FROM-THE- LIBRARYOF
TWNITYCOLLEGETORQNTO
A SYSTEM OF LOGIC,
K1TIOCINATIVE AND INDUCTIVE:
BEING A
CONNECTED VIEW OF THE PRINCIPLES OF EVIDENCE
AND THE
METHODS OF SCIENTIFIC INVESTIGATION.
BY
JOHN STUART MILL.
EIGHTH EDITION.
NEW YORK:
HARPER & BROTHERS, PUBLISHERS,
FRANKLIN SQUARE.
1882.
PREFACE TO THE FIRST EDITION,
THIS book makes no pretense of giving to the world a new theory of the
intellectual operations. Its claim to attention, if it possess any, is ground-
ed 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 sub-
ject by speculative writers, or conformed to by accurate thinkers in their
scientific inquiries.
To cement together the detached fragments of a subject, never yet treat-
ed as a whole ; to harmonize the true portions of discordant theories, by
supplying the links of thought necessary to connect them, and by disentan-
gling them from the errors with which they are always more or less inter-
woven, must necessarily require a considerable amount of original specula-
tion. To other originality than this, the present work lays no claim. In
the existing state of the cultivation of the sciences, there would be a very
strong presumption against any one who should imagine that he had effect-
ed 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 per-
forming more systematically and accurately operations with which, at least
in their elementary form, the human intellect, in some one or other of its
employments, is already familiar.
In the portion of the work which treats of Ratiocination, the author has
not deemed it necessary to enter into technical details which may be ob-
tained 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 par-
ticipates ; though the scientific theory on which its defense is usually rest-
ed appears to him erroneous : and the view which he has suggested of the
nature and functions of the Syllogism may, perhaps, afford the means of
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 Propositions ; because many useful principles and dis-
iv PREFACE.
tinctions which were contained in the old Logic have been gradually omit-
ted 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 chapters 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 Asser-
tions, will not regard these discussions as either frivolous, or irrelevant to
the topics considered in the later Books.
On the subject of Induction, the task to be performed was that of gener-
alizing the modes of investigating truth and estimating evidence, by which
so many important and recondite laws of nature have, in the various sci-
ences, 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 pronounce it impossible.* The
author has endeavored to combat their theory in the manner in which Di-
ogenes confuted the skeptical reasonings against the possibility of motion ;
remembering that Diogencs's argument would have been equally conclu-
sive, though his individual perambulations might not have extended be-
yond the circuit of his own tub.
Whatever may be the value of what the author has succeeded in effect-
ing on this branch of his subject, it is a duty to acknowledge that for much
of it he has been indebted to several important treatises, partly historical
and partly philosophical, on the generalities and processes of physical sci-
ence, which have been published within the last few years. To these trea-
tises, and to their authors, he has endeavored 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 incum-
bent on him in this place to declare, that without the aid derived from the
* In the Inter editions of Archbishop Whately 's "Logic," he states his meaning to be, not
that "rules" for the ascertainment of truths by inductive investigation can not be laid down,
or that they may not be "of eminent sen-ice," but that they "must always be comparatively
vague and general, and incapable of being built up into a regular demonstrative theory like
that of the Syllogism." (Book iv., ch. iv., 3.) And he observes, that to devise a system
for this puqxise, capable of being "brought into a scientific form," would be an achievement
which " lie must be more sanguine than scientific 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.
PREFACE. V
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 toward the solution of
a question which the decay of old opinions, and the agitation that disturbs
European society to its inmost depths, render as important in the present
day to the practical interests of human life, as it must at all times be to the
completeness of our speculative knowledge viz. : Whether moral and so-
cial phenomena are really exceptions to the general certainty and uniformi-
ty 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 irrevo-
cably acquired and universally assented to, can be made instrumental to
the formation of a similar body of received doctrine in moral and political
science.
PREFACE TO THE THIRD AND FOURTH EDITIONS.
SEVERAL criticisms, of a more or less controversial character, on this
work, have appeared since the publication of the second edition ; and Dr.
"VVhewell 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,
cither by myself or by my critics, I have, in general silently, corrected : but
it is not to be inferred that I agree with the objections which have been
made to a passage, in every instance in which I have altered or canceled 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 for controversy, but because the opportunity was favorable for pla-
cing my own conclusions, and the grounds of them, more clearly and com-
pletely 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, af-
ter hearing and comparing what each can say against the other, and what
the other can urge in its defense.
Even the criticisms from which I most dissent have been of great serv-
ice 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 by addi-
tions and corrections, suggested by criticism or by thought, has been con-
* Now forming a chapter in his volume on "The Philosophy of Discovery."
viii PREFACE.
tinucd. The additions and corrections in the present (eighth) edition,
which arc not very considerable, are chiefly such as have been suggested
by Professor Bain's " Logic," a book of great merit and value. Mr. Bain's
view of the science is essentially the same with that taken in the present
treatise, the differences of opinion being few and unimportant compared
with the agreements ; and he has not only enriched the exposition by many
applications and illustrative details, but has appended to it a minute and
very valuable discussion of the logical principles specially applicable to
eacli of the sciences a task for which the encyclopedical character of his
knowledge peculiarly qualified him. I have in several instances made use
of his exposition to improve my own, by adopting, and occasionally by
controverting, matter contained in his treatise.
The longest of the additions belongs to the chapter on Causation, and is
a discussion of the question how far, if at all, the ordinary mode of stating
the law of Cause and Effect requires modification to adapt it to the new
doctrine of the Conservation of Force a point still more fully and elabo-
rately treated in Mr. Bain's work.
CONTENTS.
INTRODUCTION.
PAGE
1. A definition at the commencement of a sub-
ject must be provisional IT
2. Is logic the art and science of reasoning ?. IT
3. Or the art and science of the pursuit of
truth ? 18
4. Logic is concerned with inferences, not
with intuitive truths .^. 19
5. Relation of logic to the other sciences 21
C. Its utility, how shown 22
7. Definition of logic stated and illustrated. . 23
BOOK I.
OF NAMES AND PROPOSITIONS.
CHAPTER I. Of the Necessity of commencing with an
Analysis of Language.
5 1. Theory of names, why a necessary part of
logic 26
2. First step in the analysis of Propositions.. 2T
3. Names must be studied before Things 23
CHAPTER II. Of Names.
51. Names are names of things, not of our ideas 29
2. Words which are not names, but parts of
names 30
3. General and Singular names 32
4. Concrete and Abstract 33
5. Connotative and Non-counotative 34
6. Positive and Negative 41
7. Relative and Absolute 42
8. Uuivocal and Equivocal 44
CHAPTER III. Of the Things denoted by Names.
1. Necessity of an enumeration of Namable
Things. The Categories of Aristotle 45
2. Ambiguity of the most general names 46
3. Feelings, or states of consciousness 48
4. Feelings must be distinguished from their
physical antecedents. Perceptions, what. 49
6. Volitions, and Actions, what 81
6. Substance and Attribute 51
1. Body 52
8. Mind 56
9. Qualities 5T
10. Relations 59
11. Resemblance 60
12. Quantity 62
13. All attributes of bodies are grounded on
states of consciousness 63
14. So also all attributes of mind 64
15. Recapitulation C4
CHAPTER IV. Of Propositions.
5 1. Nature and office of the copula GO
2. Affirmative and Negative propositions 6T
3. Simple and Complex 69
4. Universal, Particular, and Singular 71
CHAPTER V. Of the Import of Propositions.
1. Doctrine that a proposition is the expres-
sion of a relation between two ideas 73
2. that it is the expression of a relation be-
tween the meanings of two names 75
3. that it consists in referring something
to, or excluding something from, a class. 77
4. What it really is 80
5. It asserts (or denies) a sequence, a co-exist-
ence, a simple existence, a causation 81
6. or a resemblance 83
7. Propositions of which the terms are ab-
stract 86
CHAPTER VI. Of Propositions merely Verbal.
1. Essential and Accidental propositions 88
2. All essential propositions are identical
propositions 89
3. Individuals have no essences 91
4. Real propositions, how distinguished from
verbal 92
5. Two modes of representing the import of
a Real proposition 93
CHAPTER VII. Of the Nature of Classification, and
the Five Predicables.
1. Classification, how connected with Naming 94
2. The Predicables, what 95
3. Genus and Species 95
4. Kinds have a real existence in nature 97
5. Differentia 100
6. Differentiae for general purposes, and differ-
entia? for special or technical purposes. . . 101
7. Proprium 103
8. Accidens 104
CHAPTER VIII. Of Definition.
1. A definition, what 105
2. Every name can be defined, whose meaning
is susceptible of analysis 106
3. Complete, how distinguished from incom-
plete definitions 107
4. and from descriptions 108
5. What are called definitions of Things, are
definitions of Names with an implied as-
sumption of the existence of Things cor-
responding to them Ill
6. even when such things do not in reality
exist H6
CONTENTS.
57. Definitionf, though of names only, must be
grounded on knowledge of the corre-
sponding things 117
BOOK II.
OF REASONING.
CHAPTER I. Of Inference, or Reasoning, in general.
5 1. Retrospect of the preceding hook 121
2. Inferences improperly so called 122
3. Inferences proper, distinguished into in-
ductions and ratiocinations 125
CHATTER II. Of Hat iocinat ion, or Syllogism.
51. Analysis of the Syllogism 126
2. The dictum tie. omni not the foundation of
reasoning, but a mere identical proposi-
tion 132
3. What is the really fundamental axiom of
Ratiocination 135
4. The other form of the axiom 137
CHAPTER III. Of the Functions, and Logical Value
of the Syllogism.
{ 1. Is the Syllogism a petitio principii T 139
2. Insufficiency of the common theory 139
3. All inference is from particulars to partic-
ulars 141
4. General propositions are a record of such
inferences, and the rules of the syllogism
are rules for the interpretation of the
record 140
5. The syllogism not the type of reasoning,
but a test of it 148
6. The true type, what 151
7. Relation between Induction and Deduc-
tion 153
8. Objections answered 154
9. Of Formal Logic, and its relation to the
Logic of Truth 15C
CHAPTER IV. Of Trains of Reasoning, and Deduct-
ive Sciences.
51. For what purpose trains of reasoning exist. 153
2. A train of reasoning is a series of induct-
ive inferences 15?
3. from particulars to particulars through
marks of marks ICO
4. Why there are deductive sciences 161
6. Why other sciences still remain experi-
mental 164
6. Experimental sciences may become deduct-
ive by the progress of experiment, 165
7. In what manner this usually takes place. . 166
CHAPTER V. Of Demonstration, and Xecessary
Truth*.
{ 1. The Theorems of geometry are necessary
truths only in the sense of necessarily fol-
lowing from hypotheses 16S
2. Those hypotheses are real facts with some
of their circumstances exaggerated or
omitted 170
3. Some of the first principles of geometry are
axioms, and these are not hypothetical.. 171
4. but are experimental truths 172
PAGE
{ 5. An objection answered 174
C. Dr. Whewell's opinions on axioms exam-
ined 176
CHAPTER VI. The game Subject continued.
5 1. All deductive sciences are inductive 187
2. The propositions of the science of number
are not verbal, but generalizations from
experience 18S
3. In what sense hypothetical 191
4. The characteristic property of demonstra-
tive science is to be hypothetical 192
6. Definition of demonstrative evidence 193
CHAPTER VII. Examination of some Ojnnions op-
posed to the preceding doctrines.
1. Doctrine of the Universal Postulate 193
2. The test of inconceivability does not rep-
resent the aggregate of past experience. . 195
3. nor is implied in every process of
thought 197
4. Objections answered 201
5. Sir W. Hamilton's opinion on the Princi-
ples of Contradiction and Excluded Mid-
dle.... .... 204
BOOK III.
OF INDUCTION.
CHAPTER I. Preliminary Observations on Induc-
tion in general.
{1. Importance of an Inductive Logic 207
2. The logic of science is also that of business
and life 208
CHAPTER II. Of Inductions improperly so called.
5 1. Inductions distinguished from verbal trans-
formations 210
2. from inductions, falsely so called, in math-
ematics 212
3. and from descriptions 213
4. Examination of Dr. Whewell's theory of
Induction 214
6. Further illustration of the preceding re-
marks 221
CHAPTER III. Of the Ground of Induction.
51. Axiom of the uniformity of the course of
nature 2-23
2. Not true in every sense. Induction per
enumerationetn simplicem 226
3. The question of Inductive Logic stated 227
CHAPTEB IV. Of Laws of Nature,
} 1. The general regularity in nature is a tissue
of partial regularities, called laws 229
2. Scientific induction must be grounded on
previous spontaneous inductions 231
3. Are there any inductions fitted to be a test
of all others? 232
CHAPTER V. Of the Law of Universal Causation.
{ 1. The universal law of successive phenomena
is the Law of Causation 234
2. ?'. c., the law that every consequent has
an invariable antecedent 23C
CONTENTS.
XI
PAGE
5 3. The cause of a phenomenon is the assem-
blage of its conditions 23T
4. The distinction of agent and patient illu-
sory 241
5. Case in which the effect consists in giving
a property to an object 243
6. The cause is not the invariable antecedent,
but the unconditional invariable anteced-
ent 244
7. Can a cause be simultaneous with its ef-
fect? 24T
8. Idea of a Permanent Cause, or original nat-
ural agent 248
9. Uniformities of co- existence between ef-
fects of different permanent causes, are
not laws 251
10. Theory of the Conservation of Force 251
11. Doctrine that volition is an efficient cause,
examined 255
CHAPTER VI. Of the Composition of Causes.
J 1. Two modes of the conjunct action of causes,
the mechanical and the chemical 260
2. The composition of causes the general
rule ; the other case exceptional 263
3. Are effects proportional to their causes?.. 270
CHAPTER VII. Of Observation and Experiment.
} 1. The first step of inductive inquiry is a men-
tal analysis of complex phenomena into
their elements 272
2. The next is an actual separation of those
elements 273
3. Advantages of experiment over observa-
tion 274
4. Advantages of observation over experi-
ment 276
CHAPTER VIII. Of the Four Methods of Experi-
mental Inquiry.
1. Method of Agreement 278
2. Method of Difference 280
3. Mutual relation of these two methods 281
4. Joint Method of Agreement and Difference. 283
5. Method of Residues 284
6. Method of Concomitant Variations 285
7. Limitations of this last method 289
CHAPTER IX. Miscellaneous Examples of the Four
Methods.
51. Liebig's theory of metallic poisons 292
2. Theory of induced electricity 294
3. Dr. Wells's theory of dew 296
4. Dr. Brown-St-qnard's theory of cadaveric
rigidity 301
5. Examples of the Method of Residues 305
6. Dr. Whewell's objections to the Four
Methods 307
CUAPTER X. Of Plurality of Causes ; and of the
Intermixture of Effects.
1. One effect may have several causes 311
2. which is the source of a characteristic
imperfection of the Method of Agree-
ment 311
3. Plurality of Causes, how ascertained 314
4. Concurrence of Causes which do not com-
pound their effects 315
5. Difficulties of the investigation, when
causes compound their effects. 317
6. Three modes of investigating the laws of
complex effects 320
7. The method of simple observation inap-
plicable 321
8. The purely experimental method inappli-
cable 322
CHAPTER XL Of the Deductive Method.
1. First stage; ascertainment of the laws of
the separate causes by direct induction. . 325
2. Second stage ; ratiocination from the sim-
ple laws of the complex cases 328
3. Third stage ; verification by specific expe-
rience 329
CHAPTER XII. Of the Explanation of Laics of Ma-
ture.
5 1. Explanation defined 332
2. First mode of explanation, by resolving the
law of a complex effect into the laws of
the concurrent causes and the fact of
their co-existence 332
3. Second mode ; by the detection of an in-
termediate link in the sequence 332
4. Laws are always resolved into laws more
general than themselves 333
5. Third mode ; the subsumption of less gen-
eral laws under a more general one 335
6. What the explanation of a law of nature
amounts to 337
CHAPTER XIII. Miscellaneous Examples of the Ex-
planation of Laws of Mature.
1. The general theories of the sciences 338
2. Examples from chemical speculations 339
3. Example from Dr. Brown - Sequard's re-
searches on the nervous system 340
4. Examples of following newly -discovered
laws into their complex manifestations.. 341
5. Examples of empirical generalizations, af-
terward confirmed and explained deduct-
ively 342
6. Example from mental science 343
7. Tendency of all the sciences to become de-
ductive 344
CHAPTER XIV. Of the Limits to the Explanation
of Laws of Xature; and of Hypotheses.
1. Can all the sequences in nature be resolva-
ble into one law? 345
2. Ultimate laws can not be less numerous
than the distinguishable feelings of our
nature 346
3. In what sense ultimate facts can be ex-
plained 343
4. The proper use of scientific hypotheses 349
5. Their indispensableness 353
6. The two degrees of legitimacy in hypoth-
eses 355
7. Some inquiries apparently hypothetical are
really inductive 359
CHAPTER XV. Of Progressive Effects ; and of the
Continued Action of Causes.
51. How a progressive effect results from the
simple continuance of the cause 361
2. and from the progressiveness of the
cause 3C3
3. Derivative laws generated from a single
ultimate law 365
Xll
CONTENTS.
CHAPTER XVI. Of Empirical Laws.
1. Definition of an empirical law 366
2. Derivative laws commonly depend on col-
locations 367
3. The collocation? of the permanent causes
are not reducible to any law 3C7
4. Hence empirical laws can not be relied on
beyond the limits of actual experience. . . 3CS
5. Generalizations which rest only on the
Method of Agreement can only be re-
ceived ns empirical laws 3G9
& Signs from which an observed uniformity
of sequence may be presumed to be re-
solvable 3C9
7. Two kinds of empirical laws 371
CHAPTER XVII. Of Chance, and ite Elimination.
{ 1. The proof of empirical laws depends on
the theory of chance 372
2. Chauce defined and characterized 373
3. The elimiu.ition of chance 37C
4. Discovery of residual phenomena by elim-
inating chance 377
5. The doctrine of chances 37S
CHAPTER XVIII. Of the Calculation of Chances.
{ 1. Foundation of the doctrine of chances, as
taught by mathematics 379
2. The doctrine tenable 380
3. On what foundation it really rests 381
4. Its ultimate dependence on causation 3S3
5. Theorem of the doctrine of chances which
relates to the cause of a given event 385
6. How applicable to the elimination of
chancf 386
CHAPTER XIX. Of the Extension af Derivative Laics
to Adjacent Cases.
5 1. Derivative laws, when not casual, arc al-
most always contingent on collocations.. 3SS
2. On what grounds they can be extended to
cases beyond the bounds of actual expe-
rience 389
3. Those cases must be adjacent cases 390
CHAPTER XX. Of Analogy.
{ 1. Various senses of the word analogy 393
2. Nature of analogical evidence 393
3. On what circumstances its value depends. . 39G
CHAPTER XXI. Of the Evidence of the Law of i'ni-
vemal Causation.
1. The law of causality does not rest on an
instinct 397
2. but on an induction by simple enumera-
tion 400
3. In what cases such induction is allowable. 402
4. The universal prevalence of the law of cau-
sality, on what grounds admissible 403
CHAPTER XXII. Of Uniformities of Co-existence
not dependent on Causation.
}1. Uniformities of co-existence which result
from laws of sequence 406
2. The properties of Kinds are uniformities
of co-existence 408
3. Some are derivative, others ultimate 409
4. No universal axiom of co-existence 410
B. The evidence of uniformities of co-exist-
ence, how measured 411
PAGE
{ G. When derivative, their evidence is that of
empirical laws 412
So also when ultimate 413 '
The evidence stronger in proportion as the
law is more general 413
Every distinct Kind must be examined 414
CHAPTER XXIII. Of Approximate Generalizations,
ami Probable Evidence.
{ 1. The inferences called probable, rest on ap-
proximate generalizations 416
2. Approximate generalizations less useful
in c cieuce than in life 416
3. In what cases they may be resorted to 41T
4. In what manner proved 418
5. With what precautions employed 420
6. The two modes of combining probabilities. 421
7. IIow approximate generalizations may be
converted into accurate generalizations
equivalent to them 423
CHAPTER XXIV. Of the Remaining Laics of JVa-
ture.
51. Propositions which assert mere existence. 425
2. Resemblance, considered as a subject of
science 426
3. The axioms and theorems of mathematics
comprise the principal laws of resem-
blance 427
4. and those of order in place, and rest oil
induction by simple enumeration 42S
5. The propositions of arithmetic affirm the
modes of formation of some given num-
ber 429
C. Those of algebra affirm the equivalence
of different modes of formation of num-
bers generally 432
7. The propositions of geometry are laws of
outward nature 433
8. Why geometry is almost entirely deduct-
ive 435
9. Function of mathematical truths in the
other sciences, and limits of that function. 436
CHAPTER XXV. Of the Grounds of Disbelief.
51. Improbability and impossibility 438
2. Examination of Ilume's doctrine of mir-
acles 438
3. The degrees of improbability correspond
to differences in the nature of the gener-
alization with which an assertion con-
flicts 441
4. A fact is not incredible because the charces
are against it 443
5. Are coincidences less credible than other
facts? 444
G. An opinion of Laplace examined 446
BOOK IV.
OF OPERATIONS SUBSIDIARY TO IN-
DUCTION.
CHAPTER I. Of Observation and Description.
51. Observation, how far a subject of logic 449
2. A great part of what seems observation is
really inference 450
CONTENTS.
Xlll
PAGE
3. The description of an observation affirms
more than is contained in the observa-
tion 452
4. namely, an agreement among phenom-
ena ; and the comparison of phenomena
to ascertain such agreements is a prelim-
inary to induction 453
CHAPTEB II. Of A bstraction, or the Formation of
Conceptions.
1. The comparison which is a preliminary to
induction implies general conceptions. . . 455
2. but these need not be pre-existent 456
3. A general conception, originally the result
of a comparison, becomes itself the type
of comparison 45S
4. What is meant by appropriate conceptions. 459
5. and by clear conceptions 461
6. Farther illustration of the subject 462
CHAPTER III. Of Xaming as Subsidiary to Induc-
tion.
1. The fundamental property of names as an
instrument of thought 464
2. Names are not indispensable to induc-
tion 465
3. In what manner subservient to it 465
4. General names not a mere contrivance to
economize the use of language 406
CHAPTER IV. Of the Requisites of a Philosophical
Language, and the Principles of Definition.
1. First requisite of philosophical language,
a steady and determinate meaning for ev-
ery general name 46T
2. Names in common use have often a loose
connotation 467
3. which the logician should fix, with as
little alteration as possible 469
4. Why definition is often a question not of
words but of things 470
5. How the logician should deal with the
transitive applications of words 472
6. Evil consequences of casting off any por-
tion of the customary connotation of
words 476
CHAPTER V. On the Natural History of the Varia-
tions in the Meaning of Terms.
1. How circumstances originally accidental
become incorporated into the meaning of
words 480
2. and sometimes become the whole mean-
ing 481
3. Tendency of words to become generalized. 482
4. and to become specialized 485
CUAPTEK VI. The Principles of Philosophical Lan-
guage farther connulercd.
SI. Second requisite of philosophical language,
a name for every important meaning 487
2. viz., first, an accurate descriptive ter-
minology 487
3. secondly, a name for each of the more
important results of scientific abstrac-
tion 490
4. thirdly, a nomenclature, or system of
the names of Kinds 491
6. Peculiar nature of the connotation of
names which belong to a nomenclature.. 493
TA.UA
5 6. In what cases language may, and may not,
be used mechanically 494
CHAPTER VII. Of Classification, as Subsidiary to
Induction.
1. Classification as here treated of, wherein
different from the classification implied
in naming 497
2. Theory of natural groups 493
3. Are natural groups given by type, or by
definition ? 501
4. Kinds are natural groups 502
5. How the names of Kinds should be con-
structed 505
CHAPTER VIII. Of Classification by Series.
1. Natural groups should be arranged in a
natural series 507
2. The arrangement should follow the de-
grees of the main phenomenon 503
3. which implies the assumption of a type
species 509
4. How the divisions of the series should be
determined 510
5. Zoology affords the completest type of sci-
entific classification 511
BOOK V.
ON FALLACIES.
CUAPTEK I. Of Fallacies in General.
j$l. Theory of fallacies a necessary part of
logic 512
2. Casual mistakes are not fallacies 513
3. The moral sources of erroneous opinion,
how related to the intellectual 513
CHAPTER II. Classification of Fallacies.
51. On what criteria a classification of fallacies
should be grounded 515
2. The five classes of fallacies 516
3. The reference of a fallacy to one or an-
other class is sometimes arbitrary 513
CHAPTER III. Fallacies of Simple Inspection, or
A J*riori Fallacies. ^ ....
1. Character of this class of fallacies 520
2. Natural prejudice of mistaking subjective
laws for objective, exemplified in popular
superstitions 521
3. that things which we think of together
must exist together, and that what is in-
conceivable must be false 523
4. of ascribing objective existence to ab-
abstractions 527
5. Fallacy of the Suflicieut Reason 528
6. Natural prejudice, that the differences in
nature correspond to the distinctions in
language 529
7. Prejudice, that a phenomenon can not have
more than one cause 532
8. that the conditions of a phenomenon
must resemble the phenomenon 533
CHAPTER IV. Fallacies of Observation.
51. Non-observation, and Mai-observation 638
XIV
CONTENTS.
PAOB
52. Non- observation of instances, and non-
observntion of circumstances ............ 638
3. Examples of the former ................... 639
4. and of the latter ........................ 542
6. Mai-observation characterized and exem-
plified ................................... 645
CHAPTER V. Fallacies of Generalization.
} 1. Character of the class ..................... 647
2. Certain kindf of generalization must al-
ways be groundless ...................... 547
3. Attempts to resolve phenomena radically
different into the same .................. 648
4. Fallacy of mistaking empirical for casual
laws ..................................... 519
5. Post hoc, eryo projttfr hoc; and the deduct-
ive fallacy corresponding to it ........... 551
6. Fallacy of False Analogies ............... 553
7. Function of metaphors in reasoning ....... 557
8. How fallacies of generalization grow out
of bad classification ...................... 658
CHAPTER VI. Fallacies of Ratiocination.
{1. Introductory Remarks ....................
2. Fallacies in the conversion and lequipol-
lency of propositions ...................
3. in the syllogistic process ...............
4. Fallacy of changing the premises ..........
CHAPTKR VII. Fallacies of Confusion.
5 1. Fallacy of Ambiguous Terms ..............
2. of Petitio Principii .....................
3. of Iguorulio Eleuchi ....................
BOOK VI.
ON THE LOGIC OF THE MORAL SCI-
ENCES.
CHAPTER I. Introductory Remarks.
51. The backward state of the Moral Sciences
can only be remedied by applying to them
the methods of Physical Science, duly ex-
tended and generalized 579
2. How far this can be attempted in the pres-
ent work 580
CHAPTER II. Of Liberty and Xeccssity.
Are human actions subject to the law of
causality? 5*1
The doctrine commonly called Philosoph-
ical Nere-sity, in what sense true 5S1
Inappropriateness and pernicious effect of
the term Necessity 5S3
A motive not always the anticipation of a
pleasure or a pain 585
CHAPTER III. That there is, or may be, a Science of
Unman Mature.
{ 1. There may be sciences which are not exact
sciences 5^6
2. To what scientific type the Science of Hu-
man Nature corresponds 5S3
CH \PTKK IV. Of the IAWS of Mind.
' 1. What if meant by Laws of Mind 689
2. Is there a Science of Psychology ? 590
PAGE
{3. The pr'rOpat inve?tigations of Psychology
characterized 691
4. Relation of mental facta to physical con-
ditions 694
tiiAPTKR V. Of Ethology, or th* Science of the For
motion of Character.
1. The Empirical Laws of Human Nature 59
,' 2. are merely approximate generalizations.
The universal laws are those of the for-
mation of character 697
3. The laws of the formation of character can
not be ascertained by observation and
experiment 699
4. but must be studied deductively 601
'5. The principles of Ethology are the axio-
mata media of mental science 603
; 6. Ethology characterized 604
CHAPTER VI. General Considerations on the Social
Science.
5 1. Are Social Phenomena a subject of Sci-
ence ? 606
2. Of what nature the Social Sciecce must
be 607
CHAPTER VII. Of the Chemical or Experimental
Method in the Social Science.
51. Characters of the mode of thinking which
deduces political doctrines from specific
experience 603
2. In the Social Science experiments are im-
possible 610
3. the Method of Difference inapplicable.. 610
4. and the Methods of Agreement, and of
Concomitant Variations, inconclusive 611
5. The Method of Residues also inconclusive,
and presupposes Deduction 612
CHAPTER VIII. Of the Geometrical, or Abstract
Method.
51. Characters of this mode of thinking 614
2. Examples of the Geometrical Method C15
3. The interest-philosophy of the Beuthum
school 616
CHAPTER IX. Of the Phyxical, or Concrete Deductive
Method.
5 1. The Direct and Inverse Deductive Meth-
ods 619
2. Difficulties of the Direct Deductive Meth-
od in the Social Science 621
3. To what extent the different branches of
sociological speculation can be studied
apart. Political Economy characterized. 623
4. Political Ethology, or the science of nation-
al character 626
5. The Empirical Laws of the Social Sci-
ence 623
6. The Verification of the Social Science 629
CHAPTER X. Of the Inverse Deductive, or Historical
Method.
S 1. Diftinction between the general Science of
Society, and special sociological inquiries. 630
2. What is meant by a State of Society ? fi.'U
3. The Progressiveness of Man and Society. . 631
4. The laws of the succession of estates of so-
ciety can only be ascertained by the In-
verse Deductive Method 633
CONTENTS.
XV
PAGE
} 5. Social Static?, or the science of the Co-ex-
istences of Social Phenomena 635
0. Social Dynamics, or the science of the Suc-
cessions of Social Phenomena. 639
7. Outlines of the Historical Method 640
8. Future prospects of Sociological Inquiry. . 642
CHAPTER XI. Additional Elucidations of the Sci-
ence of History.
5 1. The subjection of historical facts to uni-
form laws is verified by statistics 644
2. does not imply the insignificance of
moral causes 646
3. nor the ineflBcacy of the characters of
individuals and of the acts of govern-
ments 647
4. The historical importance of eminent men
PAGE
and of the policy of governments illus-
trated G50
CII.VPTEK XII. Of the Logic of Practice, or Art; in-
cluding Morality and Policy.
5 1. Morality not a Science, but an Art 652
2. Relation between rules of art and the the-
orems of the corresponding science 653
3. What is the proper function of rules of art? 654
4. Art can not be deductive C55
5. Every Art consists of truths of Science, ar-
ranged in the order suitable for some prac-
tical use 055
6. Teleology, or the Doctrine of Ends 656
7. Necessity of an ultimate standard, or first
principle of Teleology 657
8. Conclusion... ... 659
INTRODUCTION.
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 themselves of the same language as a means of delivering
different ideas. Ethics and jurisprudence are liable to the remark in com-
mon 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 favor.
This diversity is not so much an evil to be complained of, as an inevita-
ble 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 any thing, until there is agreement about the thing itself.
To define, is to select from among all the properties of a thing, those which
shall be understood to be designated and declared by its name ; and the
properties must be well known to us before we can be competent to deter-
mine which of them are fittest to be chosen for this purpose. According-
ly, in the case of so complex an aggregation of particulars as are compre-
hended in any thing which can be called a science, the definition we set
out with is seldom that which a more extensive knowledge of the subject
shows to be the most appropriate. Until we know the particulars them-
selves, we can not fix upon the most correct and compact mode of circum-
scribing them by a general description. It was not until after an extensive
and accurate acquaintance with the details of chemical phenomena, that it
was found possible to frame a rational definition of chemistry ; and the
definition of the science of life and organization is still a matter of dispute.
So long as the sciences are imperfect, the definitions must partake of their
imperfection ; and if the former are progressive, the latter ought to be so
too. As much, therefore, as is to be expected from a definition placed at
the 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 subject of this volume.
2. Logic has often been called the Art of Reasoning. A writer* who
has done more than any other person to restore this study to the rank from
which it had fallen ia the estimation of the cultivated class in our own
country, has adopted the above definition with an amendment ; he has de-
* Archbishop Whately.
2 '
18 INTRODUCTION.
fined Logic to bo 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 analy-
sis, for conducting the process correctly. 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 ev-
ery art does not bear the name of a science, it is only because several sci-
ences are often necessary to form the groundwork of a single art. So com-
plicated are the conditions which govern our practical agency, that to ena-
ble one thing to be done, it is often requisite to know the nature and prop-
erties of many things.
