
tive property of the earth, and its magnetic property : the
gravitative, luminiferous, and calorific properties of the sun :
the colour, shape, weight, and hardness of a crystal. These
are mere phrases, which explain nothing, and add nothing to
our knowledge of the subject ; but, considered as abstract
names denoting the connexion between the different effects
produced and the object which produces them, they are a very
powerful instrument of abridgment, 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 Permanent
Cause, or original natural agent There exist in nature a
number of permanent causes, which have subsisted ever since
the human race has been in existence, and for an indefinite
and probably an enormous length of time previous. The sun,
the earth, and planets, with their various constituents, air,
water, and other distinguishable substances, whether simple or

384 INDUCTION.

compound, of which nature is made up, are such Permanent
Causes. These have existed, and the effects or consequences
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 account of
the origin of the Permanent Causes themselves. Why these
particular natural agents existed originally and no others, or
why they are commingled in such and such proportions, 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 coexistence, therefore, of Primeval Causes,
ranks, to us, among merely casual concurrences : and all those
sequences or coexistences among the effects of several such
causes, which, though invariable while those causes coexist,
would, if the coexistence terminated, terminate along with it,
we do not class as cases of causation, or laws of nature : we
can only calculate on finding these sequences or coexistences
where we know by direct evidence, that the natural agents on
the properties of which they ultimately 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
natural agent, but the earth's rotation is so too : it is a cause
which has produced, from the earliest period, (by the aid of
other necessary conditions,) 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 rotation which is mysterious to
us : once begun, its continuance is accounted for by the first
law of motion (that of the permanence of rectilinear motion

LAW OF CAUSATION. 385

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 except the primeval causes, are effects either im
mediate or remote of those primitive facts, or of some combi
nation of them. There is no Thing produced, no event
happening, in the known universe, which is not connected
by an uniformity, or invariable 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 coun
teracting cause shall coexist. These antecedent phenomena,
again, were connected in a similar manner with some that
preceded them ; and so on, until we reach, as the ultimate
step attainable by us, either the properties of some one
primeval cause, or the conjunction of several. The whole of
the phenomena of nature were therefore the necessary, or in
other words, the unconditional, consequences of some former
collocation of the Permanent Causes.

The state of the whole universe at any instant, we believe
to be the consequence of its state at the previous instant ;
insomuch that one who knew all the agents which exist at the
present moment, their collocation in space, and all their pro
perties, 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

* To the universality which mankind are agreed in ascribing to the Law of
Causation, 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, according to as strict
laws as those which they suppose to exist in the world of mere matter. This
controverted point will undergo a special examination when we come to treat
particularly of the Logic of the Moral Sciences (Book vi. ch. 2). In the mean
time I may remark that these metaphysicians, who, it must be observed, ground
the main part of their objection on the supposed repugnance of the doctrine 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

VOL. I. 25

386 INDUCTION.

entire universe could ever recur a second time, all subsequent
states would return too, and history would, like a circulating
decimal of many figures, periodically repeat itself:—

Jam redit et virgo, redeunt Saturnia regna. . . .
Alter erit turn Tiphys, et altera quse vehat Argo
Delectos heroaa ; erunt quoque altera bella,
Atque iterum ad Trojam magnus mittetur Achilles.

And though things do not really revolve in this eternal round,
the whole series of events in the history of the universe, past
and future, is not the less capable, in its own nature, of being
constructed a priori 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 laws of
succession existing between them and their effects : saving the
far more than human powers of combination and calculation
which would be required, even in one possessing the data, for
the actual performance of the task.

§ 8. Since everything which occurs is determined by
laws of causation and collocations of the original causes, it
follows that the coexistences 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 coexistence as of succession, among effects; but
these must in all cases be a mere result either of the identity
or of the coexistence of their causes : if the causes did not
coexist, 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 or remotely to one and the

would, I think, on strict self-examination, find to be, the application to human
actions and volitions of the ideas involved in the common 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 would certainly predict how
he would act in any supposable case ; they probably would not find this doctrine
either contrary to their experience or revolting to their feelings. And no more
than this is contended for by any one but an Asiatic fatalist.

LAW OF CAUSATION. 387

same cause) the coexistences of phenomena can in no case be
universal, unless the coexistences of the primeval causes to
which the effects are ultimately traceable, 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 coexistence, between effects
of different causes ; if they coexist, it is only because the
causes have casually coexisted. The only independent and
unconditional coexistences which are sufficiently invariable to
have any claim to the character of laws, are between different
and mutually independent effects of the same cause ; in other
words, between different properties 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.
^ v-*' •'-<--'

§ 9. It is proper in this place to advert to a rather
ancient doctrine respecting causation, which has been revived
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 exclusive 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 inanimate 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 accom
panied by a consciousness 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 know
ledge a priori ; assurance, prior to experience, that we have
the power of causing effects. Volition, therefore, it is
asserted, is something more than an unconditional antecedent;

25—2

388 INDUCTION.

it is a cause, in a different sense from that in which physical
phenomena are said to cause one another : it is an Efficient
Cause. From this the transition is easy to the further doc
trine, that Volition is the sole Efficient Cause of all pheno
mena. " It is inconceivable that dead force could continue
unsupported for a moment beyond its creation. We cannot
even conceive of change or phenomena 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
produced by physical causes, but they are in reality produced,
say these writers, by the immediate agency of mind. All
things which do not proceed 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 coinciding 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 ajjiysical, 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 gunpowder. The volition,
a state of our mind, is the antecedent ; the motion of our
limbs in conformity to the volition, is the consequent. This
sequence I conceive to be not a subject of direct consciousness,
in the sense intended by the theory. The antecedent, indeed,
and the consequent, are subjects of consciousness. But the
connexion between them is a subjecU)f ^experience. I cannot

LAW OF CAUSATION*. 389

admit that our consciousness of the volition contains in itself
any a priori knowledge that the muscular motion will follow.
If our nerves of motion were paralyzed, 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 anything of voli
tion as a physical power, or been conscious of any tendency
in feelings of our mind to produce motions 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 ending
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 conscious
of it, I conceive, only as a kind of uneasiness, accompanying
our feelings of desire.

It is well argued by Sir William Hamilton against the
theory in question, that it " is refuted by the consideration,
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 causal connexion between the extreme links of this
chain, the volition to move and the limb moving, as this
hypothesis asserts. No one is immediately 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 paralysis is conscious of no inability in
his limb to fulfil the determinations of his will; and it is only
after having willed, and finding that his limbs do not obey his

390

INDUCTION.

volition, that he learns by this experience, that the external
movement does not follow the internal act. But as the para
lytic 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 contending have never pro
duced, and do not pretend to produce, any positive evidencef
that the power of our will to move our bodies would be known
to us 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 explanation with it, while the
action of matter upon matter seems to require something else
to explain it; and is even, according to them, " inconceivable"

* Lectures on Metaphysics, vol. ii. Lect. xxxix. pp. 391-2.

I regret that I cannot invoke the authority of Sir William Hamilton in
favour of my own opinions on Causation, as I can against the particular
theory which I am now combating. But that acute thinker has a theory of
Causation peculiar to himself, 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 insufficient psychological theories which
strew the ground in such numbers under his potent metaphysical scythe.
(Since examined and controverted in the sixteenth chapter of An Examination
of Sir William Hamilton's Philosophy).

•f- 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
accomplished is preconsidered or meditated, and is therefore known a priori,
or before experience." — (Bo wen's Lowell Lectures on the Application of Meta
physical 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 residing in us, we
nevertheless must already have known that we possessed them, since we cannot
will that which we do not believe to be in our power. But the impossibility is
perhaps in the words onty, and 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 com
plicated 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 Causation. Our knowing, previous to experience, 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.

LAW. OF CAUSATION.

391

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 spon
taneous tendencies of its uncultured 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
experience 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 motion. Now,
it is the natural tendency of the mind to be always attempting
to facilitate its conception of unfamiliar facts by assimilating
them to others which are familiar. Accordingly, our volun
tary acts, being the most familiar to us of all cases of causa
tion, are, in the infancy and early youth of the human race,
spontaneously taken as the type of causation in general, and
all phenomena are supposed to be directly produced by the
will of some sentient being. This original Fetichism I shall
not characterize 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 subject 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 external 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 Abbe Raynal, ' wherever they
see motion which they cannot account for, there they suppose
a soul.' All men may be considered as savages in this respect,

392 INDUCTION.

until they are capable of instruction, and of using their facul
ties in a more perfect manner than savages do.

" The Abbe Raynal's observation is sufficiently confirmed,
both from fact, and from the structure of all languages.

" Rude nations do really believe sun, moon, and stars,
earth, sea, and air, fountains, and lakes, to have understanding
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 structure the marks of their
being formed when this belief prevailed. The distinction of
verbs and participles into active and passive, which is found in
all languages, must have been originally intended to distin
guish what is really active from what is merely passive ; and
in all languages, we find active verbs applied to those objects,
in which, according to the Abbe Raynal's observation, savages
suppose a soul.

"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 proper and natural to express their motions 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 lan
guage, which, notwithstanding the changes produced in it by
time, will always retain some signatures 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 intellectual abilities, find leisure
for speculation, they begin to philosophize, 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 vulgar superstitions, and invites to further disco
veries of the same kind.

" As philosophy advances, life and activity in natural

LAW OF CAUSATION. 893

objects retires, and leaves them dead and inactive. Instead of
moving voluntarily, we find them to be moved necessarily ;
instead 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 succes
sion may reach, the philosopher does not know."*

There is, then, a spontaneous tendency 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, before it has become familiar with any other invariable
sequences than those between its own volitions or those of other
human beings and their voluntary acts. As the notion of fixed
laws of succession .among external phenomena gradually
establishes itself, the propensity to refer all phenomena to volun
tary agency slowly gives way before it. The suggestions, how
ever, of daily life continuing 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 throw
ing 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 in
herent mental law, is proved by superabundant evidence.
The history of science, from its earliest dawn, shows that
mankind have not been unanimous in thinking either that the
action of matter upon matter 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 modern 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

* Reid's Essays on the Active Powers, Essay iv. ch. 3.

394 INDUCTION.

affording it to others, and even of serving as the ultimate ex
planation of things in general.

One of the ablest recent supporters of the Volitional
t. -}ory has furnished an explanation, at once historically true
au* philosophically acute, of the failure of the Greek philo
sophers in physical inquiry, in which, as I conceive, he un
consciously depicts his own state of mind. " Their stumbling-
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 connexion, where they
meant by natural that which would per se carry some pre
sumption to their own mind. . . . They wanted to see some
reason why the physical antecedent should produce this par
ticular 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 per
ceives in the nature of the phenomenon Volition. And to
complete the statement 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 he does not believe that there exist
any relations between material phenomena which can account
for their producing one another : but the very fact of the per-

* Prospective Review for February 1850.

LAW OF CAUSATION. 395

sistency of the Greeks in this error, shows that their minds
were in a very different state : they were able to derive from
the assimilation of physical facts to other physical facts, the
kind of mental satisfaction which we connect with the w>- :d
explanation, and which the reviewer would have us think i*an
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 infi
nitely various sensible manifestations ; when Anaxime*nes
predicated the same thing of air, Pythagoras of numbers, and
the like, they all thought that they had found a real expla
nation ; and were content to rest in this explanation as
ultimate. The ordinary sequences of the external universe
appeared to them, no less than to their critic, to be incon
ceivable without 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 otherwise 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 par
ticular consequent," some connexion "which would per se
carry some presumption to their own mind." Among modern
philosophers, Leibnitz laid it down as a self-evident principle
that all physical causes without exception 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 internal evidence of its own power, and as
the real bond of connexion between physical antecedents and
their consequents, he demanded some naturally and per se
efficient physical antecedent as the bond of connexion between
Volition itself and its effects. He distinctly refused to admit
the will of God as a sufficient explanation of anything except
miracles; and insisted upon finding something that would

396

INDUCTION*.

account better for the phenomena of nature than a mere refe
rence to divine volition.*

Again, and conversely, the action of mind upon matter
(which, we are now told, not only needs no explanation 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 connexion, no relation a 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 measure 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 systenvis the only efficient
cause, not qua mind, or qua endowed with volition, but qua
omnipotent. This hypothesis was, as I said, originally sug
gested by the supposed inconceivability of any real mutual
action between Mind and Matter : but it was afterwards
extended to the action of Matter upon Matter, for on a nicer
examination they found this inconceivable too, and therefore,
according to their logic, impossible. The deus ex machind
was '...Itimately called in to produce a spark 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 knowing that one
fact is invariably antecedent and another consequent, but to look
out for something which may seem to explain their being so.
But we also see that this demand may be completely satisfied

* Vide supra, p. 270, note.

LAW OF CAUSATION. 397

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 inconceivable that the antecedents
which we see in nature, should produce the consequents ; but
perfectly natural that water, or air, should produce them. The
writers whom I oppose declare this inconceivable, but can con
ceive 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 confirmation
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 requisite
associations of ideas, people may make themselves unable to
conceive 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 history
which determine what is or is not conceivable to him, deter
mine also which among the various sequences 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,
independent equally of experience and of explanation.

By what rule is any one to decide between one theory of
this description and another ? The theorists do not direct us
to any external evidence ; they appeal each to his own sub
jective feelings. One says, the succession C, B, appears to me
more natural, conceivable, and credible per se, than the succes
sion A, B ; you are therefore mistaken in thinking t1 -. 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 natural and conceivable,
or the latter more so than the former: A is quite capable 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 sequence D, B, still more natural than C, B, or
of nearer kin to the subject matter, and prefers his D theory

398 INDUCTION.

to the 0 theory. It is plain that there is no universal law
operating here, except the law that each person's conceptions
are governed and limited by his individual experience 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 conceivable
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 because Volition is an efficient
cause, therefore it is the only cause^jand the. direcjLagent in
producing even what is apparently produced by something
else. Volitions are not known to produce anything directly
except nervous action, for the will influences even the muscles
only through the nerves. Though it were granted, then, that
every phenomenon has an efficient, and not merely a pheno
menal 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 inference 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 effi
cient cause of which we are conscious, being the only one of
which in the nature of the case we can be conscious, since it is
the 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 peculiarly human or animal, phenomenon ? The
nearest parallel to this specimen of generalization is suggested

LAW OF CAUSATION. 399

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 tbat this is inhabited we know
absolutely, and without possibility of doubt. Now if on this
evidence any one were to infer that every heavenly body
without exception, sun, planet, satellite, comet, fixed star or
nebula, is inhabited, and must be so from the inherent consti
tution of things, his inference would exactly resemble that of
the writers who conclude that because volition is the efficient
cause of our own bodily motions, it must be the efficient cause
of everything else in the universe. It is true there are cases
in which, with acknowledged propriety, we generalize from, a
single instance to a multitude of instances. But they must be
instances which resemble the one known instance, and not
such as have no circumstance 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 because I am. I ascribe to certain other
creatures a life like my own, because they manifest it by the
same sort of indications by which mine is manifested. 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 conclusion
beyond the grounds for it. Earth, fire, mountains, trees,
are remarkable agencies, but their phenomena do not conform
to the same laws as my actions do, and I therefore do not
believe earth or fire, mountains or trees, to possess animal
life. But the supporters of the Volition Theory ask us to
infer that volition causes everything, for no reason except that
it causes one particular thing ; although that one pheno
menon, far from being a type of all natural phenomena, is
eminently peculiar ; its laws bearing scarcely any resemblance
to those of any other phenomenon, whether of inorganic or of
organic nature.

400 INDUCTION.

NOTE SUPPLEMENTARY TO THE PRECEDING CHAPTER.

The author of the Second Burnett Prize Essay (Dr. Tulloch), who has em
ployed a considerable number of pages in controverting the doctrines of the pre
ceding 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 explanations of phenomena the same complete mental satisfaction
which we are told is only given by volitional explanation, and others who de
nied the Volitional Theory on the same ground of inconceivability on which it
is defended. The assertion of the Essayist is countersigned still more positively
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 inconceivability. In counterstatement
as to the first of these cases the author shows— what we believe now hardly
admits of doubt— that the Greek philosophers distinctly recognised as beyond
and above their primal material source, the VOVQ, or Divine Intelligence, 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 represented
as inconceivable."

A greater quantity of historical error has seldom been comprised in a single
sentence. With regard to Thales, the assertion that he considered water as a
mere material in the hands of VOVQ rests on a passage of Cicero de Naturd
Deorum : and whoever will refer to any of the accurate historians of philo
sophy, will find that they treat this as a mere fancy of Cicero, resting on no
authority, opposed to all the evidence ; and make surmises as to the manner
in which Cicero may have been led into the error. (See Ritter, vol. i. p. 211,
2nd ed. ; Brandis, vol. i. pp. 118-9, 1st ed. ; Preller, Historia Philosophic
Grceco-Romance, p. 10. " Schiefe Ansicht, durchaus zu verwerfen ;" "augen-
scheinlich folgernd statt zu berichten ;" " quibus vera sententia Thaletis plane
detorquetur ;" are the expressions of these writers.) As for Anaxiraenes, 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 [Diis] aerem factum, sed
ipsos ex acre ortos credidit." Those who are not familiar with the metaphy
sical terminology of antiquity, must not be misled by finding it stated that
Anaximenes attributed fy>xn (translated scmZ, or life) to his universal element,
the air. The Greek philosophers acknowledged several kinds of ^v^n, the
nutritive, the sensitive, and the intellective.t Even the moderns with ad
mitted correctness attribute life to plants. As far as we can 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 external
to itself : so that he conceived it as exercising spontaneous force, and as the

* Westminster Review for October 1855.

f See the whole doctrine in Aristotle de Animd : where the OpiirTiKT} ^i/x»)
is treated as exactly equivalent to 0p£7T7iK>}

LAW OF CAUSATION. 401

principle of life and activity in all things, men and gods inclusive. If
this be not representing it as the Efficient Cause, the dispute altogether has
no meaning.

If either Anaximenes, or Thales, or any of their cotemporaries, had held the
doctrine thai vovc; was the Efficient Cause, that doctrine could not have been
reputed, as it was throughout antiquity, to have originated with Anaxagoras.
The testimony 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 philo
sophers recognised only the second kind of Cause, the Matter of a thing, TO.Q iv
v\r]£ ilSti /novae yriOijaav apx«C tlvai iravTW. As his first example he
specifies Thales, whom he describes as taking the lead in this view of the sub
ject, 6 Djf ToiavTtji; ap%r)ybc; QiXouotyiaG, and goes on to Hippon, Anaximenes,
Diogenes (of Apollonia), Hippasus of Metapontum, Heraclitus, and Empe-
docles. Anaxagoras, however, (he proceeds to say,) taught a different i!octrine,
as we know, and it is alleged that Hermotimus of Clazomense taught it before
him. Anaxagoras represented, that even if these various theories of the uni
versal 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 df) TO yt vTroKsijjivov avrb iroitl fitTafidXXtiv iavro' Xsyw
<T olov ovTt TO ZvXov ovTt o ^aX/coc, amoc, TOV [itTafiaXXeiv ticaTtpov avTwv,
oiiCi trottl TO /j.fv %uXov K\ivt]v o Ss ^aXfcog dvBpiavTa, d\\' trtpov TL Trjg
(iiiTafioXrjf; atTiov, viz., the other kind of cause, oOtv rj d(>\rj r/}<; Kivi'iatdtQ — an
Efficient Cause. Aristotle expresses great approbation of this doctrine (which
he says made its author appear the only sober man among persons raving,
olov vrjipwv itpdvri Trap' tltcfj Xsyoirac; rcv£ TrpoTipov); but while describing the
influence which it exercised over subsequent speculation, he remarks that the
philosophers against whom this, as he thinks, insuperable difficulty was urged,
had not felt it to be any difficulty : ouStv tSva^pdvav iv tavToiQ. It is surely
unnecessary to say more in proof of the matter of fact which Dr. Tulloch and
his reviewer deny.

Having pointed out what he thinks the error of these early speculators in
not recognising the need of an efficient cause, Aristotle goes on to mention two
other efficient causes to which they might have had recourse, instead of intel
ligence : ri\r), chance, and TO avTOftaTov, spontaneity. He indeed puts these
aside as not sufficiently worthy causes for the order in the universe, oi'd" av Tip
ai/TOfjidTy Kai TJJ Tvxy ToffoiJTov iiriTptyai Trpay/j.a KaXwf tl^tv: but he does
not reject them as incapable of producing any effect, but only as incapable of
producing that effect. He himself recognises Tv%t) and TO avropaTov as co
ordinate agents with Mind in producing the phenomena of the universe ; the de
partment allotted to them being composed of all the classes of phenomena which
are not supposed to follow 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 modem speculation 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

VOL. i. 26

402 INDUCTION.

the results of abstraction. Chance could make out as good a title to that dig
nity 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 rb avrofidrov, 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-deter
mining 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
necessities 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.*

With regard to the modern philosophers (Leibnitz and the Cartesians) whom
I had cited as having maintained that the action of mind upon matter, so far from

* It deserves notice that the parts of nature, which Aristotle regards as pre
senting evidence of design, are the Uniformities : the phenomena in so far as re
ducible to law. Tv^/; and TO avTopaTov 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 nature, is there-
verse of this. The events in which men spontaneously see the hand of a super
natural being, are those which cannot, 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 they
already recognise such an author, might be conceived, they think, to arise from
a blind 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 Natural 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.e. 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 inatter have been so placed
as to promote beneficent ends, is what he regards as the proof of a Divine Pro
vidence. Mr. Baden Powell, in his Essay entitled " Philosophy of Creation,"
has returned to the point of view of Aristotle and the ancients, and vigorously
reasserts the doctrine that the indication of design in the universe is not
special adaptations, but Uniformity and Law, these being the evidences 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 acknowledgment due to the philosophic spirit
which pervades generally the three Essays composing it, forming in the case
of one of them (the "Unity of Worlds") an honourable contrast with the other
dissertations, so far as they have come under my notice, which have appeared
on either side of that controversy.

LAW OF CAUSATION.

being the only conceivable origin of material phenomena, is itself inconceivable ;
the attempt to rebut this argument by asserting that the mode, not the fact, of
the action of mind on matter was represented as inconceivable, is an abuse of
the privilege of writing confidently about authors without reading them : for
any knowledge whatever of Leibnitz would have taught those who thus speak
of him, that the inconceivability of the mode, and the impossibility of the thing,
were in his mind convertible expressions. What was his famous Principle of
the Sufficient Keason, the very corner stone of his philosophy, from which the
Preestablished Harmony, the doctrine of Monads, and all the opinions most
characteristic of Leibnitz, were corollaries ? 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 some
thing in their nature showing them to be capable of producing those particular
effects. And this "something" which accounts for the production of physical
effects, he was able to find in many physical causes, but could not find it in any
finite minds, which therefore he unhesitatingly asserted to be incapable of pro
ducing any physical effects whatever. "On ne saurait concevoir," he says,
"une action re"ciproque de la matiere et de 1'intelligence 1'une sur 1'autre," and
there is therefore (he contends) no choice but between the Occasional Causes
of the Cartesians, and his own Preestablished Harmony, according to which
there is no more connexion 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 similar difficulty as to physical causes : and throughout
his speculations, as in the passage I have already cited respecting gravitation,
he distinctly refuses to consider as part of the order of nature any fact which is
not explicable from the nature of its physical cause.

With regard to the Cartesians (not Descartes ; 1 did not make that mistake,
though the reviewer of Dr. Tulloch's Essay attributes it to me) I 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 Occasional Causes, is its principal
expositor. In Part 2, chap. 3, 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 I'ide'e que 1'on a de
tous les esprits finis, on ne voit point de liaison ne"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 con-
clure, si on veut raisonner selon ses lumieres, qu'il n'y a aucun esprit cre'e' qui
puisse remuer quelque corps que ce soit comme cause veritable ou principale, de
meme que 1'on a dit qu'aucun corps ne se pouvait remuer soi-meme :" thus the
idea of Mind is according to him as incompatible 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 the idea of a Divine Mind includes omni
potence ; and the idea of omnipotence does contain the idea of being able to
move bodies. Thus it is the nature of omnipotence which renders the motion
of bodies even by the divine mind credible or conceivable, while, so far as
depended on the mere nature of mind, it would have been inconceivable and

26—2

404 INDUCTION.

incredible. If Malebranche had not believed in an omnipotent being, be -would
have beld all action of mind on body to be a demonstrated impossibility.*

A doctrine more precisely the reverse of the Volitional tbeory of causation
cannot well be imaged. The volitional tbeory is. that we know by intuiti<
or by direct experience tbe 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 Tinder the govern
ment of 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 tbe
existence of an all-governing Being, and that Being omnipotent, which can
acconnt for tbe 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 extremes of possible divergence from one another, invokes
not only as its evidence, but as its sole evidence, tbe absolute inconceivability
of any theory but itself, we are enabled to measure tbe worth of this kind of
evidence : and when we find the Volitional theory entirely built upon tbe asser
tion that by our mental constitution we are compelled to recognise our volitions
as efficient '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,
1 think we hnve a right to say, that this supposed law of our mental constitu
tion does not exist.

Dr. Tulloch (pp. 4?-7) thinks it a snfficient answer to this, that Leibnitz
and the Cartesians were Theists, 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 such cause, Dr. TnDooh mistakes the nature of the
question. I was not writing on Theism, as Dr. Tulloch is, but against a par-
t.cular theory of causation, which if it be unfounded, can give no effective sup
port to Theism or to anything else. I found it asserted that volition is the
only efficient cause., on tbe 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 positiveness that volition as an efficient cause is itself not
conceivable, and that omnipotence, which renders all things conceivable, can
alone take away the impossibility. This I taught and think, a conclusive
answer to the arenment on which this theory of causation avowedly depends.
But I certainly did not imagine that Theism was bound up with that theory ;
nor expected to be charged with denying Leibnitz and the Cartesians to be
Theists because I denied that they held the theory.

* In the words of Fontenelle, another celebrated Cartesian, u tes philosophes
anssi bien que le peuple avaient cm qne lame et le corps agissaient reellement
M physiquement Tun sur 1'autre, Descartes vint qui pronva qne leur nature
ne permettait point cette sorte de communication veritable, et qu'ik nWf
vaient avoir qn'une apparente, dont Dieu etait k Mediateur."— CEwam
Font.cneUc. ed. 1767, torn, T. p. 5S4.

CHAPTER VI.

ON THE COMPOSITION OF CAUSES.

§ 1. To complete the general notion of causation on
•which the rules of experimental inquiry into the laws of
nature must be founded, one distinction still remains to be
pointed out : a distinction so radical, and of so much impor
tance, as to require a chapter to itself.

The preceding discussions have rendered us familiar with
the case in which several agents, or causes, concur as condi
tions to the production of an effect ; a case, in truth, almost
universal, 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, instead 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 different from the joint effect
of the two, and more or less dissimilar to it. Xow, 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 enable us to do
this, it is only necessary that the same law which expresses
the effect of each cause acting by itself, shall also correctly
express the part due to that cause, of the effect which follows
from the two together. This condition is realized in the
extensive and important class of phenomena commonly
called mechanical, namely the phenomena of the communi
cation of motion ^or of pressure, which is tendency to motion)
from one body to another. In this important class of cases
of causation, one cause never, properly speaking, defeats or

406 INDUCTION.

frustrates another ; both have their full effect. If a body is
propelled in two directions by two forces, one tending 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
expression, I shall give the name of the Composition of Causes
to the principle which is exemplified in all cases in which the
joint effect 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 combina
tion of two substances produces, as is well known, a third
substance with properties entirely different from those of
either of the two substances separately, or both of them
taken together. Not a trace of the properties of hydrogen
or of oxygen is observable in those of their compound,
water. The taste of sugar of lead is not the sum of the
tastes of its component elements, acetic acid and lead or its
oxide ; nor is the colour of blue vitriol a mixture of the
colours of sulphuric acid and copper. This explains why
mechanics is a deductive or demonstrative science, and
chemistry not. In the one, we can compute the effects of
all combinations of causes, whether real or hypothetical,
from the laws which we know to govern those causes when
acting separately; because they continue to observe the
same laws when in combination which they observed when
separate : 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 altogether when they
are conjoined; and we are not, at least in the present state
of our knowledge, able to foresee what result will follow

COMPOSITION OF CAUSES. 407

from any new combination, until we have tried the specific
experiment.

If this be true of chemical combinations, it is still more
true of those far more complex combinations of elements
which constitute organized bodies ; and in which those extra
ordinary new uniformities arise, which are called the laws
of life. All organized 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 knowledge 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.

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

•108 INDUCTION.

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 amount
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 com
monly 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 of the algebraical
calculus, which has so vastly increased its powers as an instru
ment of discovery, by introducing into its reasonings (with
the sign of subtraction prefixed, and under the name of
Negative Quantities) every description whatever of positive
phenomena, provided they are of such a quality in reference to
those previously 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 anni
hilate 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 cer
tain proportions, instantly become, not a larger amount of
liquid, but a solid mass.

§ 2. This difference between the case in which the joint
effect of causes is the sum of their separate effects, and the

* I omit, for simplicity, to take into account the effect, in 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 applicability of the
principle, since when the two causes act simultaneously the conditions of that
diminution of pressure do not arise.

COMPOSITION OF CAUSES. 409

case in which it is heterogeneous 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 prin
ciple of the Composition of Causes ; none that have not some
laws which are rigidly fulfilled in every combination 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
organized body, is equal to the sum of the weights of the
elements which compose it. The weight either of the ele
ments or of the compound 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 chemical laws, in
so far as the operation of those laws is not counteracted by
the new laws which govern them as organized 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 coexist
with another portion, 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, heteropathic laws, are not capable of composition with
one another. The causes which by one combination have

410 INDUCTION.

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 condition 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 moderate number of not very complex combina
tions. The Laws of Life will never be deducible from the
mere laws of the ingredients, but the prodigiously complex
Facts of Life may all be deducible from comparatively simple
laws of life ; which laws (depending indeed on combinations,
but on comparatively simple combinations, of antecedents)
may, in more complex circumstances, be strictly compounded
with one another, and with the physical and chemical laws of
the ingredients. The details of the vital phenomena, even
now, afford innumerable exemplifications 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 cir
cumstances 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 properties 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 substance is compounded before we have analysed

COMPOSITION OF CAUSES. 411

it. The law of definite proportions, first discovered in its full
generality by Dalton, is a complete solution of this problem
in one, though but a secondary aspect, that of quantity : and
in respect to quality, we have already some partial generaliza
tions sufficient to indicate the possibility of ultimately pro
ceeding farther. We can predicate some common properties
of the kind of compounds which result from the combination,
in each of the small number of 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 whenever the new combinations which
result produce an insoluble compound, or one less soluble than
the two former. Another uniformity is that called the law
of isomorphism ; the identity of the crystalline forms of sub
stances which possess in common certain peculiarities of
chemical composition. Thus it appears that even heteropathic
laws, such laws of combined 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 principle. There
may, therefore, be laws of the generation of laws from others
dissimilar to them j and in chemistry, these undiscovered
laws of the dependence of the properties of the compound
on the properties of its elements, may, together with the
laws of the elements themselves, furnish the premises by
which the science is perhaps destined one day to be rendered
deductive.

It would seem, therefore, that there is no class of pheno
mena 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 transition from separate to
united action, the laws change, and an entirely new set of
effects are either added to, or 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 com
position, to an indefinite extent, like the laws which they
superseded.

INDUCTION.

§ 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 reason
ings respecting the laws of nature, though it is iucumbered
with many difficulties 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 identical with the sum of their separate effects. If a
force equal to one hundred weight will raise a certain body
along an inclined plane, a force equal to two hundred weight
will raise two bodies exactly similar, and thus the effect is
proportional to the cause. But does not a force equal to two
hundred weight actually contain in itself two forces each
equal to one hundred weight, which, if employed apart,
would separately raise the two bodies in question ? The fact,
therefore, 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
oan 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. Suppose
that the application of a certain quantity of heat to a body
merely increases its bulk, that a double quantity melts it, arid
a triple quantity decomposes it : these three effects being
heterogeneous, no ratio, whether corresponding 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 prin
ciple 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

COMPOSITION OF CAUSES. 413

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 introduction to the theory of the inductive process, may
here terminate. That process is essentially an inquiry into
cases of causation. All the uniformities which exist in the
succession of phenomena, and most of the uniformities in their
coexistence, are either, as we have seen, themselves laws of
causation, or consequences resulting from, and corollaries
capable of being deduced from, such laws. If we could deter
mine what causes are correctly assigned to what effects, and
what effects to what causes, we should be virtually acquainted
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 parti
cular 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
Induction ; and to point out how this is done is the chief
object of Inductive Logic.

CHAPTER VII.

OF OBSERVATION AND EXPERIMENT.

§ 1. IT results from the preceding exposition, that the
process of ascertaining what consequents, in nature, are inva
riably connected with what antecedents, or in other words
what phenomena are related to each 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 somewhere among the facts which imme
diately preceded the occurrence, may be taken for certain.
The whole of the present facts are the infallible result of all
past facts, and more immediately of all the facts which
existed 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 followed by the present state. The question is, how to
resolve this complex uniformity into the simpler uniformities
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 resolution of a complex whole into the component
elements, is more than a merely mental analysis. No mere
contemplation 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 mul
titude of distinct antecedents, in the chaotic consequent a
multitude of distinct consequents. This, supposing it done,

OBSERVATION AND EXPERIMENT. 415

will not of itself tell us on which of the antecedents each conse
quent is invariably attendant. To determine that point, we
must endeavour to effect a separation of the facts from one an
other, not in our minds only, but in nature. The mental ana
lysis, 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 eyes, 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, confound
ing it with what he imagines, or with what he infers ; another
takes note of the kind of all the circumstances, bat being inex
pert in estimating their degree, leaves the quantity of each
vague and uncertain; 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 sepa
rating others which might more conveniently be considered as
one, that the result is much the same, sometimes 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 Edu
cation, in the most enlarged sense of the term. There is not
properly an Art of Observing. There may be rules for ob
serving. But these, like rules for inventing, are properly
instructions 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 observation which may be
requisite, and the degree of decomposition to which it may be
necessary to carry the mental analysis, depend on the parti
cular purpose in view. To ascertain the state of the whole

416 INDUCTION.

universe at any particular moment is impossible, but would
also be useless. In making chemical experiments, we do not
think it necessary to note the position of the planets ; because
experience has shown, as a very superficial experience is suffi
cient 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 ascertaining the
precise condition of those bodies at the moment of the experi
ment. As to the degree of minuteness of the mental sub
division ; 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 un
necessary. 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 observations
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 imprisoned 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 elements but those which ordinary language already
recognised.