Logic, then, comprises the science of reasoning, as well as an art, found-
ed on that science. But the word Reasoning, again, like inost other scien-
tific terms in popular use, abounds in ambiguities. In one of its accepta-
tions, it means syllogi/ing ; 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 acceptation of the
term : the latter, and more extensive signification is that in which I mean
to use it. I do this by virtue of the right I claim for every author, to give
whatever provisional definition he pleases of his own subject. But suffi-
cient 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 language, the wider signification, I believe,
accords better than the more restricted one.
3. But reasoning, even in the widest sense of which the word is sus-
ceptible, 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
Argumentation, is derived from the Aristotelian, or, as they are commonly
termed, the scholastic, logicians. Yet even with them, in their systematic
treatises, Argumentation was the 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 con-
nection with reasoning, and as a preparation for the doctrine and rules of
the syllogism. Yet they were treated with greater minuteness, and dwelt
on at greater length, than was required for that purpose alone. More re-
cent writers on logic have generally understood the term as it was employ-
ed by the able author of the Port Royal Logic; viz., as equivalent to the
Art of Thinking. Nor is this acceptation confined to books, and scientific
inquiries. Even in ordinary conversation, the ideas connected with the
word Logic include at least precision of language, and accuracy of classifi-
cation : and we perhaps oftener hear persons speak of a logical arrange-
ment, or of expressions logically defined, than of conclusions logically de-
duced from premises. Again, a man is often called a great logician, or a
DEFINITION AND PROVINCE OF LOGIC. 19
man of powerful logic, not for the accuracy 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 'beino-
ample, is well under his command for argumentative use. Whether, ^here-
fore, 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 Argu-
mentation.
These various operations might be brought within the compass of the
science, and the additional advantage be obtained of a very simple defini-
tion, if, by an extension of the term, sanctioned by high authorities, we
were to define logic as the science which treats of the operations of the hu-
man understanding in the pursuit of truth. For to this ultimate end, nam-
ing, classification, definition, and all other operations over which logic has
ever claimed jurisdiction, are essentially subsidiary. They may all be re-
garded 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 re-
gard to this purpose, they have never been considered as within the prov-
ince of the logician. The sole object of Logic is the guidance of one's own
thoughts: the communication of those thoughts to others falls under the
consideration of Rhetoric, in the large sense in which that art was con-
ceived by 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 but one rational being in the universe, that being
might be a perfect logician ; and the science and art of logic would be the
same for that one person as for the whole human race.
4. But, if the definition which we formerly examined included too lit-
tle, that which is now suggested has the opposite fault of including too
much.
Truths are known to us in two ways : some are known directly, and of
themselves; some through the medium of other truths. The former are
the subject of Intuition, or Consciousness ;* 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 consciousness, 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 Avhich we know only by way of inference, are occur-
rences which took place while we were absent, the events recorded in his-
tory, or the theorems of mathematics. The two former we infer from the
testimony adduced, or from the traces of those past occurrences which still
* 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 Intui-
tion 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.
JO INTRODUCTION.
exist ; the latter, from the premises laid clown in books of geometry, under
the title of definitions and axioms. "Whatever we are capable of knowing
must belong to the one class or to 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 knowledge; with
their number or nature, the mode in which they are obtained, or the tests
by which they may be distinguished ; logic, in a direct way at least, has,
iii the sense in which I conceive the science, nothing to do. These ques-
tions are partly not a subject of science at all, partly that of a very differ-
ent science.
Whatever is known to us by consciousness is known beyond possibility
of question. What one sees or feels, whether bodily or mentally, one can
not but be sure that one sees or feels. No science is required for the pur-
pose 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.
Hut 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 intuitively. It has long been agreed by thinkers of
the most opposite schools, that this mistake is actually made in so familiar
an instance as that of the eyesight. There is nothing of which we appear
to ourselves to be more directly conscious than the distance of an object
from us. Yet it has long been ascertained, that what is perceived by the
eye, is at most nothing more than a variously colored surface; that when
we fancy we see distance, all we really see is certain variations of apparent
size, and degrees of faintness of color; 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 color of the object as they appear at the time, and the size and color
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 per-
ception of distance by the eye, which seems so like intuition, is thus, in re-
ality, an inference grounded on experience ; an inference, too, which we
learn to make ; and which we make with more and more correctness 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 perceptions of color.*
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 dis-
tinct department of science, to which the name metaphysics more particu-
larly belongs: that portion of mental philosophy which attempts to deter-
mine what part of the furniture of the mind belongs to it originally, and
* This important theory 1ms of late been called in question by a writer of deserved reputa-
tion, Mr. Samuel Hailey ; but I do not conceive that the grounds on which it has been ad-
mitted as an established doctrine for a century past, have been at all shaken by that gentle-
man's objections. I have elsewhere said what appeared to me necessary in reply to his argu-
ments. (Westminster Review for October. Ib42 ; reprinted in " Dissertations and Discus-
sions," vol. ii.)
DEFINITION AND PROVINCE OF LOGIC. 21
what part is constructed out of materials furnished to it from without. To
this science appertain the great and much debated questions of the exist-
ence 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 uni-
versally allowed that the existence of matter or of spirit, of space or of
time, is in its nature unsusceptible of being proved ; and that if any tiling
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 understanding in the pursuit
of truth ; but with which, as phenomena of the mind, or with the possibili-
ty which may or may not exist of analyzing any of them into simpler phe-
nomena, the logician as such has no concern. To this science must also be
referred the following, and all analogous questions : To what extent our in-
tellectual 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 a 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 knowl-
edge which consists of inferences from truths previously known ; whether
those antecedent data be general propositions, or particular obsei'vations
and perceptions. Logic is not the science of Belief, but the science of
Proof, or Evidence. In so far as belief professes to be founded on proof,
the office of logic is to supply a test for ascertaining whether or not the be-
lief is well grounded. With the claims which any proposition has to be-
lief 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 au-
thority of logic. To draw inferences has been said to be the great business
of life. Every one has daily, hourly, and momentary need of ascertaining
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 accordingly.
They all have to ascertain certain facts, in order that they may afterward
apply certain rules, either devised by themselves or prescribed for their
guidance by others ; and as they do this well or ill, so they discharge well
or ill the duties of their several callings. It is the only occupation in which
the mind never ceases to be engaged ; and is the subject, not of logic, but
of knowledge in general.
Logic, however, is not the same thing with knowledge, though the field
of logic is co-extensive with the field of knowledge. Logic is the com-
mon judge and arbiter of all particular investigations. It does not under-
take to find evidence, but to determine whether it lias 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
22 INTRODUCTION.
accompany .1 violent death. This he must learn from his own experience
and observation, or from that of others, his predecessors in his peculiar
pursuit. Kut logic sits in judgment on the sufficiency of that observation
and experience to justify his rules, and on the sufficiency of his rules to
justify his conduct. It does not give him proofs, but teaches him what
makes them proofs, and how he is to judge of them. It does not teach
that any particular fact proves any other, but points out to what conditions
all facts must conform, in order that they may prove other facts. To de-
cide whether any given fact fulfills these conditions, or whether facts can
be found which fulfill them in a given case, belongs exclusively to the par-
ticular art or science, or to our knowledge of the particular subject.
It is in this sense that logic is, what it was so expressively called by the
schoolmen and by Bacon, <(rs urtium; 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 every thing
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 con-
form 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 the ob-
servance of the laws which it is the province of logic to investigate. If
the conclusions are just, and the knowledge real, those laws, whether known
or not, have been observed.
0. We need not, therefore, seek any further for a solution of the ques-
tion, 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 discussing 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 em-
pirically 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 with-
out 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 precur-
sor, or as its accompaniment and necessary condition, a corresponding im-
provement in the notions and principles of logic received among the most
advanced thinkers. And if several of the more difficult sciences are still
DEFINITION AND PROVINCE OF LOGIC. 23
in so defective a state ; if not only so little is proved, but disputation has
not terminated even about the little which seemed to be so; the reason
perhaps is, that men's logical notions have not yet acquired the decree of
extension, or of accuracy, requisite for the estimation of the evidence prop-
er to those particular departments of knowledge.
1. Logic, then, is the science of the operations of the understanding
which are subservient to the estimation of evidence: both the process it-
self of advancing from known truths to unknown, and all other intellectual
operations in so far as auxiliary to this. It includes, therefore, the opera-
tion of Naming ; for language is an instrument of thought, as well as a
means of communicating our thoughts. It includes, also, Definition, and
Classification. For, the use of these operations (putting all other minds
than one's own out of consideration) is to serve not only for keeping our
evidences and the conclusions from them permanent and readily accessible
in the memory, but for so marshaling 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, therefore, 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
connection 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 anal-
ysis, and pari passu with it, to bring together or frame a set of rules or
canons for testing the sufficiency of any given evidence to prove any given
proposition.
With respect to the first part of this undertaking, I do not attempt to
decompose the mental operations in question into their ultimate elements.
It is enough if the analysis as far as it goes is correct, and if it goes far
enough for the practical purposes of logic considered as an art. The sep-
aration of a complicated phenomenon into its component parts is not like
a connected and interdependent chain of proof. If one link of an argu-
ment breaks, the whole drops to the ground; but one step toward an anal-
ysis holds good and has an independent 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 discovered that
all which we now call simple substances are really compounds. All other
things are at any rate compounded of those elements: whether the ele-
ments 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 analyze the process of inference, and the
processes subordinate to inference, so far only as may be requisite for as-
certaining the difference between a correct and an incorrect performance
of those processes. The reason for thus limiting our design, is evident.
It has been said by objectors to logic, that we do not learn to use our
muscles by studying their anatomy. The fact is not quite fairly stated;
for if the action of any of our muscles were vitiated by local weakness, or
other physical defect, a knowledge of their anatomy might be very neccs-
24 INTRODUCTION.
sary for effecting a cave. But we should be justly liable to the criticism
involved in this objection, were we, in a treatise on logic, to carry the anal-
ysis 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, analyze 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 analyze the mental processes
with which Logic is concerned. Logic has no interest in carrying the anal-
ysis beyond the point at which it becomes apparent whether the operations
have iii any individual case been rightly or wrongly performed : in the
same manner as the science of music teaches us to discriminate 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, ami 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 neces-
sary connection with any particular views respecting 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 metaphysicians ; but the field on
which their principal battles have been fought, lies beyond the boundaries
of our science.
It can not, 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 favorable to the adoption of some one opinion, on these
controverted subjects, rather than another. For metaphysics, in endeavor-
ing to solve its own peculiar problem, must employ means, the validity of
which falls under the cognizance of logic. It proceeds, no doubt, as far as
possible, merely by a closer and more attentive interrogation of our con-
sciousness, 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 evi-
dence. Now, the moment this science begins to draw inferences from evi-
dence, logic becomes the sovereign judge whether its inferences arc well
grounded, or what other inferences would be so.
This, however, constitutes no nearer or other relation between logic and
metaphysics, than that which exists between logic and every other science.
And I can conscientiously affirm that no one proposition laid down in this
work has been adopted for the sake of establishing, or with any reference
to its fitness for being employed in establishing, preconceived opinions in
any department of knowledge or of inquiry on which the speculative world
is still undecided.*
* The view taken in the text, of the definition ami purpose of Logic, stands in marked op-
position to that of the school of philosophy which, in this country, is represented hy the writ-
DEFINITION AND PROVINCE OF LOGIC. 25
ings 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 pur-
pose of excluding, as irrelevant 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 Consistency. 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 18G5, and entitled "An Examina-
tion of Sir William Hamilton's Philosophy, and of the Principal Philosophical Questions dis-
cussed in his Writings." For the purposes of the present Treatise, I am content that the jus-
tification 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 PROPOSITIONS.
"La scolastiquc, qui proiluisit dans la logique, comme dans la morale, et dans une partie
de la inctaphysiqiu* une snbtilite, une precision d'ide'es, dont 1'habitude inconnne aux anciens,
n contribue' plus qu'on ne croit au progres de la bonne philosophic.'' CONUORCKT, Vie de
Turqot.
"To tlie schoolmen tlie vulgar languages are principally indebted for what precision and
analytic subtlety they possess." SIK W. HAMILTON*, Discussions in Philosophy.
CHAPTER I.
OF THE NECESSITY OF COMMENCING WITH AX ANALYSIS OF LANGUAGE.
1. IT is so much tlie established practice of writei'S on logic to com-
mence their treatises by a few general observations (in most cases, it is
true, rather meagre) on Terms and their varieties, that it will, perhaps,
scarcely be required from me, in merely 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 Think-
ing : Language is evidently, and by the admission of all philosophers, one
of the principal instruments 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 at-
tempt 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 Reasoning, or Inference, the principal subject of logic, is an opera-
tion which usually takes place by means of words, and in complicated cases
can take place in no other way; those who have not a thorough insight
into the signification and purposes of words, will be under chances, amount-
ing almost to certainty, of reasoning or inferring incorrectly. And logi-
cians have generally felt that unless, in the very first stage, they removed
this source of error; unless they taught their pupil to put away the glasses
which distort the object, and to use those which are adapted to his pur-
pose in such a manner as to assist, not perplex, his vision; he would not be
in a condition to practice 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, lias at
all times been deemed a necessary preliminary to the study of logic.
NECESSITY OF AN ANALYSIS OF NAMES. 27
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 considera-
tion : because without it he can not examine into the import of Proposi-
tions. Now this is a subject which stands on the very threshold of the
science of logic.
The object of logic, as defined in the Introductory Chapter, is to ascer-
tain how we come by that portion of our knowledge (much the greatest
portion) which is not intuitive : and by what criterion we can, in matters
not self-evident, distinguish between 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 in-
quire what are those which offer themselves ; what questions are conceiva-
ble; 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. All 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. To know
the import of all possible propositions would be to know all questions
which can be raised, all matters which are susceptible of being either be-
lieved or disbelieved. How many kinds of inquiries can be propound-
ed; 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 Be-
lief and of all Inquiry express themselves in propositions, a sufficient scru-'
tiny of Propositions and of their varieties will apprise us what questions
mankind have actually asked of themselves, and what, in the nature of an-
swers 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, according to the common simple defi-
nition, which is sufficient for our purpose is, discourse, in which something
is affirmed or denied of something. Thus, in the proposition, Gold is yel-
low, the quality yellow is affirmed of the substance gold. In the proposi-
tion, 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
the word is, which serves as the connecting mark between the subject and
28 NAMES AND PROPOSITIONS.
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 here-
after, every proposition, then, consists of at least two names brings to-
gether two names, in a particular manner. This is already a first step to-
ward what we are in quest of. It appears from this, that for an act of be-
lief, one object is not sufficient ; the simplest act of belief supposes, and has
something to do with,f0 objects two names, to say the least; and (since
the names must be names of something) two namable 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 bring-
ing (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 of belief
tiro objects are in some manner taken cognizance of; that there can be no
belief claimed, or question propounded, which does not embrace two dis-
tinct (either material or intellectual) subjects of thought; each of them
capable, or not, of being conceived by itself, but incapable of being believed
by itself.
I may say, for instance, " the sun." The word has a meaning, and sug-
gests that meaning to the mind of any one who is listening to me. But
suppose I ask him, Whether it is true: whether he believes it? He can
give no answer. There is as yet nothing to believe, or to disbelieve. Now,
however, let me make, of all possible assertions respecting the sun, the one
which involves the least of reference to any object besides itself; let me
say, " the sun exists." Here, at once, is something which a person can say
he believes. . But here, instead of only one, we find two distinct objects of
conception : the sun is one object ; existence is another. Let it not be said
'that this second conception, existence, is involved in the first; for the sun
may be conceived as no longer existing. "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 square" does not include the meaning of "a round square exists,"
for it does not and can not 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 without a preliminary survey of language.
If we attempt to proceed further in the same path, that is, to analy/e any
further the import of Propositions ; we find forced upon us, as a subject of
previous consideration, the import of Names. For every proposition con-
sists 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
NAMES. 29
themselves, that we make the affirmation or denial. Here, therefore, we
find a new reason why the signification of names, and the relation general-
ly between names and the things signified by them, must occupy the pre-
liminary 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 man-
kind 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 fol-
low) is in reality an exhortation to discard the whole fruits of the labors 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 per-
sonal knowledge of Things amount to, after subtracting all which he has
acquired by means of the words of other people ? Even after he has learn-
ed as much as people usually do learn from others, will the notions of
things contained in his individual mind afford as sufficient a basis for a
catalogue raisonne as the notions which are in the minds of all mankind ?
In any enumeration and classification of Things, which does not set out
from their names, no varieties of things will of course be comprehended
but those recognized by the particular inquirer ; and it Avill still remain to
be established, by a subsequent examination of names, that the enumera-
tion has omitted nothing which ought to have been included. But if we
o o
begin with names, and use them as our clue to the things, we bring at once
before us all the distinctions which have been recognized, not by a single
inquirer, but by all inquirers taken together. It doubtless may, and I be-
lieve it will, be found, that mankind have multiplied the varieties unneces-
sarily, and have imagined distinctions among things, where there were only
distinctions in the manner of naming them. But we are not entitled to as-
sume this in the commencement. We must begin by recognizing the dis-
tinctions made by ordinary language. If some of these appear, on a close
examination, not to be fundamental, the enumeration of the different kinds
of realities may be abridged accordingly. But to impose upon the facts in
the first instance the yoke of a theory, while the grounds of the theory are
reserved for discussion in a subsequent stage, is not a course which a logi-
cian 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 defini-
tion of a name, as a word (or set of words) serving the double purpose of
a mark to recall to ourselves the likeness of a former thought, and a sign
* Computation or Loqic, 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.
30 NAMES AND PROPOSITIONS.
to make it known to others, appears unexceptionable. Names, indeed, do
much more than this ; but whatever else they do, grows out of, and is the
result of this: as will appear in its proper place.
Are names more properly said to be the names of things, or of our ideas
of things? The first is the expression in common use; the last is that of
some metaphysicians, who conceived that in adopting it they were intro-
ducing a highly important distinction. The eminent thinker, just quoted,
seems to countenance the latter opinion. "But seeing," he continues,
" names ordered in speech (as is defined) are signs of our conceptions, it
is manifest they are not signs of the things themselves ; for that the sound
of this word stone should be the sign of a stone, can not 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 not the thing itself,
is recalled by the name, or imparted to the hearer, this of course can not
be denied. Nevertheless, there seems good reason for adhering to the
common usage, and calling (as indeed Ilobbes himself does in other places)
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 inform 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 prop-
er to consider a word as the name of that which we intend to be under-
stood 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 ; th<; inflected
cases of nouns substantive, as me, him, John's; and even adjectives, as
large, heavy. These words do not express things of which any thing can
be affirmed or denied. We can not 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 col-
lections of written characters. This employment of a word to denote the
mere letters and syllables of which it is composed, was termed by the
schoolmen the suppositio mater ialis of the word. In any other sense we
can not introduce one of these words into the subject of a proposition,
unless in combination with other words ; as, A heavy body fell, A truly
important fact was asserted, A member of parliament was in the room.
NAMES. 31
An adjective, however, is capable of standing by itself as the predicate
of a proposition; as when we say, Snow is white; and occasionally oven
as the subject, for we may say, White is an agreeable color. The adjec-
tive 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 color, instead of'
A white color, or, The color white, is agreeable. The Greeks and Romans
were allowed, by the rules of their language, to employ this ellipsis uni-
versally in the subject as well as in the predicate of a proposition. In
English this can not, generally speaking, be done. We may say, The earth
is round ; but we can not say, Round is easily moved ; we must say, A
round object. This distinction, however, is rather grammatical than "log-
ical. Since there is no difference of meaning between round, and a round
object, it is only custom which prescribes that on any given occasion one
shall be used, and not the other. We shall, therefore, without scruple,
speak of adjectives as names, whether in their own right, or as representa-
tive of the more circuitous forms of expression above exemplified. The
other classes of subsidiary words have no title whatever to be considered
as names. An adverb, or an accusative case, can not under any circum-
stances (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 as names, but only as parts
of names, were called by some of the schoolmen Syncategorematic terms :
from avv, with, and (,-ar?jyopew, 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 Cate-
gorematic term. A combination of one or more Categorematic, 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 multiplica-
tion of technical expressions. A mixed term is, in the only useful sense of
the word, Categorematic. It belongs to the class of what have been called
many-worded names.
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 predication 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 : one, that John Nokes
died yesterday ; the other, that the mayor of the town died yesterday.
It being needless to illustrate at any greater length the subject of many-
worded names, we proceed to the distinctions which have been established
32 NAMES AND PROPOSITIONS.
among names, not according to the words they are composed of, but ac-
cording to their signification.
o o
3. All names are names of something, real or imaginary ; but all things
have not names appropriated to them 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 nam-
ing 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 mo-
ment, 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 lim-
iting 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 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 in-
dividual or singular names, is fundamental ; and may be considered 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 tTohn 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 upon them to indicate any qualities, or any
thing which belongs to them in common ; and can not be said to be affirm-
ed 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 can not 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 un-
derstood, may justly be regarded as an individual name.
It is not unusual, by way of explaining what is meant by a general name,
to say that it is the name of a class. But this, though a convenient mode
of expression for some purposes, is objectionable as a definition, since it
explains the clearer of two things by the more obscure. It would be more
logical to reverse the proposition, and turn it into a definition of the word
class: "A class is the indefinite multitude of individuals denoted by a gen-
eral 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
NAMES.
33
collective name can not 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 can
not be predicated of them severally. We may say, Jones is a soldier, and
Thompson is a soldier, and Smith is a soldier, but we can not 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.
4. The second general division of names is into concrete and abstract.
A concrete name is a name which stands for a thing; an abstract name is
a name which stands for an 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 attribute of those
things. Man is a name of many things; humanity is a name of an attri-
bute 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 unrivaled in the construction of technical language, and
whose definitions, in logic at least, though they never went more than a lit-
tle way into the subject, have seldom, I think, been altered but to be spoil-
ed. 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, in-
stead of confining it to the names of attributes. The metaphysicians of the
Condillac school whose admiration of Locke, passing over the profound-
est 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 meaning of a
word is rarely to be met with ; for the expression general name, the exact
equivalent of which exists in all languages I am acquainted with, was al-
ready available for the purpose to which abstract has been misappropri-
ated, while the misappropriation leaves that important class of words, the
names of attributes, without any compact distinctive appellation. The old
acceptation, however, has not gone so completely out of use as to deprive
those who still adhere to it of all chance of being understood. By abstract,
then, I shall always, in Logic proper, mean the opposite of concrete; by an
abstract name, the name of an attribute ; by a concrete name, the name of
an object.
Do abstract names belong to the class of general, or to that of singular
names? Some of them are certainly general. I mean those which are
names not of one single and definite attribute, but of a class of attributes.
Such is the word color, which is a name common to whiteness, redness,
etc. Such is even the word whiteness, in respect of the different shades of
3
34 NAMES AND PROPOSITIONS.
whiteness to which it is applied in common: the word magnitude, in re-
spect 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 attri-
butes. But when only one attribute, neither variable in degree nor in
kind, is designated by" the name; as visibleness; tangibleness ; equality;
squareness; milk-whiteness; then the name can hardly be considered gen-
eral; for though it denotes an attribute of many different objects, the at-
tribute itself is always conceived as one, not many.* To avoid needless lo-
gomachies, 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 exam-
ple, is as much the name of the color as whiteness is. But (as before re-
marked) 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 color. We mean that they are things having the color. The reverse
is the case with the word whiteness ; what we affirm to be whiteness is not
snow, but the color of snow. Whiteness, therefore, is the. name of the col-
or exclusively: white is a name of all things whatever having the color; 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, the things of which it can be predicated. We shall presently see
that all names which can be said to have any signification, all names by ap-
plying which to an individual we give any information respecting that in-
dividual, 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 connotfitice and non-connotutice, the latter sometimes, but improperly,
called absolute. This is one of the most important distinctions which we
shall have occasion 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 attri-
bute only. A connotative term is one which denotes a subject, and implies
an attribute. By a subject is here meant any thing which possesses attri-
butes. Thus John, or London, or England, are names which signify a sub-
ject only. Whiteness, length, virtue, signify an attribute only. None of
these names, therefore, are connotative. But white, long, virtuous, are con-
notative. The word white, denotes all white things, as snow, paper, the
foam of the sea, etc., and implies, or in the language of the schoolmen, con-
notes,} the attribute whiteness. The word white is not predicated of the
attribute, but of the subjects, snow, etc. ; but when we predicate it of
them, we convey the meaning that the attribute whiteness belongs to them.
The same may be said of the other words above cited. Virtuous, for ex-
* Vide infra, note at the end of 3, book ii., chap. ii.
t Notare, to mark ; connotare, to mark along with ; to mark one thing with or in addition
to another.
NAMES.
35
ample, is the name of a class, which includes Socrates, Howard, the Man of
Ross, and an undefinable number of other 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 con-
sidered.
All concrete general names are connotative. The word man, for exam-
ple, denotes Peter, Jane, John, and an indefinite number of other individu-
als, 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 exter-
nal form, which for distinction we call the human. Every existing thing,
which possessed all these attributes, would be called a man ; and any thing
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 Houyhnhnms would not be so called.
Or if such newly-discovered beings possessed the form of man without any
vestige of reason, it is probable that some other name than that of man
would be found for them. How it happens that there can be any doubt
about the matter, will appear hereafter. The word man, therefore, signi-
fies 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, thei'efore, is said to signify the sub-
jects directly, the attributes indirectly ; it denotes the subjects, and im-
plies, 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, because
the subject which 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
attributes 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 connotative. Even
abstract names, though the names only of attributes, may in some instances
be justly considered as connotative; for attributes themselves may have
attributes ascribed to them ; and a word which denotes attributes may con-
note 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
* 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 substi-
tute for "Connotative" (p. 22, 9th edit.)- The expression is, in itself, appropriate; but as
it has not the advantage of being connected with any verb, of so markedly distinctive a char-
acter as " to connote," it is not, I think, fitted to supply the place of the word Connotative in
scientific use.
36 NAMES AND PROPOSITIONS.
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 thin*;, but that the property or
peculiarity of the horse, from which it derives that name, the quality of be-
ing a slow mover, is an undesirable peculiarity.
In regard to those concrete names which are not general but individual,
a distinction must be made.
Proper names are not connotative : they denote the individuals who are
called by them ; but they do not indicate or imply any attributes as belong-
ing to those individuals. When we name a child by the name Paul, or a
dog by the name Caisar, 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 those names rather than
any others ; and this is true ; but the name, once given, is independent
of the reason. A man may have been named John, because that was the
name of his father; a town may have been named Dartmouth, because it is
situated at the mouth of the Dart. But it is no part of the signification of
the word John, that the father of the person so called bore the same name ;
nor even of the word Dartmouth, to be situated at the mouth of the Dart.
If sand should choke up the mouth of the river, or an earthquake change
its course, and remove it to a distance from the town, the name of the
town would not necessarily be changed. That fact, therefore, can form no
part of the signification of the word ; for otherwise, when the fact confess-
edly ceased to be true, no one would any longer think of applying the
name. Proper names are attached to the objects themselves, and are not
dependent on the continuance of any attribute of the object.
But there is another kind of names, which, although they are individual
names that is, predicable only of one object are really connotative. For,
though we may give to an individual a name utterly unmeaning, which we
call a proper name a word which answers the purpose of showing what
thing it is we are talking about, but not of telling any thing about it; yet
a name peculiar to an individual is not necessarily of this description. It
may be significant of some attribute, or some union of attributes, which,
being possessed by no object but one, determines the name exclusively to
that individual. "The sun" is a name of this description; "God," when
used by a monotheist, is another. These, however, are scarcely examples
of what we are now attempting to illustrate, being, in strictness of lan-
guage, general, not individual names : for, however they may be in, fact
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 man-
kind have believed, and still believe, that there are many gods. But it is
easy to produce words which are real instances of connotative individual
names. It may be part of the meaning of the connotative name itself, that
there can exist but one individual possessing the attribute which it con-
notes : as, for instance, " the only son of John Stiles ;" " the first emperor
of Rome." Or the attribute connoted may be a connection with some de-
terminate event, and the connection may be of such a kind as only one in-
dividual 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 Qua-
tre," of the second. For, though it is conceivable that more persons than
NAMES. 37
one might have participated in the authorship of the Iliad, or in the mur-
der 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 oth-
er cases by the context : thus, " Caesar's army " is an individual name, if it
appears from the context that the army meant is that which Caesar com-
manded 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 affirm-
ed 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 predi-
cated of one object, consistently with the meaning of the general term.
This is exemplified 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 possessed 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 afterward 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 meaning of the name, without any extrinsic proof, it is strictly an indi-
vidual name.
From the preceding observations it will easily be collected, that when-
ever the names given to objects convey any information that is, whenever
they have properly any meaning the meaning resides not in what they de-
note, but in what they connote. The only names of objects which connote
nothing are proper names ; and these have, strictly speaking, no significa-
tion.*
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 any thing 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
distinction. I say to myself, All these houses are so nearly alike that if I
lose sight of them I shall not again be able to distinguish that which I am
now 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 here-
after 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. Mor-
giana 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.
* 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 re-
minded to how great a length perverse misquotation (for, strange as it appears, I do not be-
lieve 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 invert-
ed commas, of maintaining something more than commonly absurd, not to give implicit cre-
dence to the assertion without verifying the reference.
38 NAMES AND PROPOSITIONS.
When we impose .1 proper name, we perform an operation in some de-
gree analogous to what the robber intended in chalking 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 ena-
bles us to distinguish it when it is spoken of, either in the records of our
own experience, 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 in-
dividual thing with which we were previously acquainted.
When we predicate of any thing its proper name; when we say, point-
ing to a man, this is Brown or .Smith, or pointing to a city, that it is York,
we do not, merely by so doing, convey to the reader any information about
them, except that those are their names. By enabling him to identify the
individuals, we may connect them with information previously possessed
by him ; by saying, This is York, we may tell him that it contains the Min-
ster. But this is in virtue of what he has previously heard concerning
York; not by any thing implied in the name. It is otherwise when ob-
jects are spoken of by connotative names. When we say, The town is
built of marble, we give the hearer what may be entirely new information,
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 recognized 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 individual which it
is predicated of, so (as well from the importance of adhering to analogy, as
for the other reasons formerly assigned) 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 Sophronis-
cus : I call him by another name, The father of Socrates. Both these are
names of the same individual, but their meaning is altogether different;
they are applied to that individual for two different purposes: the one,
merely to distinguish him from other persons who are spoken of; the other
to indicate a fact relating to him, the fact that Socrates was his son. I
further apply to him these other expressions: a man, a (rreek, 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 Sophroniscus for a different reason, and by each whoever under-
stands its meaning is apprised of a distinct fact or number of facts con-
cerning him; but those who knew nothing about the names except that
they were applicable to Sophroniscus, would be altogether 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
NAMES.
39
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 difference 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 a newly-discovered race to make
us refuse them the name of man. Rationality, also, being a quality which
admits of degrees, it has never been settled what is the lowest degree of
that quality which would entitle any creature to be considered a human
being. In all such cases, the meaning of the general name is so far un-
settled 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 lan-
guage are better promoted by it than by complete precision ; in order that,
in natural history for instance, individuals 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 precautions. 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 pre-
cise 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 ac-
quire, and inevitably so, our first knowledge of our vernacular language.
A child learns the meaning of the words man, or ichite, by hearing them ""
applied to a variety of individual objects, and finding out, by a process of
generalization 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 assistance 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 pos-
session of which in common by them all, their general resemblance depends.
When this is the case, people use the name without any recognized con-
notation, that is, without any precise meaning ; they talk, and consequently
think, vaguely, and remain contented to attach only the same degree of
significance to their own words, which a child three years old attaches to
the words brother and sister. The child at least is seldom puzzled by the
starting up of new individuals, on whom he is ignorant whether or not to
confer the title ; because there is usually an authority close at hand com-
petent 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 proprio
motu. They, accordingly, do this on no other principle than that of super-
40 NAMES AND PROPOSITIONS.
ficinl 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 disappear, 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 distinctions, and,
consequently, to express them in a manner progressively more and more
imperfect.