§ 2. The different antecedents and consequents, being,
then, supposed to be, so far as the case requires, ascertained
and discriminated from one another ; we are to inquire which
is connected with which. In every instance which comes
under our observation, there are many antecedents and many

OBSERVATION AND EXPERIMENT. 417

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 conse
quents, and observe by what they are preceded. We must,
in short, follow 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 circumstances, we may
have recourse (according to a distinction commonly made)
either to observation or to experiment ; we may either find an
instance in nature, suited to our purposes, or, by an artificial
arrangement of circumstances, make one. The value of the
instance depends on what it is in itself, not on the mode in
which it is obtained : its employment for the purposes of in
duction 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 importance 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 spontaneously offers, but also, in thousands of cases, to
produce the precise sort of variation which we are in want of
for discovering the law of the phenomenon ; a service which
nature, being constructed on a quite different scheme from
that of facilitating our studies, is seldom so friendly as to
bestow upon us. For 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
VOL. i. 27

4-18 INDUCTION.

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 experimentation over simple ob
servation is universally recognised : all are aware that it enables
us to obtain innumerable combinations of circumstances which
are not to be found in nature, and so add to nature's experi
ments a multitude of experiments of our own. But there is
another superiority (or, as Bacon would have expressed it,
another prerogative) of instances artificially 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 phenomenon 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 accu
rately 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 discretion, 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 simultaneous state of every
thing else which is within the reach of A's influence, we have
only to observe what alteration 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 thunder
storms, and compare it with that which they have gained,
and may expect to gain, from electrical and galvanic experi
ments. This example is the more striking, now that we have

OBSERVATION AND EXPERIMENT. 419

reason to believe that electric action is of all natural pheno
mena (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 con
tinued to be regarded either as supernatural, or as a sort of
anomalies and eccentricities in the order of the universe.

^When we have succeeded in insulating 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 obtain assurance of the
manner in which the phenomenon behaves under an indefinite
variety of possible circumstances. Thus, chemists, after
having obtained some newly-discovered substance in a pure
state, (that is, having made sure that there is nothing present
which can interfere with and modify its agency,) introduce
various other substances, one by one, to ascertain whether it
will combine with them, or decompose them, and with what
result; and also apply heat, or electricity, or pressure, to dis
cover what will happen to the substance under each of these
circumstances.

But if, on the other hand, it is out of our power to pro
duce the phenomenon, and we have to seek for instances in
which nature produces it, the task before us is very different.
Instead of being able to choose what the concomitant cir
cumstances shall be, we now have to discover what they are ;
which, when we go beyond the simplest and most accessible
cases, it is next to impossible to do, with any precision and
completeness. Let us take, as an exemplification of a phe
nomenon which we have no means of fabricating artificially,
a human mind. Nature produces many; but the consequence

27-2

420 INDUCTION.

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 unascertainable 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 connexion with it, a
body ; that is, a vast complication of physical facts, in no two
cases perhaps exactly similar, and most of which (except the
mere structure, which we can examine in a sort of coarse
way after it has ceasad to act), are radically out of the reach
of our means of exploration. If, instead of a human mind,
we suppose the subject of investigation to be a human society
or State, all the same difficulties recur in a greatly augmented
degree.

We have thus already come within sight of a conclusion,
hich the progress of the inquiry will, I think, bring before
us with the clearest evidence, : 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 prac
tised at a disadvantage in most cases equivalent to impractica
bility : from which it follows that the methods of those sciences,
in order to accomplish anything worthy 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 th" others, is probably one of the reasons why they are
not in a moi'e advanced state.

§ 4. If what is called pure observation is at so great a
disadvantage, compared with artificial experimentation, in one
department of the direct exploration of phenomena, there is
another branch in which the advantage is all on the side of
the former.

Inductive inquiry having for its object to ascertain what

OBSERVATION AND EXPERIMENT. 421

causes are connected 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 effects of a
given cause, or into the causes 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 inquiring
into the circumstances. The effect of the urali poison might
have become known either by administering it to animals, or
by examining how it happened that the wounds which the
Indians of Guiana inflict with their arrows prove so uniformly
mortal. Now it is manifest from the mere statement of
the examples, without any theoretical discussion, that arti
ficial 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 pro
duced, 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 un
known, we are obliged to commence 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 contrary, 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

422 INDUCTION.

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 antece
dents, we are necessarily destitute of the resource of artificial
experimentation. We cannot, at our choice, obtain conse
quents, as we can antecedents, under any set of circumstances
compatible with their nature. There are no means of pro
ducing effects but through their causes, and by the supposi
tion 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 ante
cedents or among some other order of antecedents, something
which is always found when the effect is found, however
various the circumstances, and never found when it is not;
we may discover, by mere observation 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 induction when not founded on experimentation. Sup
pose that, by a comparison of cases of the effect, we have
lound 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,
aud produced the effect by means of that antecedent. If we
can produce the antecedent artificially, and if, when we do so,
the effect follows, the induction is complete ; that antecedent
is the cause of that consequent.* But we have then added

* Unless, indeed, the consequent was generated not by the antecedent, but
by the means employed to produce the antecedent. As, however, these
means are under our power, there is so far a probability that they are also
sufficiently within our knowledge, to enable us to judge whether that could be
the case or not.

OBSERVATION AND EXPERIMENT. 423

the evidence of experiment to that of simple observation.
Until we had done so, we had only proved invariable ante
cedence within the limits of experience, but not unconditional
antecedence, or causation. Until it had been shown by the
actual production of the antecedent under known circum
stances, and the occurrence thereupon of the consequent, that
the antecedent was really the condition on which it depended ;
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 ulte
rior cause. Observation, in short, without experiment (sup
posing no aid from deduction) can ascertain sequences and
coexistences, but cannot prove causation.

In order to see these remarks verified 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 coexistence, others
of succession, to many of which, notwithstanding considerable
variations of the attendant circumstances, we know not any
exception : but the antecedents, for the most part, are such as
we cannot artificially produce ; or if we can, it is only by set
ting in motion the exact process by which nature produces
them; and this being to us a mysterious process, of which
the main circumstances are not only unknown but unobserv-
able, we do not succeed in obtaining 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 strictness of arrangement, premature in this place, it
seemed that a few general remarks on the difference between

424

INDUCTION.

sciences of mere observation and sciences of experimentation,
and the extreme disadvantage under which directly inductive
inquiry is necessarily 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.

OF THE FOUR METHODS OF EXPERIMENTAL INQUIRY.

§ 1. 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 comparing
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 similar in which
it does not. These two methods may be respectively deno
minated, the Method of Agreement, and the Method of Dif
ference.

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 properties of a given cause.
We shall consider the methods in their application 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 inquiry be to ascertain what are the 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 pro
duced in all our trials, is indicated as the effect of A. Sup
pose, for example, that A is tried along with B and C, and
that the effect is a b 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

426 INDUCTION.

are d and e, for they were not produced in the first. Whatever
is really the effect of A must have been produced in both
instances ; now this condition is fulfilled by no circumstance
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 substance 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 detersive or saponaceous substance: it is therefore con
cluded that the combination 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 inquire 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
experiment : we cannot take a phenomenon of which we know
not the origin, and try to find its mode of production by pro
ducing it : if we succeeded in such a random trial it could only
be by accident. But if we can observe a in two different com
binations, a b 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 reasoning
similar to that in the preceding example, that A is the ante
cedent 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 circumstances, was found among the antecedents of a
in both instances.

For example, let the effect a be crystallization. We com
pare 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-

THE FOUR EXPERIMENTAL METHODS. 427

elude, therefore, that the solidification of a substance from a
liquid state is an invariable antecedent of its crystallization.

ID this example we may go farther, and say, it is not only
the invariable antecedent but the cause ; or at least the proxi
mate event which completes the cause. For in this case we
are able, after detecting the antecedent A, to produce it arti
ficially, and by finding that <i follows it, verify the result of
our induction. The importance of thus reversing the proof
was strikingly manifested when by keeping a phial of water
charged with siliceous particles undisturbed for years, a
chemist (I believe Dr. Wollaston) succeeded in obtaining
crystals of quartz ; and in the equally interesting experiment
in which Sir James Hall produced artificial marble, by the
cooling of its materials from fusion under immense pressure :
two admirable examples of the light which may be thrown
upon the most secret processes of nature by well-contrived
interrogation of her.

But if we cannot artificially produce the phenomenon A,
the conclusion that it is the cause of a remains 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 assuring ourselves that A is the only
immediate antecedent common to both the instances. If we
could be certain of having ascertained all the invariable ante
cedents, we might be sure that the unconditional invariable
antecedent, or cause, must be found somewhere among them.
Unfortunately it is hardly ever possible to ascertain all the
antecedents, unless the phenomenon is one which we can
produce artificially. Even then, the diificulty is merely
lightened, not removed : men knew how to raise water in
pumps long before they adverted to what was really the
operating circumstance in the means they employed, 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 made by ourselves, than the whole
complex mass of the agencies which nature happens to be
exerting at the moment of the production of a given phe-

428 INDUCTION.

nomenon. We may overlook some of the material circum
stances in an experiment with an electrical machine ; but we
shall, at the worst, be better acquainted with them than with
those of a thunder-storm.

The mode of discovering and proving laws of nature, which
we have now examined, proceeds on the following 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 causation.
The casual circumstances being thus eliminated, if only one
remains, that one is the cause which we are in search of: if
more than one, they either are, or contain among them, the
cause ; and so, mutatis mutandis, of the effect. As this method
proceeds 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 phenomenon under investiga
tion have only one circumstance in common, the circumstance 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 proceed 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 circumstance 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 procure 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, b c, it is

THE FOUR EXPERIMENTAL, METHODS. 429

evident that the effect of A is a. So again, if we begin at
the other end, and desire to investigate the cause of an effect
a, we must select an instance, as a b 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, b c, occur without a. If the antecedents, in
that instance, are B C, we know that the cause of a must he
A : either A alone, or A in conjunction with some of the other
circumstances present.

It is scarcely necessary to give examples of a logical
process to which we owe almost all the inductive conclusions
we draw in daily life. When a man is shot through the
heart, it is by this method we know that it was the gun-shot
which killed him,: for he was in the fulness of life imme
diately before,, all circumstances being the same, except the
wound.

The axioms implied in this method are evidently the
following. Whatever 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 difference in the antecedents than the absence
of a particular one, is the effect of that one. Instead of
comparing different instances of a phenomenon, to discover
in what they agree, this method compares an instance of its
occurrence with an instance of its non-occurrence, to discover
in what they differ. The canon which is the regulating
principle of the Method of Difference may be expressed as
follows :

SECOND CANON.

If an instance in which the phenomenon under investigation
occurs, and an instance in which it does not occur, have every
circumstance in common 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 indispensable part of
the cause, of the phenomenon.

§ 3. The two methods which we have now stated have
many features of resemblance, but there are also many dis-

430 INDUCTION.

tinctions between them. Both are methods of elimination.
This term (employed in the theory of equations 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 relation
between the remaining elements 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 cir
cumstances which are found to accompany 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 con
nected with the phenomenon by a law.

Of these methods, that of Difference is more particularly
a method of artificial experiment; while that of Agreement is
more especially the resource employed where experimentation
is impossible. A few reflections will prove the fact, and point
out the reason of it.

It is inherent in the peculiar character of the Method of
Difference, that the nature of the combinations which it
requires is much more strictly defined than in the Method of
Agreement. The two instances which are to be compared
with one another must be exactly similar, in all circumstances
except the one which we are attempting to investigate : they
must be in the relation of A B C and B C, or of 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 coexistent
phenomena of the universe may be either present or absent
without affecting the given phenomenon; or, if present, 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

THE FOUR EXPERIMENTAL METHODS. 431

•very seldom that nature affords two instances, of which we
can be assured that they stand in this precise relation to one
another. In the spontaneous operations of nature there is
generally such complication and such obscurity, they are
mostly either on so overwhelmingly large or on so inaccessibly
minute a scale, we are so 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 ex
actly alike in any two cases, that a spontaneous experiment, of
the kind required by the Method of Difference, is commonly
not to be found. When, on the contrary, we obtain a pheno
menon by an artificial experiment, a pair of instances such as
the method requires is obtained almost as a matter of course,
provided the process does not last a long time. A certain
state of surrounding circumstances existed before we com
menced 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 (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 possible, 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 pro-
. duced, differ in nothing except the presence or absence 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 repetitions) 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 is one
doubt, indeed, which may remain in some cases of this descrip
tion ; the effect may have been produced not by the change,
but by the means employed to produce the change. The pos
sibility, however, of this last supposition generally admits of

432 INDUCTION.

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 requisitions of the Method of Dif
ference ; but that by the spontaneous operations of nature
those requisitions are seldom fulfilled.

The reverse of this is the case with the Method of Agree
ment. We do not here require instances of so special and deter
minate a kind. Any instances 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 agree
ment is the only one ; but this ignorance does not, as in the
Method of Difference, vitiate the conclusion ; the certainty
of the result, 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 unascertained. 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,ade,afg, all number A among their antecedents, then
A is connected as an antecedent, by some invariable law,
with a. But to determine whether this invariable antecedent
is a cause, or this invariable consequent 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 assur
ance of having produced anything, namely, an instance in
which the effect, a, has come into existence, with no other
change in the pre-existing circumstances than the addition of
A. And 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 im
properly, 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

THE FOUR EXPERIMENTAL METHODS. 433

remain undecided. The Method of Agreement is chiefly to
be resorted to, as a means of suggesting 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 antece
dent on which to try the experiment whether it could produce
a) ; or as an inferior resource, in case the Method of Difference
is impracticable ; which, as we before showed, generally arises
from the impossibility of artificially producing the phenomena.
And hence it is that the Method of Agreement, though appli
cable in principle to either case, is more emphatically the
method of investigation on those subjects where artificial ex
perimentation is impossible : because on those it is, generally,
our only resource of a directly inductive nature ; while, in the
phenomena which we can produce at pleasure, the Method of
Difference generally affords a more efficacious 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 complete, 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 inquiry to be the cause of the double
refraction of light. We can produce this phenomenon at
pleasure, by employing any one of the many substances 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 phenomenon depends, we can make no
use, for that purpose, of the Method of Difference ; for we
cannot find another substance precisely resembling Iceland
spar except in some one property. The only mode, therefore,
of prosecuting this inquiry is that afforded by the Method of
Agreement; by which, in fact, through a comparison of all
the known substances which have the property of doubly
VOL. i. 28

434 INDUCTION.

refracting light, it was ascertained that they agree in the
circumstance of heing 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 connexion between these two pro
perties ; 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 peculiar 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 agree
ing in every antecedent except A, or in every consequent except
a ; we may yet be able, by a double employment of the Method
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 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 connexion between
A and a. In order to convert this evidence of connexion 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 supposing (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 advantage will be the same. Suppose, then,
that as we previously examined a variety of instances in which
a occurred, 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 connexion between the
absence of A and the absence of a, which was before esta
blished 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

THE FOUR EXPERIMENTAL METHODS. 435

have by the one proposition A B 0, a b c, by the other B C,
b c, the positive and negative instances which the Method of
Difference requires.

This method may be called the Indirect Method of Dif
ference, 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 corro
borating it. But it is not equivalent to a proof by the direct
Method of Difference. For the requisitions of the Method of
Difference are not satisfied, unless we can be quite sure either
that the instances affirmative of a agree in no antecedent
whatever but A, or that the instances negative of a agree in
nothing but the negation 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 tivo or more instances in which the phenomenon occurs
have only one circumstance in common, while two or more in
stances in which it does not occur have nothing in common
save the absence of that circumstance; the circumstance 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 Agree
ment 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 exposi
tion without introducing a new element of complexity into
this long and intricate discussion, I shall postpone it to a sub
sequent chapter, and shall at once proceed to a statement of
two other methods, which will complete the enumeration of

28—2

436 INDUCTION,

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 Residues. Its principle is very simple. Subduct
ing from any given phenomenon all the portions which, by
virtue of preceding inductions, can be assigned to known
causes, the remainder will be the effect of the antecedents
which had been overlooked, 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 induc
tions (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 apprised that
the effect of A is a, and that the effect of B is 6. 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 A B C, a b 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 Differ
ence. 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 pro
duce separately, what effect they must produce in the case
ABC where they act together. Of the two instances, there
fore, which the Method of Difference requires, — the one posi
tive, 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 deduc
tion. 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 referred ; the only agent of

THE FOUR EXPERIMENTAL METHODS. 437

which we had not already calculated and subducted the effect.
But as we can never be quite certain of this, the evidence de
rived from the Method of Eesidues is not complete unless we
can obtain C artificially and try it separately, 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 dis
covery. Of all the methods of investigating laws of nature,
this is the most fertile in unexpected results ; often informing
us of sequences in which neither the cause nor the effect were
sufficiently conspicuous to attract 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 disguised by its intermixture
with a and b, that it would scarcely have presented itself
spontaneously as a subject 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 follows : —

FOURTH CANON.

Subduct from any phenomenon such part as is knoivn by pre
vious inductions to be the effect of certain antecedents, and the
residue of the phenomenon is the effect of the remaining ante
cedents.

§ 6. There remains a class of laws which it is imprac
ticable to ascertain by any of the three methods which I have
attempted to characterize ; 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 present, 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 phenomena with which they cannot be prevented from
coexisting. In respect, indeed, to most of the permanent
causes, no such difficulty exists ; since though we cannot

438 INDUCTION.

eliminate them as coexisting 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 pendulum to a sufficient distance
from the mountain, and the disturbance ceases : from these
data we can determine by the Method of Difference, the amount
of effect due to the mountain ; and beyond a certain distance
everything goes on precisely as it would do if the mountain
exercised no influence whatever, which, accordingly, we, with
sufficient reason, conclude to be the fact.

The difficulty, therefore, in applying the methods already
treated of to determine the eifects of Permanent Causes, is
confined to the cases in which it is impossible for us to get
out of the local limits of their influence. 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 pendulum, nor the pendulum from
the earth, to ascertain whether it would continue to vibrate
if the action which the earth exerts upon it were withdrawn.
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 in
stance, is wanting. Nor by the Method of Agreement ; for
though all pendulums agree in this, that during their oscil
lations the earth is always 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.
Independently 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 cer
tain, that no one ever perceived heat not emanating from a
body. Being unable, then, to separate Body and Heat, we
cannot effect such a variation of circumstances as the fore-

THE FOUR EXPERIMENTAL METHODS. 439

going three methods require ; we cannot ascertain, 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 nothing but heat, and
therefore not characterized also by the presence of a body, we
could ascertain the effects of heat, from an instance of heat
with a body and an instance of heat without a body, by the
Method of Agreement ; 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 solution of this problem would be illusory. It would
be idle, for instance, to attempt 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
investigation than these three, we should be unable to deter
mine the effects due 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
modification in the antecedent A is always followed by a
change in the consequent a, the other consequents b and c
remaining the same ; or vice versa, 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-

440 INDUCTION.

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 observation
already treated of, that such increase or diminution of heat is
followed by expansion or contraction of the body. In this
manner we arrive at the conclusion, otherwise unattainable 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 surface 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 ; but when we find that all the variations
in the position of the moon are followed by corresponding
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 remote from, the moon, we have ample evidence
that the moon is, wholly or partially, the cause which deter
mines the tides. It very commonly happens, as it does in this
instance, that the variations of an effect are correspondent, 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 indispensable 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 pendulum are caused by the
earth, is proved by similar evidence. Those oscillations take

THE FOUR EXPERIMENTAL METHODS. 441

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 characterized, that all terrestrial bodies tend to the earth,
and not to some unknown fixed point lying in the same direc
tion. 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 fancied by some,
to a fixed point of space.

The method by which these results were obtained, may be
termed the Method of Concomitant Variations : it is regulated
by the following canon : —

FIFTH CANON.

Whatever phenomenon varies in any manner whenever
another phenomenon varies in some particular manner, is
either a cause or an effect of that phenomenon, or 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, supposing them to be two dif
ferent effects of a common cause : and by this method alone it
would never be possible to ascertain which of the suppositions
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, by
increasing the temperature of a body we increase its bulk, but
by increasing its bulk we do not increase its temperature ; on
the contrary, (as in the rarefaction of air under the receiver of
an air-pump,) we generally diminish it : therefore heat is not

442

INDUCTION.

an effect, but a cause, of increase of bulk. If we cannot our
selves produce the variations, we must endeavour, though it is
an attempt which is seldom successful, 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 concomitance of variations in the effect with varia
tions 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 retain all the other antecedents un
changed, 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 concomitance 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 fol
lowed by a change in the effect. And it does usuallv happen

. -i . _ v Xrf

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 quantity 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 moreover 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
connexion between the sun and the earth's gravitation, but
that two of the relations of the sun, its position with respect
to the earth and its distance from the earth, are invariably
connected as antecedents with the quantity and direction of
the earth's gravitation. The cause of the earth's gravitating
at all, 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

THE FOUR EXPERIMENTAL METHODS. 443

strange that a modified cause, which is in truth a different
cause, should produce a different effect.

Although it is for the most part true that a modification of
the cause is followed hy a modification of the 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, modifi
cations of an effect are invariably consequent, must be the
cause (or connected with the cause) of that effect ; a propo
sition, 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 oppositions of different stars can have
no such power.

Although the most striking applications 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 additional precision to
a solution which that has found. When by the Method of
Difference it has first been ascertained that a certain object
produces a certain effect, the Method of Concomitant Varia
tions 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 employment, is that in which the variations of the
cause are variations of quantity. Of such variations we may
in general affirm with safety, that they will be attended not
only with variations, 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 Compo
sition 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 exceptional. Suppose,

444 INDUCTION.

then, that when A changes in quantity, a also changes in
quantity, and in such a manner that we can trace the numerical
relation 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 precautions, 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 annihilated, 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 sometbing
else : its changes, for example, may be such as would occur if
part of it remained constant, or varied on some other prin
ciple, and the remainder varied in some numerical relation to
the variations of A. In that case, when A diminishes, a will
be seen to approach not towards zero, but towards some other
limit : and when the series of variations is such as to indicate
what that limit is, if constant, or the law of its variation if
variable, the limit will exactly measure 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 precautions. In the first place, the possibility of
drawing them at all, manifestly supposes that we are ac
quainted not only with the variations, but with the absolute
quantities both of A and a. If we do not know the total
quantities, we cannot, of course, determine the real numerical
relation according to which those quantities vary. It is there
fore an error to conclude, as some have concluded, that because
increase of heat expands bodies, that is, increases the dis
tance between their particles, therefore the distance is wholly
the effect of heat, and that if we could entirely exhaust the

THE FOUR EXPERIMENTAL METHODS. 445

body of its heat, the particles would be in complete contact.
This is no more than a guess, and of the most hazardous 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 distance does or does not follow the diminu
tion of the quantity of heat according to such a numerical re
lation that the two quantities would vanish simultaneously.

In contrast with this, let us consider a case in which the
absolute quantities are known ; the case contemplated in the
first law of motion ; viz. that all bodies in motion continue 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 accord
ingly the ancients, with their inductio per enumerationem sim-
plicem, imagined to be the law. Every moving body, however,
encounters various obstacles, as friction, the resistance of the
atmosphere, &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 obstacles could have
been entirely removed, the case would have been amenable to
the Method of Difference. They could not be removed, they
could only be diminished, and the case, therefore, admitted
only of the Method of Concomitant Variations. This accord
ingly being employed, it was found that every diminution 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 consequent were
known ; it was practicable to estimate, with an approach to
accuracy, both the amount of the retardation 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 perpendicular, which in ordinary circum-

446 INDUCTION.

stances lasts but a few minutes, was prolonged in Borda's ex
periments to more than thirty hours, by diminishing 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 hesitation in
assigning the whole of the retardation of motion to the influence
of the obstacles ; and since, after subducting this retardation
from the total phenomenon, the remainder was an uniform velo
city, 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 experience, some counteract
ing cause might develop itself; either a new agent, or a new
property of the agents concerned, which lies dormant in the
circumstances we are able to observe. This is an element of
uncertainty which enters largely into all our predictions of
effects ; but it is not peculiarly applicable to the Method of
Concomitant Variations. The uncertainty, however, of which
I am about to speak, is characteristic of that method ; espe
cially in the cases in which the extreme limits of our observa
tion are very narrow, in comparison with the possible variations
in the quantities of the phenomena. Any one who has the
slightest acquaintance with mathematics, is aware that very
different laws of variation may produce numerical results
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
results given by one law and by another becomes appreciable.
When, therefore, such variations in the quantity of the ante
cedents as we have the means of observing, are small in com
parison with the total quantities, there is much danger lest
we should mistake the numerical law, and be led to miscalcu
late the variations which would take place beyond the limits ; a
miscalculation which would vitiate any conclusion respecting

THE FOUR EXPERIMENTAL METHODS. 447

the dependence of the effect upon the cause, that could be
founded on those variations. 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 beyond 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 connexion between them, or to the
permanency of the same numerical relation between their
variations when 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 induction. All that in
such a case can be regarded as proved on the subject of causa
tion is, that there is some connexion 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 de
scribe, are the only possible modes of experimental inquiry —
of direct induction a posteriori, as distinguished from deduc
tion : at least, I know not, nor am able to imagine, any
others. And even of these, the Method of Residues, as we
have seen, is not independent of deduction ; though, as it
also requires specific experience, it may, without impro
priety, be included among methods of direct observation and
experiment.

These, then, with such assistance as can be obtained from

* Discourse on the Study of Natural Philosophy, p. 179.

448 INDUCTION.

Deduction, compose the available resources of the human mind
for ascertaining the laws of the succession of phenomena.
Before proceeding to point out certain circumstances, hy which
the employment 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, accordingly, will
f form the subject of the succeeding chapter.

CHAPTER IX.

MISCELLANEOUS EXAMPLES OP THE FOUR METHODS.

V

§ 1. I SHALL select, as a first example, an interesting N)
speculation of one of the most eminent of theoretical chemists,
Baron Liebig. The object in view, is to ascertain the imme- — */
diate cause of the death produced by metallic poisons.

Arsenious acid, and the salts of lead, bismuth, copper,
and mercury, if introduced 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
generalization ; but it was reserved for Liebig, by an apt em
ployment of the first two of our methods of experimental
inquiry, to connect these truths together by a higher induc
tion, pointing out what property, common to all these dele
terious substances, is the really operating cause of their fatal
effect.

When solutions of these substances are placed in suffi
ciently close contact with many animal products, albumen,
milk, muscular fibre, and animal membranes, the acid or salt
leaves the water in which it was dissolved, and enters into com
bination with the animal 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 substances 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 reparative process taking
place in the healthy parts.
VOL. i. 29

450 INDUCTION.

These three sets of instances admit of being treated accord
ing to the Method of Agreement. In all of them the metallic
compounds are brought into contact with the substances which
compose the human or animal body ; and the instances do not
seem to agree in any other circumstance. The remaining
antecedents are as different, and even opposite, as they could
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 organization, in others not even in that.
And what is the result which follows in all the cases?
The conversion of the animal substance (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 condition of sensitive life) consisting in a
continual state of decomposition and recomposition of the
different organs and tissues ; whatever incapacitates them for
this decomposition destroys life. And thus the proximate
cause of the death produced by this description of poisons,
is ascertained, as far as the Method of Agreement 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 incapable of putrefaction,
(and a fortiori incapable of the chemical actions which con
stitute life,) and the consequent 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
insoluble 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 approaches very closely in composition to the organic
arsenious compounds 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

EXAMPLES OF THE FOUR METHODS. 451

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 antecedent which
we had already good ground for considering as the proximate
cause.

But the rigorous conditions of the Method of Difference
are not yet satisfied ; for we cannot be sure that these un-
poisonous bodies agree with the poisonous substances in every
property, except the particular one, of entering into a difficultly
decomposable compound with the animal tissues. To render
the method strictly applicable, we need an instance, not of a
different substance, but of one of the very same substances, in
circumstances 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 suboxide, neither
of which enters into combination with animal matter. The
disease called painter's colic, so common in manufactories 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 sul
phuric acid has the property of decomposing all compounds 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 con
flict with the theory. Soluble salts of silver, such for instance
as the nitrate, have the same stiffening antiseptic effect on
decomposing animal substances as corrosive sublimate and
the most deadly metallic poisons; and when applied to
the external parts of the body, the nitrate is a powerful

29—2

452 INDUCTION.

eaustic, depriving 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 excep
tion arises the strongest confirmation which the theory has yet
received. Nitrate of silver, in spite of its chemical pro
perties, 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, combining 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
influence, though an entirely different class of organic

actions.

The preceding instances have afforded 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 Difference, in its most perfect
exemplification, is capable of affording. For (let us not
forget) the positive instance and the negative one which the
rigour of that method requires, ought to differ only in the
presence or absence 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 know
ing what number of real differences are involved in what is
nominally and apparently only one difference. It is conceiv
able 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 generalizations in chemistry, is how
ever reduced in the present case to almost the lowest degree

EXAMPLES OF THE FOUR METHODS. 453

possible, when we find that not only one substance, but many
substances, possess tbe capacity of acting as antidotes to
metallic poisons, and that all these agree in the property of
forming insoluble compounds with the poisons, while they
cannot be ascertained to agree in any other property what
soever. We have thus, in favour of the theory, all the evidence
which can be obtained by what we termed the Indirect Method
of Difference, or the Joint Method of Agreement and Differ
ence; the evidence of which, though it never can amount to
that of the Method of Difference properly so called, may ap
proach indefinitely near to it.

§ 2. Let the object be* to ascertain the law of what is
termed induced electricity; to find under what conditions any
electrified body, whether positively or negatively electrified,
gives rise to a contrary electric state in some other body adja
cent to it.

The most familiar exemplification 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 con
ductor itself. Near and around the positive prime conductor
there is negative electricity, and near and around the negative
prime conductor there is positive electricity. When pith balls
are brought near to either of the conductors, they become elec
trified with the opposite electricity to it ; either receiving a
share from the already electrified atmosphere 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 withdrawn in their electrified state,

* For this speculation, as for many other of my scientific illustrations,
I am indebted to Professor Bain, of Aberdeen, who has since, in his profound
treatises entitled "The Senses and the Intellect," and " The Emotions and the
Will," carried the analytic investigation of the mental phenomena according
to the methods of physical science, to the most advanced point which it has yet
reached, and has worthily inscribed his name among the successive constructors
of an edifice to which Hartley, Brown, and James Mill had each contributed
their part.

454 INDUCTION.

they will be attracted by any other oppositely charged body.
In like manner the hand, if brought near enough to the con
ductor, receives or gives an electric discharge; now we have
no evidence that a charged conductor can be suddenly dis
charged unless by the approach of a body oppositely electri
fied. In the case, therefore, of the electric machine, it appears
that the accumulation of electricity in an insulated conductor
is always accompanied by the excitement of the contrary elec
tricity 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, resembling 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 substan
tial identity of magnetism and electricity, we may cite the
magnet, both the natural and the electro-magnet, in neither of
which it is possible to produce one kind of electricity 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 Agree
ment, a general law appears to result. The instances 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 connected, and that the excitement of elec
tricity in any body has for one of its necessary conditions the
possibility of a simultaneous excitement of the opposite elec
tricity in some neighbouring body.

EXAMPLES OF THE FOUR METHODS. 455

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 example
of the Leyden jar. It needs scarcely be here remarked that in
the Leyden jar, electricity can be accumulated and retained in
considerable quantity, by the contrivance of having two con
ducting surfaces of equal extent, and parallel to each other
through the whole of that extent, with a non-conducting sub
stance such as glass between them. When one side of the jar
is charged positively, the other is charged negatively, and it
was by virtue of this fact that the Leyden jar served just now
as an instance in our employment of the Method of Agree
ment. Now it is impossible to discharge one of the coatings
unless the other can be discharged at the same time. A con
ductor held to the positive side cannot convey away any elec
tricity 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 admits of corroboration
by the Method of Concomitant Variations. The Leyden jar
is capable of receiving a much higher charge than can ordi
narily 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 receiving and retaining the one electricity, as
the opposite surface of receiving and retaining the other ; but
in the machine, the neighbouring body which is to be op
positely electrified 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 conductor itself, their limited power imposes a correspond
ing 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.

456 INDUCTION.

A further and most decisive confirmation by the Method
of Difference, is to be found in one of Faraday's experiments
in the course of his researches on the subject of induced
electricity.

Since common or machine electricity, and voltaic electri
city, may be considered for the present purpose to be identical,
Faraday wished to know whether, as the prime conductor de-
velopes opposite electricity upon a conductor in its vicinity, so
a voltaic current running along a wire would induce an oppo
site current upon another wire laid parallel to it at a short
distance. Now this case is similar to the cases previously ex
amined, 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 neigh
bouring body. But in Faraday's experiment this indispensable
opposition 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 accommodated 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 posi
tive and a negative surface. The exciting cause can and does
produce all the effect which its laws require, independently of
any electric excitement of a neighbouring body. Now the
result of the experiment with the second wire was, that no op
posite 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 phenomena of a different class.
There was no induced electricity in the sense in which this is
predicated of the Leyden jar; there was no sustained current
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 Variations, and the
most rigorous form of the Method of Difference, that neither
of the two kinds of electricity can be excited without an equal

EXAMPLES OF THE FOUR METHODS. 457

excitement of the other and opposite kind : that both are effects
of the same cause ; that the possibility of the one is a condition
of the possibility of the other, and the quantity of the one an
impassable limit to the quantity of the other. A scientific
result of considerable interest in itself, and illustrating 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 happily-selected exemplifications of induc
tive 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 characterized 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 specimens" which can be cited " of inductive
experimental inquiry lying within a moderate compass;" the
theory of dew, first promulgated by the late Dr. Wells, and
now universally adopted by scientific authorities. The pas
sages in inverted commas are extracted verbatim from the
Discourse.f

" Suppose dew were the phenomenon proposed, whose cause
we would know. In the first place" we must determine pre
cisely what we mean by dew : what the fact really is, whose

This view of the necessary coexistence 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 existence
of the negative charge on the rubber was equally dependent on a contrary state
of the surfaces 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 machine.
t Pp. 159-162..