To what a degree this loose mode of classing and denominating objects
has rendered the vocabulary of mental and moral philosophy unfit for the
purposes of accurate thinking, is best known to whoever has most medi-
tated on the present condition of those branches of knowledge. Since,
however, the introduction of a new technical language as the vehicle of
speculations on subjects belonging to the domain of daily discussion, is ex-
tremely dith'cult to effect, and would not be free from inconvenience even
if effected, the problem for the philosopher, 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 attri-
butes, 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 con-
notation to a name, with the least possible change in the objects which the
name is habitually employed to denote; with the least possible disarrange-
ment, 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 com-
monly received as true.
This desirable purpose, of giving a fixed connotation where it is want-
ing, is the end aimed at whenever any one attempts to give a definition of
a general name already in use ; every definition of a connotative name be-
ing an attempt either merely to declare, or to declare and analyze, the con-
notation of the name. And the fact, that no questions which have arisen
in the moral sciences have been subjects of keener controversy than the
* "Take the familiar term Stone. It is applied to mineral and rocky materials, to the
kernels of fruit, to the accumulations in the gall-Madder and in the kidney ; while it is re-
fused to polished minerals (called gems), to rocks that have the cleavage suited for roofing
(slates), and to baked clay (bricks). It occurs in the designation of the magnetic oxide of
iron (loadstone), and not in speaking of other metallic ores. Such a term is wholly unfit for
accurate reasoning, unless hedged round on every occasion by other phrases; as building
stone, precious stone, gall-stone, etc. Moreover, the methods of definition are battled for
want of sufficient community to ground upon. There is no quality uniformly present in the
cases where it is applied, and uniformly absent where it is not applied; hence the dcfiner
would have to employ largely the license of striking off existing applications, and taking in
new ones." UAIN, Logic, ii., 172.
NAMES.
41
definitions of almost all the leading expressions, is a proof how reat an
extent the evil to which we have adverted has attained.
Names with indeterminate connotation are not to be confounded with
names which have more than one connotation, that is to say, ambiguous
words. A word may have several meanings, but all of them fixed and rec-
ognized 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 ex-
isting names, in comparison with the demand for them, may often render
it advisable and even necessary to retain a name in this multiplicity of ac-
ceptations, distinguishing these so clearly as to prevent their being con-
founded with one another. Such a word may be considered as two or
more names, accidentally written and spoken alike.*
6. The fourth principal division of names, is into positive and nega-
tive. Positive, as man, tree, good; negative, as not-man, not-tree, not-good.
To every positive concrete name, a corresponding negative one might be
framed. After giving a name to any one thing, or to any plurality of
things, we might create a second name which should be a name of all things
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 con-
notative, the corresponding negative name is connotative likewise; but in a
* 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 the Human Mind, employs it in a signification dif-
ferent from that in which it is here used. He uses the word in a sense co-extensive witli its
etymology, applying 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 general 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 attribute. And he describes abstract names as being properly concrete names
with their connotation dropped; whereas, in my view, it is the t/enotation which would be
said to be dropped, what was previously connoted becoming the whole signification.
In adopting a phraseology at variance with that which so high an authority, and one which
I am less likely than any other person to undervalue, has deliberately sanctioned. I have been
influenced by the urgent necessity for a term exclusively appropriated to express the manner
in which a concrete general name serves to mark the attributes which are involved in its signi-
fication. 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 philosophy of language
without such a word. It is hardly an exaggeration to say, that some of the most prevalent of
the errors with which logic has been 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 admirable 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 di-
verted from that purpose by being taken to fulfill 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, etc. By
employing 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.
42 NAMES AND PROPOSITIONS.
peculiar way, connoting not the presence but the absence of an attribute.
Thus, not-white denotes all things whatever except white things; and con-
notes the attribute of not possessing 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 oth
ers are really positive though their form is negative. The word inconven-
ient, for example, does not express the mere absence of convenience; it ex-
presses a positive attribute that of being the cause of discomfort or an-
noyance. 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 posi-
tive. 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 dis})osed to work- and sober, either by not
drunk or by not drunken.
There is a class of names called privative. A privative name is equiva-
lent in its signification to a positive and a negative name taken together;
being the name of something which has once had a particular attribute, or
for some other reason might have been expected to have it, but which has
it not. Such is the word blind, which is not equivalent to not seeing, or to
not capable of seeing, for it would not, except by a poetical or rhetorical
figure, be applied to stocks and stones. A thing is not usually said to be
blind, unless the class to which it is most familiarly referred, or to which
it is referred on the particular occasion, be chiefiy 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, there-
fore, connote two things ; the absence of certain attributes, and the pres-
ence 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 metaphysics, not to be willingly spared when
its services can be dispensed with. It resembles the word civil in the lan-
guage of jurisprudence, which stands for the opposite of criminal, the op-
posite of ecclesiastical, the opposite of military, the opposite of political
in short, the opposite of any positive word which wants a negative.
Relative names are such as father, son; ruler, subject; like; equal; un-
like; unequal; longer, shorter ; cause, effect. Their characteristic property
is, that they are always given in pairs. Every relative name which is pred-
icated 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
* Professor Bain (Logic, i., >(!) thinks that negative names are not names of all things
whatever except those denoted by the correlative positive name, but only for all things of some
particular class: not-white, for instance, he deems not to be a name for every thing in nature
except white things, but only for every colored thing other than white. In this case, however,
as in all others, the test of what a name denotes is what it can he predicated of: and we can
certainly predicate of a sound, or a smell, that it is not white. The affirmation and the nega-
tion of the .same attribute can not but divide the whole h'eld of predication between them.
NAMES.
43
suppose other persons who must be called parents. "When we call any event
a cause, we suppose another event which is an effect. When we" say of
any distance that it is longer, we suppose another distance which is shorter.
When we say of any object that it is like, we mean that it is like some
other object, which is also said to be like the first. In this last case both
objects receive the same name; the relative term is its own correlative.
It is evident that these words, when concrete, are, like other concrete
general names, connotative; they denote a subject, and connote an attri-
bute; 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 con-
notes 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 at-
tainable. 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 can not, however, perceive in what respect it is more
so than any other attribute ; indeed, it appears to me to be so in a some-
what less degree. I conceive rather, that it is by examining into the sig-
nification of relative names, or, in other words, into the nature of the at-
tribute which they connote, that a clear insight may best be obtained into
the nature of all attributes : of all that is meant by an attribute.
It is obvious, in fact, that if we take any two correlative names, father
and son for instance, though the objects Quoted by the names are differ-
ent, they both, in a certain sense, connote the same thing. They can not,
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 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 focts, in which two different objects
are implicated, and which is therefore predicable of both of them, may be
either considered as constituting an attribute of the one, or an attribute of
the other. According as we consider it in the former, or in the latter as-
pect, it is connoted by the one or the other of the two correlative names.
Father connotes the fact, regarded as constituting an attribute of A ; son
connotes the same fact, as constituting an attribute of B. It may evident-
ly 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 concerned, an attribute ground-
ed on that fact may be ascribed to either of these individuals.
44 NAMES AND PROPOSITIONS.
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 ob-
ject, also deriving a denomination from the. same fact which is the ground
of the first name. Or (to express the same meaning in other words) a
name is relative, when, being the name of one thing, its signification can
not be explained but by mentioning another. Or we may state it thus
when the name can not be employed in discourse so as to have a meaning,
unless the name of some other thing than what it is itself the name of, be
either expressed or understood. These definitions are all, at bottom, equiva-
lent, being modes of variously expressing this one distinctive circumstance
that every other attribute of an object might, without any contradiction,
be conceived still to exist if no object besides that one had ever existed;*
but those of its attributes which are expressed by relative names, would on
that supposition be swept away.
8. Names have been further distinguished into univocal and (Kquivocal:
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 a?quiv-
ocal, or applied aequivocally, as respects those things of which it is predi-
cated 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 ambiguous word is not one name, but
two names, accidentally coinciding in sound. File meaning a steel instru-
ment, and t /irYtf meaning a line of soldiers, have no more title to be consid-
ed 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 metaphor-
ically; 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 derived one from the other, one of them may be consid-
ered 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 just as
properly two names instead of one, in this case, as in that of the most per-
fect ambiguity. And one of the commonest 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.
* Or ratlier, 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 jiiven 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 1'heuomena. of the Human Miud.
THINGS DENOTED BY NAMES. 45
CHAPTER III.
OF THE THINGS DENOTED BY NAMES.
1. LOOKING back now to the commencement of our inquiry, let us at-
tempt to measure how far it has advanced. Logic, we found, is the Theory
of Proof. But proof supposes something provable, which must be a Prop-
osition 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 every thing
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 de-
nied of a subject. We have accordingly, in the preceding chapter, re-
viewed 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 predicates, or of having
any thing predicated of them : after which to determine the import of
Predication, that is, of Propositions, can be no arduous task.
The necessity of an enumeration of 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 phi-
losophers. The Categories, or Predicaments the former a Greek word,
the latter its literal translation in the Latin language were believed to be
an enumeration of all things capable of being named ; an enumeration by
the summa genera, i. e., the most extensive classes into which things could
be distributed ; which, therefore, were so many highest Predicates, one or
other of which was supposed capable of being affirmed with truth of every
namable thing whatsoever. The following are the classes into which, ac-
cording to this school of philosophy, Things in general might be reduced :
Ovcia, Substantia.
Tioabv, Quantitas.
TLot6v, Qualitas.
Hp6f TI, Relatio.
Tloielv, Actio.
Passio.
Ubi.
Quando.
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, however
46 NAMES AND PROPOSITIONS.
superficially conducted, would have shown the enumeration to be both re-
dundant 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 Relation which could ex-
clude action, passivity, and local situation from that category. 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 yemis the
class which forms the tenth category is manifest. On the other hand, the
enumeration takes no notice of any thing 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, judgment, conception, and the like? Probably all these would
have been placed by the Aristotelian school in the categories of actio and
passio; and the relation of such of them as are active, to their objects, and
of such of them as are passive, to their causes, would rightly be so placed ;
but the things themselves, the feelings or states of mind, wrongly. Feel-
ings, or states of consciousness, are assuredly to be accounted among reali-
ties, but they can not be reckoned either among substances or attributes.*
2. Before recommencing, under better auspices, the attempt made with
such imperfect success by the early logicians, we must take notice of an
unfortunate ambiguity in all the concrete names which correspond to the
most general of all abstract terms, the word Existence. When we have
occasion for a name which shall be capable of denoting whatever exists,
as contradistinguished from non-entity or Nothing, there is hardly a word
applicable to the purpose which is not also, and even more familiarly, taken
in a sense in which it denotes only substances. But substances are not all
that exists ; attributes, if such things are to be spoken of, must be said to
exist; feelings certainly exist. Yet when we speak of an object, or of a
* On the preceding passage Professor Hain remarks (Logic, i.. 265): " The Categories do not
seem to have been intended as a classification of Namahle Things, in the sense of 'an enu-
meration of all kinds of Tilings which are capable of being made predicates, or of having any
thing predicated of them.' They seem to have been rather intended as a generalization
of predicates ; an analysis of the final import of predication. Viewed in this light, they
are not open to the objections offered by Mr. Mill. The proper question to ask is not In
what Category are we to place sensations or other feelings or states of mind ? but, Under
what Categories can we predicate regarding states of mind? Take, for example. Hope.
When we say that it is a state of mind, we predicate Substance : we may also describe how
great it is (Quantity), what is the quality of it, pleasurable or painful (Quality), what it has
reference to (Relation). Aristotle seems to have framed the Categories on the plan Here is
an individual ; what is the final analysis of all that we can predicate about him?''
This is doubtless a true statement of the leading idea in the classification. The Category
O'uaia was certainly understood by Aristotle to be a general name for all possible answers to
the question Quid sit ? when asked respecting a concrete individual ; as the other Categories
are names comprehending all possible answers to the questions Quantum sit? Quale sit? etc.
In Aristotle's conception, therefore, the Categories may not have been a classification of
Things; but they were soon converted into one by his Scholastic followers, who certainly re-
garded and treated them as a classification of Things, and carried them out as such, dividing
down the Category Substance as a naturalist might do, into the different classes of physical
or metaphysical objects as distinguished from attributes, and the other Categories into the
principal varieties of quantity, quality, relation, etc. It is, therefore, a just subject of com-
plaint against them, that they had no Category of Feeling. Feeling is assuredly predicable as
a summum genus, of every particular kind of feeling, for instance, as in Mr. Haiti's example, of
Hope : but it can not be brought within any of the Categories as interpreted either by Aristo-
tle or by his followers.
THINGS DENOTED BY NAMES. 47
thing, we are almost always supposed to mean a substance. There seems
a kind of contradiction in using such an expression as that one thing is
merely an attribute of another thing. And the announcement of a Classi-
fication of Things would, I believe, prepare most readers for an enumera-
tion like those in natural history, beginning with the great divisions of an-
imal, vegetable, and mineral, and subdividing them into classes and orders.
If, rejecting the word Thing, we endeavor 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 equiv-
alent to the verb exists ; and therefore suitable, even by its grammatical
formation, to be the concrete of the abstract existence. But this 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 synonymous with substance ; except that it is free
from a slight taint of a second ambiguity; being implied impartially to
matter and to mind, while substance, though originally and in strictness
applicable to both, is apt to suggest in preference the idea of matter. At-
tributes are never called Beings; nor are feelings. A Being is that which
excites feelings, and which possesses attributes. The soul is called a Be-
ing ; God and angels are called Beings ; but if we were to say, extension,
color, wisdom, virtue, are beings, we should perhaps be suspected of think-
ing with some of the ancients, that the cardinal virtues are animals; or, at
the least, of holding with the Platonic school the doctrine of self-existent
Ideas, or with the followers of Epicurus that of Sensible Forms, which de-
tach 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, philosophers look-
ing 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 un-
derwent a more complete transformation when, from being the abstract
of the verb to be, it came to denote something sufficiently concrete to be
inclosed 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 mentioned. Yet the same gradual
decay to which, after a certain age, all the language of psychology seems
liable, has been at work even here. If you call virtue an entity, you are
indeed somewhat less strongly suspected of believing it to be a substance
than if you called it a being; but you are by no means free from the sus-
picion. Every word which was originally intended to connote mere ex-
istence, seems, after a time, to enlarge its connotation to separate existence,
or existence freed from the condition of belonging to a substance; which
condition being precisely what constitutes an attribute, attributes are grad-
ually 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
48 NAMES AND PROPOSITIONS.
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 tiling is to un-
derstand thoroughly the defects of those we have. I have therefore warn-
ed 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 endeavor 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 ex-
press what is signified by a known word in some one or other of its senses :
unless authors had an unlimited license 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 familial-
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 Avhich must
be made to use vague words so as to convey a precise meaning, is not
wholly a matter of regret. It is not unfitting that logical treatises should
afford an example of that, to facilitate which is among the most important
uses of loijic. Philosophical language will for a long time, and popular
language still longer, retain so much of vagueness and ambiguity, that logic
would be of little value if it did not, among its other advantages, exercise
the understanding in doing its work neatly and correctly with these im-
perfect tools.
After this preamble it is time to proceed to our enumeration. We shall
commence with Feelings, the simplest class of namable things; the term
Feeling being of course understood in its most enlarged sense.
I. FEELIXGS, OR STATES OF CONSCIOUSNESS.
3. A Feeling and a State of consciousness are, in the language of phi-
losophy, equivalent expressions : every thing is a feeling of which the mind
is conscious; every thing which it feels, or, in other words, which forms a
part of its own sentient existence. In popular language Feeling is not al-
ways synonymous with State of Consciousness; being often taken more
peculiarly for those states which are conceived as belonging to the sensi-
tive, 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 with-
drawn from its rightful generality of signification, and restricted to the
intellect. The still greater perversion by which Feeling is sometimes con-
fined not only to bodily sensations, 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
THINGS DENOTED BY NAMES. 49
is here to be included whatever we are internally conscious of when we are
said to think ; from the consciousness we have when we think of a red col-
or without having it before our eyes, to the most recondite thoughts of a
philosopher or poet. Be it remembered, however, that by a thought is to
be understood what passes in the mind itself, and not any object external
to the mind, which the person is commonly said to be thinking of. He may
be thinking of the sun, or of 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 mav
think of the loaf which was eaten yesterday, or of the flower which will
bloom to-morrow. But the hobgoblin which never existed is not the same
thing with my idea of a hobgoblin, any more than the loaf which once ex-
isted 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 ob-
ject which causes the sensation; our sensation of white from a white object:
nor is it less to be distinguished from the attribute whiteness, which we
ascribe to the object in consequence of its exciting the sensation. Unfor-
tunately for clearness and due 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 sen-
sation : the name ichiteness. But when we speak of the sensation itself
(as we have not occasion to do this often except in our scientific specula-
tions), language, which adapts itself for the most part only to the common
uses of life, has provided us with no single-worded or immediate designa-
tion ; we must employ a circumlocution, and say, The 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, with-
out any thing whatever to excite it. We can conceive it as arising spon-
taneously in the mind. But if it so arose, we should have no name to de-
note 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 a universe with nothing in it except sounds, and ourselves
hearing them: and what is easily conceived separately, easily obtains a
separate name. But in general our names of sensations denote indiscrim-
inately the sensation and the attribute. Thus, color stands for the sensa-
tions of white, red, etc., but also for the quality in the colored object. We
talk of the colors of things as among their properties.
4. In the case of sensations, another distinction has also to be kept in
view, which is often confounded, and never without mischievous conse-
quences. This is, the distinction between the sensation itself, and the state
4
50 NAMES AND PROPOSITIONS.
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 color blue, is a feeling of blue color, 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 ap-
prised me of. These are states of my body ; but the sensation of blue,
which is the consequence of these states of body, is not a state of body:
that which perceives and is conscious is called Mind. When sensations
are called bodily feelings, it is only as being the class of feelings which are
immediately occasioned by bodily states ; whereas the other kinds of feel-
ings, thoughts, for instance, or emotions, are immediately excited not by
any thing acting upon the bodily organs, but by sensations, or by previous
thoughts. This, however, is a distinction not in our feelings, but in the
agency which produces our feelings: all of them when actually produced
are states of mind.
Besides the affection of our bodily organs from without, and the sensa-
tion thereby produced in our minds, many writers admit a third link in the
chain of phenomena, which they call a Perception, and which consists in
the recognition of an external object as the exciting cause of the sensation.
This perception, they say, is an act of the mind, proceeding from its own
spontaneous activity ; while in a sensation the mind is passive, being mere-
ly acted upon by the outward object. And according to some metaphysi
cians, it is by an act of the mind, similar to perception, except in not being
preceded by any sensation, that the existence of God, the soul, and other
hyperphysical objects, is recognized.
These acts of what is termed perception, whatever be the conclusion ul-
timately 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 legitimate or the
reverse. Far less do I mean (as Dr. Whewell seems to suppose must be
meant in an analogous case*) to indicate that as they are "merely states of
mind," it is superfluous to inquire into their distinguishing 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, wheth-
er physical or spiritual, which are external to itself, I can see only cases of
belief; but of belief which claims to be intuitive, or independent of exter-
nal evidence. When a stone lies before me, I am conscious of certain sen-
sations which I receive from it; but if I say that these sensations 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.
* Philosophy of the Inductive Sciences, vol. i., p. 40.
THINGS DENOTED BY NAMES. 51
To the same region of speculation belongs all that can be said respecting
the distinction which the German metaphysicians and their French and
English followers so elaborately draw between the acts of the mind and its
merely passive states; between what it receives from, and what it gives to
the crude materials of its experience. I am aware that with reference to
the view which those writers take of the primary elements of thought and
knowledge, this distinction is fundamental. 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 be-
tween active and passive states of mind is of secondary importance. For
us, they all are states of mind, they all are feelings ; by which, let it lie.
said once more, I mean to imply nothing of passivity, but simply that they
are psychological facts, facts which take place in the mind, and are to be
carefully distinguished from the external or physical facts with which they
may be connected either as effects or as causes.
5. Among active states of mind, there is, however, one species which
merits particular attention, because it forms a principal part of the conno-
tation of some important classes of names. I mean volitions, or acts of
the will. When we speak of sentient beings by relative names, a large
portion of the connotation of the name usually consists of the actions of
those beings; actions past, present, and possible or probable future. Take,
for instance, the words Sovereign and Subject. What meaning do these
words convey, but that of innumerable actions, done or to be done by the
sovereign and the subjects, to or in regard to one another reciprocally ?
So with the words physician and patient, leader and follower, tutor and
pupil. In many cases the words also connote actions which would be
done under certain contingencies by persons other than those denoted : as
the words mortgagor and mortgagee, 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 correlative ; as the word brother.
From these instances, it may be seen how large a portion of the connota-
tion of names consists of actions. Now what is an action ? Not one thing,
but a series of two things : the state of mind called a volition, followed 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 mov-
ing my arm ; that is a state of my mind : my arm (not being tied or par-
alytic) moves in obedience to my purpose ; that is a physical fact, conse-
quent 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 namable things, viz., Feelings or
States of Consciousness, we began by recognizing three subdivisions ; Sen-
sations, 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. We shall now proceed to the two remaining class-
es of namable things; all things which are regarded as external to the
5-2 NAMES AND PROPOSITIONS.
mind being considered as belonging either to the class of Substances or to
that of Attributes.
II. SUBSTANCES.
Logicians have endeavored to define Substance and Attribute ; but their
definitions are not so much attempts to draw a distinction between the
things themselves, as instructions what difference it is customary to make
in the grammatical structure of the sentence, according as we are speak-
ing of substances or of attributes. Such definitions are rather lessons of
English, or of Greek, Latin, or German, than of mental philosophy. An
attribute, say the school logicians, must be the attribute of something ;
color, for example, must be the color 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 attri-
bute would be at an end. A substance, on the contrary, is self-existent; in
speaking about it, we need not put of after its name. A stone is not the
stone of any thing; the moon is not the moon of any thing, but simply the
moon. Unless, indeed, the name which we choose to give to the substance
be a relative 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 sub-
sist. 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 whole universe except himself were destroyed. But destroy
all white substances, and where would be the attribute whiteness? White-
ness, 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 any thing else. And as for the
self-existence of substance, it is very true that a substance may be con-
ceived to exist without any other 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 satisfactory than this. Substances
are usually distinguished as Bodies or Minds. Of each of these, philoso-
phers have at length provided us with a definition which seems unexcep-
tionable.
7. A body, according to the received doctrine of modern metaphysi-
cians, may be defined, the external cause to which we ascribe our sensa-
tions. When I see and touch a piece of gold, I am conscious of a sensa-
tion of yellow color, and sensations of hardness and weight ; and by vary-
ing the mode of handling, I may add to these sensations many others com-
pletely distinct from them. The sensations are all of which I aui directly
THINGS DENOTED BY NAMES. 53
conscious ; but I consider them as produced by something not only exist-
ing 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 extei'-
nal cause? And is there sufficient ground for so ascribing them? It is
known, that there are metaphysicians who have raised a controversy on
the point; maintaining that we are not warranted in referring our sensa-
tions to a cause such as we understand by the word Body, or to any ex-
ternal cause whatever. Though we have no concern here with this con-
troversy, nor with the metaphysical niceties on which it turns, one of the
best ways of showing what is meant by Substance is, to consider what po-
sition 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 compounded of its visible form and size, which are com-
plex sensations 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 color, which is a sensa-
tion of sight ; its hardness, which is a sensation of the muscles ; its com-
position, which is another word for all the varieties of sensation which we
receive under various circumstances from the wood of which it is made,
and so forth. All or most of these various sensations frequently are, and,
as we learn by experience, always might be, experienced simultaneously, or
in many different orders of succession at our own choice: and hence the
thought of any one of them makes us think of the others, and the whole
becomes mentally amalgamated into one mixed state of consciousness,
which, in the language of the school of Locke and Hartley, is termed a
Complex Idea.
Now, there are philosophers who have argued as follows : If we con-
ceive an orange to be divested of its natural color without acquiring any
new one; to lose its softness without becoming hard, its roundness without
becoming square or pentagonal, or of any other regular or irregular figure
whatever ; to be deprived of size, of weight, of taste, of smell ; to lose all
its mechanical and all its chemical properties, and acquire no new ones ; to
become, in short, invisible, intangible, imperceptible not only by all our
senses, but by the senses of all other sentient beings, real or possible;
nothing, say these thinkers, would remain. For of what nature, they ask,
could be the residuum? and by what token could it manifest its presence?
To the unreflecting its existence seems to rest on the evidence of the senses.
But to the senses nothing is 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 connection,
making the sensations occur together, does not, say these philosophers,
necessarily require what is called a substratum to support them. Tho con-
ception of a substratum is but one of many possible forms in which that
connection presents itself to our imagination ; a mode of, as it were, real-
izing the idea. If there be such a substratum, suppose it at this instant
miraculously annihilated, and let the sensations continue to occur in the
54 NAMES AND PROPOSITIONS.
same order, and how would the substratum l>e 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 any
thing intrinsically different from the sensations which the body is said to
produce in us; it is, in short, a set of sensations, or rather, of possibilities
of sensation, joined together according to a fixed law.
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 sensations (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 connection, 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 sub-
stratuni and its attributes (as they expressed themselves) inhered, literally
stuck, in it. To this substratum the name Matter is usually given in phil-
osophical discussions. It was soon, however, acknowledged by all who re-
flected on the subject, that the existence of matter can not be proved by ex-
trinsic 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 sen-
sations 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 intui-
tive. And here the question merges in the fundamental problem of meta-
physics properly so called: to which science we leave it.
But although the extreme doctrine of the Idealist metaphysicians, that
objects are nothing but our sensations and the laws which connect them,
has not been generally adopted by subsequent thinkers ; the point of most
real importance is one on which those metaphysicians are now very gen-
erally considered to have made out their ease: vi/., that all ice know of ob-
jects 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 Berke-
ley or Locke. However firmly convinced that there exists a universe of
"Tilings in themselves," totally distinct from the universe of phenomena,
or of things as they appear to our senses; and even when bringing into
use a technical expression (Noumenori) to denote what the thing is in it-
self, as contrasted with the representation of it in our minds ; he allows
that this representation (the matter of which, he says, consists of our sen-
sations, though the form is given by the laws of the mind itself) is all we
know of the object: and that the real nature of the Thing is, and by the
constitution of our faculties ever must remain, at least in the present state
of existence, an impenetrable mystery to us. "Of things absolutely or in
themselves," says Sir William Hamilton,* "be they external, be they in-
ternal, we know nothing, or know them only as incognizable; and become
aware of their incomprehensible existence, only as this is indirectly and
* Discussions on Philosophy, etc. Appendix I., pp. 643, G44.
THINGS DENOTED BY NAMES. 55
accidentally revealed to us, through certain qualities related to our faculties
of knowledge, and which qualities, again, we can not think as uncondition-
al, irrelative, existent in and of ourselves. All that we know is therefore
phenomenal phenomenal of the unknown."* 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 ontological character of his philosophy in other respects,
they may be regarded as the admissions of an opponent.f
There is not the slightest reason for believing that what we call the sen-
sible qualities of the object are a type of any 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 boiling 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 ?J Or on what principle are we
* It is to be regretted that Sir William Hamilton, though he often strenuously 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.
t "Nous savons qu'il existe quelque chose liors de nous, parceque nous ne pouvons expli-
quer nos perceptions sans les rattacher a des causes distinctes de nous merries ; nous savons
de plus que ces causes, dont nous ne connaissons pas d'ailleurs 1'essence, produisent les eft'ets
les plus variables, les plus divers, et meme les plus contraires, selon qu'elles rencontrent telle
nature ou telle disposition du sujet. Mais savons-noiis quelque chose de plus ? et meme, 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 enquerir si nous percevons les choses telles qu'elles
sorit ? Non e'videmment Je ne dis pas que le probleme est insoluble, je dis
qu'il est absurde et enferme une contradiction. Nous ne savons pas ce que ces causes sont en
el/es-memes, et la raison nous defend de chercher a le connaitre : mais il est bien evident a
priori, qu'el/es ne sont pas en elles-memes ce qu'elles sont par rapport a nous, puisque la pre-
sence du sujet modih'e ne'cessairement leur action. Supprimez tout sujet sentant, il est certain
que ces causes agiraient encore puisqu'elles continueraient d'exister; mais elles agiraient au-
trement ; elles seraient encore des qualites et des proprie'te's, mais qui ne ressembleraient a
riende ce que nous connaissons. Le feu ne manifesterait plus aucune des proprie'tes que nous
lui connaissons: que serait-il? C'est ce que nous ne saurons jamais. C'est d'ailleurs peut-
etre un probleme qui ne repugne pas seulement a la nature de notre esprit, mais a 1'essence mume
des choses. Quand meme en eff'et on supprimerait par le pense'e tons les sujets sentants, il
faudrait encore admettre que nul corps ne manifesterait ses proprie'te's autrement qu'en rela-
tion avec un sujet quelconque, et dans ce cas ses proprie'te's ne seraient encore que relatives:
en sorte qu'il me parait fort raisonnable d'admettre que les proprie'te's de'termiiiees des corps
n'existent pas inde'pendamment d'un sujet quelconque, et que quand on demande si les pro-
priete's de la matiere sont telles que nous les percevons, il faudrait voir auparavant si elles sont
en tant que de'terminees, et dans quel sens il est vrai de dire qu'elles sont." Cours d'Histoire
de la Philoso/ihie Morale au I8me siecle, 8me Ie9on.
t An attempt, indeed, has been made by Reid and others, to establish that although some
of the properties we ascribe to objects exist only in our sensations, others exist in the things
themselves, being such as can not 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 anal-
ysis than had previously been applied to the notions of extension and figure, pointed out that
the sensations from which those notions are derived, are sensations 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 analytic power,
Mr. Herbert Spencer's Principles of Psychology.
On this point M. Cousin may again be cited in favor of the better doctrine. M. Cousin
recognizes, in opposition to Reid, the essential subjectivity of our conceptions of what are called
the primary qualities of matter, as extension, solidity, etc., equally with those of color, heat,
and the remainder of the so-called secondary qualities. Cours, ut supra, Ume Ie9on.
50 NAMES AND PROPOSITIONS.
authorized to deduce from the effects, any thing concerning the cause, ex~
ccpt that it is a cause adequate to produce those effects? It may, there-
fore, safely be laid down as a truth both obvious iu 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 sen-
sations which we experience from it.*
8. l>ody 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. Xor, after
the preceding observations, will this be difficult. For, as our conception
of a bodv is that of an unknown exciting cause of sensations, so our con-
ception of a mind is that of an unknown recipient or percipient, of them ;
and not of them alone, but of all our other feelings. As body is under-
stood to be the mysterious something which excites the mind to feel, so
mind is the mysterious something which feels and thinks. It is unneces-
sary to give in the case of mind, as we gave in the case of matter, a par-
ticular statement of the skeptical system by which its existence as a Thing
in itself, distinct from the series of what are denominated its states, is call-
ed in question, lint 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 al-
ways remain, entirely in the dark. All which we are aware of, even in our
own minds, is (in the words of James Mill) a certain "thread of conscious-
ness;" 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, rny mind, which I consider
as distinct from these sensations, thoughts, etc. ; a something which I con-
ceive to be not the thoughts, but the being that has the thoughts, and
* This doctrine, which is the most complete form of the philosophical theory known as the
Relativity of Human Knowledge, lias, since the recent revival in this country of an active in-
terest in metaphysical speculation, been the subject of a greatly increased amount of discussion
and co-itrovers\ ; and dissentients have manifested themselves in considerably greater number
than ! hail any knowledge of when the passage in the text was written. The doctrine has
been attacked from two sides. Some thinkers, among whom are the late Professor Ferrier,
in his Institutes of Metaphysic, and Professor John Grote, in his Exploratio Philosophica, ap-
pear to deny ; altogether the reality of Noumena, or Tilings in themselves of an unknowable
substratum or support for the sensations which we experience, and which, according to the
theory, constitute all our knowledge of an external world. It seems to me, however, that in
Professor (Irote'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. Hailey in his valuable Let-
ters (,n ike riiilsphy of the Human Mind, and (in spite of the striking passage quoted in
the text) also Sir William Hamilton, who contend for a direct knowledge by the human mind
of more than the sensations of certain attributes or properties as they exist not in us, but
in the Tilings 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 concerning it, I must content myself with referring to a
work already mentioned An Examination of S(V \Villiam Hamilton's P/iiloso/>hy ; several
chapters of which are devotjd to a full discussion of the questions and theories relating to
the supposed direct perception of external objects.