458 INDUCTION.

cause we desire to investigate. " We must separate dew from
rain, and the moisture of fogs, and limit the application of the
term to what is really meant, which is the spontaneous appear
ance of moisture on substances exposed in the open air when
no rain or visible wet is falling." This answers to a prelimi
nary operation which will be characterized in the ensuing book,
treating of operations subsidiary to induction.*

" Now, here we have analogous phenomena in the mois
ture which bedews a cold metal or stone when we breathe
upon it ; that which appears 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." Comparing these cases, we find
that they all contain the phenomenon which was proposed as
the subject of investigation. 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 ? Certainly not, one
would at first be inclined to say ; for what is to make it so ?
But .... the experiment is easy : we have only to lay
a thermometer 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 invariably in the affirr
mative. Whenever an object contracts dew, it is colder than
the air."

Here then is a complete application of the Method of
Agreement, establishing the fact of an invariable connexion
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.

* Infra, book iv. ch. ii. On Abstraction.

EXAMPLES OF THE FOUR METHODS. 459

" We must collect more facts, or, which comes to the same
thing, vary the circumstances ; since every instance in which
the circumstances 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 in
stances 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 exposed 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 between 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 circumstances by
which the former substance is distinguished from the latter.
But if we could be sure that glass, and the various other sub
stances on which dew is deposited, have only one quality in
common, and that polished metals arid 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 substances, the cause of dew. This, 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 substances 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

460

INDUCTION.

on this occasion ; for the quality of conducting heat could not
be excluded, since all substances conduct heat in some degree.
The conclusion obtained is, that ctsteris paribus the deposition
of dew is in some proportion to the power which the body pos
sesses of resisting the passage of heat ; and that tin's, 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 influence. 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 Variations ; 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 appli
cation 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
promote 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 unfavourable, 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 tex
ture of no substance is absolutely firm or absolutely loose.
Looseness of texture, therefore, or something which is the cause

EXAMPLES OF THE FOUR METHODS. 461

of that quality, is another circumstance which promotes the
deposition of dew ; but this third cause resolves itself into the
first, viz. the quality of resisting the passage of heat : for sub
stances 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 corro
borative of a former induction.

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 circumstance of agreement, than that by
virtue of either, the body tends to lose heat from the surface
more rapidly than it can be restored from within. The in
stances, on the contrary, in which no dew, or but a small
quantity of it, is formed, and which are also extremely
various, agree (as far as we can observe) in nothing except
in not having this same property. We seem, therefore, to
have detected the characteristic difference between the sub
stances on which dew is produced, and those on which it is not
produced. And thus have been realized 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 manner 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 interesting
speculation.

We might now consider the question, on what the depo
sition of dew depends, to be completely solved, if we could be
quite sure that the substances on which dew is produced differ
from those on which it is not, in nothing but in the property
of losing heat from the surface faster than the loss caii 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

462 INDUCTION.

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 coincidence
which affords a strong presumption of a community of cause,
and a consequent invariable coexistence between the two pro
perties ; so that the property of being a better radiator than
conductor, if not itself the cause, almost certainly always
accompanies the cause, and, for purposes of 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 instance
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 the cause of dew, or its
effect. This doubt we are now able to resolve. We have
found that, in every such instance, the substance is one which,
by its own properties or laws, would, if exposed in the night,
become colder than the surrounding air. The coldness there
fore being accounted for independently of the dew, while it
is proved that there is a connexion 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 corrob oration 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 experiment 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 temperature diminishes. From
this it follows, deductively, that if there is already as much
vapour suspended as the air will contain at its existing tern-

EXAMPLES OF THE FOUR METHODS. 463

perature, any lowering of that temperature will cause a portion
of the vapour to be condensed, and become water. But, again,
we know deductively, 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 with a portion
of its water, which accordingly will, by the ordinary laws of
gravitation or cohesion, attach itself 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 coexistence ; and it has the additional advan
tage that it also accounts for the exceptions to the occurrence
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- sup
plied with aqueous vapour, comparatively 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 suspended in it : thus in a very dry
summer there are no dews, in a very dry winter no hoar frost.
Here, therefore, is an additional condition of the production
of dew, which the methods we previously made use of failed
to detect, and which might have remained still undetected, if
recourse had not been had to the plan of deducing the effect
from the ascertained properties of the agents known to be
present.

The second corroboration of the theory is by direct experi
ment, according 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 hygrometric condition,) at which dew will
begin to be deposited. 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 produce 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

464 INDUCTION.

shown them to be, in which nature works the experiment for
us in the same manner in which we ourselves perform it ; in
troducing into the previous state of things a single and per
fectly 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 presently begins, and goes on in
creasing 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 uninterrupted communication with the sky causes the de
position or non-deposition 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 consequent follows accordingly : a
natural experiment which satisfies the requisitions of the
Method of Difference.*

* I must, however, remark, that this example, which seems to militate
against the assertion we made of the compar.itive inapplicability of the Method
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, she has only succeeded in producing the like
ness of man's most imperfect experiments ; namely, those in which, though he
succeeds in producing the phenomenon, he does so by employing complex
means, which he is unable perfectly to analyse, and can form therefore no
sufficient judgment what portion of the effects may be due, not to the supposed
cause, but to some unknown agency of 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
a priori that it might not operate upon the deposition of dew independently of

EXAMPLES OF THE FOUR METHODS. 465

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 causation
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.
Brovvn-Sequard afford brilliant examples of the application
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 Pro
ceedings of the Royal Society for May 16, 1861) on the rela
tions between muscular irritability, cadaveric rigidity, and
putrefaction.

The law which Dr. Browu-Sequard's investigation tends
to establish, is the following :— " The greater the degree of
muscular irritability at the time of death, the later the cada
veric 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 ap
pearance, arising from the circumstance that the conclusion to
be tested is itself a fact of concomitant variation. For the
establishment of that fact any of the 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 particular
investigation.

The evidences by which Dr. Brown-Sequard establishes the
law may be enumerated as follows : —

1st. Paralysed muscles have greater irritability than
healthy muscles. Now, paralysed muscles are later in as
suming the cadaveric rigidity than healthy muscles, the rigidity

any thermometric effect at the earth'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 attained through other
means.

VOL. I. 30

466 INDUCTION.

lasts longer, and putrefaction sets in later and proceeds more
slowly.

Both these propositions had to be proved hy experiment ;
and for the experiments which prove them, science is also in
debted to Dr. Brown-Sequard. 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 irritability 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 para
lysed muscle remained irritable twice, three times, or even four
times as long as the healthy one." This is a case of induction
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 presence and
absence of which, therefore, the difference in the muscular
irritability 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, be
cause 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 re
peated sufficiently often in different animals to exclude the
supposition that any abnormal circumstance could be present
in them all, the conditions of the Method of Difference were
adequately secured.

In the same manner in which Dr. Brown-Sequard proved
that paralysed muscles have greater irritability, he also proved
the correlative proposition 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 re
mained 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

EXAMPLES OF THE FOUR METHODS. 467

of the Method of Difference, requiring no comment. A further
and very important 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 irritable than those on the healthy side. This
gives the A B C, a b c, and B C, b c, of the Method of Dif
ference. One antecedent, increased irritability, being changed,
and the other circumstances being the same, the consequence
did not follow ; and moreover, when a new antecedent, con
trary to the first, was supplied, it was followed by a contrary
consequent This instance is attended with the special advan
tage, of proving that the retardation and prolongation of the
rigidity do not depend directly on the paralysis, since that was
the same in both the instances ; but specifically on one effect
of the paralysis, namely, the increased irritability ; since they
ceased when it ceased, and were reversed when it was reversed.
2ndly. Diminution of the temperature of muscles before
death increases their irritability. But diminution of their tem
perature also retards cadaveric rigidity and putrefaction.

Both these truths were first made known by Dr. Brown-
Sequard himself, through experiments which conclude accord
ing to the Method of Difference. There is nothing in the
nature of the process requiring specific analysis.

Srdly. Muscular exercise, prolonged to exhaustion, dimi
nishes 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, con
stantly 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

30—2

468

INDUCTION.

in no circumstance, directly connected with the muscles, except
that these have just heen subjected to exhausting exercise.
Under the canon, therefore, of the Method of Agreement, it
may be inferred that there is a connexion between the two
facts. The Method of Agreement, indeed, as has been shown,
is not competent to prove causation. The present case, how
ever, is already known to be a case of causation, it being cer
tain that the state of the body after death must somehow
depend upon its state at the time of death. We are therefore
warranted in concluding that the single circumstance in which
all the instances agree, is the part of the antecedent which is
the cause of that particular consequent.

4thly. In proportion as the nutrition 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 Method of Difference. Now,
in the case of those who die from accident or violence, with
their muscles in a good state of nutrition, the muscular irrita
bility 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 rigidity
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 mus
cular nutrition ; a connexion is therefore inductively proved
between the degree of the nutrition, and the slowness and pro
longation of the rigidity.

Sthly. 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 very rapidly, and after a very brief
duration, gives place to putrefaction. This is another ex
ample of the Method of Agreement, of the same character
with No. 3.

EXAMPLES OF THE FOUR METHODS. 469

Gthly. The series of instances which we shall take last, is
of a more complex character, and requires a more minute
analysis.

It has long been observed that in some cases of death by
lightning, cadaveric 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 rapid. In other cases,
however, the usual cadaveric rigidity appears. There must be
some difference in the cause, to account for this difference in
the effect. Now " death by lightning may be the result of,
1st, a syncope by fright, or in consequence of a direct or reflex
influence of lightning on the par vagum ; 2ndly, hemorrhage
in or around the brain, or in the lungs, the pericardium, &c. ;
3rdly, concussion, or some other alteration in the brain ;" none
of which phenomena have any known property capable of
accounting 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 intensity, the known
effect would be that "muscular irritability ceases almost at
once." If Dr. Brown-Sequard's generalization 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 tc
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-
Sequard galvanized 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, except the
single one of producing muscular convulsions. If, therefore,
after the bodies have been galvanized, the duration of rigidity
is much shortened and putrefaction much accelerated, 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-

470 INDUCTION.

Sequard 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 dura
tion 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 destroyed, the rigidity only
lasted fifteen minutes. On the principle, therefore, of the
Method of Concomitant Variations, it may be inferred that the
duration of the rigidity depends on the degree of the irrita
bility ; and that if the charge had been as much stronger than
Dr. Brown-Sequard'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 corre
sponding 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 correspondence between the
irritability of the muscle and the duration of rigidity.

All these instances are summed up in the following state-
ment : — " That when the degree of muscular irritability at the
time of death is considerable, 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 putre
faction appears late, and progresses slowly :" but " that when
the degree of muscular irritability at the time of death is slight,
either in consequence of a bad state of nutrition, or of exhaus
tion 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. Eigidity begins late and
lasts long in cases which agree only in the contrary circum
stance, of a muscular irritability high and unusually prolonged.
It follows that there is a connexion through causation between
the degree of muscular irritability after death, and the tardiness

EXAMPLES OF THE FOUR METHODS. 471

and prolongation of the cadaveric rigidity. This investigation
places in a strong light the value and efficacy 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 causation. 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 douht that the rigidity altogether, and the putrefaction
which follows it, are caused by the fact of death : the obser
vations and 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 con
sequents, whatever of the circumstances attending the death
can be shown to be followed in all its variations by variations
in the effect under investigation, must be the particular feature
of the fact of death on which that effect depends. The degree
of muscular irritability at the time of death fulfils this con
dition. The only point that could be brought into question,
would be whether the effect depended on the irritability itself,
or on something 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 pro
duced, 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 concep
tion of the use and practical management of three of the four
methods 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 pre
ceding 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 phenomena

472 INDUCTION.

which Nature presents are very complicated ; and when the
effects of all known causes are estimated with exactness, and
subducted, the residual facts are constantly appearing in the
form of phenomena altogether new, and leading to the most
important conclusions.

" For example : the return of the comet predicted Jby Pro
fessor Encke, a great many times in succession, and the
general good agreement of its calculated with its observed
place during any one of its periods of visibility, would lead us
to say that its gravitation towards the sun and planets is the
sole and sufficient cause of all the phenomena of its orbitual
inotion ; 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 otherwise ascertained to exist, which is a small anticipa
tion of the time of its reappearance, or a diminution of its
periodic time, which cannot be accounted for by gravity, and
whose cause is therefore to be inquired into. Such an antici
pation would be caused by the resistance of a medium dis
seminated 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.*

" 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
eases there were two verce causce " (antecedents known to
exist) "why it should come at length to rest, viz. the resist
ance 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
known by the observation made in the 'absence of the copper,
and being thus allowed for and subducted, a residual pheno
menon appeared, in the fact that a retarding influence was

* In his subsequent work, Outlines of Astronomy (§ 570), Sir John
Herschel suggests another possible explanation of the acceleration of the revolu
tion of a comet.

EXAMPLES OP THE FOUR METHODS. 473

exerted by the copper itself ; and this fact, once ascertained,
speedily led to the knowledge of an entirely new and unex
pected class of relations." This example belongs, however,
not to the Method of Residues but to the Method of Differ
ence, the law being ascertained 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 a priori, from the laws obtained by separate and
foregone experiments.

"Unexpected and peculiarly striking confirmations of
inductive laws frequently occur in the form of residual phe
nomena, in the course of investigations of a widely different
nature from those which gave rise to the inductions them
selves. A very elegant example may be cited in the unex
pected confirmation of the law of the development of heat in
elastic fluids by compression, which is afforded by the phe
nomena 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 calculations were performed ; but, 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 philosophers 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 condensation 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
strking confirmation of the general law of the development
of heat by compression, under circumstances beyond 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

474

INDUCTION.

in the sulphate produced from a small portion 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 chemical ingredients : witness
iodine, hrome, selenium, and the new metals accompanying
platina in the experiments 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 same author,f " have resulted from the consideration of
residual phenomena of a quantitative or numerical 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 the
fixed stars. Thus, also, aberration and nutation resulted as
residual phenomena from that portion of the changes of the
apparent places of the fixed stars which was left unac
counted for by precession. And thus again the apparent
proper motions of the stars are the observed residues of
their apparent movements outstanding and unaccounted for
by strict calculation of the effects of precession, 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 possible, 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 effects mutually produced 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 consideration solely of their gravitation

* Discourse, pp. 156-8, and 171. f Outlines of Astronomy, § 856.

EXAMPLES OF THE FOUR METHODS. 475

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
catastrophists, 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 existence 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 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 substantiate their proposition by
subtracting from the differences of intellect which we in fact
see, all that can be traced by known laws either to the ascer
tained differences of physical organization, or to the dif
ferences 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 assertors of such sup
posed differences have not provided themselves with these
necessary logical conditions of the establishment of their
doctrine.

The spirit of the Method of Residues being, it is hoped,
sufficiently intelligible from these examples, and the other
three methods having already 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 combinations of phenomena.

§ 6. Dr. Whewell has expressed a very unfavourable
opinion of the utility of the Four Methods, as well as of the

476 INDUCTION.

aptness of the examples by -which I have attempted to illus
trate 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
formulae 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 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, b, 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 com
bination 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 dis
coveries 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 enumerated ? Who will tell us which of the methods
of inquiry those historically real and successful inquiries
exemplify ? Who will carry these formulas 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 formulse ?"

He adds that, in this work, the methods have not been
applied " to a large body of conspicuous and undoubted ex
amples of discovery, extending 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.)

* Philosophy of Discovery, pp. 263, 264.

EXAMPLES OF THE FOUR METHODS.