THINGS DENOTED BY NAMES. 57
which I can conceive as existing forever in a state of quiescence, without
any thoughts at all. But what this being is, though it is myself, I have no
knowledge, other than the series of its states of consciousness. As bodies
manifest themselves to me only through the sensations of which I regard
them as the causes, so the thinking principle, or mind, in my own nature,
makes itself known to me only by the feelings of which it is conscious. I
know nothing about myself, save my capacities of feeling or being con-
scious (including, of course, thinking and willing) : and were I to learn
any thing new concerning my own nature, I can not with my present facul-
ties conceive this new information to be any thing else, than that I have
some additional capacities, 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 feelings, so mind may be de-
scribed 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
any thing; and if any thing, logic has nothing to do with it, or with the
manner in which the knowledge is acquired. With this result we may
conclude this portion of our subject, and pass to the third and only remain-
ing class or division of Namable Things.
III. ATTRIBUTES : AND, FIRST, QUALITIES.
9. From what has already been said of Substance, what is to be said
of Attribute is easily deducible. For if we know not, and can not know,
anything of bodies but the sensations which they excite in us or in others,
those sensations must be all that we can, at bottom, mean by their attri-
butes ; and the distinction which we verbally make between the properties
of things and the sensations we receive from them, must originate in the
convenience of discourse rather than in the nature of what is signified by
the terms.
Attributes are usually distributed under the three heads of Quality,
Quantity, and Relation. We shall come to the two latter presently : in the
first place we shall confine 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 whiteness. When we ascribe
whiteness to any substance, as, for instance, snow; when we say that snow
has the quality whiteness, what do we really assert? Simply, that when
snow is present to our organs, we have a particular 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 composing
this group or series, that which I call the sensation of white color 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 noth-
ing of sensible objects, except the sensations they excite in us ; that the
fact of our receiving from sno\v the particular sensation which is called a
sensation of white, is the ground on which we ascribe to that substance the
quality whiteness; the sole proof of its possessing that quality. But be-
cause one thing may be the sole evidence of the existence of another thing,
58 NAMES AND PROPOSITIONS.
it docs not follow that the two arc one and the same. The attribute white-
ness (it may be said) is not the fact of receiving the sensation, but some-
thing in the object itself; a poirer inherent in it; something in virtue of
which the object produces the sensation. And when we affirm that snow
possesses the attribute whiteness, we do not merely assert that the pres-
ence 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 met-
aphysics ; 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 ex-
cept in a tendency of the human mind which is the cause of many delu-
sions. I mean, the disposition, wherever we meet with two names which
are not precisely synonymous, to suppose that they must be the names of
two different things ; whereas in reality they may be names of the same
thing viewed in two different lights, or under different suppositions as to
surrounding circumstances. Because quality and sensation can not be put
indiscriminately one for the other, it is supposed that they can not 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 feel-
ing may be called a sensation when considered merely in itself, and a quali-
ty when looked at in relation to any one of the numerous objects, the pres-
ence 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 any thing in fact but a lingering remnant
of the old doctrine of occult causes; the very absurdity which Moliere so
happily ridiculed when he made one of his pedantic physicians account for
the fact that opium produces sleep by the maxim, Because it has a soporific
virtue.
It is evident that when the physician stated that opium has a soporific
virtue, he did not account for, but merely asserted over again, the fact that
it produces sleep. In like manner, when we say that snow is white because
it has the quality of whiteness, we arc 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 intelli-
gible cause, to suppose an occult cause besides, for the purpose of enabling
the real cause to produce its effect. If I am asked, why does the presence
of the object cause this sensation in me, I can not tell: I can onlv 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.
THINGS DENOTED BY NAMES. 59
But, as the difficulties which may be felt in adopting this view of the
subject can not 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 na-
ture of qualities. I shall say what at least admits of no dispute that
the quality of whiteness ascribed to the object snow, is grounded on its
exciting in us the sensation of white ; and adopting the language already
used by the school logicians in the case of the kind of attributes called
Relations, I shall term the sensation of white i\\Q foundation of the quality
whiteness. For logical purposes the sensation is the only essential part of
what is meant by the word ; the only part which we ever can be concerned
in proving. When that is proved, the quality is proved ; if an object ex-
cites a sensation, it has, of course, the power of exciting it.
IV. RELATIONS.
10. The qualities of a body, we have said, are the attributes grounded
on the sensations which the presence of that particular body to our organs
excites in our minds. But when we ascribe to any object the kind of at-
tribute called a Relation, the foundation of the attribute must be some-
thing in which other objects are concerned besides itself and the percipient.
As there may with propriety be said to be a relation between any two
things to which two correlative names are or may be given, we may ex-
pect to discover what constitutes a relation in general, if we enumerate the
principal cases in which mankind have imposed correlative names, and ob-
serve what these cases have in common.
"What, then, is the character which is possessed in common by states of
circumstances so heterogeneous and discordant as these : one thing like
another; one thing unlike another; one thing near another; one thing
far from another; one thing before, after, along icith another; one thing
greater, equal, less, than another; one thing the cause of another, the effect
of another; one person the master, servant, child, parent, debtor, creditor,
sovereign, subject, attorney, client, of another, and so on ?
Omitting, for the present, the case of Resemblance, (a relation which re-
quires to be considered separately,) there seems to be one thing common
to all these cases, and only one ; that in each of them there exists or occurs,
or has existed or occurred, or may be expected to exist or occur, some fact
or phenomenon, into which the two things which are said to be related to
each other, both enter as parties concerned. This fact, or phenomenon, is
what the Aristotelian logicians called the fandamentum relationis. Thus
in the relation of greater and less between two magnitudes, \\\e fundamen-
tum relationis is the fact that one of the two magnitudes could, under cer-
tain conditions, be included in, without entirely filling, the space occupied
by the other magnitude. In the relation of master and servant, the fun-
damentum relationis is the fact that the one has undertaken, or is com-
pelled, to perform certain services for the benefit and at the bidding of the
other. Examples might be indefinitely multiplied ; but it is already obvi-
ous that whenever two things are said to be related, there is some fact, or
series of facts, into which they both enter; and that whenever any two
things are involved in some one fact, or series of facts, we may ascribe to
those two things a mutual relation grounded on the fact. Even if they
have nothing in common but what is common to all things, that they are
members of the universe, we call that a relation, and denominate them
fellow-creatures, fellow-beings, or fellow-denizens of the universe. But in
y o /
60 NAMES AND PROPOSITIONS.
proportion as the fact into which the t\vo 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 be jointly
concerned.
In the same manner, therefore, as a quality is an attribute grounded on
the fact that a certain sensation or sensations are produced in us by the
object, so an attribute grounded on some fact into which the object enters
jointly with another object, is a 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 and creditor, principal and
agent, guardian and ward, the fiuulamentum relationis consists entirely of
thoughts, feelings, and volitions (actual or contingent), either of the persons
themselves or of other persons concerned in the same series of transactions ;
as, for instance, the intentions which would be formed by a judge, in case
a complaint were made to his tribunal of the infringement of any of the
legal obligations imposed by the relation; and the acts which the judge
would perform in consequence; acts being (as we have already seen) an-
other word for intentions followed by an effect, and that effect being but
another word for sensations, or some other feelings, occasioned either to
the agent himself or to somebody else. There is no part of what the names
expressive of the relation imply, that is not resolvable into states of con-
sciousness ; outward objects being, no doubt, supposed throughout as the
causes by which some of those states of consciousness are excited, and
minds as the subjects by which all of them are experienced, but neither
the external objects nor the minds making their existence known other-
wise 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, lor 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 succession of the two objects .1
third thing; but their succession is not something added to the things
themselves; it is something involved in them. Dawn and sunrise announce
themselves to our consciousness by two successive sensations. Our con-
sciousness 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 feel-
ing 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 analyze the matter any further.
11. In a somewhat similar position are two other sorts of relations,
Likeness and Unlikeness. I have two sensations; we will suppose them
to be simple ones; two sensations of white, or one sensation of white and
Another of black. I call the first two sensations like ; the last two unlike.
What is the fact or phenomenon constituting the fntnlamentum of this
relation? The two sensations first, and then what we call a feeling of re-
semblance, or of want of resemblance. Let us confine ourselves to the fcv-
THINGS DENOTED BY NAMES. 61
mer case. Resemblance is evidently a feeling ; a state of the consciousness
of the observer. Whether the feeling of the resemblance of the two colors
be a third state of consciousness, which I have after having the two sensa-
tions of color, or whether (like the feeling of their succession) 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 presupposed in every attempt to analyze 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 consciousness,
but on states which are peculiar, unresolvable, and inexplicable.
But, though likeness or unlikeness can not be resolved into any thing
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 likenesses 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 com-
plex 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, wheth-
er by word, countenance, or gesture.
All likeness and unlikeness of which we have any cognizance, resolve
themselves into likeness and unlikeness between states of our own, or some
other, mind. When we say that one body is like another, (since we know
nothing of bodies but the sensations 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 attri-
butes except the sensations or states of feeling on which they are ground-
ed), 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 resem-
blance 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, resembles the relation in ^ which
Philip stood to Alexander; resembles it so closely that they are called the
same relation. The relation in which Cromwell stood to England resem-
bles the relation in which Xapoleon 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 resemblance being in the two fundamenta relationis, in each of which
there occurs a germ, producing by its development a multitude of other
02 NAMES AND PROPOSITIONS.
things similar to itself. And as, whenever two objects are jointly concern-
ed in a phenomenon, 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 two phenomena is sufficient to ad-
mit of its being said that the two relations resemble; provided, of course,
the points of resemblance arc found in those portions of the two phenom-
ena respectively which are connoted by the relative names.
While speaking of resemblance, it is necessary to take notice of an am-
biguity of language, against which scarcely any one is sufficiently on his
guard. Resemblance, when it exists in the highest degree of all, amount-
ing to undistinguishableness, is often called identity, and the two similar
things are said to be the same. I say often, not always; for we do not say
that two visible objects, two persons, for 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 per-
son. 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 can not 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 understandings, 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 iden-
tity and undistinguishable resemblance. Among modern writers, Arch-
bishop Whately stands almost alone in having drawn attention to this dis-
tinction, and to the ambiguity connected with it.
Several relations, generally called by other names, are really 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 sensa-
tions which it excites. Ten gallons of water are also an external object,
making its presence known to us in a similar manner; and as we do not
mistake ten gallons of water for a gallon of water, it is plain that the set
of sensations is more or less different in the two cases. Jn 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 dif-
ferent from each other. In the first case, however, we say that the differ-
ence is in quantity ; in the last there is a difference in quality, while the
THINGS DENOTED BY NAMES. QQ
quantity of the water and of the wine is the same. "What is the real dis-
tinction between the two cases? It is not within the province of Logic to
analyze it ; nor to decide whether it is susceptible of analysis or not. For
us the following considerations are sufficient: It is evident that the sen-
sations 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 altogether unlike : they are partly similar, partly dissimilar ; and that
in which they resemble is precisely that in which alone the gallon of wa-
ter and the ten gallons do not resemble. That in which the gallon of wa-
ter 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 quan-
tity. This 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 sensations 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 drink-
ing 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 un-
dertake to say what the difference in the sensations is. Every body knows,
and nobody can tell ; no more than any one could tell what white is to a
person who had never had the sensation. But the 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 ex-
cited by them.
VI. ATTRIBUTES CONCLUDED.
13. 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 ex-
citing those sensations. And the same general explanation has been found
to apply to most of the attributes usually classed under the head of Rela-
tion. They, too, are grounded on some fact or phenomenon into which the
related objects enter as parts; that fact or phenomenon having no mean-
ing and no existence to us, except the series of sensations or other states
of consciousness 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 production of that series of sensa-
tions or states of consciousness. We have been obliged, indeed, to recog-
nize a somewhat different character in certain peculiar relations, those of
succession 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 relations, 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 succession. Or,
if this be disputed (and we can not, 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 be-
tween sensations, or other states of consciousness ; for, though we ascribe
resemblance, or succession, or simultaneity, to objects and to attributes, it
04 NAMES AND PROPOSITIONS.
is always in virtue of resemblance or succession or simultaneity in the sen-
sations or states of consciousness which those objects excite, and on which
those attributes are grounded.
14. In the preceding investigation we have, for the sake of simplicity,
considered bodies only, and omitted minds. But what we have said, is ap-
plicable, 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 attribute of a mind consists either
in being itself affected in a certain way, or affecting other minds in a certain
way. Considered in itself, we can predicate nothing of it but the series
of its own feelings. When we say of any mind, that it is devout, or super-
stitious, 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 till up the sentient ex-
istence 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 not, indeed, like a body, excite sensations, but
it may excite thoughts or emotions. The most important example of attri-
butes ascribed on this ground, is the employment of terms expressive of
approbation or blame. When, for example, we say of any character, or (in
other words) of any mind, that it is admirable, we mean that the contem-
plation of it excites the sentiment of admiration ; and indeed somewhat
more, for the word implies that we not only feel admiration, but approve
that sentiment in ourselves. In some cases, under the semblance of a sin-
gle 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 say of any one that he is generous. The word gene-
rosity expresses a certain state of mind, but being a term of praise, it also
expresses that this state of mind excites in us another mental state, called
approbation. The assertion made, therefore, is twofold, and of the follow-
ing purport: Certain feelings form habitually a part of this person's sen-
tient existence ; and the idea of those feelings of his, excites the sentiment
of approbation in ourselves or others.
As we thus ascribe attributes to minds on the ground of ideas and emo-
tions, 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. GKNERAL 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 predi-
cations is now concluded.
Our enumeration commenced with Feelings. These we scrupulously dis-
tinguished from the objects which excite them, and from the organs by
which they are, or may be supposed to be, conveyed. Feelings are of four
sorts: Sensations, Thoughts, Emotions, and Volitions. What are called
Perceptions are merely a particular case of Belief, and Belief is a kind of
thought. Actions are merelv volitions followed bv an effect.
THINGS DENOTED BY NAMES.
65
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 ob-
jective 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 Namable Things is Attributes; and these
are of three kinds, Quality, Relation, and Quantity. Qualities, like sub-
stances, are known to us no otherwise than by the sensations or other
states of consciousness which they excite : and while, in compliance with
common usage, we have continued to speak of them as a distinct class of
Tilings, we showed that in predicating them no one means to predicate any
thing but those sensations or states of consciousness, on which they may be
said to be grounded, and by which alone they can be defined or described.
Relations, except the simple cases of likeness and unlikeness, succession
and simultaneity, are similarly grounded on some fact or phenomenon, that
is, on some series of sensations or states of consciousness, more or less
complicated. The third species of Attribute, Quantity, is also 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 inextricably in-
volved therein; and to this even the peculiar and simple relations just ad-
verted to arc not exceptions. Those peculiar relations, however, are so im-
portant, and, even if they might in strictness be classed among states of
consciousness, are so fundamentally distinct from any other of those states,
that it would be a vain subtlety to bring them under that common descrip-
tion, and it is necessary that they should be classed apart.*
As the result, therefore, of our analysis, we obtain the following as an
enumeration and classification of all Namable Things :
1st. Feelings, or States of Consciousness.
2d. The Minds which experience those feelings.
3d. The Bodies, or external objects which excite certain of those feelings,
together w r ith the powers or properties whereby they excite them ; these
latter (at least) being included rather in compliance with common opinion,
and because their existence is taken for granted in the common language
from which I can not prudently deviate, than because the recognition of
such powers or pi'operties as real existences appears to be warranted by a
sound philosophy.
4th, and last. The Successions and Co-existences, the Likenesses and Un-
likenesses, between feelings or states of consciousness. Those relations,
when considered as subsisting between other things, exist in reality only
between the states of consciousness which those things, if bodies, excite, if
minds, either excite or experience.
* Professor Bain (Logic, i., 49) defines attributes as "points of community among classes."'
This definition expresses well one point of view, but is liable to the objection that it applies
only to the attributes of classes ; though an object, unique in its kind, may be said to have at-
tributes. Moreover, the definition is not ultimate, since the points of community themselves
admit of, and require, further analysis ; and Mr. Bain does analyze them into resemblances in.
the sensations, or other states of consciousness excited by the object.
5
66 NAMES AND PROPOSITIONS.
This, xmtil a better can be suggested, may serve as a substitute for the
Categories of Aristotle considered as a classification of Existences. The
practical application of it will appear when we commence the 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 correct, all Xamable
Things, these or some of them must of course compose the signification of
all names: and of these, or some of them, is made up whatever we call a
fact.
For distinction's sake, every fact which is solely composed of feelings 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 attri-
butes, is called an Objective fact. We may say, then, that every objective
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
psychological 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 that analysis of the
import conveyed by them, which is the real subject and purpose of this
preliminary book.
A proposition, we have before said, is a portion of discourse in which a
predicate is 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 can not
conclude from merely seeing two names put together, that they are a predi-
cate 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 predi-
cation from any other kind of discourse. 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 subject fire. But this
function is more commonly fulfilled by the word fa, 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 respecting it are among the causes which have spread
mysticism over the field of logic, and perverted its speculations into logoma-
chies.
It is apt to be supposed that the copula is something more than a mere
sign of predication; that it also signifies existence. In the 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 fa, that is to say,
PROPOSITIONS. 6 7
exists. This, however, only shows that there is an ambiguity in the word
is ; a word which not only performs the function of the copula in affirma-
tions, but has also a meaning of its own, in virtue of which it may itself be
made the predicate of a proposition. That the employment of it as a cop-
ula does not necessarily include the affirmation of existence, appears from
such a proposition as this, A centaur is a fiction of the poets ; where it can
not possibly be implied that a centaur exists, since the proposition itself ex-
pressly asserts that the thing has no real existence.
Many volumes might be filled with the frivolous speculations concerning
the nature of Being (TO ov, ovaia, Ens, Entitas, Essentia, and the like), which
have arisen from overlooking this double meaning of the word to be; from
supposing that when it signifies to evist, 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 Aristotle because
we are now able to preserve ourselves from many errors into which they,
perhaps inevitably, fell. The fire-teazer of a modern 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 lan-
guages which eminent thinkers have used as the vehicle of their thoughts,
is the practical lesson we learn respecting the ambiguities of words, by find-
ing that the same word in one language corresponds, on different occasions,
to different words in another. When not thus exercised, even the strong-
est understandings find it difficult to believe that things which have a com-
mon name, have not in some respect or other a common nature ; and often
expend much labor very unprofitably (as was frequently done by the two
philosophers just mentioned) in vain attempts to discover in what this com-
mon nature consists. But, the habit once formed, intellects much inferior
are capable of detecting even ambiguities which are common to many lan-
guages: and it is surprising that the one now under consideration, though
it exists in the modern languages as well as in the ancient, should have
been overlooked by almost all authors. The quantity of futile speculation
which had been caused by a misapprehension of the nature of the copula,
was hinted at by Hobbes ; but Mr. James Mill* was, I believe, the first who
distinctly characterized the ambiguity, and 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 completely emancipated from
their influence, do not appear equally irrational.
We shall now briefly review the principal distinctions which exist among
propositions, and the technical terms most commonly in use to express
those distinctions.
2. A proposition being a portion of discourse in which something is
affirmed or denied of something, the first division of propositions is into
* Analysis of the Human Mind, i., 126 et seq.
68 NAMES AND PROPOSITIONS.
affirmative and negative. An affirmative proposition is that in which the
predicate is affirmed of the subject; as, Ca)sar is dead. A negative prop-
osition is that in which the predicate is denied of the subject; as, Ciesar
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 Ilobbes, state this dis-
tinction differently; they recognize only one form of copula, is, and attach
the negative sign to the predicate. " Caesar is dead," and " Crcsar is not
dead,'' according to these writers, are propositions agreeing not in the sub-
ject and predicate, but in the subject only. They do not consider " dead,"
but " not dead," to be the predicate of the second proposition, and they ac-
cordingly define a negative proposition to be one in which the predicate is
a negative name. The point, though not of much practical moment, de-
serves notice as an example (not 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 distinction between affirming and denying, by treating
every case of denying as the affirming of a negative name. But what is
meant by a negative name? A name expressive of the absence of an attri-
bute. So that when we affirm a negative name, what we are really predi-
cating is absence and not presence; we are asserting not that any thing is,
but that something is not; to express which operation no word seems so
proper as the word denying. The fundamental distinction is between a
fact and the non-existence of that fact; between seeing something and
not seeing it, between Caesar's being dead and his not being dead ; and if
this were a merely verbal distinction, the generalization which brings both
within the same form of assertion would be a real simplification : the dis-
tinction, however, being real, and in the facts, it is the generalization con-
founding 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 distinc-
tions among propositions which are said to have reference to their modali-
ty ; as, difference of tense or time; the sun did rise, the sun is rising, the
suii will rise. These differences, like that between affirmation and nega-
tion, 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 belong-
ing to the event asserted, to the sun's rising to-day. They affect, not the
predicate, but the applicability of the predicate to the particular subject.
That which we affirm to be past, present, or future, is not what the subject
signifies, nor what the predicate signifies, but specifically and expressly
what the predication signifies; what is expressed only by the proposition
as such, and not by either or both of the terms. Therefore the circum-
stance of time is properly considered as attaching to the copula, which is
the sign of predication, and not to the predicate. If the same can not be
said of such modifications as these, Caesar may be dead ; Caesar is perhaps
dead; it is possible that Ca?sar is dead; it is only because these fall alto-
PROPOSITIONS.
09
gethcr under another head, being properly assertions not of any thino- re-
lating to the fact itself, but of the state of our own mind in regard to it
namely, our absence of disbelief of it. Thus " Caesar may be dead" means
" I am not sure that Caesar is alive."
3. The next division of propositions is into Simple and Complex ; more
aptly (by Professor Bain*) termed Compound. A simple proposition is
that in which one predicate is affirmed or denied of one subject. A com-
pound proposition is that in which there is more than one predicate, or
more than one subject, or both.
At first sight this division has the air of an absurdity; a solemn distinc-
tion of things into one and more than one; as if we were to divide horses
into single horses and teams of horses. And it is true that what is called
a complex (or compound) proposition is often not a proposition at all, but
several propositions, held together by a conjunction. Such, for example, is
this : Caesar is dead, and Brutus is alive : or even this, Caesar is dead, but
Brutus is alive. There are here two distinct assertions ; and we might as
well call a street a complex house, as these two propositions a complex
proposition. It is true that the 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 abbrevia-
tions, 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 :
Ca3sar is dead; Brutus is alive; it is desired that the two preceding prop-
ositions should be thought of together. If the words were, Cassar is dead,
but Brutus is alive, the sense would be equivalent to the same three propo-
sitions 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 sub-
ject. For brevity, however, and to avoid repetition, the propositions are
often blended together : as in this, " Peter and James preached at Jerusa-
lem 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
assertions, which, if true when joined, are true also when separated. But
there is a kind of proposition which, though it contains a plurality of sub-
jects and of predicates, and may be said in one sense of the word to con-
sist of several propositions, contains but one assertion ; and its truth does
not at all imply that of the simple propositions which compose it. An ex-
ample of this is, when the simple propositions are connected by the parti-
cle 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 lat-
ter, conditional: the name hypothetical was originally common to both.
Logic, i., 85.
70 XAMKS AND PROPOSITIONS.
As has been well remarked by Archbishop Whately and otlicrs, the dis-
junctive form is resolvable into the conditional; every disjunctive proposi-
tion being equivalent to two or more conditional ones. "Either A is B or
C is D," means, " if A is not B, C is D ; and if C is not D, A is B." All
hypothetical propositions, therefore, though disjunctive in form, are condi-
tional in meaning; and the words hypothetical and conditional may be, as
indeed they generally are, used synonymously. Propositions in which the
assertion is not dependent on a condition, are said, in the language of logi-
cians, to be categorical.
A hypothetical proposition is not, like the pretended complex proposi-
tions which we previously considered, a mere aggregation of simple propo-
sitions. 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, Mohammed is the prophet of God, we
do not intend to affirm either that the Koran does come from God, or that
Mohammed is really his prophet. Neither of these simple propositions may
be true, and yet the truth of the hypothetical proposition may be indis-
putable. 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 proposition? "The Koran"
is not the subject of it, nor is "Mohammed:" for nothing is affirmed or de-
nied either of: the Koran or of Mohammed. The real subject of the pred-
ication is the entire proposition, "Mohammed is the prophet of God;" and
the affirmation is, that this is a legitimate inference from the proposi-
tion, " The Koran comes from God." The subject and predicate, therefore,
of a 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 is here afforded of the remark, that particles are abbreviations ;
since " If A. is B, C is D," is found to be an abbreviation of the follow-
ing: "The proposition C is D, is a legitimate inference from the proposi-
tion A is B."
The distinction, therefore, between hypothetical and categorical proposi-
tions is not so great as it at first appears. In the conditional, as well as in
the categorical form, one predicate 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 a hypo-
thetical proposition, is that of being an inference from a certain other prop-
osition. 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 math-
ematics : 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 re-
nounced by Parliament at the Revolution: The infallibility of the Pope
has no countenance from Scripture. In all these cases the subject of the
predication is an entire proposition. That which these different predicates
are affirmed of, is tlie proposition," the whole is greater than its part;" the
proposition, "the Holy Ghost proceeds from the Father alone;" the propo-
sition, " kings have a divine right ;" the proposition, " the Pope is infallible."
Seeing, then, that there is much less difference between hypothetical
propositions aud any others, than one might be led to imagine from their
PROPOSITIONS. 7!
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 remem-
ber 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.
4. The next of the common divisions of Propositions is into Universal,
Particular, Indefinite, and Singular : a distinction founded on the degree
of generality in which the name, which is the subject of the proposition,
is to be understood. The following are examples :
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 individual name.
The individual name needs not be a proper name. "The Founder of
Christianity was crucified," is as much a singular proposition as " Christ
was crucified."
When the name which is the 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 uni-
versal propositions. No man is immortal, is also a universal proposition,
since the predicate, immortal, is denied of each and every individual de-
noted 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 ev-
ery 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 singu-
lar proposition, or into a universal proposition with a different subject;
as, for instance, " all properly instructed men are wise." There are other
forms of particular propositions ; as, "Most men are imperfectly educated:"
it being immaterial how large a portion of the subject the predicate is as-
serted of, as long as it is left uncertain how that portion is to be distin-
guished from the rest.*
When the form of the expression does not clearly show whether the
general name which is the subject of the proposition is meant to stand for
all the individuals denoted by it, or only for some of them, the proposition
is, by some logicians, called Indefinite ; but this, as Archbishop Whately ob-
* Instead of Universal and Particular as applied to propositions, Professor Bain proposes
(Logic, i., 81) the terms Total and Partial; reserving the former pair of terms for their in-
ductive meaning, "the contrast between a general proposition and the particulars or individ-
uals that we derive it from." This change in nomenclature would be attended with the further
advantage, that Singular propositions, which in the Syllogism follow the same rules as Univer-
sal, would be included along with them in the same class, that of Total predications. It is not
the Subject's denoting many things or only one, that is of importance in reasoning, it is that
the assertion is made of the whole or a part only of what the Subject denotes. The words
Universal and Particular, however, are so familiar and so well understood in both the senses
mentioned by Mr. Bain, that the double meaning does not produce any material inconvenience.
72 NAMES AND PROPOSITIONS.
serves, is a solecism, of the same nature as that committed by some gram-
marians when in their list of genders they enumerate the doubtful gender.
The speaker must mean to assert the proposition either as a universal or
as a particular proposition, though lie has failed to declare which : and it
often happens that though the words do not show which of the two he in-
tends, the context, or the custom of speech, supplies the deficiency. Thus,
when it is affirmed that <; Man is mortal," nobody doubts that the asser-
tion is intended of all human beings; and the word indicative of universal-
ity 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.* As is observed by Professor Bain,f the
chief examples of Indefinite propositions occur "with names of material,
which are the subjects sometimes of universal, and at other times of partic-
ular predication. 'Food is chemically constituted by carbon, oxygen, etc.,'
is a proposition of universal quantity; the meaning is all food all kinds
of food. 'Food is necessary to animal life' is a case of particular quan-
tity; the meaning is some sort of food, not necessarily all sorts. 'Metal
is requisite in order to strength' does not mean all kinds of metal. ' Gold
will make a way,' means a portion of gold."
When a general name stands for each and every individual which it is a
name of, or in other words, which it denotes, it is said by logicians to be
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 hap-
pen to be men; while the word may, for aught that appears, and in fact
dut-s, comprehend within it an indefinite number of objects besides men.
In the proposition, Some men are mortal, both the predicate and the sub-
ject are undistributed. In the following, No men have wings, both the
predicate and the subject are distributed. Xot only is the attribute of
having wings denied of the entire class Man, but that class is severed and
cast out from the whole of the class Winged, and not merely from some
part of that class.
This phraseology, which is of great service in stating and demonstrating
the rules of the syllogism, enables us to express very concisely the defini-
tions of a universal and a particular proposition. A universal proposition
is that of which the subject 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 importance. But, for ex-
plaining and illustrating these, more suitable opportunities will occur in the
sequel.
* It may, however, be considered ns equivalent to a universal proposition with a different
predicate, viz. : "All wine is good qua wine," or "is good in respect of the qualities which
constitute it wine."
t Logic, i., 82.
IMPORT OF PROPOSITIONS.
CHAPTER V.
OF THE IMPORT OF PROPOSITIONS.
1. Ax inquiry into the nature of propositions must have one of two
objects: to analyze the state of mind called Belief, or to analyze what is
believed. All language recognizes a difference between a doctrine or opin-
ion, 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. Phi-
losophers, however, from Descartes downward, 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 analyze the im-
port of Propositions, unless founded on an analysis of the act of Judgment.
A proposition, they would have said, is but the expression in words t>f a
Judgment. The thing expressed, not the mere verbal expression, is the
important matter. When the mind assents to a proposition, it judges.
Let us find out what the mind does when it judges, and we shall know
what propositions mean, and not otherwise.
Conformably to these views, almost all the writers on Logic in the last
two centuries, whether English, German, or French, have made their the-
ory of Propositions, from one end to the other, a theory of Judgments.
They considered a Proposition, or a Judgment, for they used the two
words indiscriminately, to consist in affirming or denying one idea of an-
other. To judge, was to put two ideas together, or to bring one idea un-
der another, or to compare two ideas, or to perceive the agreement or disa-
greement between two ideas : and the whole doctrine of Propositions, to-
gether with the theory of Reasoning (always necessarily founded on the
theory of Propositions), was stated as if Ideas, or Conceptions, or whatever
other term the writer preferred as a name for mental representations gen-
erally, constituted essentially the subject-matter and substance of those op-
erations.
It is, of course, true, that in any case of judgment, as for instance when
we judge that gold is yellow, a process takes place in our minds, of which
some one or other of these theories is a partially correct account. We
must have the idea of gold and the idea of yellow, and these two ideas
must be brought together in our mind. But in the first place, it is evident
that this is only a part of what takes place; for we may put two ideas to-
gether without any act of belief; as when we merely imagine something,
such as a golden mountain ; or when we actually disbelieve : for in order
even to disbelieve that Mohammed was an apostle of God, we must put the
idea of Mohammed 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,
74 NAMES AND PROPOSITIONS.
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 tilings themselves. In order to believe that gold is yellow,
I must, indeed, have the idea of gold, and the idea of yellow, and some-
thing having reference to those ideas must take place in my mind ; but
my belief has not reference to the ideas, it has reference to the things.
What I 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 every thing
else that I do. I can not dig the 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 an-
other. Digging is an operation which is performed upon the things them-
selves, though it can not 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? Xo : I mean that the natural
phenomenon, fire, causes the natural phenomenon, heat. When I mean to
assert any thing respecting the ideas, I give them their proper name, I
call them ideas: as when I say, that a child's idea of a battle is unlike the
reality, or that the ideas entertained of the Deity have a great effect on the
characters of mankind.
The notion that what is of primary importance to the logician in a prop-
osition, is the relation between the two ideas corresponding to the subject
and predicate (instead of the relation between the two phenomena which
they respectively express), seems to me one of the most fatal errors ever
introduced into the philosophy of Logic; and the principal cause why the
theory of the science has made such inconsiderable progress during the last
two centuries. The treatises on Logic, and on the branches of Mental Phi-
losophy connected with Logic, which have been produced since the intru-
sion 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 and handling our ideas,
or conceptions of things, instead of the things themselves: a doctrine tan-
tamount 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 incessant-
ly establishing great and fruitful truths on most important subjects, by
processes upon which these views of the nature of Judgment and Reason-
ing threw no light, and in which they afforded no assistance whatever. No
wonder that those who knew by practical experience how truths are ar-
rived at, should deem a science futile, which consisted chiefly of such spec-
* Dr. Whewell (Philotophy of Ltiicavery, p. 242) questions this statement, and asks, "Are
we to say that a mole can not dig the ground, except he has an idea of the ground, and of
the snout and paws with which he digs it?" I do not know what passes in a mole's mind,
nor what amount of mental apprehension may or may not accompany his instinctive actions.
But a human being does not use n 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 OF PROPOSITIONS. 75
ulations. What has been done for the advancement of Los:ic since these
doctrines came into vogue, has been done not by professed logicians, but
by discoverers in the other sciences ; in whose methods of investio-ation
many principles of logic, not previously thought of, have successively come
forth into light, but who have generally committed the error of supposing
that nothing whatever was known of the art of philosophizing by the old
logicians, because their modern interpreters have written to so little pur-
pose respecting it.
We have to inquire, then, on the present occasion, not into Judgment,
but judgments; not into the act of believing, but into the thing believed.
What is the immediate object of belief in a Proposition? What is the
matter of fact signified by it? What is it to which, when I assert the
proposition, I give my assent, and call upon others to give theirs ? What is
that which is expressed by the form of discourse called a Proposition, and
the conformity of which to fact constitutes the truth of the proposition ?
2. One of the clearest and most consecutive thinkers whom this coun-
try or the world has produced, I mean Hobbes, has given the following an-
swer to this question. In every proposition (says he) what is signified is,
the belief of the speaker that the predicate is a name of the same thing of
which the subject is a name ; and if it really is so, the proposition is true.
Thus the proposition, All men are living beings (he would say) is true,
because living being is a name of every thing of which man is a name.
All men are six feet high, is not true, because six feet high is not a name
of every tiling (though it is of some things) of which man is a name.
What is stated in this theory as the definition of a true proposition, must
be allowed to be a property which all true propositions possess. The sub-
ject 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 sig-
nification, be predicated of the other. If it be true that some men are cop-
per-colored, 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-colored. 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 who-
ever asserts that all oxen ruminate, undoubtedly does assert that this rela-
tion subsists between the two names.
The assertion, therefore, which, according to Hobbes, is the only one
made in any proposition, really is made in every proposition : and his anal-
ysis has consequently one of the requisites for being the true one. We
may go a step further; it is the only analysis that is rigorously true of Jill
propositions without exception. What he gives as the meaning of propo-
sitions, is part of the meaning of all propositions, and the whole meaning
of some. This, however, only shows what an extremely minute fragment
of meaning it is quite possible to include within the logical formula of a
proposition. It does not show that no proposition means more. To war-
rant us in putting together two words with a copula between them, it is
really enough that the thing or things denoted by one of the names should
be capable, without violation of usage, of being called by the other name also.
If, then, this be all the meaning necessarily implied in the form of discourse
called a Proposition, why do I object to it as the scientific definition of what
a proposition means? Because, though the mere collocation which makes
the proposition a proposition, conveys no more than this scanty amount of
76 NAMES AND PROPOSITIONS.
meaning, that same collocation combined with other circumstances, that
form combined with other matter, does convey more, and the proposition
in those other circumstances does assert more, than merely that relation
between the two names.
The only propositions of which Hobbes's principle is a sufficient 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 ob-
jects: and when a proper name is predicated of another proper name, all
the signification conveyed is, that both the names arc marks for the same
object. But this is precisely what Hobbes produces as a theory of predi-
cation in general. His doctrine is a full explanation of such predications
as these: Hyde was Clarendon, or, Tally is Cicero. It exhausts the mean-
ing of those propositions. Hut it is a sadly inadequate theory of any oth-
ers. That it should ever have been thought of as such, can be accounted
for only by the fact, that Hobbes, in common with the other Nominalists,
bestowed little or no attention upon the connotation of words; and sought
for their meaning exclusively in what they denote: as if all names had been
(what none but proper names really are) marks put upon individuals ; and
as if there were no difference between a proper and a general name, except
that the first denotes only one individual, and the last a greater number.
It has been seen, however, that the meaning of all names, except proper,
names and that portion of the class of abstract names which are not conno-
tative, resides in the connotation. AVhen, therefore, we are analyzing the
meaning of any proposition in which the predicate and the subject, or
either of them, are connotative names, it is to the connotation of those
terms that we must exclusively look, and not to what they denote, or in the
language of Hobbes (language so far correct) are names of.
In asserting that the truth of a proposition depends on the conformity of
import between its terms, as, for instance, that the proposition, Socrates is
wise, is a true proposition, because Socrates and wise are names applicable
to, or, as he expresses it, names of, the same person ; it is very remarkable
that so powerful a thinker should not have asked himself the question, But
how came they to be names of the same person ? Surely not because such
was the intention of those who invented the words. When mankind h'xed
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 in-
vented. 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 at-
tributes, 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 mart is a name: but why? Those
objects are brought under the name, by possessing the attributes connoted
by it: but their possession of the attributes is the real condition on which
IMPORT OF PROPOSITIONS. 77
the truth of the proposition depends ; not their being called by the name.
Connotative names do not precede, but follow, the attributes which they
connote. If one attribute happens to be always found in conjunction with
another attribute, the concrete names which answer to those attributes will
of course be predicable of the same subjects, and may be said, in Hobbes's
language (in the propriety of which on this occasion I fully concur), to be
two names for the same things. But the possibility of a concurrent appli-
cation of the two names, is a mere consequence of the conjunction between
the two attributes, and Avas, 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 dreamed of when the words
Diamond and Combustible first received their meaning; and could not
have been discovered by the most ingenious and refined analysis of the sig-
nification 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 combustibility existed in the diamonds upon which the experiment was
tried ; the number or character of the experiments being such, that what
was true of those individuals might be concluded to be true of all sub-
stances " called by the name," that is, of all substances possessing the at-
tributes which the name connotes. The assertion, therefore, when ana-
lyzed, is, that wherever we find certain attributes, there will be found a cer-
tain other attribute : which is not a question of the signification of names,
but of laws of nature ; the order existing among phenomena.
3. Although Hobbes's theory of Predication has not, in the terms in
which he stated it, met with a very favorable reception from subsequent
thinkers, a theory virtually identical with it, and not by any means so per-
spicuously expressed, may almost be said to have taken the rank of an es-
tablished opinion. The most generally received notion of Predication de-
cidedly is that it consists in referring something to a class, i. e., either pla-
cing 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 philoso-
pher," 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 proposition, The elephant is not carnivorous ; what
is asserted (according to this theory) is, that the elephant is excluded from
the class carnivorous, or is not numbered among the things comprising that
class. There is no real difference, except in language, between this theory
of Predication and the theory of Hobbes. For a class is absolutely noth-
ing but an indefinite number of individuals denoted by a general name.
The name given to them in common, is what makes them a class. To re-
fer any thing to a class, therefore, is to look upon it as one of the things
which are to be called by that common name. To exclude it from a class,
is to say that the common name is not applicable to it.
How widely these views of predication have prevailed, is evident from
this, that they are the basis of the celebrated dictum de or/mi 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 logicians, the propositions of which reasonings
78 NAMES AND PROPOSITIONS.
:ire compose*! can be the expression of nothing but the process of dividing
tilings into classes, and referring every thing to its proper class.
This theory appears to me a signal example of a logical error very often
committed in logic, that of vertpot' Trpor/por, or explaining a thing by some-
thing which presupposes it. When I say that snow is white, I may and
ought to be thinking of snow as a class, because I am asserting a proposi-
tion as true of all snow: but I am certainly not thinking of white objects
as a class ; I am thiuking of no white object whatever except snow, but
only of that, and of the sensation of white which it gives me. When, in-
deed, I have judged, or assented to the propositions, that snow is white,
and that several other things are also white, I gradually begin to think of
white objects as a class, including snow and those other things. But this
is a conception which followed, not preceded, those judgments, and there-
fore can not be given as an explanation of them. Instead of explaining the
effect by the cause, this doctrine explains the cause by the effect, and is, I
conceive, founded on a latent misconception of the nature of classification.
There is a sort of language very generally prevalent in these discussions,
which seems to suppose that classification is an arrangement and grouping
of definite and known individuals: that when names were imposed, man-
kind took into consideration all the individual objects in the universe, dis-
tributed them into parcels or lists, and gave to the objects of each list a
common name, repeating this operation totics quoties until they had invent-
ed all the general names of which language 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 con-
ferred, 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 sup-
posed) have predetermined all the objects that arc 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 rec-
onciled 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, ex-
cept by accident, has a fixed meaning at all, or ever long retains the same
meaning. The only mode in which any general name has a definite mean-
ing, is by being a name of an indefinite variety of things ; namely, of all
things, known or unknown, past, present, or future, which possess certain
definite attributes. When, by studying not the meaning of words, but the
phenomena of nature, we discover 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 place the indi-
vidual in the class because the proposition is true; the proposition is not
true because the object is placed in the class.*
* Professor Bain remarks, in qualification of the statement in the text (Logic, i., 50), that
IMPORT OF PROPOSITIONS. 79
It will appear hereafter, in treating of reasoning, bo\v much the theory
of that intellectual process has been vitiated by the influence of these erro-
neous notions, and by the habit which they exemplify of assimilating all
the operations of the human understanding which have truth for their ob-
ject, to processes 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's theory of Predication, according to the
well-known remark of Leibnitz, and the avowal of Hobbes himself,* renders
truth and falsity completely arbitrary, with no standard but the will of
men, it must not be concluded that either Hobbes, or any of the other
thinkers who have in the main agreed with him, did in fact consider the
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 speculations. But this shows how little
hold their doctrine possessed over their own minds. No person, at bot-
tom, ever imagined that there was nothing more in truth than propriety of
expression ; than using language in conformity to a previous convention.
When the inquiry was brought down from generals to a particular case, it
has always been acknowledged that there is a distinction between verbal
and real questions ; that some false propositions are uttered from ignorance
of the meaning of words, but that in others the source of the error is a
misapprehension of things ; that a person who has not the use of language
at all may form propositions mentally, and that they may be untrue that
is, he may believe as matters of fact what are not really so. This last ad-
mission can not be made in stronger terms than it is by Hobbes himself,!
though he will not allow such erroneous belief to be called falsity, but only
error. And he has himself laid down, in other places, doctrines in which
the true theory of predication is by implication contained. He distinctly
the word Class has two meanings; "the class definite, and the class indefinite. The class
definite is an enumeration of actual individuals, as the Peers of the Realm, the oceans of the
globe, the known planets. . . . The class indefinite is unenumerated. Such classes are
stars, planets, gold-bearing rocks, men, poets, virtuous. ... In this last acceptation of the
word, class name and general name are identical. The class name denotes an indefinite num-
ber of individuals, and connotes the points of community or likeness."
The theory controverted in the text, tacitly supposes all classes to be definite. I have as-
sumed them to be indefinite ; because, for the purposes of Logic, definite classes, as such, are
almost useless ; though often serviceable as means of abridged expression. (Vide infra, book
iii., chap, ii.)
* "From hence also this may be deduced, that the first truths were arbitrarily made by
those that first of all imposed names upon things, or received them from the imposition of oth-
ers. 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, chap,
iii., sect. 8.
t " 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 pass-
ing 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." Computation or Logic, chap, v., sect. 1.
80 NAMES AND PROPOSITIONS.
says that general names arc given to tilings on account of their attributes,
ami that abstract names are the names of those attributes. " Abstract is
that which in any subject denotes the cause of the concrete name
Ami 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 any thing works upon our senses, but by
most men they arc called accidents.''''* It is strange that having gone so
far, he should not have gone one step further, 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 at-
tribute (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 sum-
mit of Chimborazo is white." The word white connotes an attribute which
is possessed by the individual object designated by the words "summit of
Chimborazo;" which attribute consists in the physical fact, of its exciting
in human beings the sensation which we call a sensation of white. It will
be admitted that, by asserting the proposition, we wish to communicate in-
formation of that physical fact, and are not thinking of the names, except
as the necessary means of making that communication. The meaning of
the proposition, therefore, is, that the individual thing denoted by the sub-
ject, has the attributes connoted by the predicate.
It we now suppose the subject also to be a connotative name, the mean-
ing expressed by the proposition has advanced a step further in complica-
tion. Let us first suppose the proposition to be universal, as well as affirm-
ative : "All men are mortal." In this case, as in the last, what the propo-
sition asserts (or expresses a belief of) is, of course, that the objects de-
noted by the subject (man) possess the attributes connoted by the predi-
cate (mortal). Hut 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 at-
tributes connoted by the name man ; and the only thing known of them
may be those attributes: indeed, as the proposition is general, and the ob-
jects 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, etc., but that those attributes are possessed by each and ev-
ery individual possessing certain other attributes ; that whatever has the
attributes connoted by the subject, has also those connoted by the predi-
cate; that the latter set of attributes constantly accompany the former set.
Whatever has the attributes of man has the attribute of mortality; mortal-
ity constantly accompanies the attributes of man.f
* Chap, iii., sect. 3.
t To the preceding statement it has been objected, that " we naturally construe the subject
of n proposition in its extension, and the predicate (which therefore may be an adjective) in
its intension (connotation): and that consequently co-existence 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 my-
self laid down and exemplified a few pages back (p. 77). But though it is true that we nat-
urally "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.
IMPORT OF PROPOSITIONS. 81
If it be remembered that every attribute is grounded on some fact or
phenomenon, either of outward sense or of inward consciousness, and that
to possess an attribute is another phrase for being the cause of, or formin^
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 as-
serts thereby no other thing than this, that one phenomenon always accom-
panies another phenomenon ; insomuch that where we find the latter, we
have assurance of the existence of the former. Thus, in the proposition,
All men are mortal, the word man connotes the attributes which we ascribe
to a certain kind of living creatures, on the ground of certain phenomena
which they 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 further than to the occurrence of the phenomenon at some
time or other, leaving the particular time undecided.
5. We have already proceeded far enough, not only to demonstrate the
error of Hobbes, but to ascertain ^the real import of by far the most numer-
ous class of propositions. The object of belief in a proposition, when it
asserts any thing 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 propo-
sition affirms (or denies) to subsist between them, namely, either succession
or co-existence. And this case includes innumerable instances which no
one, previous to reflection, would think of referring to it. Take the follow-
ing example : A generous person is worthy of honor. Who would expect
to recognize here a case of co-existence between phenomena ? But so it is.
The attribute which causes a person to be termed generous, is ascribed to
him on the ground of states of his mind, and particulars of his conduct:
both are phenomena : the former are facts of internal consciousness ; the
latter, so far as distinct from the former, are physical facts, or perceptions
of the senses. Worthy of honor admits of a similar analysis. Honor, as
here used, means a state of approving and admiring emotion, followed on
occasion by corresponding outward acts. " Worthy of honor" connotes all
this, together with our approval of the act of showing honor. All these
are phenomena ; states of internal consciousness, accompanied or followed
by physical facts. When we say, A generous person is worthy of honor,
It is both apprehended and indicated 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 Phi-
losophy, chap. xxii.
6
82 NAMES AND PROPOSITIONS.
we affirm co-existence between the two complicated phenomena connoted
by the two terms respectively. We affirm, that wherever and whenever
the inward feelings and outward facts implied in the word generosity
have place, then and there the existence and manifestation of an inward
feeling, honor, would be followed in our minds by another inward feeling,
approval.
After the analysis, in a former chapter, of the import of names, many
examples are not needed to illustrate the import of propositions. When
there is any obscurity, or difficulty, it does not lie in the meaning of the
proposition, but in the meaning of the names which compose it; in the
extremely complicated connotation of many words; the immense multitude
and prolonged series of facts which often constitute the phenomenon con-
noted 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 proposi-
tion is, the co-existence of one such phenomenon with another ; or the suc-
cession of one such phenomenon to another: so that where the one is found,
we may calculate on finding the other, though perhaps not conversely.
This, however, though the most common, is not the only meaning which
propositions are ever intended to convey. In the first place, sequences and
co-existences are not only asserted respecting Phenomena ; we make propo-
sitions 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 unknowable en-
tities, except in virtue of the Phenomena by which alone they manifest
themselves to our faculties. When we say Socrates was contemporary with
the Peloponnesian war, the foundation of this assertion, as of all assertions
concerning 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 as commonly
understood does not assert that alone ; it asserts that the Thing in itself,
the noumenon Socrates, was existing, and doing or experiencing those vari-
ous facts during the same time. Co-existence and sequence, therefore, may
be affirmed or denied not only between phenomena, but between noumena,
or between a noumenon and phenomena. And both of noumena and of
phenomena we may affirm simple existence. But what is a noumenon?
An unknown cause. In affirming, therefore, the existence of a noumenon,
we affirm causation. Here, therefore, are two additional kinds of fact,
capable of being asserted in a proposition. Besides the propositions which
assert Sequence or Co-existence, there are some which assert simple Exist-
ence ;* and others assert Causation, which, subject to the explanations
* Professor Bain, in bis Logic (i., 2.~>(>), excludes Existence from the list, considering it as a
mere name. All propositions, he says, which predicate mere existence "are more or less ab-
breviated, or elliptical : when fully expressed they fall tinder either co-existence or succession.
When we say there exists a conspiracy for a particular purpose, we mt>;ui that at the present
time a body of men have formed themselves into n society for n particular object; which is a
complex affirmation, resolvable into propositions of co-existence and success 1 ion (as causation).
The assertion that the dodo does not exist, points to the fact that this animal, once known in
a certain place, has disappeared or become extinct; is no longer associated with the locality;
all which may be better suited without the use of the verb 'exist,' There is a debated ques-
tion Does an ether exist? but the concrete form would be this 'Are heat and light and
IMPORT OF PROPOSITIONS. 83
which will follow in the Third Book, must be considered provisionally as a
distinct and peculiar kind of assertion.
6. To these four kinds of matter-of-fact or assertion, must be added
a fifth, Resemblance. This was a species of attribute which we found it
impossible to analyze ; for which no fundamentum, distinct from the ob-
jects 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 color is like
that color ; 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 asser-
tion that the simultaneous contemplation of the two colors is followed by
a specific feeling termed the feeling of resemblance. But there would be
nothing gained by incumbering ourselves, especially in this place, with a
generalization which may be looked upon as strained. Logic does not un-
dertake to analyze mental facts into their ultimate elements. Resemblance
between two phenomena is more intelligible in itself than any explanation
could make it, and under any classification must remain specifically distinct
from the ordinary cases of sequence and co-existence.
It is sometimes said, that all propositions whatever, of which the pred-
icate is a general name, do, in point of fact, affirm or deny resemblance. AH
snch propositions affirm that a thing belongs to a class ; but things being
classed together according to their resemblance, every thing is of course
classed with the things which it is supposed to resemble most ; and thence,
it may be said, when we affirm that Gold is a metal, or that Socrates is a
man, the affirmation intended is, that gold resembles other metals, and Soc-
other radiant influences propagated by an ethereal medium diffused in space ;' which is a prop-
osition of causation. In like manner the question of the Existence of a Deity can not be dis-
cussed in that form. It is properly a question as to the First Cause of the Universe, and as to
the continued exertion of that Cause in providential superintendence." (i., 407.)
Mr. Bain thinks it "fictitious and unmeaning language" to carry up the classification of
Nature to one summum genus, Being, or that which Exists ; since nothing can be perceived or
apprehended but by way of contrast with something else (of which important truth, under the
name of Law of Relativity, he has been in our time the principal expounder and champion),
and we have no other class to oppose to Being, or fact to contrast with Existence.
I accept fully Mr. Bain's Law of Relativity, but I do not understand by it that to enable us
to apprehend or be conscious of any fact, it is necessary that we should contrast it with some
other positive fact. The antithesis necessary to consciousness need not, I conceive, be an an-
tithesis between two positives ; it may be between one positive and its negative. Hobbes was
undoubtedly right when he said that a single sensation indefinitely prolonged would cease to be
felt at all ; but simple intermission, without other change, would restore it to consciousness.
In order to be conscious of heat, it is not necessary that we should pass to it from cold ; it
suffices that we should pass to it from a state of no sensation, or from a sensation of some other
kind. The relative opposite of Being, considered as a summum genus, is Nonentity, or
Nothing ; and we have, now and then, occasion to consider and discuss things merely in con-
trast with Nonentity.
I grant that the decision of questions of Existence usually if not always depends on a pre-
vious question of either Causation or Co-existence. But Existence is nevertheless a different
tiling from Causation or Co-existence, and can be predicated apart from them. The meaning
of the abstract name Existence, and the connotation of the concrete name Being, consist, like
the meaning of all other names, in sensations or states of consciousness : their peculiarity is
that to exist, is to excite, or be capable of exciting, any sensations or states of consciousness :
no matter what, but it is indispensable that there should be some. It was from overlooking
this that Hegel, finding that Being is an abstraction reached by thinking away all particular
attributes, arrived at the self-contradictory proposition on which he founded all his philosophy,
that Being is the same as Nothing. It is really the name of Something, taken in the most
comprehensive sense of the word.
84 NAMES AND PROPOSITIONS.
rates 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
resemblance : the resemblance it is grounded on consists in the possession
by all those things, of certain common peculiarities ; and those peculiarities
it is which the terms connote, and which the propositions consequently as-
sert ; not the resemblance. For though when I say, Gold is a metal, I say
by implication 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 possess the attri-
butes constituting the class, are so far from asserting nothing but resem-
blance, that they do not, properly speaking, 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 characteris-
tic 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 rec-
ognized ; and almost every great family of plants or animals has a few anom-
alous 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 resem-
blance 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 af-
firm, 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 oth-
er 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 consider-
ed, 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 unequiv-
ocally 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 unanalyzablc resemblance. The classes in question are those into
which our simple sensations, or other simple feelings, are divided. Sensa-
tions of white, for instance, are classed together, not because we can take
them to pieces, and say they are alike in this, and not alike in that, but be-
* Book iv., chap. vii.
IMPORT OF PROPOSITIONS. 85
cause we feel them to be alike altogether, though in different degrees.
When, therefore, I say, The color I saw yesterday was a white color, or
The sensation I feel is one of tightness, in both cases the attribute I affirm
of the color or of the other sensation is mere resemblance simple likeness
to sensations which I have had before, and which have had those names be-
stowed upon them. The names of feelings, like other concrete general
names, are connotative; but they connote a mere resemblance. When
predicated of any individual feeling, the information they convey is that of
its likeness to the other feelings which we have been accustomed to call by
the same name. Thus much may suffice in illustration of the kind of prop-
ositions in which the matter-of-fact asserted (or denied) is simple Resem-
blance.
Existence, Co-existence, Sequence, Causation, Resemblance : one or other
of these is asserted (or denied) in every proposition which is not merely
verbal. This five-fold division is an exhaustive classification of matte rs-of-
fact ; of all things that can be believed, or tendered for belief ; of all ques-
tions that can be propounded, and all answers that can be returned to them.
Professor Bain* distinguishes two kinds of Propositions of Co-existence.
" In the one kind, account is taken of Place ; they may be described as
propositions of Order in Place." In the other kind, the co-existence which
is predicated is termed by Mr. Bain Co-inherence of Attributes. " This is a
distinct variety of Propositions of Co-existence. Instead of an arrangement
in place with numerical intervals, we have the concurrence of two or more
attributes or powers in the same part or locality. A mass of gold contains,
in every atom, the concurring attributes that mark the substance weight,
hardness, color, lustre, incorrosibility, etc. An animal, besides having parts
situated in place, has co-inhering functions in the same parts, exerted by
the very same masses and molecules of its substance. . . . The Mind,
which affords no Propositions of Order in Place, has co-inhering functions.
We affirm mind to contain Feeling, Will, and Thought, not in local separa-
tion, but in commingling exercise. The concurring properties of minerals,
of plants, and of the bodily and the mental structure of animals, are united
in affirmations of co-inherence."
The distinction is real and important. But, as has been seen, an Attri-
bute, when it is any thing but a simple unanalyzable Resemblance between
the subject and some other things, consists in causing impressions of some
sort on consciousness. Consequently, the co-inherence of two attributes
is but the co-existence of the two states of consciousness implied in their
meaning : with the difference, however, that this co-existence is sometimes
potential only, the attribute being considered as in existence, though the
fact on which it is grounded may not be actually, but only potentially pres-
ent. Snow, for instance, is, with great convenience, said to be white even
in a state of total darkness, because, though we are not now conscious of
the color, we shall be conscious of it as soon as morning breaks. Co-in-
herence of attributes is therefore still a case, though a complex one, of
co-existence of states of consciousness ; a totally different thing, however,
from Order in Place. Being a part of simultaneity, it belongs not to Place
but to Time.
We may therefore (and we shall sometimes find it a convenience) instead
of Co-existence and Sequence, say, for greater particularity, Order in Place
and Order in Time : Order in Place being a specific mode of co-existence,
* Logic, i., 103-105.
86 NAMES AND PROPOSITIONS.
not necessary to be more particularly analyzed here ; while tho mere fact of
co-existence, whether between actual sensations, or between the potentiali-
ties of causing them, known by the name of attributes, may be classed, to-
gether with Sequence, under the head of Order in Time.
7. In the foregoing inquiry into the import of propositions, we have
thought it necessary to analyze directly those alone, in which the terms of
the proposition (or the predicate at least) are concrete terms. ]>ut, in do-
ing so, we have indirectly analyzed 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 general name is, as we have so often
said, its connotation ; and what the concrete term connotes, forms the en-
tire meaning of the abstract name. Since there is nothing in the import
of an abstract name which is not in the import of the corresponding con-
crete, it is natural to suppose that neither can there be any thing in the im-
port 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 cor-
responding concrete is a name given to things, because of, and in order to
express, their possessing that attribute, or that combination of attributes.
"When, therefore, we predicate of any thing a concrete name, the attribute
is what we in reality predicate of it. But it has now been shown that in
all propositions of which the predicate is a concrete name, what is really
predicated is one of five things : Existence, Co-existence, Causation, Se-
quence, or Resemblance. An attribute, therefore, is necessarily either an
existence, a co-existence, 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 any thing an abstract name, we am'rm
of the thing that it is one or other of these five things ; that it is a case of
Existence, or of Co-existence, or of Causation, or of Sequence, or of Re-
semblance.
It is impossible to imagine any proposition expressed in abstract terms,
which can not be transformed into a precisely equivalent proposition in
which the terms are concrete ; namely, either the concrete names which
connote the attributes themselves, or the names of the fund-amenta of those
attributes; the facts or phenomena on which they are grounded. To il-
lustrate the latter case, let us take this proposition, of which the subject
only is an abstract name, " Thoughtlessness is dangerous." Thoughtless-
ness is an attribute, grounded on the facts which we call thoughtless ac-
tions; 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 color;" or "The color of snow is a white-
ness." These attributes being grounded on sensations, the equivalent prop-
ositions in the concrete would be, The sensation of white is one of the sen-
sations called those of color The sensation of sight, caused by looking at
snow, is one of the sensations called sensations of white. In these proposi-
tions, as we have before seen, the matter-of-fact asserted is a Resemblance.
In the following examples, the concrete terms are those which directly cor-
respond to the abstract names ; connoting the attribute which these de-
note. " Prudence is a virtue :" this may be rendered, " All prudent per-
IMPORT OF PROPOSITIONS. 87
sons, in so far as prudent, are virtuous :" " Courage is deserving of hon-
or ;" thus, "All courageous persons are deserving of honor in so far as they
are courageous:" which is equivalent to this "All courageous persons
deserve an addition to the honor, or a diminution of the disgrace, which
would attach to them on other grounds."
In order to throw still further light upon the import of propositions of
which the terms are abstract, we will subject one of the examples given
above to a minuter analysis. The proposition we shall select is the follow-
ing: "Prudence is a virtue." Let us substitute for the word virtue an
equivalent 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 se-
quence, accompanied with causation; 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 analyze the antecedent. Prudence is an at-
tribute; and, in connection with it, two things besides itself are to be con-
sidered ; prudent persons, who are the subjects of the attribute, and pru-
dential 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 persons ? No ; except
in so far as they are prudent; for prudent persons who are scoundrels can
seldom, on the whole, be beneficial to society, nor can they be acceptable to
a good being. Is it upon prudential conduct, then, that divine appi'obalion
and benefit to mankind are supposed to be invariably consequent ? Neither
is this the assertion meant, when it is said that prudence is a virtue; ex-
cept 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 benefi-
cial to society, may yet, by reason of some other of its qualities, be produc-
tive of an injury outweighing the benefit, and deserve a displeasure exceed-
ing the approbation which would be due to the prudence. Neither the
substance, therefore (viz., the person), nor the phenomenon (the conduct),
is an antecedent on which the other term of the sequence is universally
consequent. But the proposition, " Prudence is a virtue," is a universal
proposition. What is it, then, upon which the proposition affirms the ef-
fects 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 cor-
rect 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 attribute Prudence ; since wherever these states of mind exist we may
predicate prudence, even before we know whether any conduct has fol-
lowed. And in this manner every assertion respecting an attribute, may
be transformed into an assertion exactly equivalent respecting the fact or
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 enumerated : it is
either simple Existence, or it is some Sequence, Co-existence, Causation, or
Resemblance.
And as these five are the only things which can be affirmed, so are they
88 NAMES AND PROPOSITIONS.
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 nega-
tions. " Some birds are web-footed," affirms that, with the attributes con-
noted by bird, the phenomenon web-feet is sometimes co-existent : " Some
birds are not web-footed," asserts that there are other instances in which
this co-existence does not have place. Any further explanation of a thing
which, if the previous exposition has been assented to, is so obvious, may
here be spared.
CHAPTER 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 sus-
ceptible 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 ex-
treme Nominalists, that it is the expression of an agreement or disagree-
ment 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 Propositions, and found that, with the
exception of those which are merely verbal, they assert five different kinds
of matters of fact, namely, Existence, Order in Place, Order in Time, Causa-
tion, and Resemblance ; that in every proposition one of these five is either
affirmed, or denied, of some fact or phenomenon, or of some object the un-
known source of a fact or phenomenon.
In distinguishing, however, the different kinds of matters of fact asserted
in propositions, we reserved one class of propositions, which do not relate
to any matter of fact, in the proper sense of the term at all, but to the
meaning of names. Since names and their signification are entirely arbi-
trary, such propositions are not, strictly speaking, susceptible of truth or
falsity, but only of conformity or disconfonnity to usage or convention ;
and all the proof they are capable of, is proof of usage; proof that the
words have been employed by others in the acceptation in which the speak-
er 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 prop-
ositions 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
Ilobbes's theory of predication, vix., those of which the subject and predi-
cate 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 attention of phi-
losophers. But the class of merely verbal propositions embraces not only
much more than these, but much more than any propositions which at first
VERBAL AND REAL PROPOSITIONS. 89
sight present themselves as verbal; comprehending a kind of assertions
which have been regarded not only as relating to things, but as havino-
actually a more intimate relation with them than any other propositions
whatever. The student in philosophy will perceive 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 predi-
cates which are said to be of the essence of the subject. The essence of a
thing, they said, was that without which the thing could neither be, nor
be conceived to be. Thus, 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 respect-
ing it, than any other proposition could do. All properties, not of the es-
sence of the thing, were called its accidents ; were supposed to have noth-
ing 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 Acci-
dental Propositions. A connection may be traced between this distinction,
which originated with the schoolmen, and the well-known dogmas of sub-
stantice secundce or general substances, and substantial forms, doctrines
which under varieties of language pervaded alike the Aristotelian and the
Platonic schools, and of which more of the spirit has come down to mod-
ern times than might be conjectured from the disuse of the phraseology.