There is a striking similarity between the objections here
made against Canons of Induction, and what was alleged, in
the last century, by as able men as Dr. Whewell, against the
acknowledged Canon of Eatiocination. Those who protested
against the Aristotelian Logic said of the Syllogism, what
Dr. Whewell says of the Inductive Methods, that it " takes
for granted the very thing which is most difficult to discover,
the reduction of the argument to formula such as are here
presented to us." The grand difficulty, they said, is to obtain
your syllogism, not to judge of its correctness 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 conclusiveness. But if we try to reduce it without know
ing to what, we are not likely to make much progress. It is
a more difficult thing to solve 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 finding 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 superfluous ; 'for
erroneous inductions, false inferences from experience, are quite
as common, on some subjects much commoner, than true ones.
The business of Inductive Logic is to provide rules and models
(such as the Syllogism and its rules are for ratiocination) to
which if inductive arguments conform, those arguments are
conclusive, and not otherwise. This is what the Four
Methods profess to be, and what I believe they are universally
considered to be by experimental 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.
Whewell says, or seems to say, that none were ever made by
the four Methods of Induction. To the former objectors,
Archbishop Whately very pertinently answered, that their
argument, if good at all, was good against the reasoning pro-

478 INDUCTION.

cess altogether; for whatever cannot be reduced to syllogism,
is not reasoning. And Dr. Whewell's argument, if good at
all, is good against all inferences from experience. In saying
that no discoveries were ever made by the four Methods, he
affirms that none were ever made by observation and experi
ment ; 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 examples give him ; for I did not select them with
a view to satisfy any one who required to be convinced that
observation and experiment are modes of acquiring knowledge :
I confess that in the choice of them I thought only of illus
tration, and of facilitating the conception of the Methods by
concrete instances. If it had been my object to justify the
processes themselves as means of investigation, there would
have been no need to look far off, or make use of recondite or
complicated instances. As a specimen of a truth ascertained
by the Method of Agreement, I might have chosen the pro
position "Dogs bark." This dog, and that dog, and the
other dog, answer to A B C, A D E, A F G. The circum
stance of being a dog, answers to A. Barking answers to a.
As a truth made known by the Method of Difference, " Fire
burns" 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,
aB C.

Such familiar experimental processes are not regarded as
inductions by Dr. Whewell ; but they are perfectly homo
geneous 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 most arbitrary
restrictions on the choice of examples admissible as instances
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 ordinary obser
vation and practical life (pp. 241 — 247). They must be
taken exclusively from the generalizations by which scientific
thinkers have ascended to great and comprehensive laws of
natural phenomena. Now it is seldom possible, in these com-

EXAMPLES OF THE FOUR METHODS. 479

plicated 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 il
lustrate 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 generalizations, there would have been no mate
rials 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
historically a deduction from the first law of motion ; but the
experiments by which it was verified, and by which it might
have been discovered, were examples of the Method of Agree
ment; and the apparent variation from the true law, caused
by the resistance of the air, was cleared up by experiments
in vacua, constituting an application of the Method of Dif
ference. The law of "refracted rays" (the constancy of the
ratio between the sines of incidence and of refraction for each
refracting substance) was ascertained by direct measurement,
and therefore by the Method of Agreement. The " cosmical
motions" were determined by highly complex processes of
thought, in which Deduction was predominant, but the
Methods of Agreement and of Concomitant 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 smallest difficulty in setting out "the ABC
and a b c elements" of these cases.

* See, on this point, the second chapter of the present Book.

480 INDUCTION.

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 generalizations which begin as Hypo
theses, must end by being proved, and are in reality (as will
be shown hereafter) proved, by the Four Methods. 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 Induction, 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 simpler 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 misgiving 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 gene
ral, 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 process, that of inves
tigation only, not that of proof. A knowledge of many laws
of nature has doubtless been arrived 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 independently

EXAMPLES OF THE FOUR METHODS. 481

of the facts which disproved the specific conclusion. Hence
it is, that while the thoughts of mankind have on many sub
jects worked themselves practically right, the thinking 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 prin
ciples of inductive evidence.

VOL. i. 31

CHAPTEE X.

OF PLURALITY OF CAUSES; AND OF THE INTERMIXTURE
OF EFFECTS.

§ 1. IN the preceding exposition of the four methods of
observation and experiment, by which we contrive to distin
guish among a mass of coexistent phenomena the particular
effect due to a given cause, or the particular 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 ana
lytical operation is encumbered by no other difficulties than
what are essentially inherent in its nature ; and to represent
to ourselves, therefore, every effect, on the one hand as con
nected exclusively with a single cause, and on the other hand
as incapable of being mixed and confounded with any other
coexistent effect. We have regarded abode, the aggregate
of the phenomena existing at any moment, as consisting of
dissimilar facts, a, b, 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
antecedent circumstances, A, B, C, D, and E. The cause
indeed may not be simple ; it may consist of an assemblage of
conditions; but we have supposed 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 investigate 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

PLURALITY OF CAUSES.

483

may produce not a and b, but different portions of an effect a.
The obscurity and difficulty of the investigation of the laws of
phenomena is singularly increased by the necessity of ad
verting to these two circumstances ; Intermixture of Effects,
and Plurality of Causes. To the latter, being the simpler of
the two considerations, we shall first direct our attention.

It is not true, then, that one effect must be connected with
only one cause, or assemblage of conditions ; that each phe
nomenon can be produced 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 sequences; it may follow, with equal uni
formity, any one of several antecedents, or collections of ante
cedents. Many causes may produce motion: many causes
may produce some kinds of sensation : many causes may pro
duce 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 consequences 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 by 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 difficulty 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 possibly 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 philo-
31—2

484

INDUCTION.

sophers, that two extremely selfish, or extremely generous
characters, were compared together as to the circumstances of
their education and history, and the two cases were found to
agree only in one circumstance : would it follow that this one
circumstance was the cause of the quality which characterized
both those individuals ? Not at all ; for the causes which
may produce any type of character are innumerable ; and the
two persons might equally have agreed in their character,
though there had been no manner of resemblance in their pre
vious history.

This, therefore, is a characteristic imperfection of the
Method of Agreement ; 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 conclusions which that yields,
when the number of instances compared is small, are of no
real value, except as, in the character of suggestions, they may
lead either to experiments bringing them to the test of the
Method of Difference, or to reasonings which may explain and
verify them deductively.

It is only when the instances, being indefinitely multiplied
and varied, continue to suggest the same result, that this re
sult acquires any high degree of independent value. If there
are but two instances, ABC and A D E, though these in
stances have no antecedent in common except A, 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

PLURALITY OF CAUSES. 485

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 addi
tion, therefore, 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 separately, appeal to the Method of Difference
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 nume
rous, 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
imperfection, and reduced to a virtual certainty ? This is a
question which we cannot be exempted from answering : but
the consideration of it belongs to what is called the Theory of
Probability, which will form the subject of a chapter hereafter.
It is seen, however, at once, that the conclusion does amount
to a practical certainty after a sufficient 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 infe
riority in the Method of Agreement as compared with other
modes of investigation, and new reasons for never resting con
tented with the results obtained by it, without attempting to
confirm them either by the Method of Difference, or by con
necting them deductively with some law or laws already ascer
tained by that superior method. And, in the second place,
we learn from this the true theory of the value of mere number

486 INDUCTION.

of instances in inductive inquiry. 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 circum
stances are or are not eliminated by means of them. Most
people hold their conclusions with a degree of assurance pro
portioned to the mere mass of the experience on which they
appear to rest; not considering that by the addition of in
stances to instances, all of the same kind, that is, differing
from one another only in points already recognised as imma
terial, 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
circumstances, we cannot too scrupulously repeat the same
experiment or observation without any change. But when
once this assurance has been obtained, the multiplication of
instances 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 modifica
tion of the Method of Agreement, which, as partaking in some
degree of the nature of the Method of Difference, I have called
the Joint Method of Agreement and Difference, is not affected
by the characteristic imperfection now pointed out. For, in
the joint method, it is supposed not only that the instances in
which a is, agree only in containing A, but also that the
instances 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 containing A. This, therefore,

PLURALITY OF CAUSES.

487

constitutes an immense advantage of the joint method over
the simple Method of Agreement. It may seem, indeed, that
the advantage does not helong so much to the joint method,
as to one of its two premises, (if they may he 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 characteristic imper
fection which affects it in the affirmative case. The negative
premise, it might therefore be supposed, could he worked as
a simple case of the Method of Agreement, without requiring
an affirmative premise to he joined with it. But though this
is true in principle, it is generally 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 affirmation. For instance, let the
question he, what is the cause of the transparency of bodies ;
with what prospect of success could we set ourselves to inquire
directly in what the multifarious substances which are not
transparent, 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 examin
ing whether the absence of this one circumstance be not pre
cisely the point in which all opaque substances will be found

to resemble.

The Joint Method of Agreement and Difference, therefore,
or, as I have otherwise called it, the Indirect Method of Diffe
rence (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 instruments of inductive investiga
tion ; 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

488

INDUCTION.

a possible supposition, which, until removed, renders our induc
tions uncertain ; and have only considered by what means, where
the plurality does not really exist, we may be enabled to dis
prove 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
establishing. For this, however, there is required 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 sets 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 circum
stance in which they all agree, and fail in doing so. We find
it impossible to trace, in all the cases in which the effect is
met with, any common circumstance. We find that we can
eliminate all the antecedents, that no one of them is present
in all the instances, no one of them indispensable to the effect.
On closer scrutiny, however, it appears that though no one is
always present, one or other of several always is. If, on fur
ther 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 produce the
effect.

We here close our remarks on the Plurality of Causes, and
proceed to the still more peculiar and more complex 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

INTERMIXTURE OF EFFECTS. 489

with which the four only possible methods of directly induc
tive investigation 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 pre
mises for, and a verification of, our deductions.

§ 4. A concurrence of two or more causes, not separately
producing each its own effect, but interfering with or modify
ing the effects of one another, takes place, as has already
been explained, in two different ways. In the one, which is
exemplified by the joint operation of different forces in
mechanics, the separate effects of all the causes continue to
be produced, but are compounded with one another, and dis
appear in one total. In the other, illustrated by the case of
chemical action, the separate effects cease entirely, and are
succeeded by phenomena altogether 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 cease entirely, and a phenomenon makes its appearance,
which, with reference to those laws, is quite heterogeneous ;
when, for example, two gaseous substances, 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 effects
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

490 INDUCTION.

actual production of the phenomenon are most frequently in
accessible to our observation. If we could not have learned
the composition of water until we found instances in which it
was actually produced 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 taper into it, merely to try what
would happen. Besides, many substances, though they can
be analysed, cannot by any known artificial means be recora-
pounded. Further, even if we could have ascertained, by the
Method of Agreement, that oxygen and hydrogen were both
present when water is produced, no experimentation on oxygen
and hydrogen separately, no knowledge of their laws, could
have enabled us deductively to infer that they would produce
water. We require a specific experiment on the two com
bined.

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 experimenta
tion 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 combination 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 analysis is the process of
searching for the causes of a phenomenon among its effects,
or rather among the effects produced by the action of some
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 was then called red precipitate,
while the air, on being examined after the experiment, proved

INTERMIXTURE OF EFFECTS. 491

to have lost weight, and to have become incapable of sup
porting life or combustion. When red precipitate was ex
posed 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 precipitate when acted upon by heat. So, if we
decompose water by means of iron filings, we produce two
effects, rust and hydrogen : now rust is already known by
experiments upon the component substances, to be an effect
of the union of iron and oxygen : the iron we ourselves supplied,
but the oxygen must have been produced from the water.
The result therefore is that water has disappeared, and hydro
gen 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 existence, and the
causes of water are found among its effects.

Where two phenomena, between the laws or properties of
which considered in themselves no connexion 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 transformation. The idea of chemical composition
is an idea of transformation, but of a transformation which is
incomplete ; since we consider the oxygen and hydrogen to be
present in the water as oxygen and hydrogen, and capable of
being discovered in it if our senses were sufficiently keen : a
supposition (for it is no more) grounded solely on the fact,
that the weight of the water is the sum of the separate
weights of the two ingredients. If there had not been this
exception to the entire disappearance, in the compound, 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

492

INDUCTION.

results ; we should never, probably, have had the notion now
implied by the words chemical composition : and, in the facts
of water produced from hydrogen and oxygen, and hydrogen
and oxygen produced from water, as the transformation would
have been complete, we should have seen only a transformation.
The very promising generalization now commonly known
as the Conservation or Persistence of Force, bears a close resem
blance to what the conception of chemical composition would
become, if divested of the one circumstance which now dis
tinguishes it from simple transformation. It has long been
known that heat is capable of producing electricity, and
electricity heat ; that mechanical motion in numerous cases
produces and is produced by them both ; and so of all other
physical forces. It has of late become the general belief of
scientific inquirers that mechanical force, electricity, magnetism,
heat, light, and chemical action (to which has subsequently
been added vital action) are not so much causes of one
another as convertible into one another ; and they are now
generally spoken of as forms of one and the same force,
varying only in its manifestations. This doctrine may
be admitted, without by any means implying that Force
is a real entity, a Thing in itself, distinct from all its
phenomenal manifestations to our organs. Supposing the
doctrine true, the several kinds of phenomena which it iden
tifies in respect of their origin would nevertheless remain diffe
rent facts ; facts which would be causes of one another —
reciprocally causes and effects, which is the first element in the
form of causation properly called transformation. What the
doctrine contains more than this, is, that in each of these cases
of reciprocal causation, the causes are reproduced without
alteration in quantity. This is what takes place in the trans
formations of matter : when water has been converted into
hydrogen and oxygen, these can be reconverted into precisely
the same quantity of water from which they were produced.
To establish a corresponding law in regard to Force, it has to
be proved that heat is capable of being converted into elec
tricity, electricity into chemical action, chemical action into
mechanical force, and mechanical force back again into the
exact quantity of heat which was originally expended ; and so

INTERMIXTURE OF EFFECTS. 493

through all the interchanges. Were this proved, it would
establish what constitutes transformation, as distinguished
from the simple fact of reciprocal causation. The fact in issue
is simply the quantitative equivalence of all these natural
agencies ; whereby a given quantity of any one is convertible
into, and interchangeable with, a given, and always the same,
quantity of any other : this, no less, but also no more. It cannot
yet be said that the law -has been fully proved of any case, ex
cept that of interchange between heat and mechanical motion.
It does seem to be ascertained, not only that these two are
convertible into each other, but that after any number of con
versions the original quantities reappear without addition or
diminution, like the original quantities of hydrogen and oxygen
after passing through the condition of water. If the same
thing comes to be proved true of all the other forces, in rela
tion to these two and to one another, the law of Conservation
will be established ; and it will be a legitimate mode of ex
pressing the fact, to speak of Force, as we already speak of
Matter, as indestructible. But Force will not the less remain,
to the philosopher, a mere abstraction of the mind. All that
will have been proved is, that in the phenomena of Nature,
nothing actually ceases without generating a calculable, and
always the same, quantity of some other natural phenomenon,
which again, when it ceases, will in its turn either generate a
calculable, and always the same, quantity of some third phe
nomenon, or reproduce the original quantity of the first.

In these cases, where the heteropathic effect (as we called it
in a former chapter)* is but a transformation of its cause, or
in other words, where the effect and its cause are reciprocally
such, and mutually convertible 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 investiga
tion is not applicable. Take, for instance, the heteropathic
laws of mind; that portion of the phenomena of our mental
nature which are analogous to chemical rather than to dvna-

* Ante, ch. vii. § 1.

494 INDUCTION.

mical phenomena ; as when a complex passion 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 the
product; just as a youth can grow into an old man, but an old
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,
therefore, discover these laws by the slow process of studying
the simple feelings 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
according to the same laws to which it conforms in its separate
state, would have presented fewer difficulties 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 diffi
culties. When a concurrence 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 absence among any number
of surrounding phenomena. It admits therefore of being easily
brought under the canons of Induction, provided instances 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 investiga
tions ; a difficulty not logical, but in some sort physical. It is
otherwise with cases of what, in a preceding chapter, has been
denominated the Composition of Causes. There, the effects of

INTERMIXTURE OF EFFECTS. 495

the separate causes do not terminate and give place to others,
thereby ceasing to form any part of the phenomenon to be
investigated ; on the contrary, they still take place, but are
intermingled with, and disguised by, the homogeneous and
closely allied effects of other causes. They are no longer
a, b, c, d, e, existing side by side, and continuing to be sepa
rately discernible; they are + a, — a, ^ b, — b, 2 b, &c., some
of which cancel one another, while many others do not appear
distinguishably, but merge in one sum : forming altogether
a result, between which and the causes whereby it was pro
duced there is often an insurmountable difficulty in tracing by
observation any fixed relation whatever.

The general idea of the Composition of Causes has been
seen to be, that though two or more laws interfere with one
another, and apparently frustrate or modify one another's
operation, yet in reality all are fulfilled, the collective effect
being the exact sum of the effects of the causes taken sepa
rately. A familiar instance is that of a body kept in equili
brium by two equal and contrary 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 distance ;
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 con
flict 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 direc
tions making an angle with one another, moves in the diago
nal ; and it seems a paradox to say that motion in the diagonal

496 INDUCTION.

is the sum of two motions in two other lines. Motion, how
ever, 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 alternate instants instead of acting in the same
instant ; (saving that if we suppose two forces to act succes
sively 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 instant, all the effect which
belonged to it ; and that the modifying influence 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 compound their effects may be treated as
if they produced simultaneously each of them its own effect,
and all these effects coexisted 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 assertion 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,
retarded by the action of gravity and other resisting forces,
and at last stopped 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 pheno
mena, 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 pre
vented, or except in so far as prevented, by some counteracting

INTERMIXTURE OF EFFECTS. 497

cause. But the body does not only move in that manner
unless counteracted ; it tends to move in that manner even
when counteracted ; it still exerts, in the original direction,
the same energy of movement as if its first impulse had been
undisturbed, and produces, by that energy, an exactly equiva
lent quantity of effect. This is true even when the force
leaves the body as 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
neutralizing 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
contrary 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 results. In
those sciences of causation which have an accurate nomen
clature, there are special words which signify a tendency to
the particular effect with which the science is conversant;
thus pressure, in mechanics, is synonymous with tendency to
motion, and forces are not reasoned on as causing actual
motion, but as exerting pressure. A similar improvement
in terminology would be very salutary in many other branches
of science.