The false views of the nature of classification and generalization which pre-
vailed among the schoolmen, and of which these dogmas were the technical
expression, afford the only explanation 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 can not be con-
ceived without rationality. But though man can not, a being may be con-
ceived exactly like a man in all points except that one quality, and those
others which are the conditions or consequences of it. All, therefore, which
is really true in the assertion that man can not be conceived without ration-
ality, 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 conventions 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 mean-
ing of the word man : is one of the attributes connoted by the name. The
essence of man, simply means the whole of the attributes connoted 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 properties to which mankind have chosen to attach
that name, but by participation in the nature of a general substance, called
90 NAMES AND PROPOSITIONS.
gold in general, which substance, together with all the properties that be-
longed 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 prop-
erties from a universal substance, and that the rest belonged to it individu-
ally : the former they called its essence, and the latter its accidents. The
scholastic doctrine of essences long survived the theory on which it rested,
that of the existence of real entities corresponding to general terms ; and it
was reserved for Locke, at the end of the seventeenth century, to convince
philosophers that the supposed essences of classes were merely the signifi-
cation 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 ob-
ject, each of which attributes separately 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 proposition will be true; since what-
ever possesses the whole of any set of attributes, must possess any part of
that same set. A proposition of this sort, however, conveys no informa-
tion to any one who previously understood the whole meaning of the terms.
The propositions, Every man is a corporeal being, Every man is a living
creature, Every man is rational, convey no knowledge to any one who was
already aware of the entire meaning of the word man, for the meaning of
the word includes all this: and that every man has the attributes connoted
by all these predicates, is already asserted when he is called a man. Now,
of this nature are all the propositions which have been called essential.
They are, in fact, identical propositions.
It is true that a proposition which predicates any attribute, even though
it be one implied in the name, is in most cases understood to involve a tacit
assertion that there exists a thing corresponding to the name, and possess-
ing the attributes connoted by it ; and this implied assertion may convey
information, 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 existence is, after all, the result of an imper-
fection 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 act-
ual existence of the subject of the proposition is therefore only apparently,
not really, implied in the predication, if an essential one : we may say, A
ghost is a disembodied spirit, without believing in ghosts. But an acci-
dental, 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 proposition as, The ghost of a murdered
person haunts the couch of the murderer, can only have a meaning if un-
derstood as implying a belief in ghosts; for since the signification of the
* 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
afterward given to them by the Realists of the Middle Ages. Aristotle himself (in his Trea-
'tise on the Categories) expressly denies that the 6ev7f(>at ovotai, or Substantial Secimda:, in-
here in a subject. They are only, he says, predicated of it.
VERBAL AND REAL PROPOSITIONS. 91
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 reallv
taken place.
It will be hereafter seen that when any important consequences seem to
follow, as in mathematics, from an essential proposition, oi', 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 proposi-
tions in which the predicate is of the essence of the subject (that is, in
which the predicate connotes the whole or part of what the subject con-
notes, but nothing besides) answer no purpose but that of unfolding the
whole or some part of the meaning of the name, to those who did not pre-
viously know it. Accordingly, the most useful, and in strictness the only
useful kind of essential propositions, are Definitions : which, to be com-
plete, 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 usu-
ally 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 distinc-
tions give rise to, und the purposes to which they are respectively subserv-
ient, will be minutely considered in the proper place.
3. According to the above view of essential propositions, no proposi-
tion can be reckoned such which relates to an individual by name, that is,
in which the subject is a proper name. Individuals have no essences.
When the schoolmen talked of the essence of an individual, they did not
mean the properties implied in its name, for the names of individuals imply
no properties. They regarded as of the essence of an individual, whatever
was of the essence of the species in which they were accustomed to place
that individual ; i. e., of the class to which it was most familiarly referred,
and to which, therefore, they conceived that it by nature belonged. Thus,
because the proposition Man is a rational being, was an essential proposi-
tion, they affirmed the same thing of the proposition, Julius Cajsar 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 sup-
posed to accompany it; to inhere in John Thompson, and to form the
common essence of Thompson and Julius Caesar. It might then be fairly
said, that rationality, being of the essence of Man, was of the essence also
of Thompson. But if Man 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 vic-
tory. 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, Real and Nominal.
His nominal essences were the essences of classes, explained nearly as we
92 NAMES AND PROPOSITIONS.
have now explained them. Nor is any thing wanting to render the third
book of Locke's Essay a nearly unexceptional treatise on the connotation
of names, except to free its language from the assumption of what are
called Abstract Ideas, which unfortunately is involved in the phraseology,
though not necessarily connected with the thoughts contained in that im-
mortal Third Book.* But besides nominal essences, he admitted real es-
sences, 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 acknowledgment rendered the fiction comparatively in-
nocuous) ; but if we did, we could, from them alone, demonstrate the sen-
sible properties of the object, as the properties of the triangle are demon-
strated 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 en-
tities, 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 accidental propositions, on the contrary, may be called Real Proposi-
tions, 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 connoted by that name. Such are all proposi-
tions concerning things individually designated, and all general or partic-
ular propositions in which the predicate connotes any attribute not con-
noted by the subject. All these, if true, add to our knowledge : they con-
vey 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. f
Nothing has probably contributed more to the opinion so long prevalent
of the futility of the school logic, than the circumstance that almost all the
examples used in the common school books to illustrate the doctrine of
* The always acute and often profound author of An Outline of Sematology (Mr. B. II.
Smart) justly says, " Locke will he 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) our
Knowledge, or Belief, concerning the thing itself.
t 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. 93
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, which included nothing but what was of the es-
sence of the species : Omne corpus est substantia, Omne animal est corpus,
Omnis homo est corpus, Omnis homo est animal, Omnis homo est rationalis,
and so forth. It is far from 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 professed teachers, it was
employed to prove, were such as every one assented to without proof the
moment he comprehended the meaning of the words ; and stood exactly
on a level, in point of 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 prin-
ciple to be illustrated specifically required them.
5. "With respect to propositions which do convey information which
assert something of a Thing, under a name that does not already presup-
pose 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 consid-
ered : 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 proposition as a portion of
our theoretical knowledge, All men are mortal, means that the attributes
of man are always accompanied by the attribute mortality : No men are
gods, means that the attributes of man are never accompanied by the at-
tributes, 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 adapt-
ed to indicate the office which the proposition performs. The practical 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 proposi-
tion. In reference to this purpose, the proposition, All men are mortal,
means that the attributes of man are evidence of, are a mark of, mortality ;
an indication by which the presence of that attribute is made manifest.
No men are gods, means that the attributes of man are a mark or 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 proposition means, the latter
to the manner in which it is to be used.
Now it is to be observed that Reasoning (the subject to which we are
next to proceed) is a process into which propositions enter not as ultimate
results, but as means to the establishment of other propositions. We may
expect, therefore, that the mode of exhibiting the import of a general prop-
osition which shows it in its application to practical use, will best express
the function which propositions perform in Reasoning. And accordingly,
in the theory of Reasoning, the mode of viewing the subject which consid-
ers a Proposition as asserting that one fact or phenomenon is a mark or ev-
idence of another fact or phenomenon, will be found almost indispensable.
For the purposes of that Theory, the best mode of defining the import of
94 NAMES AND PROPOSITIONS.
a proposition is not the mode which shows most clearly what it is in itself,
but that which most distinctly suggests the manner in which it may be
made available for advancing from it to other propositions.
CHAPTER VII.
OF THE NATURE OF CLASSIFICATION, AND THE FIVE PREDICABLES.
1. IN examining into the nature of general propositions, we have ad-
verted much less than is usual with logicians to the ideas of a Class, and
Classification ; ideas which, since the Realist doctrine of General Substances
went out of vogue, have formed the basis of almost every attempt at a
philosophical theory of general terms and general propositions. We have
considered general names as having a meaning, quite independently of their
being the names of classes. That circumstance is in truth 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 signification of which is constituted by attributes, is po-
tentially a name of an indefinite number of objects ; but it needs not be
actually the name of any; and if of any, it may be the name of only one.
As soon as we employ a name to connote attributes, the things, be they
more or fewer, which happen to possess those attributes, are constituted
ipso facto a class. But in predicating the name we predicate only the at-
tributes ; and the fact of belonging to a class does not, in many cases, come
into view at all.
Although, however, 'Predication does not presuppose Classification, and
though the theory of Names and of Propositions is not cleared up, but only
encumbered, by intruding the idea of classification into it, there is never-
theless a close connection between Classification and the employment of
General Names. By every general name which we introduce, we create a
class, if there be any things, real or imaginary, to compose it; that is, any
Things corresponding to the signification of the name. Classes, therefore,
mostly owe their existence to general language. But general language,
also, though that is not the most common case, sometimes owes its exist-
ence 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, however, be supposed that such names, when introduced, differ
in any respect, as to their mode of signification, from other connotative
names. The classes which they denote are, as much as any other classes,
constituted by certain common attributes, and their names are significant
of those attributes, and of nothing else. The names of Cuvier's classes and
CLASSIFICATION AND THE PREDICABLES. 95
orders, Plantigrades, Digitigrades, etc., are as much the expression of at-
tributes as if those names had preceded, instead of grown out of, his clas-
sification of animals. The only peculiarity of the case is, that the conven-
ience of classification was here the primary motive for introducing the
names ; while in other cases the name is introduced as a means of predica-
tion, and the formation of a class denoted by it is only an indirect conse-
quence.
The principles which ought to regulate Classification, as a logical process
subservient to the investigation of truth, can not be discussed to any pur-
pose until a much later stage of our inquiry. But, of Classification as re-
sulting from, and implied in, the fact of employing general language, we
can not forbear to treat here, without leaving the theory of general names,
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 hand-
ed down from Aristotle, and his follower Porphyry, many of which have
taken a firm root in scientific, and some of them even in popular, phraseolo-
gy. The predicables are a fivefold division of General Xames, not ground-
ed 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
A species
A differentia
A proprium u&ov)
An accidens
It is to be remarked of these distinctions, that they express, 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 ex-
clusively species, or differentia ; but the same name is referred 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. Rectangu-
lar is one of the Differentia of a geometrical square ; it is merely one of
the Accidentia of the table at which I am writing. The words genus, spe-
cies, etc., 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 classi-
fication, that class occupies relatively to the particular subject.
3. Of these five names, two, Genus and Species, are not only used by
naturalists in a technical acceptation not precisely agreeing with their phil-
osophical meaning, but have also acquired a popular acceptation, much
more general than either. In this popular sense any two classes, one of
which includes the whole of the other and more, may be called a Genus
and a Species. Such, for instance, are Animal and Man ; Man and Mathe-
matician. Animal is a Genus; Man and Brute are its two species; or we
may divide it into a greater number of species, as man, horse, dog, etc.
Biped, or two-footed animal, may also be considered a genus, of which
96 NAMES AND PROPOSITIONS.
man and bird arc two species. Taste is a genus, of which sweet taste, sour
taste, salt taste, etc., are species. Virtue is a genus; justice, prudence,
courage, fortitude, generosity, etc., are its species.
The same class which is a genus with reference to the sub-classes or
species included in it, may be itself a species with reference to a more
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. Vir-
tue, a genus with reference to justice, temperance, etc., 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 importance which of the two modes
of speaking we adopt, provided the rest of our language is consistent with
it ; but, if we call the class itself the genus, we must not talk of predica-
ting the genus. We predicate of man the name mortal ; and by predica-
ting the name, we may be said, in an intelligible sense, to predicate what
the name expresses, the attribute mortality; but in no allowable sense of
the word predication do we predicate of man the class mortal. AVe predi-
cate of him the fact of belonging to the class.
By the Aristotelian logicians, the terms genus and species were used in
a more restricted sense. They did not admit every class which could be
divided into other classes to be a genus, or every class which could be in-
cluded 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, how-
ever, would not have been admitted to be a genus with reference to man,
but a proprium or accidens only. It was requisite, according to their
theory, that genus and species should be of the essence of the subject.
Animal was of the essence of man ; biped was not. And in every classi-
fication they considered some one class as the lowest or infirna species.
Man, for instance, was a lowest species. Any further divisions into which
the class might be capable of being broken down, as man into white, black,
and red man, or into priest and layman, they did not admit to be species.
It has been seen, however, in the preceding chapter, that the distinction
between the essence of a class, and the attributes or properties which are
not of its essence a distinction which has given occasion to so much ab-
struse 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 in-
dividuals, the word Essence, we found, has no meaning, except in connec-
tion with the exploded 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.
CLASSIFICATION AND THE PREDICABLES. 97
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 differ-
ences which exist among objects as differences in kind (genere or specie)
and others only as differences in the accidents? Were the schoolmen ri^ht
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, ground-
ed on differences of a comparatively superficial nature? Examination will
show that the Aristotelians did mean something by this distinction, and
something important; but which, being but indistinctly conceived, was in-
adequately 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, there-
fore, is boundless ; and there are as many actual classes (either of real or
of imaginary things) as there are general names, positive and negative to-
gether.
But if we contemplate any one of the classes so formed, such as the class
animal or plant, or the class sulphur or phosphorus, or the class white or
red, and consider in what particulars the individuals included in the class
differ from those which do not come within it, we find a very remarkable
diversity in this respect between some classes and others. There are some
classes, the things contained in which differ from other things only in cer-
tain particulars which may be numbered, while others differ in more than
can be numbered, more even than we need ever expect to know. Some
classes have little or nothing in common to characterize them by, except
precisely what is connoted by the name : white things, for example, 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 observations and ex-
periments, in the full confidence of discovering new properties which were
by no means implied in those we previously knew. While, if any one were
to propose for investigation the common properties of all things which are
of the same color, the same shape, or the same specific gravity, the absurd-
ity would be palpable. We have no ground to believe that any such com-
mon properties exist, except such as may be shown to be involved in the
supposition itself, or to be derivable from it by some law of causation. It
appears, therefore, that the properties, on which we ground our classes,
sometimes exhaust all that the class has in common, or contain it all by
some mode of implication ; but in other instances we make a selection of a
few properties from among not only a greater number, but a number inex-
haustible by us, and to which as we know no bounds, they may, so far as
we are concerned, be regarded as infinite.
There is no impropriety in saying that, of these two classifications, the
one answers to a much more radical distinction in the things themselves,
than the other does. And if any one even chooses to say that the one clas-
08 NAMES AND PROPOSITIONS.
sification is made by nature, the other by us for our convenience, lie will be
right ; provided he means no more than this : Where a certain apparent
difference between things (though perhaps in itself of little moment) an-
swers to we know not what number of other differences, pervading not
only their known properties, but properties yet undiscovered, it is not op-
tional but imperative to recognize this difference as the foundation of a
specific distinction ; 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 1 for which the classification is made does
not require attention to those particular properties. The differences, how-
ever, are made by nature, in both cases ; while the recognition of those dif-
ferences 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 classifica-
tion would be subverted if no notice were taken of the difference, while in
the other case, the necessity of taking notice of it depends on the impor-
tance or unimportance of the particular qualities in which the difference
happens to consist.
No\v, 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 hind, 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, Isaac Newton would be said to be of the species man. There arc
indeed numerous sub-classes included in the class man, to which Newton
also belongs; for example, Christian, and Englishman, and Mathematician.
But these, though distinct classes, are not, in our sense of the term, distinct
Kinds of men. A Christian, for example, differs from other human be-
ings; 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 should never think of inquiring what properties, unconnected with
Christianity, either as cause or effect, are common to all Christians and pe-
culiar to them ; while in regard to all Men, physiologists are perpetually
carrying on such an inquiry ; nor is the answer ever likely to be completed.
Man, therefore, we may call a species ; Christian, or Mathematician, we
can not.
Note here, that it is by no means intended to imply that there may not
be different Kinds, or logical species, of man. The various races and tem-
peraments, the two sexes, and even the various ages, may be differences of
kind, within our meaning of the term. I do not say that they are so. For
in the progress of physiology it may almost be said to be made out, that
the differences which really exist between different races, sexes, etc., follow
CLASSIFICATION AND THE PREDICABLES. 99
as consequences, under laws of nature, from a small number of primary
differences which can be precisely 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 afterward proved not to be so.
But if it turned out that the differences were not capable of being thus ac-
counted for, then Caucasian, Mongolian, Negro, etc., would be really differ-
ent 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 supposed that they 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 differences can all be traced
to climate and habits, or to some one or a few special differences in struc-
ture, they are not, in the logician's view, specifically distinct.
When the injima species, or proximate Kind, to which an individual
belongs, has been ascertained, the properties common to that Kind include
necessarily the whole of the common properties of every other real Kind
to which the individual can be referrible. Let the individual, for example,
be Socrates, and the 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 ani-
mals 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 fiat-nosed; that
being a class which includes Socrates, without including all men. To de-
termine whether it is a real Kind, we must ask ourselves this question :
Have all flat-nosed animals, in addition to whatever is implied in their flat
noses, any 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 proxi-
mate Kind. Therefore, the properties of the proximate Kind do compre-
hend 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 popu-
lar 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 distinguished from all other classes
by an indeterminate multitude of properties not derivable from one an-
other, is either a genus or a species. A Kind which is not divisible into
other Kinds, can not 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
100 NAMES AND PROPOSITIONS.
genera above (Species Pnedicabilis and Species Subjicibilis). But every
Kind which admits of division into real Kinds (as animal into mammal,
bird, fish, etc., 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 predica-
bles, 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 the attribute which distin-
guishes 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 signifies. For we have seen that every Kind (and a species must be a
Kind) is distinguished from other Kinds, not by any one attribute, but by
an indefinite number. Man, for instance, is a species of the genus 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
Differentia ; 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 at-
tributes by which the species man is distinguished from other species of
the same genus: would this attribute serve equally well for a differentia?
The Aristotelians say No ; having laid it down that the differentia must,
like the genus and species, be of the essence of the subject.
And here we lose even that vestige of a meaning grounded in the nature
of the things themselves, which may be supposed to be attached to the
word essence when it is said that genus and species must be of the essence
of the thing. There can be no doubt that when the schoolmen talked of
the essences of things as opposed to their accidents, they had confusedly
in view the distinction between differences of kind, and the differences
which are not of kind ; they meant to intimate that genera and species
must be Kinds. Their notion of the essence of a thing was a vague notion
of a something which makes it what it is, i. e., which makes it the Kind of
thing that it is which causes it to have all that variety of properties which
distinguish its Kind. But when the matter came to be looked at more
closely, nobody could discover what caused the thing to have all those prop-
erties, nor even that there was any thing which caused it to have them.
Logicians, however, not liking to admit this, and being unable to detect
what made the thing to be what it was, satisfied themselves with what
made it to be what it was called. Of the innumerable properties, known
and unknown, that are 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 beer, thus distinguished from the rest either for their
greater obviousness, or for greater supposed importance. These prop-
erties, then, which were connoted by the name, logicians seized upon, and
called them the essence of the species; and not stopping there, they af-
firmed them, in the case of the injima species, to be the essence of the in-
dividual too ; for it was their maxim, that the species contained the " whole
essence" of the thing. Metaphysics, that fertile field of delusion propa-
gated 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 cook-
ing their food, not being connoted, was relegated to the class of accidental
properties.
CLASSIFICATION AND THE PREDICABLES. 1Q1
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 attributes which the genus connotes, or there would be
nothing to prevent it from denoting individuals not included in the genus.
And it must connote something besides, otherwise it would include the
whole genus. Animal denotes all the individuals denoted by man, and
many more. Man, therefore, must connote all that animal connotes, other-
wise there might be men who are not animals ; and it must connote some-
thing more than animal connotes, otherwise all animals would be men.
This surplus of connotation this which the species connotes over and
above the connotation of the genus is the Differentia, or specific differ-
ence ; or, to state the same proposition in other words, the Differentia is
that which must be added to the connotation of the genus, to complete the
connotation of the species.
The word man, for instance, exclusively of what it connotes 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 h'uman. The Differentia,
or specific difference, therefore, of man, as referred to the genus animal, is
that outward form and the possession of reason. The Aristotelians said,
the possession of reason, without the 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 suf-
ficed 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 classification of them most in ac-
cordance with the order in which, for zoological purposes, he considers it
desirable that we should think of them. With this view he finds it advisa-
ble 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 carnivorous, and frugivorous or graminiv-
orous ; 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 spon-
taneously referred ; nor should we ever think of assigning to them so prom-
inent a position in our arrangement of the animal kingdom, unless for a pre-
conceived 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
102 NAMES AND PROPOSITIONS.
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 demarkations in our arrangement of objects run in lines not coin-
ciding with any distinction of Kind, and so creating genera and species in
the popular sense which are not genera or species in the rigorous sense at
all ; (I fortiori must we be warranted, when our genera and species are real
genera and species, in marking the distinction between them by those of
their properties which considerations of practical convenience most strong-
ly recommend. If we cut a species out of a given genus the species man,
for instance, out of the genus animal with an intention on our part that
the peculiarity by which we are to be guided in the application of the
name man should be rationality, then rationality is the differentia of the
species man. Suppose, however, that being naturalists, we, for the pur-
poses of our particular study, cut out of the genus animal the same species
man, but with an intention that the distinction 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 rational-
ity, 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 inaxim,
that wherever there is a Genus, and a Species marked out from that genus
by an assignable differentia, the name of the species must be connotative,
and must connote the differentia ; but the connotation may be special not
involved in the signification of the term as ordinarily used, but given to it
when employed as a term of art or science. The word Man in common
use, connotes rationality and a certain form, but does not connote the num-
ber or character of the teeth; in the Linnoean system it connotes the num-
ber of incisor and canine teeth, but does not connote rationality nor any
particular form. The word man has, therefore, two different meanings;
though not commonly considered as ambiguous, because it happens in both
cases to denote the same individual objects. But a case is conceivable in
which the ambiguity would become evident: we have only to imagine that
some new kind of animal were discovered, having Linna-us's three char-
acteristics of humanity, but not rational, or not of the human form. In
ordinary parlance, these animals would not be called men; but in natural
history' they must still be called so by those, if any there should be, who
adhere to- the Linnaean 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 nothing; it merely denotes the at-
tribute corresponding to a certain sensation : but if we are making a clas-
sification of colors, and desire to justify, or even merely to point out, the
particular place assigned to whiteness in our arrangement, we may define
it "the color 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,
CLASSIFICATION AND THE PREDICABLES. 1Q3
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 tech-
nical, which distinguishes the species in question from all other species of
the genus to which on the particular occasion we are referring it.
V. Having disposed of Genus, Species, and Differentia, we shall not find
much difficulty in attaining a clear conception of the distinction between
the other two predicables, as well as between them and the first three.
In the Aristotelian phraseology, Genus and Differentia are of the essence
of the subject ; by which, as we have seen, is really meant that the proper-
ties signified by the genus and those signified by the differentia, form part
of the connotation of the name denoting the species. Propriimi and Ac-
cidens, 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 only,
Proprium being another sort. Proprium, continue the schoolmen, is pred-
icated accidentally, indeed, but necessarily; or, as they further explain it,
signifies an attribute which is not indeed part of the essence, but which
flows from, or is a 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 necessarily be possessed by whatever
comes under that definition. Accidens, on the contrary, has no connection
whatever with the essence, but may come and go, and the species still 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 neces-
sarily consequent, and therefore without its essence, without that which con-
stitutes 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 sup-
posing any of the essential properties of the species to be altered, since
with them an Accidens has no connection.
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
purpose), 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 con-
sequently 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 connoted by it,
namely, from having the opposite sides straight lines and parallel, and the
number of sides four. The attribute, therefoi'e, of having the opposite
sides equal, is a Proprium of the class parallelogram ; and a Proprium of
the first kind, which follows from the connoted attributes by way of dem-
* If we allow a differentia to what is not really a species. For the distinction of Kinds,
in the sense explained by us, not being in anyway 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.
104 NAMES AND PROPOSITIONS.
onstration. The attribute of being capable of understanding language, is
a Proprium of the species man, since without being connoted by the word,
it follows from an attribute 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 causation. How it is that one property of a thing fol-
lows, or can be inferred, from another; under what conditions this is pos-
sible, and what is the exact meaning of the phrase; are among the ques-
tions which will occupy us in the two succeeding Books. At present it
needs only be said, that whether a Proprium follows by demonstration 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 constitu-
tion either of our thinking faculty or of the universe.
8. Under the remaining practicable, Accidens, are included all attri-
butes 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 connection with attributes which are so involved. They are
commonly divided into Separable and Inseparable Accidents. Inseparable
accidents are those which although we know of no connection between
them and the attributes constitutive of the species, and although, therefore,
so far as we are aware, they might be absent without making the name in-
applicable 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 attribute of a crow, and, as far
as we know, a 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 con-
note, 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, how-
ever, none but black crows are known to exist, blackness, in the present
state of our knowledge, ranks as an accident, but an inseparable accident,
of the species crow.
Separable Accidents are those 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 color of a European is one of the separable accidents of the spe-
cies 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 spe-
cies 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.
DEFINITION. 105
CHAPTER VIII.
OF DEFINITION.
1. ONE necessary part of the theory of Names and of Propositions re-
mains to be treated of in this place: the theory of Definitions. As being
the most important of the class of propositions which we have character-
ized as purely verbal, they have already received some notice in the chapter
preceding the last. But their fuller treatment was at that time postponed,
because definition is so closely connected with classification, that, until the
nature of the latter process is in some measure understood, the former can
not 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, can not 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 can not of course be declared ;
though we may indicate by language, as we might indicate still more con-
veniently 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 propo-
sitions 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 him, which, however, has not been esteemed one of the modes of defi-
nition.
In the case of connotative names, the meaning, as has been so often ob-
served, is the connotation ; and the definition of a connotative name, is the
proposition which declares its connotation. This might be done either di-
rectly 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 any thing,
signifies the possession of such and such attributes by that thing." Or
thus : Man is every thing which possesses such and such attributes : Man
is every thing which possesses corporeity, organization, life, rationality, and
certain peculiarities of external form.
This form of definition is the most precise and least equivocal of any;
but it is not brief enough, and is besides too technical for common discourse.
The more usual mode of declaring the connotation of a name, is to predi-
cate 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 syn-
onymous, as, " Man is a human being," which is not commonly accounted a
106 NAMES AND PROPOSITIONS.
definition at all ; or by predicating t\vo 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 con-
notative 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 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 in-
cluded in the definition, if complete, and may be evolved from it 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 be an
analysis. To resolve any complex whole into the elements of which it is
compounded, 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 in-
stance, " 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 explanation may be
given of its meaning than is contained in the proposition, " Rational is that
which possesses the attribute of reason ;" since the attribute reason itself
admits of being defined. And here we must turn our attention to the def-
initions of attributes, or rather of the names of attributes, that is, of ab-
stract names.
In regard to such names of attributes as are connotative, and express
attributes of those attributes, there is no difficulty: 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 a
union of several : we have only, therefore, to put together the names of all
the attributes taken separately, and we obtain the definition of the name
which belongs to them all taken together; a definition which will corre-
spond exactly to that of the corresponding concrete name. For, as we de-
fine 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 compli-
DEFINITION. 10 <7
cation 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 for-
mer chapter the foundation of the attribute, we must, therefore, have re-
course for its definition. Now, the foundation of the attribute may be
a phenomenon of any degree of complexity, consisting of many different
parts, either co-existent or in succession. To obtain a definition of the attri-
bute, we must analyze 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 ascribe 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 analyze, that is, to distinguish into parts, the attri-
bute or set of attributes which constitute the meaning both of the concrete
name and of the corresponding abstract : if a set of attributes, by enumer-
ating them ; if a single attribute, by dissecting the fact or phenomenon
(whether of perception or of internal consciousness) which is the foundation
of the attribute. But, further, even when the fact is one of our simple
feelings or states of consciousness, and therefore unsusceptible of analy-
sis, the names both of the object and of the attribute still admit of defini-
tion ; or rather, would do so if all our simple feelings had names. White-
ness may be defined, the property or power of exciting the sensation of
white. A white object may be defined, an object which excites the sensation
of white. The only names which are unsusceptible of definition, because
their meaning is unsusceptible of analysis, are the names of the simple feel-
ings themselves. These are in the same condition as proper names. They
are not indeed, like proper names, unmeaning ; for the words sensation
of white signify, that the sensation which I so denominate resembles other
sensations which I remember to have had before, and to have called by that
name. But as we have no words by which to recall those former sensations,
except the very word which we seek to define, or some other which, being
exactly synonymous with it, requires definition as much, words can not un-
fold 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, I pro-
ceed to examine some opinions of philosophers, and some popular concep-
tions 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 man-
ner inconsistent with custom and convention. Any thing, therefore, is to
them a sufficient definition of a term, which will serve as a correct index
to what the term ffenotes ; though not embracing the whole, and some-
times, 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 Definitions, or Descriptions. In the former, a
connotative name is defined by a part only of its connotation ; in the latter,
by something which forms no part of the connotation at all.
108 NAMES AND PROPOSITIONS.
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
enumerated attributes, possess also those which are omitted : so that the
field of predication which the word covers, and the employment 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 constitutive of the species, but some one of those peculiarities
only, a complete definition would be per genus et differentias, rather than
differentiavn. It would include, with the name of the superior genus, not
merely some attribute which distinguishes the species intended to be de-
fined from all other species of the same genus, but all the attributes im-
plied 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 differentia. 1 , is not tenable. It was early
remarked by logicians, that the summum genus in any classification, hav-
ing 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.
4. Although the first kind of imperfect definition (which defines a con-
notative term by a part only of what it connotes, but a part sufficient to
mark out correctly the boundaries of its denotation), has been considered
by the ancients, and by logicians in general, as a complete definition ; it has
always been deemed necessary that the attributes employed should really
form part of the connotation ; for the rule was that the definition must be
drawn from the essence of the class ; and this would not have 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 connotation has been rejected from the rank
of genuine Definition by all logicians, and has been termed Description.
This kind of imperfect definition, however, takes its rise from the same
cause as the other, namely, the willingness to accept as a definition any thing
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 con-
sequently to employ the term in predication without deviating from estab-
lished 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 pe-
culiar to it, though separately each of those attributes may be common to
DEFINITION. 10 g
it with some other things. It is only necessary that the definition (or de-
scription) thus formed, should be convertible with the name which it pro-
fesses to define ; that is, should be exactly co-extensive with it, being pred-
icable of every thing of which it is predicable, and of nothing of which it
is not predicable ; though the attributes specified may have no connection
with those which mankind had in view when they formed or recognized the
class, and gave it a name. The following are correct definitions of Man,
according to this test : Man is a mammiferous animal, having (by nature)
two hands (for the human species answers to this description, and no other
animal does) : Man is an animal who cooks his food : Man is a featherless
biped.
What would otherwise be a mere description, may be raised to the rank
of a real definition by the peculiar purpose which the speaker or writer
has in view. As was seen in the preceding chapter, it may, for the ends
of a particular art or science, or for the more convenient statement of an
author's particular doctrines, be advisable to give to some general name,
without altering its denotation, a special connotation, different from its or-
dinary 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 actual-
ly occurs with respect to one of the preceding examples, "Man is a mam-
miferous 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 declaration of the
meaning which in the particular instance the name is appointed to convey
it can not be said that to state the meaning of the word is the purpose r,f
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 orl a
certain principle, that is, according to a certain set of distinctions, A^nd
since the definition of Man according to the ordinary connotation oft the
word, though it would have answered every other purpose of a definPiior,
would not have pointed out the place which the species ought to oc^cury
in that particular classification ; he gave the word a special connot,'atin,
that he might be able to define it by the kind of attributes on wh'/ch,for
reasons of scientific convenience, he had resolved to found his div'isioi of
animated nature.
Scientific definitions, whether they are definitions of scientific terras, or
of common terms used in a scientific sense, are almost always of thj kind
last spoken of : their main purpose is to serve as the landmarks of scien-
tific classification. And since the classifications in any scier '^"'ire con-
tinually modified as scientific knowledge advances, the defin^^s in the
sciences are also constantly varying. A striking instance is'^'^'orded by
the words Acid and Alkali, especially the former. As expe n \i ental dis-
covery advanced, the substances classed with acids have be 1 "constantly
multiplying, and by a natural consequence the attributes coO c ^ted by the
word have receded and become fewer. At first it connoted ^ attributes,
of combining with an alkali to form a neutral substance (ci^'ed a salt) ;
being compounded of a base and oxygen ; causticity to the ta i,-^ and touch ;
fluidity, etc. The true analysis of muriatic acid, into chlor' 1 e and hydro-
110 NAMES AND PROPOSITIONS.
gen, 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 sus-
pected, there is now a tendency to include the presence of this element in
the connotation of the word. But carbonic acid, silica, sulphurous acid,
have no hydrogen in their composition; that property can not, therefore,
be connoted by the term, unless those substances are no longer to be con-
sidered acids. Causticity and fluidity have long since been excluded from
the characteristics of the class, by the inclusion of silica and many other
substances in it; and the formation of neutral bodies by combination with
alkalis, together with such electro-chemical peculiarities as this is supposed
to imply, are now the only dijferentiie 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 accordingly (as observed in the In-
troductory Chapter of this work), the definition of a science must neces-
sarily be progressive and provisional. Any extension of knowledge or al-
teration in the current opinions respecting the subject-matter, may lead to
a change more or less extensive in the particulars included in the science ;
and its composition being thus altered, it may easily happen that a different
set of characteristics will be found better adapted as differentiae for defin-
ing its name.
In the same manner in which a special or technical definition has for its
object to expound the artificial classification out of which it grows; the
Aristotelian logicians seem to have imagined that it was also the business
>f ordinary definition to expound the ordinary, and what they deemed the
natural, classification of things, namely, the division of them into Kinds;
.o nd to show the place which each Kind occupies, as superior, collateral, or
subordinate, among other Kinds. This notion would account for the rule
th.at all definition must necessarily be per genus et differentiam, and would
alsio explain why a single differentia was deemed sufficient. But to ex-
joiVnd, or express in words, a distinction of Kind, has already been shown
t> & an impossibility : the very meaning of a Kind is, that the properties
which distinguish it do not grow out of one another, and can not therefore
bese't forth in words, even by implication, otherwise than by enumerating
then ^11 : 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 crily required that the definition of a Kind should indicate what kinds
inclule it or are included by it, any definitions which expound the connota-
tion cf the names will do this: for the name of each class must necessarily
connote enough of its properties to fix the boundaries of the class. If the
definition, therefore, be a full statement of the connotation, it is all that a
definition i can be required to be.*
F
* Profes."^ Bain, in his Logic, takes a peculiar view of Definition. He holds (i., 71) with
the present U irk, that "the definition in its full import, is the sum of all the properties con-
noted by thei ame; it exhausts the meaning of a word. 1 ' Hut he regards the meaning of a
general name?' 5 including, not indeed all the common properties of the class named, hut all
of them that i,^ l , ultimate properties, not resolvable into one another. "The enumeration of
the attributes o\ oxygen, of gold, of man, should be an enumeration of the final (so far as can
be made out), ft .e underivable, powers or functions of each," and nothing less than this is a
complete Definittm (i., 7f>). An independent property, not derivable from other properties,
even if previouslV^unknown, yet as soon as discovered becomes, according to him, part of the
DEFINITION.
Ill
5. Of the two incomplete and popular modes of definition, and in what
they differ from the complete or philosophical mode, enough has now been
said. We shall next 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 treated are only one of two sorts into which defini-
tions may be divided, viz., definitions of names, and definitions of things.
The former are intended to explain the meaning of a term ; the latter, the
nature of a thing; the last being incomparably the most important.
This opinion was held by the ancient philosophers, and by their follow-
ers, 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 definitions of things has been to a certain extent in
abeyance, still continuing, however, to breed confusion in logic, by its con-
sequences 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 word, Archbishop
Whately's Logic* In a review of that work published by me in the West-
meaning of the term, and should be included in the definition. "When we are told that dia-
mond, which we know to be a transparent, glittering, hard, and high-priced substance, is com-
posed of carbon, and is combustible, we must put these additional properties on the same level
as the rest; to us they are henceforth connoted by the name"(i., 73). Consequently the
propositions that diamond is composed of carbon, and that it is combustible, are regarded by
Mr. Bain as merely verbal propositions. He carries this doctrine so far as to say that unless
mortality can be shown to be a consequence of the ultimate laws of animal organization, mor-
tality is connoted by man, and " Man is Mortal " is a merely verbal proposition. And one of
the peculiarities (I think a disadvantageous peculiarity) of his able and valuable treatise, is
the large number of propositions requiring proof, and learned by experience, which, in con-
formity with this doctrine, he considers as not real, but verbal, propositions.
The objection I have to this language is that it confounds, or at least confuses, a much
more important distinction than that which it draws. The only reason for dividing Proposi-
tions into real and verbal, is in order to discriminate propositions which convey information
about facts, from those which do not. A proposition which affirms that an object has a given
attribute, while designating the object by a name which already signifies the attribute, adds
no information to that which was already possessed by all who understood the name. But
when this is said, it is implied that, by the signification of a name, is meant the signification
attached to it in the common usage of life. I can not think we ought to say that the meaning
of a word includes matters of fact which are unknown to every person who uses the word un-
less he has learned them by special study of a particular department of Nature ; or that because
a few persons are aware of these matters of fact, the affirmation of them is a proposition con-
veying no information. I hold that (special scientific connotation apart) a name means, or
connotes, only the properties which it is a mark of in the general mind ; and that in the case
of any additional properties, however uniformly found to accompany these, it remains possible
that a thing which did not possess the properties might still be thought entitled to the name.
Ruminant, according to Mr. Bain's use of language, connotes cloven-hoofed, since the two
properties are always found together, and no connection has ever been discovered between
them: but ruminant does not mean cloven-hoofed; and were an animal to be discovered
which chews the cud, but has its feet undivided, I venture to say that it would still be called
ruminant.
* 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 im-
portant sense, distinct. He seems (9th ed., p. 145) to limit the notion of a Rer.l 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 every thing 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 De-
scription, I conceive, can only be ranked among Definitions, when taken (as in the case of the
zoological definition of man) to fulfill the true office of a Definition, by declaring the connota-
tion given to a word in some special use, as a term of science or art : which special conno-
112 NAMES AND PROPOSITIONS.
minster 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 defini-
tions of words and what are called definitions of things, though conforma-
ble to the ideas of most of the Aristotelian logicians, can not, as it appears
to us, be maintained. We apprehend that no definition is ever intended to
'explain and unfold the nature of a thing.' It is some confirmation of our
opinion, that none of those writers who have thought that there were defini-
tions of things, have ever succeeded 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 proposi-
tion in which any quality whatever is predicated of the thing, unfolds some
part of its nature. The true state of the case \ve 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, can not be
collected from the mere form of the expression. 'A centaur is an animal
with the upper parts of ti man and the lower parts of a horse,' and 'A tri-
angle is a rectilineal figure with three sides,' are, in form, expressions pre-
cisely similar; although in the former it is not implied that any thiny, con-
formable 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,' etc., the sense would remain un-
changed: in the second, 'A triangle means,' etc., the meaning would be al-
tered, 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.
" 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 proposi-
tions, 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
tation of course would not be expressed by the proper definition of the word in its ordinary
employment.
Air. I)e Morgan, exactly reversing the doctrine of Archbishop Whately, understands by a
Real Definition one which contains less than the Nominal Definition, provided only that what
it contains is sufficient for distinction. "Uy 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. !5(>. Mr. De Morgan's gen-
eral proposition and his example are at variance ; for the peculiar mode of drinking of the
elephant certainly forms no part of the meaning of the word elephant. It could not be said,
because a person happened to be ignorant of this property, that he did not know what an
elephant means.
DEFINITION. 113
latter is a mere nominal definition, or explanation of the use and applica-
tio r / 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 consequences 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.
"VVe have already made, and shall often have to repeat, the remark, that
the philosophers who overthrew Realism by no means got rid of the con-
sequences of Realism, but retained long afterward, in their own philosophy,
numerous propositions which could only have a rational meaning as part
of a Realistic system. It had been handed down from Aristotle, and prob-
ably from earlier times, as an obvious truth, that the science of Geometry
is deduced from definitions. This, so long as a definition was considered
to be a proposition " unfolding the nature of the thing," did well enough.
But Hobbes followed, and rejected utterly the notion that a definition de-
clares the nature of the thing, or does any thing but state the meaning of
a name ; yet he continued to affirm as broadly as any of his predecessors,
that the up-^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 sig-
nification 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 at-
tempt so often made, to escape from the necessity of abandoning old lan-
guage after the ideas which it expresses have been exchanged for contrary
ones. From the meaning of a name (we are told) it is possible to infer
physical facts, provided the name has corresponding to it an existing thing.
But if this proviso be 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 analyzed, con-
sists 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 with-
in 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 defini-
tion, and observe to which of the two propositions contained in it the dem-
onstration really appeals. " About the centre A, describe the circle B C D."
8
114 NAMES AND PROPOSITIONS.
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 dis-
tance from the point A." By this the definition of a circle would be got
rid of, and rendered needless; 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 C D is a circle, the radius
B A is equal to the radius C A." B A is equal to C A, not because BCD
is a circle, but because B C D is a figure with the radii equal. Our war-
rant 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 admissibility
of these postulates rests on intuition, or on proof, may be a matter of dis-
pute ; but in either case they are the premises on which the theorems de-
pend ; and while these are retained it would make no difference in the cer-
tainty 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 near-
ly self-evident; but when a distinction, obvious as it may appear, has been
confounded, and by powerful intellects, it is better to say too much than
too little for the purpose of rendering such mistakes impossible in future.
I will, therefore detain the reader while I point out one of the absurd con-
sequences 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.
This proposition, considered only as a definition, is indisputably 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 ex-
istence 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 can not be true. But the premises, considered as
parts of a definition, are true. Therefore, the premises considered as parts
of a definition can not be the real ones. The real premises must be
A dragon is a really existing thing which breathes flame :
A dragon is a really existing serpent :
which implied premises being false, the falsity of the conclusion presents
no absurdity.
If we would determine what conclusion follows from the same ostensible
premises when the tacit assumption of real existence is left out, let us, ac-
DEFINITION. 115
cording 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 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 elements. The truth of the conclusion fol-
lows from the existence of the psychological phenomenon called the idea of
a dragon ; and therefore still from the tacit assumption of a matter of fact.*
When, as in this last syllogism, the conclusion is a proposition respecting
an idea, the assumption on which it depends may be merely that of the ex-
istence of an idea. But when the conclusion is a proposition concerning a
Thing, the postulate involved in the definition which stands as the apparent
premise, is the existence of a thing conformable to the definition, and not
merely of an idea conformable to it. This assumption of real existence we
always convey the impression that we intend to make, when we profess to
define any name which is already known to be a name of really existing
objects. On this account it is, that the assumption was not necessarily
implied in the definition of a dragon, while there was no doubt of its be-
ing included in the definition of a circle.
* In the only attempt which, so far as I know, has been made to refute the preceding argu-
mentation, 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 can
not 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) serpent : from which it undoubtedly
follows, that there are serpents which are imagined to breathe flame ; but the major premise
is not a definition, nor part of a definition ; which is all that I am concerned to prove.
Let us now examine the other assertion that if the word serpent stands for none but real
serpents, the minor premise (a dragon is a serpent) is false. This is exactly what I have my-
self 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 premise can not be the definition, which is true, but the statement of fact,
which is false.
116 NAMES AND PROPOSITIONS.
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 lias 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
conclusions could rest on premises which, instead of being certainly 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 sup-
port 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 in-
dispensable that there should be found in definitions something more cer-
tain, or at least more accurately true, than the implied postulate of the real
existence of a corresponding object. And this something they flattered
themselves they had found, when they laid it down that a definition is a
statement and analysis not of the mere meaning of a word, nor yet of the
nature of a thing, but of an idea. Thus, the proposition, " A circle is a
plane figure bounded by a line all the points of which are at an equal dis-
tance from a given point within it," was considered by them, not as an as-
sertion 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 ac-
curately true.
Allowing this doctrine respecting the nature of demonstrative truth to
be correct (which, in a subsequent place, I shall endeavor to prove that it
is not) ; even on that supposition, the conclusions which seem to follow
from a definition, do not follow from the definition as such, but from an
implied postulate. Even if it be true that there is no object in nature an-
swering 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 as-
sumes 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 can not form any such notion; it can
not conceive length without breadth ; it can only, in contemplating objects,
attend to their length, exclusively of their other sensible qualities, and so
determine what properties may be predicated of them in virtue of their
length alone. If this be true, the postulate involved in the geometrical
definition of a line, is the real 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 of all physical objects in so far as possessing length. ]>ut
even what I hold to be the false doctrine on the subject, leaves the conclu-
DEFINITION. in
sion that our reasonings are grounded on the matters of fact postulated in
definitions, and not on the definitions themselves, entirely unaffected ; and
accordingly this conclusion is one which I have in common with Dr. Whe-
well, 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 eminently serviceable in clearing from confusion the initial
steps in the analysis of the mental processes, even where his views respect-
ing the ultimate analysis are such as (though with unfeigned respect) I can
not 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 in-
quiry of considerable difficulty and intricacy, but may involve considera-
tions going deep into the nature of the things which are denoted by the
name. Such, for instance, are the inquiries which form the subjects of the
most important of Plato's 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 funda-
mental question with speculative moralists in all ages, " What is virtue ?"
It would be a mistake to represent these difficult and 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 at-
tributes which it connotes, the objects were 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 dis-
tinctly 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 dis-
tinct conception in his mind of the attribute signified by the name.
But Avhere the resemblances and differences on which our classifications
are founded are not of this palpable and easily determinable kind; especial-
ly 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 discrimi-
nated, and referred each to its true source ; it often happens that names
are applied to namable objects, with no distinct connotation present to the
minds of those who apply them. They are only influenced by a general
resemblance between the new object and all or some of the old familial-
objects which they have been accustomed to call by that name. This, as
we have seen, is the law M'hich even the mind of the philosopher must fol-
low, in giving names to the simple elementary feelings of our nature : but,
where the tilings to be named are complex wholes, a philosopher is not
content with noticing a general resemblance ; he examines what the resem-
blance consists in : and he only gives the same name to things which re-
1 1 8 NAMES AND PROPOSITIONS.
soluble one another in the same definite particulars. The philosopher,
therefore, habitually employs his general names with a definite connota-
tion. 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 can not be brought
before the tribunal of the outward senses to be identified and discriminated,
connote little more than a vague gross resemblance to the things which
they were earliest, or have been most, accustomed to call by those names.
When, for instance, ordinary persons predicate the words just or unjust
of any action, noble or mean of any sentiment, expression, or demeanor,
statesman or charlatan of any personage figuring in polities, do they mean
to affirm of those various subjects any determinate attributes, of whatever
kind ? No: they merely recognize, as they think, some likeness, more or
less vague and loose, between these and some other things which they
have been accustomed to denominate or to hear denominated by those ap-
pellations.
Language, as Sir James Mackintosh used to say of governments, "is not
made, but grows." A name is not imposed at once and by previous pur-
pose upon a class of objects, but is first applied to one thing, and then ex-
tended 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 applied 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 confused huddle of
objects, having nothing whatever in common ; and connotes nothing, not
even a vague and general resemblance. When a name has fallen into this
state, in which by predicating it of any object we assert literally nothing
about the object, it has become unfit for the purposes either of thought or
of the communication of thought; and can only be made serviceable by
stripping it of some part of its multifarious denotation, and confining it to
objects possessed of some attributes in 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 con-
tinual mending in order to be passable.
From this it is already evident, why the question respecting the defini-
tion 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 an-
swer is, that having come to no precise agreement on the point, they do
not mean to predicate distinctly any attribute at all. Nevertheless, all be-
lieve that there is some common attribute belonging to all the actions which
they are in the habit of calling just. The question then must be, whether
there is any such common attribute? and, in the first place, whether man-
kind 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 ac-
tions 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 inqui-
ries 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,
DEFINITION. 119
often more arduous than all the rest, namely, how best to form a class arti-
ficially, 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 re-
model them. The classifications rudely made by established language, when
retouched, as they almost all require to be, by the hands of the logician,
are often 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 in-
strument than the latter ; but being the result of a long, though unscien-
tific, course of experience, they contain a mass of materials which may be
made very usefully available in the formation of the systematic body of
written law. In like manner, the established grouping of objects under a
common name, even when founded only on a gross and general resemblance,
is evidence, in the first place, that the resemblance is obvious, and therefore
considerable; and, in the next place, that it is a resemblance Avhich 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 common to them
all, still at every step in its progress we shall find such a resemblance. And
these transitions of the meaning of words are often an index to real con-
nections between the things denoted by them, which might otherwise escape
the notice of thinkers ; of those at least who, from using a different lan-
guage, 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
perceiving 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 any tiling else than a mere comparison of authorities, we tacit-
ly assume that a meaning must be found for the name, compatible with its
continuing to denote, if possible all, but at any rate the greater or the more
important part, of the things of which it is commonly predicated. The in-
quiry, 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 re-
semblance can be traced : and finally, what are the common attributes, the
possession of which gives to them all, or to that portion of them, the char-
acter 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 in-
* "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 intuitively, an unobvious link of connection, 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 vainglory of the mere logician, who, hobbling
after him, evinces his own superior wisdom by pausing on its brink, and giving up as desper-
ate his proper business of bridging it over."
120 NAMES AND PROPOSITIONS.
stead of a vague connotation ; and by possessing this distinct connotation,
becomes susceptible of definition.
In giving a distinct connotation to the general name, the philosopher will
endeavor 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 them-
selves ; either directly, or from the number, the conspicuousness, or the in-
teresting character, of the consequences to which they lead. He will select,
as far as possible, such differentiae as lead to the greatest number of inter-
esting propria. For these, rather than the more obscure and recondite
qualities on which they often depend, give that general character and as-
pect to a set of objects, which determine the groups into which they natu-
rally fall. But to penetrate to the more hidden agreement on which these
obvious and superficial agreements depend, is often one of the most diffi-
cult of scientific problems. As it is among the most difficult, so it seldom
fails to be among the most important. And since upon the result of this
inquiry respecting the causes of the properties of a class of things, there in-
cidentally depends the question what shall be the meaning of a word ; some
of the most profound and most valuable investigations which philosophy
presents to us, have been introduced by, and have offered themselves under
the guise of, inquiries into the definition of a name.
BOOK II.
OF SEASONING.
uiv E TOVTWV Xeyoi/utv frfr], did rivaiv, Kai TCUTI, icai TTWI; yn/frai TTCIQ
vartpov le XIKTIOV irepl ciTroSti^tojg. Uportpov yap irtpi avXXoyiapov XiKTtov, r) irtpt dirodd-
aC> Sid TO Ka96\ov ndXXov tivai TOV avXXoyiafiov. 'H fiiv yap diroSd^i^, (jvXXoyifffio^ TIQ' 6
Si ov 7ra, cafoSn^iQ. ARIST., Analyt. Prior., 1. i. ? cap. 4.
CHAPTER I.
OP INFERENCE, OR REASONING, IN GENERAL.
1. IN the preceding Book, we have been occupied not with the nature
of Proof, but with the nature of Assertion : the import conveyed by a Prop-
osition, whether that Proposition 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 nec-
essary to understand what that is to which proof is applicable; what that
is which can be a subject of belief or disbelief, of affirmation or denial;
what, in short, the different kinds of Propositions assert.
This preliminary inquiry we have prosecuted to a definite result. Asser-
tion, in the first place, relates either to the meaning of words, or to some
property of the things which words signify. Assertions respecting the
meaning of words, among which 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 analyzed 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 what-
ever be the form of the proposition, and whatever its nominal subject or
predicate, the real subject of every proposition is some one or more facts
or phenomena 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 negative, of those phenomena or those
powers, is always either Existence, Order in Place, Order in Time, Causa-
tion, or Resemblance. This, then, is the theory of the Import of Proposi-
tions, reduced to its ultimate elements : but there is another and a less ab-
struse expression for it, which, though stopping short in an earlier stage of
the analysis, is sufficiently scientific for many of the purposes for which
such a general expression is required. This expression recognizes the com-
monly received distinction between Subject and Attribute, and gives the
following as the analysis of the meaning of propositions : Every Proposi-
122 REASONING.
tion asserts, that some given subject does or does not possess sonic attri-
bute ; 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 attri-
bute.
We shall now for the present take our leave of this portion of our in-
quiry, and proceed to the peculiar problem of the Science of Logic, name-
ly, how the assertions, of which we have analy/ed the import, are proved
or disproved ; such of them, at least, as, not being amenable to direct con-
sciousness or intuition, are appropriate subjects of proof.
We say of a fact or statement, that it is proved, when we believe its truth
by reason of some other fact or statement from* which it is said to follow.
Most of the propositions, whether affirmative or negative, universal, partic-
ular, 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 proposi-
tion 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 in-
quiry, and additional motives will be suggested by the considerations on
which we are now about to enter.
2. In proceeding to take into consideration the cases in which infer-
ences can legitimately be drawn, we shall first mention some cases in which
the inference is apparent, not real; and which require notice chiefly that
they may not be confounded with cases of inference properly so called.
This occurs when the proposition ostensibly inferred from another, appears
on analysis to be merely a repetition of the same, or part of the same, as-
sertion, which was contained in the first. All the cases mentioned in books
of Logic as examples of equipollency 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 AVC 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 a universal proposition, we affect to infer
another which differs from it only in being particular: as All A is 1>, there-
fore 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 predicate: as, Socrates is a man, therefore Socrates
is a living creature; where all that is connoted by living creature was af-
firmed 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 crea-
ture, therefore he is not a man ; for if we deny the less, the greater, which
includes it, is already denied by implication. These, therefore, arc not real-
INFERENCE IN GENERAL. 123
ly cases of inference ; and yet the trivial examples by which, in manuals of
Logic, the rules of the syllogism are illustrated, are often of this ill-chosen
kind ; formal demonstrations oi 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 proposition, Some A is B,
we may infer that Some B is A. From the universal negative, No A is B,
we may conclude that No B is A. From the universal affirmative proposi-
tion, All A is B, it can not be inferred that all B is A ; though all water is
liquid, it is not implied that all liquid is water; but it is implied that some
liquid is so ; and hence the proposition, All A is B, is legitimately convert-
ible into Some B is A. This process, which converts a universal propo-
sition into a particular, is termed conversion per accidens. From the prop-
osition, Some A is not B, we can not even infer that some B is not A ;
though some men are not Englishmen, it does not follow that some English-
men are not men. The only mode usually recognized of converting a par-
ticular negative proposition, is in the form, Some A is not B, therefore
something which is not B is A; and this is termed conversion by contra-
position. In this case, however, the predicate and subject are not merely
reversed, but one of them is changed. Instead of [A] and [B], the terms
of the new proposition are [a thing which is not B], and [A]. The origi-
nal proposition, Some A is not B, is first changed into a proposition equi-
pollent with it, Some A is " a thing which is not B ;" and the proposition,
being now no longer a particular negative, but a particular affirmative, ad-
mits of conversion in the first mode, or as it is called, simple conversion.!
In all these cases there is not really any inference ; there is in the con-
clusion no new truth, nothing but what was already asserted in the prem-
ises, and obvious to whoever apprehends them. The fact asserted in the
conclusion is either the very same fact, or part of the fact, asserted in the
original proposition. This follows from our previous analysis of the Im-
port of Propositions. "When we say, for example, that some lawful sov-
ereigns are tyrants, what is the meaning of the assertion? That the attri-
butes connoted by the term " lawful sovereign," and the attributes connoted
by the term " tyrant," sometimes co-exist in the same individual. Now this
is also precisely what we mean, when we say that some tyrants are lawful
sovereigns ; which, therefore, is not a second proposition inferred from the
first, any more than the English translation of Euclid's Elements is a col-
lection of theorems different from and consequences of, those contained in
the Greek original. Again, if we assert that no great general is a rash
man, we mean that the attributes connoted by " great general," and those
connoted by " rash," never co-exist in the same subject; which is also the
exact meaning which would be expressed by saying, that no rash man is a
* The different cases of Equipollency, or "Equivalent Prepositional Forms, "are set forth
with some fullness in Professor Bain's Logic. One of the commonest of these changes of
expression, that from affirming a proposition to denying- its negative, or vice versa, Mr. Bain
designates, very happily, by the name Obversion.
t As Sir William Hamilton lias 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. g. , Europeans).
124 REASONING.
ucreat general. When we say that all quadrupeds are warm-blooded, we
assert, not only that the attributes connoted by " quadruped " and those
connoted by " warm-blooded " sometimes co-exist, but that the former nev-
er exist without the latter : now the proposition, Some warm-blooded crea-
tures are quadrupeds, expresses the first half of this meaning, dropping the
latter half; and therefore has been already affirmed in the antecedent prop-
osition, All quadrupeds are warm-blooded. I>ut that all warm-blooded
creatures are quadrupeds, or, in other words, that the attributes connoted
by "warm-blooded" never exist without those connoted by "quadruped,"
has not been asserted, and can not be inferred. In order to re-assert, in an
inverted form, the whole of what was affirmed in the proposition, All quad-
rupeds are warm-blooded, we must convert it by contraposition, thus, Noth-
ing which is not warm-blooded is a quadruped. This proposition, and the
one from which it is derived, are exactly equivalent, and either of them may
be substituted for the other ; for, to say that when the attributes of a quad-
ruped are present, those of a warm-blooded creature are present, is to say
that when the latter are absent the former are absent.
In a manual for young students, it would be proper to dwell at greater
length on the conversion and equipollency of propositions. For though
that can not be called reasoning or inference which is a mere re-assertion in
different words of what had been asserted before, there is no more impor-
tant 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 lan-
guage. That important chapter in logical treatises which relates to the Op-
position of Propositions, and the excellent technical language which logic
provides for distinguishing the different kinds or modes of opposition, are
of use chiefly for this purpose. Such considerations as these, that contrary
propositions may both be false, but can not both be true ; that subcontrary
propositions may both be true, but can not 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 universal proves the truth of the
particular, and the falsity of the particular proves the falsity of the univer-
sal, but not vied versa ;* are apt to appear, at first sight, very technical and
mysterious, but when explained, seem almost too obvious to require so form-
al a statement, since the same amount of explanation which is necessary
to make the principles intelligible, would enable the truths which they con-
vey to be apprehended in any particular case which can occur. In this
respect, however, these axioms of logic are on a level with those of mathe-
matics. That things which are equal to the same thing are equal to one
another, is as obvious in any particular case as it is in the general state-
ment: and if no such general maxim had ever been laid down, the demon-
strations 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
* All A is B>
No AiBBj- Contrarie8 -
Some A is B >
SomeAi 8 notBJ- Bubcontraries -
" A I s B ' contradictories.
Some A is not 1$)
No A is B> ,
So me AisB,- alsocontra(llctones -
All A is B) , No AisB >
Some A is B)' nnd Some A is not Bj' *I*CtiTely subalternate.
INFERENCE IN GENERAL. 12 5
one has ever censured writers on geometry, for placing a list of these ele-
mentary 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 apprehending a general truth. And the student of logic, in the discus-
sion even of such truths as we have cited above, acquires habits of cir-
cumspect interpretation of words, and of exactly measuring the length and
breadth of his assertions, which are among the most indispensable condi-
tions 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 province of Reasoning
or Inference properly so called, the cases in which the progression from one
truth to another is only apparent, the logical consequent being a mere rep-
etition 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 ideally distinct 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 : rea-
soning from particulars to generals, and reasoning from generals to partic-
ulars ; the former being called Induction, the latter Ratiocination or Syllo-
gism. It will presently be shown that there is a third species of reasoning,
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 from particu-
lars to generals, and reasoning from generals to particulars, are recom-
mended by brevity rather than by precision, 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 proposition from propositions
less general than itself, and Ratiocination 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 prop-
osition, not alone (for from a single proposition nothing can be concluded
which is not involved in the terms), but by combining it with other propo-
sitions, 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 Ratiocination.
As all experience begins with individual cases, and proceeds 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, however, be advantageous, in a science which aims at tracing our
acquired knowledge to its sources, that the inquirer should commence with
the latter rather than with the earlier stages of the process of constructing
our knowledge ; and should trace derivative truths backward to the truths
from which they are deduced, and on which they depend tor their evidence,
before attempting to point out the original spring from which both ulti-
mately take their rise. The advantages of this order of proceeding in the
present instance will manifest themselves as we advance, in a manner su-
perseding the necessity of any further justification or explanation.
126 REASONING.
Of Induction, therefore, we shall say no more at present, than that it at
least is, without doubt, a process of real inference. 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 exam-
ined ; it is a generalization 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
induction we proceed from truths which we knew, to truths which we did
not know ; from facts certified by observation, to facts Avhich 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 evi-
dence 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 Syllogism, remains to be de-
termined by the examination into which we arc about to enter.
CHAPTER II.
OF RATIOCIXATIOX, OR SYLLOGISM.
1. THE analysis of the Syllogism lias been so accurately and fully per-
formed in the common manuals of Logic, that in the present work, which
is not designed as a manual, it is sufficient to recapitulate, menwriw caitsd,
the leading results of that analysis, as a foundation for the remarks to be
afterward made on the functions of the Syllogism, and the place which it
holds in science.
To a legitimate syllogism it is essential that there should be three, and
no more than three, propositions, namely, the conclusion, or proposition to
be proved, and two other 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 conclu-
sion, and another called the middle term, which must be found in both
premises, since it is by means of it that the other two terms are to be con-
nected together. The predicate of the conclusion is called the major term
of the syllogism; the subject of the conclusion is called the minor term.
As there can be but three terms, the major and minor terms must each be
found in one, and only one, of the premises, together with the middle term
which is in them both. The premise which contains the middle term aad
the major term is called the major premise ; that which contains the mid-
dle term and the minor term is called the minor premise.
Syllogisms are divided by some logicians into three jfif/itres, 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
RATIOCINATION, OR SYLLOGISM.
127
the middle term is the subject of the major premise and the predicate of
the minor. This is reckoned as the first figure. When the middle term is
the predicate in both premises, the syllogism belongs to the second figure ;
when it is the subject in both, to the third. In the fourth figure the mid-
dle term is the subject of the minor premise and the predicate of the major.
Those writers who reckon no more than three figures, include this case in
the first.
Each figure is divided into moods, according to what are called the quan-
tity and quality of the propositions, that is, according as they are universal
or particular, affirmative or negative. 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 mid-
dle term.
FIRST FIGURE.
All B is C
All A is B
therefore
All A is C
No C is B
All A is B
therefore
No A is C
No B is C
All A is B
therefore
No A is C
All B is C
Some A is B
therefore
Some A is C
SECOND FIGURE.
All C is B No C is B
No A is B Some A is B
therefore therefore
No A is C Some A is not C
THIRD FIGURE.
No B is C
Some A is B
therefore
Some A is not C
All C is B
Some A is not B
therefore
Some A is not C
All C is B
No B is A
therefore
Some A is not C
FOURTH FIGURE.
Some C is B No C is B
All B is A All B is A
therefore therefore
Some A is C Some A is not C
No C is B
Some B is A
therefore
Some A is not C
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 Bis A All Bis A All B is A SomeBisA All B is A Seme 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
All C is B
All B is A
therefore
Some A is C
In these exemplars, or blank forms for making syllogisms, no place is
assigned to singular propositions ; not, of course, because such proposi-
tions are not used in ratiocination, but because, their predicate being af-
firmed or denied of the whole of the subject, they are ranked, for the pur-
poses of the syllogism, with universal propositions. Thus, these two syllo-
gisms
All men are mortal, All men are mortal,
All kings are men, Socrates is a man,
therefore therefore
All kings are mortal, Socrates is mortal,
are arguments precisely similar, and are both ranked in the first mood of
the first figure.*
* Professor Bain denies the claim of Singular Propositions to be classed, for the purposes
of ratiocination, with Universal ; though they come within the designation which he himself
proposes as an equivalent for Universal, that of Total. He would even, to use his own ex-
pression, banish them entirely from the syllogism. He takes as an example,
Socrates is wise,
Socrates is poor, therefore
Some poor men are wise,
or more properly (as he observes) "one poor man is wise." "Now, if wise, poor, and a
man, are attributes belonging to the meaning of the word Socrates, there is then no march of
128 REASONING.
The reasons why syllogisms in any of the above iorms are legitimate,
that is, why, if the premises are true, the conclusion must inevitably be so,
and why this is not the case in any other possible mood (that is, in any-
other combination of universal and particular, affirmative and negative
propositions), any person taking interest in these inquiries may be pre-
sumed to have either learned from the common-school books of the syllo-
gistic logic, or to be capable of discovering for himself. The reader may,
however, be referred, for every needful explanation, to Archbishop AVhate-
ly's Elements of f^ogic, where he will find stated with philosophical pre-
cision, and explained with remarkable perspicuity, the whole of the com-
mon doctrine of the syllogism.
All valid ratiocination ; all reasoning by which, from general propositions
reasoning at all. We have given in Socrates, inter alia, the facts wise, poor, and a man, and
we merely repeat the concurrence which is selected from the whole aggregate of properties
milking up the whole, Socrates. The case is one under the head 'Greater and Less Connota-
tion ' in Equivalent Prepositional Forms, or Immediate Inference.