The habit of neglecting this necessary element in the
precise expression 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 con
clusions of science, when they have been submitted to the
judgment of minds insufficiently disciplined and cultivated.
The rough generalizations suggested by common observation
VOL. i. 32

498 INDUCTION.

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 exception 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 conspicuous of
the two, is called the disturbing force, prevails sufficiently
over the other force in some one case, to constitute that case
what is commonly called an exception, the same disturbing
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
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 astronomer knows,
tend towards the earth, with a force exactly equal to that
with which the earth tends towards them. The resistance of
the atmosphere 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 is 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 correct principles

* It seems hardly necessary to say that the word impinge, as a general
term to express collision of forces, is here used by a figure of speech, and not
as expressive of any theory respecting the nature of force.

INTERMIXTURE OF EFFECTS. 499

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 according to what method
these complex 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 circumstances
in which it may be expected again to occur. The conditions
of a phenomenon which arises from a composition of causes,
may be investigated either deductively or experimentally.

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 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 a priori. The other, or a. posteriori method,
professes to proceed according to the canons of experimental
inquiry. Considering the whole assemblage of concurrent
causes which produced the phenomenon, as one single cause,
it attempts to ascertain the cause in the ordinary manner, by a
comparison of instances. This second method subdivides
itself into two different varieties. If it merely collates
instances 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 combination
which will produce the given total effect, it is a method of
experiment.

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 favourite
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 circumstances."

* Essays on some Unsettled Questions of Political Economy, Essay V.

32—2

500 INDUCTION.

We shall select for this purpose a case which as yet furnishes
no very brilliant example of the success of any of the three
methods, hut 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 mercury, and known laws of the human body,
and by reasoning from these, would attempt to discover
whether mercury will act upon the body when in the morbid
condition supposed, in such a manner as to restore health.
The experimental method would simply administer mercury in
as many cases as possible, noting the age, sex, temperament,
and other peculiarities of bodily constitution, the particular
form or variety of the disease, the particular stage of its pro
gress, &c., remarking in which of these cases it produced a
salutary effect, and with what circumstances 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

INTERMIXTURE OF EFFECTS. 501

which presented themselves, in an examination extending to a
great number of instances, were cases in which mercury had
been administered, we might generalize with confidence from
this experience, and should have obtained a conclusion of real
value. But no such basis for generalization can we, in a case
of this description, hope to obtain. The reason is that which
we have spoken of as constituting the characteristic imperfec
tion of the Method of Agreement ; Plurality of Causes. Sup
posing even that mercury does tend to cure the disease, so
many other causes, both natural and artificial, also tend to
cure it, that there are sure to be abundant instances of recovery
in which mercury has not been administered : unless, indeed,
the practice be to administer it in all cases ; on which suppo
sition 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
approximately, any one of the causes. Recovery 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 although 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 like, 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 a contribution to the theory of the
subject.

§ 8. The inapplicability of the method of simple obser
vation to ascertain the conditions of effects dependent on

502 INDUCTION.

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 arti
ficially 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 suc
cessful than the former.

The method now under consideration is called the Empi
rical Method ; and in order to estimate it fairly, we must sup
pose it to be completely, not incompletely, empirical We
must exclude from it everything which partakes of the nature
not of an experimental 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 laws to determine
how it will act upon persons affected with a particular disease,
this may be a really effectual method, but this is deduction.
The experimental method does not derive the law of a com
plex case from the simpler laws which conspire to produce it,
but makes its experiments directly upon the complex case. We
must make entire abstraction of all knowledge of the simpler
tendencies, the modi operandiof mercury in detail. Our ex
perimentation must aim at obtaining a direct answer to the
specific 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 ex
periment 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

INTERMIXTURE OF EFFECTS.

503

set of circumstances which we have exactly ascertained. It
needs hardly be remarked how far this condition is from being
realized 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 admi
nistered to a living being. This difficulty, 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. Moreover, the difficulty may
be attenuated by sufficient multiplication of experiments, in
circumstances rendering it improbable that any of the un
known causes should exist in them all. But when we have got
clear of this obstacle, we encounter another still more serious.
In other cases, when we intend to try an experiment, we do
not reckon it enough that there be no circumstance 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 agent 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 influence, 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 considering. The mercury of our experiment being tried
with an unknown multitude (or even let it be a known multi
tude) of other influencing circumstances, the mere fact of their
being influencing circumstances implies that they disguise the
effect of the mercury, and preclude us from knowing 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 suppose the very problem solved which we are con
sidering the means of solving,) 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

504

INDUCTION.

comparing the state of things following the experiment with
the state which preceded it, is thus, in the case of intermixture
of effects, entirely unavailing ; because other causes than that
whose effect we are seeking to determine, have been operating
during the transition. As for the other mode of employing
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 phenomena so com
plicated it is questionable 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 complicated cases, is therefore out of the question.
We can in the most favourable cases only discover, by a suc
cession 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 influencing
agents, is generally, 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.

If so little can be done by the experimental method to
determine the conditions of an effect of many combined causes,
in the case of medical science ; still less is this method appli
cable to a class of phenomena more complicated than even
those of physiology, the phenomena of politics and history.
There, Plurality of Causes exists in almost boundless excess,
and effects are, for the most part, inextricably interwoven
with 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 indirectly 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 methods 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

INTERMIXTURE OP EFFECTS. 505

of the speculative faculties in any age in which it is accredited.
Nothing can he more ludicrous than the sort of parodies on
experimental reasoning which one is accustomed to meet with,
not in popular discussion only, but in grave treatises, 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 intending 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
collation of individual instances, that even the impossibility,
in social phenomena, of making artificial experiments, a cir
cumstance otherwise so prejudicial to directly inductive inquiry,
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 definite circumstance. The nearest
approach to an experiment in the philosophical 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 become apparent; and as the
causes operating in so extensive a sphere are not only infinitely
numerous, but in a state of perpetual alteration, it is always
certain that before the effect of the new cause becomes con
spicuous enough to be a subject of induction, so many of the
other influencing circumstances will have changed as to vitiate
the experiment.

Two, therefore, of the three possible methods for the study
of phenomena resulting from the composition of many causes,

506 INDUCTION.

being, from the very nature of the case, inefficient and illu
sory, there remains only the third, — that which considers the
causes separately, and infers the effect from the balance
of the different tendencies which produce it: in short, the
deductive, or a priori method. The more particular con
sideration of this intellectual process requires a chapter to
itself.

CHAPTER XI.

OF THE DEDUCTIVE METHOD.

§ 1. THE mode of investigation which, from the proved
inapplicability 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 recur
rence, 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 ratiocination ; 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 Method is, to find the law
of an effect, from the laws of the different tendencies 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 Deductive 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 posi
tion on the earth. The Deductive Method, applied to social
phenomena, must begin, therefore, by investigating, or must
suppose to have been already investigated, the laws of human

INDUCTION.

action, and those properties of outward things by which the
actions 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
process.

To ascertain, then, the laws of each separate cause which
takes a share in producing the effect, is the first desideratum
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. In the case last mentioned, this first condi
tion is of easy fulfilment. That social phenomena depend on
the acts and mental impressions of human beings, never could
have been a matter of any doubt, however imperfectly it may
have been known either by what laws those impressions
and actions are governed, or to what social consequences 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 organized
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 pheno
mena. Until, by combining the laws of certain causes, it was
found that those laws explained all the facts which experience
had proved concerning the heavenly motions, and led to pre
dictions which it always verified, mankind 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
answering it, in either case it must be answered ; the laws of
the different 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,

THE DEDUCTIVE METHOD. 509

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 observation of bodies kept at rest
by the equilibrium of opposing forces. Even where the ten
dency is not, in the ordinary 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 unfavourable 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.
Notwithstanding the resources afforded in this description of
cases by the Method of Concomitant Variations, the principles
of a judicious experimentation prescribe that the law of each
of the tendencies should be studied, if possible, 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, unfortunately very numerous and
important, in which the causes do not suffer themselves to be
separated and observed 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 phenomena ; it being
seldom possible to separate the different agencies which col
lectively compose an organized body, without destroying the
very phenomena which it is our object to investigate :

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 phy-

510 INDUCTION.

siology (greatly and rapidly progressive as it now is) is embar
rassed by greater natural difficulties, and is probably susceptible
of a less degree of ultimate perfection, tban even the social
science ; inasmuch as it is possible to study the laws and ope
rations 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 common language, diseases in their different
forms and degrees, afford in the case of physiological investi
gation the most valuable equivalent to experimentation pro
perly so called ; inasmuch as they often exhibit to us a definite
disturbance in some one organ or organic function, the remain
ing organs and functions being, in the first instance at least,
unaffected. It is true that from the perpetual actions and re
actions which are going on among all parts of the organic
economy, there can be no prolonged disturbance in any one
function without 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 func
tions 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 confidence to the original local derangement; but for
this it is necessary that we should know that the original
derangement was local. If it was what is termed constitu
tional, 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 tardy, action of the
original cause.

Besides natural pathological facts, we can produce patho
logical facts artificially ; we can try experiments, even in the

THE DEDUCTIVE METHOD. 511

popular sense of the term, by subjecting the living being to
some external agent, such as the mercury of our former ex
ample, or the section of a nerve to ascertain the functions of
different parts of the nervous system. As this experimenta
tion is not intended to obtain a direct solution of any prac
tical question, but to discover general laws, from which
afterwards the conditions of any particular effect may be ob
tained 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 practical object in view. The
experiments are best tried, not in a state of disease, which is
essentially a changeable 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 physiological
phenomena would, it may generally be presumed, remain un
disturbed, were it not for the disturbing cause which we
introduce.

Such, with the occasional aid of the Method of Concomi
tant Variations, (the latter not less incnmbered than the more
elementary methods by the peculiar difficulties of the subject,)
are our inductive resources for ascertaining the laws of the
causes considered 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 surprised at the backward state of the science of physio
logy ; in which indeed our knowledge of causes is so imperfect,
that we can neither explain, nor could without specific expe
rience 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 pheno
mena, 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 organiza
tion 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 entire facts of

512 INDUCTION.

comparative anatomy and physiology, the characteristic organic
structure corresponding to each class of functions has heen
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 organized body,
and try whether it would live.

Under such disadvantages do we, in cases of this descrip
tion, 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 he obtained by an
induction from comparatively 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 unknown. And only when the induction which fur
nished the premises to the Deductive method rested on such
instances, has the application of such a method to the ascer
tainment 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 stage of the great logical operation now under
discussion satisfactorily accomplished, the second part follows ;
that of determining from the laws of the causes, what effect
any given combination of those causes will produce. This is a
process of calculation, 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 theorems 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

THE DEDUCTIVE METHOD. 513

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
inversely as the square of the distance, all the resources of the
calculus have not hitherto sufficed to obtain any general solu
tion 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 gunpowder, 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, acous
tics, astronomy. But when the complication increases, and
the effects are under the influence of so many and such shift
ing causes as to give no room either for fixed numbers, or for
straight lines and regular curves, (as in the case of physio
logical, to say nothing of mental and social phenomena,)
the laws of number and extension are applicable, if at all,
only on that large scale on which precision of details becomes
unimportant. Although 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 indis
pensable part of every such process. All that is essential in
it is reasoning from a general law to a particular case, that
is, determining by means of the particular circumstances of
that case, what result is required in that instance to fulfil the
law. Thus in the Torricellian experiment, if the fact that air
has weight had been previously known, it would have been
easy, without any numerical 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
VOL. i. 33

514 INDUCTION.

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 answering
either of the following questions : Given a certain combina
tion of causes, what effect will follow ? and, What combi
nation of causes, if it existed, would produce a given effect ?
In the one case, we determine the effect to be expected in any
complex circumstances 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 argu
ments by which the methods of direct observation and expe
riment were set aside as illusory when applied to the laws
of complex phenomena, applicable with equal force against
the Method of Deduction ? When in every single instance a
multitude, often an unknown multitude, of agencies, are
clashing and combining, what security have we that in our
computation a priori we have taken all these into our reck
oning ? How many must we not generally 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 accurately the numerical law of each, — a condition in
most cases not to be fulfilled; and even when fulfilled, to
make the calculation transcends, in any but very simple cases,
the utmost power of mathematical science with all its most
modern improvements.

These objections have real weight, and would be altogether
unanswerable, if there were no test by which, when we employ
the Deductive Method, 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 application forms, under
the name of Verification, the third essential component part of
the Deductive Method ; without which all the results it can
give have little other value than that of conjecture. To

THE DEDUCTIVE METHOD. 515

warrant reliance on the general conclusions arrived at by
deduction, these conclusions must be found, on careful com
parison, to accord with the results of direct observation
wherever it can be had. If, when we have experience to com
pare with them, this experience confirms them, we may safely
trust to them in other cases of which our specific experience
is yet to come. But if our deductions have led to the conclu
sion that from a particular combination of causes a given eifect
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 pro
bable surmise) what frustrated it : if we cannot, the theory is
imperfect, and not yet to be relied upon. Nor is the verifi
cation complete, unless some of the cases in which the theory
is borne out by the observed result, are of at least equal com
plexity with any other cases in which its application could be
called for.

If direct observation and collation of instances have fur
nished 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 uniformities, 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 pro
duced. Thus it was very reasonably deemed an essentia
requisite of any true theory of the causes of the celestial
motions, that it should lead by deduction to Kepler'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 pos
sible of the empirical laws of the phenomena should be as
certained, by a comparison of instances, conformably to the
Method of Agreement: as well as (it must be added) that
the phenomena themselves should be described, in the most
comprehensive as well as accurate manner possible; by col
lecting from the observation of parts, the simplest possible

33—2

516 INDUCTION.

correct expressions for the corresponding 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 complex instances which
would have been of no use for the discovery of the simple
laws into which we ultimately analyse their phenomena,
nevertheless, when they have served to verify the analysis,
become additional evidence of the laws themselves. Although
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 circumstances ; and occasionally serves to
eliminate some circumstance not previously 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 calculated 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 univer
sality of that law. Accordingly any law of nature is deemed
to have gained in point of certainty, by being found to explain
some complex case which had not previously been thought of
in connexion 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 characterized in its three
constituent parts, Induction, Ratiocination, and Verifica
tion, the human mind is indebted for its most conspicuous
triumphs in the investigation of nature. To it we owe all
the theories by which vast and complicated phenomena 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

THE DEDUCTIVE METHOD. 517

what the method has done for us, from the case of the celestial
motions ; one of the simplest among the greater instances of
the Composition of Causes, since (except in a few cases not
of primary importance) 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 motions of that
body depend ; a much smaller number, no doubt, than that by
which any other of the great phenomena 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 velo
cities of different planets, or the different 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 a 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 experimentation under simple
circumstances. As we shall have occasion to analyse, further
on, this great example of the Method of Deduction, we shall
not occupy any time with it here, but shall proceed to that
secondary application of the Deductive Method, the result of
which is not to prove laws of phenomena, but to explain
them.

CHAPTER XII.

OF THE EXPLANATION OP LAWS OF NATURE.

§ 1. THE deductive operation by which we derive the
law of an effect from the laws of the causes, the concurrence
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 continually 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 or uniformity in nature is said to be
explained, 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 distinguishable 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 uniform
motion in the tangent, and the law of the centripetal force

EXPLANATION OF LAWS. 519

which tends to produce an accelerating motion towards the sun;
the real motion heing a compound of the two.

It is necessary here to remark, that in this resolution of the
law of a complex effect, the laws of which it is compounded
are not the only elements. It is resolved into the laws of the
separate causes, together with the fact of their coexistence.
The one is as essential an ingredient as the other ; whether the
object be to discover 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 gravita-
tive force, hut 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 collo
cations 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 insist
ing 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, between what seemed the
cause and what was supposed to be its effect, further observa
tion detects an intermediate link; a fact caused by the ante
cedent, 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 before 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.
Touching the object, therefore, is only the remote cause of our

520 INDUCTION.

sensation ; 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 parti
cular 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 phenomenon 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, provisionally, as the proximate cause of the
affection of the nerve. The sequence, 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 affec
tion of the nerve ; and the law, that an affection of the nerve
produces sensation.

To take another example : the more powerful acids corrode
or blacken organic 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 separa
tion of some of the chemical elements of the organic structure
from the rest, and their entering into combination with the
acid. The acid causes this separation of the elements, and the
separation of the elements causes the disorganization, and often
the charring of the structure. So, again, chlorine extracts
colouring matters, (whence its efficacy in bleaching,) and
purifies the air from infection. This law is resolved into the
two following laws. Chlorine has a powerful affinity for bases
of all kinds, particularly metallic bases and hydrogen. Such
bases are essential elements of colouring matters and conta
gious compounds : which substances, therefore, are decomposed
and destroyed 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

EXPLANATION OF LAWS. 521

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 frus
trated, by the non-fulfilment of some negative condition : 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 pro
duces B. It is also less general than the law that B produces
0. For B may have other causes besides A ; and as A pro
duces 0 only by means of B, while B produces 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 sensa
tion, 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 pro
duces sensation ; since the sensation equally follows the change
in the nerve when not produced by contact with an object,
but by some other cause ; as in the well-known case, when a
person who has lost a limb, feels the same sensation which he
has been accustomed to call a pain in the limb.

Not only are the laws of more immediate 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 ultimately
found not to be universally true. From the moment when
the sequence of A and C is shown not to be immediate, but to

522

INDUCTION.

depend on an intervening phenomenon, then, however con
stant and invariable the sequence of A and C has hitherto
been found, possibilities arise of its failure, exceeding those
which can affect either of the more immediate sequences, A, B,
and B, C. The tendency of A to produce C may be defeated
by whatever is capable of defeating either the tendency of A
to produce B, or the tendency of B to produce 0 ; it is there
fore twice as liable to failure as either of those more elementary
tendencies ; and the generalization that A is always followed
by C, is twice as likely to be found erroneous. And so of the
converse generalization, 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 generalization into the other
two, not only shows that there are possible limitations of the
former, from which its two elements 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 there
be cases in which the sequence of A and C does not hold,
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, extend to more cases, and are also less
likely to require limitation from subsequent experience, than
the law which they serve to explain. They are more nearly
unconditional ; they 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 causes 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 manifest that

EXPLANATION OF LAWS. 523

the complex law is liable to be oftener unfulfilled than any one
of the simpler laws of which it is the result, since every con
tingency 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 sub
ject 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 complex effect must be less general than the laws of the
causes which conspire to produce it. The same causes, acting
according to the same laws, and differing only in the propor
tions in which they are combined, often produce effects which
differ not merely in quantity, but in kind. The combination
of a centripetal with a projectile force, in the proportions
which obtain in all the planets and satellites 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 demon
strated that the motion produced would be in a circle, or a
parabola, or an hyperbola : 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 resolvable into the very
same simple laws into which that of the elliptical motion
is resolved, namely, the law of the permanence of rectilineal
motion, 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 motion might be changed into a
motion in some other conic section ; and the complex law, that
the planetary motions take place in ellipses, would be deprived
of its universality, though the discovery would not at all de
tract from the universality of the simpler laws into which that

524) INDUCTION.

v complex law is resolved. The law, in short, of each of the
concurrent causes remains the same, however their colloca
tions 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 this it is self-evident 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 example of this operation was
when terrestrial gravity and the central force of the solar
system were brought together under the general law of gravi
tation. It had been proved antecedently that the earth and
the other planets tend to the sun ; and it had been known
from the earliest times that terrestrial bodies tend towards 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 calculation,
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
suspended, the moon would fall towards the earth through ex
actly 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 virtue of its weight : and that
the two phenomena, the tendency of the moon to the earth
and the tendency of terrestrial objects to the earth, being not

EXPLANATION OF LAWS. 525

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 tendency of the moon to the earth, and
the tendency of the earth arid planets to the sun, were already
known to be cases of the same law of causation : and thus the
law of all these tendencies, 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 recently 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 the
recognition of the same sequence in different sets of instances ;
and may, in fact, be regarded as merely one step in the pro
cess of elimination. That 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, therefore,
be ascribed to a peculiar property of the earth itself: one of
the circumstances, namely, the proximity of the earth, had
not been eliminated. To eliminate this circumstance required
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 unfavourable circum
stances for observing them. To make these observations, fell
naturally to the lot of a different set of persons from those

526

INDUCTION.

who studied terrestrial phenomena ; nnd had, indeed, been a
matter of great interest at a time when the idea of explaining
celestial facts hy terrestrial laws was looked upon as the con
founding of an indefeasible distinction. When, however, the
celestial motions were accurately ascertained, and the deduc
tive processes performed, from which it appeared that their
laws and those of terrestrial gravity corresponded, those celes
tial observations became a set of instances which exactly
eliminated the circumstance of proximity to the earth ; and
proved that in the original case, that of terrestrial objects, it
was not the earth, as such, that caused the motion or the
pressure, but the circumstance common to that case with the
celestial instances, namely, the presence of some great body
within certain limits of distance.

§ 0. 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 intermediate 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, consisting of what all those classes
of cases have in common. We may here remark that this last
operation involves none of the uncertainties attendant on
induction by the Method of Agreement, since we need not
suppose the result to be extended by way of inference to any
new class of cases, different from those by the comparison of
which it was engendered.

In all these three processes, laws are, as we have seen,
resolved into laws more general than themselves ; laws ex
tending to all the cases which the former extended to, and
others besides. In the first two modes they are also resolved

EXPLANATION OF LAWS. 527

into laws more certain, 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 condi
tionally, 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 exception 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 mystery for another ; and does nothing
to render the general course of nature other than mysterious :
we can no more assign a why for the more extensive 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 resolves 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
tendency of all particles of matter towards one another. It
must be kept constantly in view, therefore, that in science,
those who speak of explaining any phenomenon mean (or
should mean) pointing out not some more familiar, but merely
some more general, phenomenon, of which it is a partial exem
plification ; or some laws of causation which produce it by their
joint or successive action, and from which, therefore, its con
ditions 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

528

INDUCTION.

assumptions, which being granted, the order of nature as it
exists would be the result ? What are the fewest general pro
positions from which all the uniformities existing in nature
could be deduced ?

The laws, thus explained or resolved, are sometimes said
to be accounted 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 collocations, which laws and collocations
being supposed, the partial law follows without any additional
supposition.

CHAPTER XIII.

MISCELLANEOUS EXAMPLES OF THE EXPLANATION OF
LAWS OF NATURE.

§ 1. THE most striking example which the history of
science presents, of the explanation of laws of causation and
other uniformities of sequence among special phenomena, by
resolving them into laws of greater simplicity and generality,
is the great Newtonian generalization : 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 revolutions 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
affiliated by deduction to observed laws of electric action, in
which they have ever since been considered to be included 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,
VOL. i. 34

530 INDUCTION.

commenced by Bichat, and carried on by subsequent biologists,
of tbe properties of the bodily organs, to the elementary
properties of the tissues into which they are anatomically
decomposed.

Another striking instance is afforded by Dalton's gene
ralization, commonly known as the atomic theory. It had
been known from the very commencement of accurate chemical
observation, that any two bodies combine 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 100 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 perceived 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 per
ceiving, that a unit of weight might be established for each
substance, such that by supposing the substance to enter into
all its combinations 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 1 being
assumed as the unit of hydrogen, if 8 were then taken as that
of oxygen, the combination of one unit of hydrogen with one
unit of oxygen would produce the exact proportion of weight
between the two substances which is known to exist in water ;
the combination of one unit of hydrogen with two units of
oxygen would produce the proportion which exists in the other
compound of the same two elements, called peroxide of
hydrogen ; and the combinations of hydrogen and of oxygen
with all other substances, would correspond with the suppo
sition that those elements enter into combination by single
units, or twos, or threes, of the numbers assigned to them,
1 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 of the equivalent numbers, or, as they are called,
atomic weights, of all the elementary substances, comprises in
itself, and scientifically explains, all the proportions in which
any substance, elementary or compound, is found capable of

EXAMPLES OF THE EXPLANATION OF LAWS. 531

entering into chemical combination with any other substance
whatever.

§ 2. Some interesting cases of the explanation of old uni
formities by newly ascertained laws are afforded by the re
searches 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 crystal
loids 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 different from those of the
same substance when crystallized, or when in a state easily
susceptible of crystallization. Colloid substances pass with
extreme difficulty and slowness into the crystalline state, and
are extremely inert in all the ordinary chemical relations. Sub
stances 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 vege
table substances, particularly gelatine, albumen, starch, the
gums, caramel, tannin, and some others. Among substances
not of organic origin, the most notable instances are hydrated
silicic acid, and hydrated alumina, with other metallic per
oxides of the aluminous class.

Now it is found, that while colloidal substances are easily
penetrated by water, and by the solutions of crystalloid sub
stances, they are very little penetrable by one another : which
enabled Professor Graham to introduce a highly effective
process (termed dialysis) for separating the crystalloid sub
stances contained in any liquid mixture, by passing them
through a thin septum of colloidal matter, which does not
suffer 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 obser
vation, not previously explained.

For instance, " while soluble crystalloids are always highly
sapid, soluble colloids are singularly insipid," as might be ex
pected ; for, as the sentient extremities of the nerves of the

34—2

532 INDUCTION'.

palate " are probably protected by a colloidal membrane," im
permeable to otber 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 colloids." One of the mysterious processes
accompanying digestion, the secretion of free muriatic acid by
the coats of the stomach, obtains a probable hypothetical ex
planation through the same law. Finally, much light is thrown
upon the observed 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 intermediate phenomenon which is interpo
lated between the remote cause and 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 swimming
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 Kesolution of Laws. The law itself is proved by the
Method of Difference, 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 results from Liebig's
speculations. The putrefaction of animal and other azotised

* Vide Memoir by Thomas Graham, F.E.S., Master of the Mint, "On
Liquid Diffusion Applied to Analysis," in the Philosophical Transactions for
1 862, reprinted in the Jowrnal of the Chemical Society, and also separately as a
pamphlet.

EXAMPLES OF THE EXPLANATION OF LAWS. 533

bodies is a chemical process, by which they are gradually dis
sipated in a gaseous form, chiefly in that of carbonic acid and
ammonia ; now to convert the carbon of the animal substance
into carbonic acid requires oxygen, and to convert the azote
into ammonia requires hydrogen, which are the elements of
water. The extreme 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 decomposed by the action of two different
affinities upon two of their elements, 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 influ
ence of the nervous system on nutrition and secretion. By
reflex nervous action is meant, action which one part of the
nervous system exerts over another part, without any inter
mediate action on the brain, and consequently without
consciousness ; or which, if it does pass through the brain,
at least produces its effects independently 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
stomach 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-Sequard's Lectures on the
Nervous System.

The production of tears by irritation 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

538 INDUCTION.

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 cha
racter form associations more easily and strongly than other
ideas, that is, they become associated after fewer repetitions,
and the association is more durable. This is an experimental
law, grounded on the Method of Difference. By deduction
from this law, many of the more special laws which expe
rience 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 interests are excited, and the firm hold
which the facts relating to them have on our memory ; the
vivid recollection 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 acci
dental instrument of any occurrence 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 pro
portional 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. Priestley in a monthly
periodical,* that the same elementary law of our mental con
stitution, suitably followed out, would explain a variety of
mental phenomena previously inexplicable, and in particular
some of the fundamental 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 renders associations stronger in

* Since acknowledged and reprinted in Mr. Martineau's Miscellanies.

EXAMPLES OF THE EXPLANATION OF LAWS. 539

proportion to the pleasurable or painful character of the impres
sions, 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 Imagination, and is one of the peculiarities of the painter
and the poet ; while persons of more moderate susceptibility to
pleasure and pain will have a tendency to associate facts chiefly
in the order of their succession, and such persons, if they pos
sess mental superiority, will addict themselves to history or
science rather than to creative art. This interesting specula
tion the author of the present work has endeavoured, on an
other occasion, to pursue farther, and to examine how far it
will avail towards explaining the peculiarities of the poetical
temperament.* It is at least an example which may serve,
instead of many others, to show the extensive scope which
exists for deductive investigation in the important and hitherto
so imperfect Science of Mind.

§ 7. The copiousness with which the discovery and ex
planation of special laws of phenomena by deduction from
simpler and more general ones has here been exemplified, was
prompted by a desire to characterize clearly, and place in its
due position of importance, the Deductive Method ; which, in
the present state of knowledge, is destined henceforth irrevo
cably to predominate in the course of scientific investigation.
A revolution is peaceably and progressively effecting 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 to experimental, and it is now rapidly reverting
from experimental to deductive. But the deductions which
Bacon abolished were from premises hastily snatched up, or
arbitrarily assumed. The principles were neither established
by legitimate canons of experimental inquiry, nor the results

* Dissertations and Discussions, vol. i., fourth paper.

534 INDUCTION.

origin, very frequently 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 in
stance) 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 action, 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 abdomen, 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 ; consisting
in violent inflammation of the tissues of the abdomen, chest,
or 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 neu
ralgia, even when there is no paralysis :

Tetanus produced by the lesion of a nerve ; Dr. Brown-
Sequarcl thinks it highly probable that hydrophobia is a phe
nomenon of a similar nature :

Morbid changes in the nutrition of the brain and spinal
cord, manifesting themselves by epilepsy, chorea, hysteria, and
other diseases, occasioned by lesion of some of the nervous
extremities in remote places, as by worms, calculi, tumours,
carious bones, and in some cases even by very slight irrita
tions of the skin.

§ 4. From the foregoing and similar instances, we may
see the importance, when a law of nature previously unknown
has been brought to light, or when new light has been thrown
upon a known law by experiment, of examining all cases

EXAMPLES OF THE EXPLANATION OF LAWS. 535

which present the conditions necessary for bringing that law
into action ; a process fertile in demonstrations of special laws
previously unsuspected, and explanations of others already
empirically known.

For instance, Faraday discovered hy experiment, that
voltaic electricity could be evolved from a natural magnet,
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 magnets, but of that great magnet, the earth.
The law being thus established experimentally, that electricity
is evolved, by a magnet, and a conductor 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 evolu
tion of electricity. In the northern 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 electric.

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 membranes in
close, 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: 1st. 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. 2nd. The
carbonic acid gas of effervescing drinks, evolved in the stomach,

INDUCTION.

permeates its membranes, and rapidly spreads through the
system. 3rd. 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 explain the bodily warmth immediately consequent on
drinking spirituous liquors.) 4th. In any state of the body in
which peculiar gases 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 surrounding atmo
sphere 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 pro
ducts. 6th. The exchange of oxygen and carbonic acid in the
lungs is not prevented, but rather promoted, by the inter
vention 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 it is formed in the capillaries, should also find a sub
stance 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 old but not undisputed empirical generaliza
tion, that soda powders weaken the human system. These
powders, consisting of a mixture of tartaric acid with bicar
bonate of soda, from which the carbonic acid is set free, must
pass into the stomach as tartrate of soda. Now, neutral tar-
trates, 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 addi
tional quantity of oxygen, the abstraction of which must lessen
the oxygen destined for assimilation with the blood, on the

EXAMPLES OP THE EXPLANATION OF LAWS. 537

quantity of which the vigorous action of the human system
partly depends.

The instances of new theories agreeing with and explaining
old empiricisms, are innumerable. All the just remarks made
by experienced persons on human character and conduct, are
so many special laws, which the general laws of the human
mind explain and resolve. The empirical generalizations on
which the operations of the arts have usually been founded,
are continually justified and confirmed on the one hand, or
corrected and improved on the other, by the discovery of the
simpler scientific laws on which the efficacy of those operations
depends. The effects of the rotation of crops, of the various
manures, and other processes of improved agriculture, have
been for the first time resolved 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 experimental generalization : but as science
advances in discovering the simple laws of chemistry and phy
siology, 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 exploded, or their efficacy, in so far as real, explained,
better processes, founded on the knowledge of proximate
causes, are continually suggested and brought into use.*
Many even of the truths of geometry were generalizations
from experience before they were deduced from first prin-

* It was an old generalization in surgery, that tight bandaging had a ten
dency to prevent or dissipate local inflammation. This sequence, being, in the
progress of physiological knowledge, resolved into more general laws, led to
the important surgical invention 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
the part, prevents the inflammation, or the tumour, from being nourished : in
the case of inflammation, it removes the stimulus, which 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.

540

INDUCTION.

tested by that indispensable element of a rational Deductive
Method, verification by specific experience. Between the pri
mitive method of Deduction and that which I have attempted
to characterize, 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
generalizations, from which the subordinate truths of the more
backward sciences will probably at some future period be de
duced by reasoning (as the truths of astronomy are deduced
from the generalities of the Newtonian theory), will be found,
in all, or even in most cases, among truths now known and
admitted. 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 cha
racter, 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 universal 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, crystallization, 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 gravita
tion appeared to the cotemporaries of Newton ; possibly even
more so, since Newton's law, after all, was but an extension of
the law of weight — that is, of a generalization familiar from of
old, and which already comprehended a not inconsiderable
body of natural phenomena. The general laws of a similarly
commanding character, which we still look forward to the dis
covery of, may not always find so much of their foundations
already laid.

These general truths will doubtless make their first ap
pearance in the character of hypotheses ; not proved, nor even

* Written before the rise of the new views respecting the relation of heat
to mechanical force ; but confirmed rather than contradicted by them.

EXAMPLES OF THE EXPLANATION OF LAWS. 541

admitting of proof, in the first instance, but assumed as pre
mises for the purpose of deducing from them the known laws
of concrete phenomena. 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 thenceforth
be presented as conclusions, and the science will, by means of
a new and unexpected Induction, be rendered Deductive.

END OF VOL. r.

LONDON :

6AVIIX, EDWABDS AND CO., PBINTEKS, CHANDOS STBEET,
COVENT GARDEN.

PLEASE DO NOT REMOVE
CARDS OR SLIPS FROM THIS POCKET

UNIVERSITY OF TORONTO LIBRARY

BG

91

MS

1S68

v.l

, John Stuart
A system of logic

• .-•