''But the example in this form does not do justice to the syllogism of singulars. "\Ve must
suppose both propositions to be real, the predicates being in no way involved in the subject.
Tli us
Socrates was the master of Plato,
Socrates fought at Delium,
The master of Plato fought at Delium.
lt lt may fairly be doubted whether the transitions, in this instance, are any tiling more
than equivalent forms. For the proposition ' Socrates was the master of Plato and fought at
Delium,' compounded out of the two premises, is obviously nothing more than a grammatical
abbreviation. No one can say that there is here any change of meaning, or any thing beyond
a verbal modification of the original form. The next step is, ' The master of Plato fought at
Delium,' which is the previous statement cut down by the omission of Socrates. It contents
itself with reproducing a part of the meaning, or saying less than had been previously said.
The full equivalent of the affirmation is, 'The master of Plato fought at Delium, and the
master of Plato was Socrates:' the new form omits the last piece of information, and gives
only the first. Now, we never consider that we have made a real inference, a step in advance,
when we repeat /ess than we are entitled to say, or drop from a complex statement some por-
tion not desired at the moment. Such an operation keeps strictly within the domain of equiv-
alence, or Immediate Inference. In no way, therefore, can a syllogism with two singular
premises be viewed as a genuine syllogistic or deductive inference." (Logic, i., lf>9.)
The first argument, as will have been seen, rests upon the supposition that the name Soc-
rates has a meaning ; that man, wise, and poor, are parts of this meaning ; and that by predi-
cating them of Socrates we convey no information ; a view of the signification of names
which, for reasons already given,* I can not admit, and which, as applied to the class of names
which Socrates belongs to, is at war with Mr. Bain's own definition of a Proper Name (i., 148),
"a single meaningless mark or designation appropriated to the thingi" Such names, Mr.
Bain proceeded to say, do not necessarily indicate even human beings : much less then does
the name Socrates include the meaning of wise or poor. Otherwise it would follow that if
Socrates had grown rich, or had lost his mental faculties by illness, he would no longer have
been called Socrates.
The second part of Mr. Bain's argument, in which he contends that even when the premises
convey real information, the conclusion is merely the premises with a part left out, is applica-
ble, if at all, as much to universal propositions as to singular. In every syllogism the con-
clusion contains less than is asserted in the two premises taken together. Suppose the syllo-
gism to be
All bees are intelligent,
All bees are insects, therefore
Some insects are intelligent :
one might use the same liberty taken by Mr. Bain, of joining together the two premises as if
they were one "All bees are insects and intelligent" and might say that in omitting the
middle term bees we make no real inference, but merely reproduce part of what had been pre-
viously said. Mr. Bain's is really an objection to the syllogism itself, or at all events to the
third figure : it has no special applicability to singular propositions.
* Note to 4 of the chapter on Definition, supra, pp. 110, 111.
RATIOCINATION, OR SYLLOGISM. 129
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 formulae 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 syl-
logisms. It is done by the conversion of one or other, or both, of the prem-
ises. Thus an argument in the first mood of the second figure, as
No C is B
All A is B
therefore
No A is C,
may be reduced as follows. The proposition, No C is B, being a universal
negative, admits of simple conversion, and may be changed into No B is
C, which, as we 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 fol-
lowing :
All B is C
All B is A
therefore
Some A is C,
where the minor premise, All B is A, conformably to what was laid down
in the last chapter respecting universal affirmatives, does not admit of sim-
ple conversion, but may be converted per accidens, thus, Some A is B ;
which, though it does not express the whole of what is asserted in the
proposition All B is A, expresses, as was formerly shown, part of it, and
must therefore be true if the whole is true. We have, then, as the re-
sult of the reduction, the following syllogism in the third mood of the first
figure :
All B is C
Some A is B,
from which it obviously follows, that
Some A is C.
In the same manner, or in a manner on which after these examples it is
not necessary to enlarge, every mood of the second, third, and fourth fig-
ures may be reduced to some one of the four moods of the first. In other
words, every conclusion which can be proved in any of the last three fig-
ures, may be proved in the first figure from the same premises, with a
slight alteration in the mere manner of expressing them. Every valid ra-
tiocination, therefore, may be stated in the first figure, that is, in one of the
following forms :
9
130 REASONING.
Every B is C No B is C
All A ) . -p All A I . -p
Some A f 1S B > Some A \ 1S B >
therefore therefore
All A I r No A is ) r
Some A J Some A is not f
Or, if more significant symbols are preferred :
To prove an affirmative, the argument must admit of being stated in this
form :
All animals arc mortal ;
All men }
Some men v are animals;
Socrates )
therefore
All men }
Some men v 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 v are capable of self-control ;
Mr. A's negro )
therefore
No negroes are }
Some negroes are not > 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 considerably 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 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 would carry
conviction more instantly home, than the same ratiocination strained into
the first figure, thus
Aristides was virtuous,
Some pagan was Aristides,
therefore
Some pagan was virtuous.
A German philosopher, Lambert, whose Neues Organon (published in
the year 1764) contains among other things one of the most elaborate and
complete expositions which had ever been made of the syllogistic doctrine,
has expressly examined what sort of arguments fall most naturally and suit-
ably into each of the four figures ; and his investigation is characterized by
RATIOCINATION, OR SYLLOGISM. 131
great ingenuity and clearness of thought.* The argument, however, is one
and the same, in whichever figure it is expressed ; since, as we have already
seen, the premises of a syllogism in the second, third, or fourth figure, and
those of the syllogism in the first figure to which it may be reduced, are
the same premises in every thing except language, or, at least, as much of
them as contributes to the proof of the conclusion is the same. We are
therefore at liberty, in conformity 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 be 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, can not possibly happen with the only
class of arguments which are of first-rate scientific importance, those in
which the conclusion is a universal affirmative, such conclusions being sus-
ceptible of proof in the first figure alone. f
* 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 distinctions between things ; the third
to the discovery or proof of instances and exceptions ; the fourth to the discovery, or exclu-
sion, 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 diverso for the second figure,
dictum de exemplo for the third, and dictum de reciproco for the fourth. See part L, or Dia-
noiologie, chap, iv., 229 et seqq. Mr. Bailey (Theory of Reasoning, 2d ed., pp. 70-74)
takes a similar view of the subject.
t 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 Logic; or, the Calculus of Inference, Necessary
and Probable;" and the "New Analytic of Logical Forms," attached as an Appendix to Sir
William Hamilton's Discussions on P'hilosophy, and at greater length, to his posthumous Lec-
tures on Logic.
In Mr. Ue Morgan's volume abounding, in its more popular parts, with valuable observa-
tions 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 necessarily
in part consist of the same individuals. Following out this line of thought, it is equally evi-
dent 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 GO 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 examining what inferences admit of being drawn from the various com-
binations which may be made of premises of this description, Mr. De Morgan establishes uni-
versal formulaj for such inferences ; creating for that purpose not only a new technical lan-
guage, 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 legiti-
mately be drawn, and that the ordinary theory takes no account of them, I will not say that
it was not worth while to show in detail how these also could be reduced to formula) as rigor-
ous 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
mastering for any practical purpose. The practical use of technical forms of reasoning 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 de-
132 REASONING.
2. On examining, then, these two general formula?, we find that in
both of them, one premise, the major, is a universal proposition; and ac-
pend. either for purposes of speculation or of practice, do not, except in u few peculiar cases,
admit of any numerical precision ; common reasoning can not be translated into Mr. De
Morgan's forms, which therefore can not serve any purpose as a test of it.
Sir William Hamilton's theory of the "quantification of the predicate " may be described as
follows :
''Logically " (I quote his words) "we ought to take into account the quantity, always un-
derstood 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 co-extensive 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. \Ve may also make
the assertion All A is all B, which will be true if the classes A and B are exactly co-extensive.
The last three forms, though conveying real assertions, have no place in the ordinary classifi-
cation of Propositions. All propositions, then, being supposed to be translated into this lan-
guage, and written each in that one of the preceding forms which answers to its signification,
there emerges a new set of syllogistic rules, materially different from the common ones. A
general view of the points of difference may be given in the words of Sir W. Hamilton (Dis-
cussions, 2d ed. , ]). Gf>l) :
"The revocation of the two terms of a Proposition to their true relation ; a proposition be-
ing 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.
''The reduction of all the General Lairs of Categorical Syllogisms to a single Canon.
"The evolution from that one canon of all the Species and varieties of Syllogisms.
"The abrogation of all the Special Laws of Syllogism.
"A demonstration of the exclusive 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 con-
sequent absurdity of Reducing 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 subordination between a term ma-
jor 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
premises, and there are two indifferent conclusions : whereas in the first the premises are de-
terminate, and there is a single proximate conclusion."
This doctrine, like that of Mr. l)e Morgan previously noticed, is a veal addition to the syl-
logistic 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 ratioc-
ination : 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 contribution
to the Science of Logic, that is, to the analysis of the mental processes concerned in reasoning,
the new doctrine appears to me, I confess, not merely superfluous, but erroneous ; since the
form in which it clothes propositions does not, like the ordinary form, express what is in the
mind of the speaker when he enunciates the proposition. I can not think Sir William Ham-
ilton right in maintaining that the quantity of the predicate is " always understood in thought."
It is implied, but is not present to the mind of the person who asserts the proposition. The
quantification of the predicate, instead of being a means of bringing out more clearly the mean-
ing 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 our-
selves about whether it contains any other beings or not. It is only for some artificial- pur-
pose 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. 77, 78.)
For a fuller discussion of this subject, see the twenty-second chapter of a work already re-
ferred to, "An Examination of Sir William Hamilton's Philosophy."
RATIOCINATION, OR SYLLOGISM. 133
cording as this is affirmative or negative, the conclusion is so too. All
ratiocination, therefore, starts from a general proposition, principle, or as-
sumption : a proposition in which a predicate is affirmed or denied of an
entire class ; that is, in which some attribute, or the negation of some
attribute, is 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 of a class) belongs to, or is in-
cluded 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 included in the class: and this
is precisely the assertion made in the conclusion.
Whether or not the foregoing is an adequate account of the constituent
parts of the syllogism, will be presently considered ; but as far as it goes it
is a true account. It has accordingly been 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 tiling. The maxim is, That whatever can be affirmed (or denied) of
a class, may be affirmed (or denied) of every thing included in the class.
This axiom, supposed to be the basis of the syllogistic theory, is termed by
logicians the dictum de omni et nullo.
This maxim, however, when considered as a principle of reasoning, ap-
pears 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 ob
jects classed under them, the dictum de omni conveyed an important mean-
ing ; because it expressed the intercommunity of nature, which it was nec-
essary on that theory that we should suppose to exist between those gen-
eral substances and the particular substances which were subordinated to
them. That every thing predicable of the universal was predicable of the
various individuals contained under it, was then no identical proposition,
but a statement of what was conceived as a fundamental law of the uni-
verse. The assertion that the entire nature and properties of the substan-
tia secunda formed part of the nature and properties of each of the indi-
vidual substances called by the same name; that the properties of Man, for
example, were properties of all men ; was a proposition of real significance
when man did not mean all men, but something inherent in men, and vast-
ly superior to them in dignity. Xow, however, when it is known that a
class, a universal, a genus or species, is not an entity per se, but neither
more nor less than the individual 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 attributes indicated by th,e
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 con-
tained in the class ? The class is nothing but the objects contained in it :
and the dictum de omni merely amounts to the identical proposition, that
whatever is true of certain objects, is true of each of those objects. If all
ratiocination were no more than the application of this maxim to particular
cases, the syllogism would indeed be, what it has so often been, declared to
134 REASONING.
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, \ve must consider
it not as an axiom, but as a definition ; we must look upon it as intended
to explain, in a circuitous and paraphrastic manner, the meaning of the
word class.
An error which 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 have not been sparing in their contempt for the scho-
lastic dogma that genera and species are a peculiar kind of substances, 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
substances or universals, and not to the facts or particulars included un-
der them. Yet, though nominally rejected, this very doctrine, whether dis-
guised under the Abstract Ideas of Locke (whose speculations, however, it
has less vitiated than those of perhaps any other writer who has been in-
fected with it), under the ultra-nominalism of Hobbes and Condillac, or the
ontology of the later German schools, has never ceased to poison philosophy.
Once accustomed to consider scientific investigation as essentially consist-
ing in the study of universals, men did not drop this habit of thought when
they ceased to regard universals as possessing an independent existence:
and* even those who went the length of considering them as mere names,
could not free themselves from the notion that the investigation of truth
consisted entirely or partly in some kind of conjuration or juggle with those
names. When a philosopher adopted fully the Xominalist view of the
signification of general language, retaining along with it the dictum de
omni as the foundation of all reasoning, two such premises fairly put to-
gether 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 reason-
ing consists in the mere substitution of one set of arbitrary signs for an-
other; a doctrine which they suppose to derive irresistible confirmation
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 Condil-
lac, that a science is nothing, or scarcely any thing, but nne lanyue bien
fdite; 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 them properly except in propor-
tion 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 conceivable
manipulation of mere names, as such ; and that what can be learned from
names, is only what somebody who used the names knew before? Philo-
sophical analysis confirms the indication of common sense, that the func-
tion 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 mem-
ory, an instrument of which few have adequately considered the immense
potency. As an artificial memory, language truly is, what it has so often
RATIOCINATION, OR SYLLOGISM. 135
been called, an instrument of thought ; but it is one thing to be the instru-
ment, and another to be the exclusive subject upon which the instrument
is exercised. We think, indeed, to a considerable extent, by means of
names, but what we think of, are the things called by those names ; and
there can not be a greater error than to imagine that thought can be car-
ried on with nothing in our rnind 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 erro-
neous view which Ilobbes 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 any thing 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 that what was included in the
lower class is included in the higher, and the result, therefore, nothing ex-
cept that the classification 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 proposi-
tion 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 attri-
butes, or sets of attributes, do or do not (constantly or occasionally) co-ex-
ist. 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 recognize this import of propo-
sitions, can not, 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 premise, 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 at-
tribute (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, de-
noting objects and connoting attributes. The assertion in the major prem-
ise is, that along with one of the two sets of attributes, we always find
the other : that the attributes connoted by " man " never exist unless con-
joined with the attribute called mortality. The assertion in the minor prem-
ise is that the individual named Socrates possesses the former attributes ;
and it is concluded that he possesses also the attribute mortality. Or, if
both the premises are general propositions, as
136 REASONING.
All men are mortal,
All kings are men,
therefore
All kings are mortal,
the minor premise asserts that the attributes denoted by kingship only
exist in conjunction with those 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 omnipotent, 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 constituting a
king. In a similar manner we might analyze any other example of the
syllogism.
If we generalize this process, and look out for the principle or law in-
volved in every such inference, and presupposed in every syllogism, the
propositions of which are any thing more than merely verbal; we find, riot
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 co-exist with the same thing, co-exist with one another: or (still more
precisely) a thing which co-exists with another thing, which other co-exists
with a third thing, also co-exists with that third thing. The second is the
principle of negative syllogisms, and is to this effect: that a thing which
co-exists with another thing, with which other a third thing does not co-ex-
ist, is not co-existent with that third thing. These axioms manifestly relate
to facts, and not to conventions ; and one or other of them is the ground of
the legitimacy of every ai'gument 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 syl-
logism coincides with all that is essential of mine, thinks it a logical fallacy to present the two
axioms in the text, as the regulating principles of syllogism. He charges me with filling
into the error pointed out by Archbishop Whately and myself, of confounding exact likeness
with literal identity ; and maintains, that we ought not to say that Socrates possesses the
same attributes which are connoted by the word Man, but only that he possesses attributes
exactly like them : according to which phraseology, Socrates, and the attribute mortality,
are not two things co-existing with the same thing, as the axiom asserts, but two things co-
existing with two different things.
The question between Mr. Spencer and me is merely one of language; for neither of us (if
I understand Mr. Spencer's opinions rightly) believes an attribute 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 anv
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 1 have
employed, which is that commonly used by philosophers, seems to me to be the best. Mr.
Spencer is of opinion that because Socrates and Alcibiades are not the same man, the attri-
bute 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 dif-
ferent attribute in every different man. J5ut on tiiis showing, the humanity even of any one
man should be considered as different attributes now and half an hour hence ; for the sensa-
tions by which it will then manifest itself to my organs will not be a continuation of my pres-
ent sensations, but a repetition of them ; fresh sensations, not identical with, but only exactly
RATIOCINATION, OR SYLLOGISM. 137
4. It remains to translate this exposition of the syllogism from the
one into the other of the two languages in which we formerly remarked*
that all propositions, and of course therefore all combinations of proposi-
tions, 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 proposition 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 knowledge,
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 pos-
sesses the other; thus employing 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 cited as
specimens of the syllogism, will express themselves in the following
manner :
The attributes of man are a mark of the attribute mortality,
Socrates has the attributes of man,
therefore
Socrates has the attribute mortality.
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 predicated 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 individual identity. What, then, is the common
something which gives a meaning to the general name ? Mr. Spencer can only say, it is the
similarity of the feelings ; and I rejoin, the attribute is precisely that similarity. The names
of attributes are in their ultimate analysis names for the resemblances of our sensations (or
other feelings). Every general name, whether abstract or concrete, denotes or connotes one
or more of those resemblances. It will not, probably, be denied, that if a hundred sensations
are undistinguishably alike, their resemblance ought to be spoken of as one resemblance, and
not a hundred resemblances 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 sensations 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 light-
ning. 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 co-exists with a third type,
co-exist with another ; or Two powers each of which co-exists with a third power co-exist
with one another.
Mr. Spencer has misunderstood me in another particular. He supposes that the co-exist-
ence spoken of in the axiom, of two things with the same third thing, means simultaneousness
in time. The co-existence 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 sense co-existent, both being attributes of man, though ex vi termini never of
the same man at the same time.
* Supra, p. 93.
138 REASONING.
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 ax-
ioms on which the syllogistic process is founded must undergo a corre-
sponding 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 ascertain-
ment of a truth by ratiocination.*
* Professor Bain (Logic, i., 157) considers the axiom (or rather axioms) here proposed as
a substitute for the dictum de omni, to possess certain advantages, but to be " unworkable as
a basis of the syllogism. The fatal defect consists in this, that it is ill-adapted to bring out
the difference between total and partial coincidence of terms, the observation of which is the
essential precaution in syllogizing correctly. If all the terms were co-extensive, the axiom
would How on admirably ; A carries 15, all B and none but B ; B carries C in the same man-
ner; at once A carries C, without limitation or reserve. But in point of fact, we know that
while A carries B, other things carry B also ; whence a process of limitation is required, in
transferring A to C through B. A (in common with other things) carries B ; B (in common
with other tilings) carries C ; whence A (in common with other things) carries C. The ax-
iom provides no means of making this limitation ; if we were to follow A literally, we should
be led to suppose A and C co-extensive : for such is the only obvious meaning of ' the attri-
bute A coincides with the attribute C.'"
It is certainly possible that a careless learner here and there may suppose that if A carries
B, it follows that B carries A. But if any one is so incautious as to commit this mistake, the
very earliest lesson in the logic of inference, the Conversion of propositions, will correct it.
The first of the two forms in which I have stated the axiom, is in some degree open to Mr.
Bain's criticism : when B is said to co-exist with A (it must be by a lapsus calami that Mr.
Bain uses the word coincide), it is possible, in the absence of warning, to suppose the meaning
to be that the two things are only found together. But this misinterpretation is excluded by
the other, or practical, form of the maxim ; A T o/u notir est nota rei ipsius. No one would be
in any danger of inferring that because a is a mark of b, b can never exist without a ; that
because being in a confirmed consumption is a mark of being about to die, no one dies who is
not in a consumption ; that because being coal is a mark of having come out of the earth,
nothing can come out of the earth except coal. Ordinary knowledge of English seems a
sufficient protection against these mistakes, since in speaking of a mark of any thing we are
never understood as implying reciprocity.
A more fundamental objection is stated by Mr. Bain in a subsequent passage (p. 158).
"The axiom does not accommodate itself to the type of Deductive Keasoning as contrasted
. with Induction the application of a general principle to a special case. Any thing that fails
to make prominent this circumstance is not adapted as a foundation for the syllogism." But
FUNCTIONS AND VALUE OF THE SYLLOGISM. 139
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 conceived in the common theory; and
what are the fundamental axioms on which its probative force or conclu-
siveness depends. We have now to inquire, whether the syllogistic proc-
ess, that of reasoning from generals to particulars, is, or is not, a_p_roc_e_ss
of inference ; a progress from the_ known to_ the unknown : a means of com-
ingtoaTcnowledge 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 any thing more in the conclusion than was assumed in the premises.
Butthisis 1 jn_jact > to j?aj^thajLllothing ever was, or can be, proved by syl-
logism, \vlucir^a^jioJLknjaw-o, oj'iissi^ried^to be knowa. before. Is ratioci-
nation, then, not a process of inference? And is the syllogism, to which
the word reasoning has so often been represented to be exclusively appro-
priate, not really entitled to be called reasoning at all ? This seems an in-
evitable consequence of the doctrine, admitted by all writers on the sub-
ject, 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 represent 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 gen-
eral theorem respecting the logical value of the syllogism to its legitimate
corollary, have been led to impute uselessness and frivolity to the syllogis-
tic theory itself, on the ground of the petitio pr'mcipii 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 cer-
tain considerations, without which any just appreciation of the true char-
acter of the syllogism, and the functions it performs in philosophy, appears
to me impossible; but which seem to have been either overlooked, or in-
sufficiently adverted to, both by the defenders of the syllogistic theory and
by its assailants.
2. It must be granted that in every syllogism, considered as an
though it may be proper to limit the term Deduction to the application of a general principle
to a special case, it has never been held that Ratiocination or Syllogism is subject to the same
limitation ; and the adoption of it would exclude a great amount of valid and conclusive syl-
logistic reasoning. Moreover, if the dictum de omni makes prominent the fact of the applica-
tion of a general principle to a particular case, the axiom I propose makes prominent the
condition which alone makes that application a real inference.
I conclude, therefore, that both forms have their value, .and their place in Logic. The
dictum de omni should be retained as the fundamental axiom of the logic of mere consistency,
often called Formal Logic ; nor have I ever quarreled with the use of it in that character,
nor proposed to banish it from treatises on Formal Logic. But the other is the proper axiom
for the logic of the pursuit of truth by way of Deduction ; and the recognition of it can alone
show how it is possible that deductive reasoning can be a road to truth.
140 REASONING.
argument to prove the conclusion, there is a pelitio 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 as-
sumption, All men are mortal : that we can not be assured of the mortali-
ty of all men, unless we are already certain of the mortality of every indi-
vidual man : that if it be still doubtful whether Socrates, or any other in-
dividual we choose to name, be mortal or not, the same degree of uncer-
tainty must hang over the assertion, All men are mortal : that the general
principle, instead of being given as evidence of the particular case, can not
itself be taken for true without exception, until every shadow of doubt
which could affect any case comprised with it, is dispelled by evidence
al'mnde ; and then what remains for the syllogism to prove? That, in
short, no reasoning from generals to particulars can, as such, prove any
thing: since from a general principle we can not infer any particulars, but
those which the principle itself assumes as known.
This doctrine appears to me irrefragable ; and if logicians, though una-
ble 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 equal-
ly indisputable. In the syllogism last referred to, for example, or in any of
those which we previously constructed, is it not evident that the conclu-
sion may, to the person to whom the syllogism is presented, be actually
and bona fide a new truth? Is it not matter of daily experience that
truths previously unthought of, facts which have not been, and can not be,
directly observed, are arrived at by way of general reasoning? We be-
lieve that the Duke of Wellington is mortal. We do not know this by di-
rect 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 knowl-
edge of a truth not (as yet) susceptible of observation, by a reasoning
which admits of being exhibited in the following syllogism :
All men arc 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 lias cleared up the difficulty which arises from
the inconsistency between that assertion, and the principle, that if there be
any thing in the conclusion which was not already asserted in the premi-
ses, the argument is vicious. For it is impossible to attach any serious
scientific value to such a mere salvo, as the distinction drawn between be-
ing involved by implication in the premises, and being directly asserted in
them. When Archbishop Whately says* that the object of reasoning is
" merely to expand and unfold the assertions wrapped up, as it were, and
* Logic, p. 239 (9th cd.).
FUNCTIONS AND VALUE OF THE SYLLOGISM. 141
implied in those with which we set out, and to bring a person to perceive
and acknowledge the full force of that which he has admitted," he does
not, I think, meet the real difficulty requiring to be explained, namely, how
it happens that a science, like geometry, can be all " wrapped up " in a
few definitions and axioms. Nor does this defense 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 con-
sequences 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 Whate-
ly, you asserted it by implication merely : this, however, can here only
mean that you asserted it unconsciously ; that you did not know you were
asserting it ; but, if so, the difficulty revives in this shape Ought you not
to have known? Were you warranted in asserting the general proposi-
tion without having satisfied yourself of the truth of every thing which it
fairly includes? And if not, is not the syllogistic art prima facie what its
assailants affirm it to be, a contrivance for catching you in a trap, and hold-
ing you fast in it ?*
3. From this difficulty there appears to be but one issue. The propo-
sition that the Duke of Wellington is mortal, is evidently an inference ; it
is got at as a conclusion from something else ; but do we, in reality, con-
clude it from the proposition, All men are mortal? I answer, no.
The error committed is, I conceive, that of overlooking the distinction be-
tween two parts of the process of philosophizing, 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 una-
ble 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 ob-
servation. 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 compendious form for recording and preserving in the memory a
number of particular facts, all of which have been observed. Generaliza-
* 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, pres-
ent, 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, before 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 ad-
ducing 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.
142 REASONING.
tion is not a process of mere naming, it is also a process of inference.
From instances which we have observed, 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 commu-
nicate. The results of many observations and inferences, and instructions
for making innumerable inferences in unforeseen cases, are compressed
into one short sentence.
When, therefore, we conclude from the death of John and Thomas, and
every other person we ever heard of in whose case the experiment had
been fairly tried, that the Duke of Wellington is mortal like the rest; we
may, indeed, pass through the generalization, All men are mortal, as an in-
termediate stage; but it is not in the latter half of the process, the de-
scent 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 afterward is merely deciphering 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 philosophical 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 can not help thinking that the vulgar notion is, in this
case, the more correct. If, from our experience of John, Thomas, etc., who
once were living, but are now dead, we are entitled to conclude that all hu-
man beings are mortal, we might surely without any logical inconsequence
have concluded at once from those instances, that the Duke of Wellington
is mortal. The mortality of John, Thomas, and others is, after all, the
whole evidence we have for the mortality of the Duke of Wellington. Not
one iota is added to the proof by interpolating a general proposition.
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 insuf-
ficient for the one purpose, can not be sufficient for the other ; I am una-
ble to see why we should be forbidden to take the shortest cut from these
sufficient premises to the conclusion, and constrained to travel the " high
priori road," by the arbitrary fiat of logicians. I can not perceive why it
should be impossible to journey from one place to another unless we
" march up a hill, and then march down again." It may be the safest
road, and there may be a 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 infer-
ences are of this nature. PYom the first dawn of intelligence we draw in-
ferences, but years elapse before we learn the iise of general language.
The child, who, having burned his fingers, avoids to thrust them again into
the fire, has reasoned or inferred, though lie has never thought of the gen-
eral maxim, Fire burns. lie knows from memory that he has been burn-
ed, and on this evidence believes, when he sees a candle, that if he puts his
FUNCTIONS AND VALUE OF THE SYLLOGISM. 143
finger into the flame of it, he will be burned again. He believes this in ev-
ery case which happens to arise ; but without looking, in each instance, be-
yond the present case. He is not generalizing; he is inferring a partic-
ular from particulars. In the same way, also, brutes reason. There is
no ground for attributing to any of the lower animals the use of signs, of
such a nature as to render general propositions possible. But those ani-
mals profit by experience, and avoid what they have found to cause them
pain, in the same manner, though not always with the same skill, as a
human creature. Not only the burned child, but the burned dog, dreads
the fire.
I believe that, in point of fact, when drawing inferences from our per-
sonal 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
judge from an enlarged consideration of the manner in which human beings
in general, or persons of some particular character, are accustomed to feel
and act ; but much oftener from merely recollecting the feelings and con-
duct of the same pei'son 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 neighbor's child, pro-
nounces 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 practicing the habit
of stating to one's self 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 skillful 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, ungeneralized
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, or of tools, is
of a precisely similar nature. The savage who executes unerringly the ex-
act throw which brings down his game, or hi? 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, etc., owes this power to a long series of
144 REASONING.
previous experiments, the results of which lie certainly never framed into
any verbal theorems or rules. The same thing may generally be said of
any other extraordinary manual dexterity. Not long ago a Scotch manu-
facturer procured from England, at a high rate of wages, a working dyer,
famous for producing very fine colors, with the view of teaching to his
other workmen the same skill. The workman came ; but his mode of pro-
portioning the ingredients, in which lay the secret of the effects he pro-
duced, 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. lie had, from the individual cases of his own experience, es-
tablished a connection in his mind between fine effects of color, and tactual
perceptions in handling his dyeing materials ; and from these perceptions
he could, in any particular case, infer the means to be employed, and the
effects which would be produced, but could not put others in possession of
the grounds on which he proceeded, from having never 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 courts 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 suppose that the bad reason was the source of the
good decision. Lord Mansfield knew that if any reason were assigned it
would be necessarily an afterthought, the judge being in fact guided by
impressions from past experience, without the circuitous process of fram-
ing general principles from them, and that if he atteinpted 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 preferable 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 general-
ization, though a help, the most important indeed of all helps, is not an
essential.
Even the scientifically instructed, who possess, in the form of general
propositions, a systematic record of the results of the experience of man-
kind, need not always revert to those general propositions in order to ap-
ply that experience to a new case. It is justly remarked by Dugald Stew-
art, 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 under-
stood, would assent to the inference, without having ever heard of the gen-
eral 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
FUNCTIONS AND VALUE OF THE SYLLOGISM. 145
root, as I conceive, of the philosophy of ratiocination ; and it is to be re-
gretted that he himself stopped short at a much more limited application
of it. He saw that the general propositions on which a reasoning is said
to depend, may, in certain cases, be altogether omitted, without impairing
its 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 dynamics, 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 generalization, 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 exam-
ple, of the circle is to the properties of the circle, what the laws of equi-
librium and of the pressure of the atmosphere are to the rise of the mer-
cury in the Torricellian tube. Yet all that he had asserted respecting the
function to which the axioms are confined in the demonstrations of geome-
try, holds equally true of the definitions. Every demonstration in Euclid
might be crrried 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 dia-
gram 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 gen-
eral ; 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 sin-
gular proposition, combined with other propositions of a similar kind, some
of which ichen generalized are called definitions, and other axioms, we
prove that a certain conclusion is true, not of all circles, but of the partic-
ular circle ABC ; or at least would be so, if the facts precisely accorded
w r ith our assumptions. The enunciation, as it is called, that is, the gener-
al theorem which stands at the head of the demonstration, is not the propo-
sition actually demonstrated. One instance only is demonstrated : but the
process by which this is done, is a process which, when we consider its
nature, we perceive might be exactly copied in an indefinite number of oth-
er instances ; in every instance which conforms to certain conditions. The
contrivance 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 alphapet, 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 assuming an individual fact, then in
whatever case we are warranted in making an exactly similar assumption,
10
146 REASONING.
we may draw an exactly similar conclusion. The definition is a sort of
notice to ourselves and others, what assumptions we think ourselves en-
titled to make. And so in all cases, the general propositions, whether
called definitions, axioms, or laws of nature, which we lay down at the
beginning of our reasonings, are merely abridged statements, in a kind of
short-hand, of the particular facts, which, as occasion arises, we either
think we may proceed on as proved, or intend to assume. In any one
demonstration it is enough if we assume for a particular case suitably se-
lected, 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, ac-
cording 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 con-
fined to the particular case : that case, however, being chosen as a speci-
men or paradigm of the whole class of cases included in the theorem, there
can be 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 ex-
plained presently, so far as explanation is requisite. But, that nnpracticed
learners, even in making use of one theorem to demonstrate another, rea-
son 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 dia-
gram by which the original theorem was demonstrated. A difficulty
which, except in cases of unusual mental power, long practice can alone re-
move, and removes chiefly by rendering us familiar with all the configura-
tions consistent Avith the general conditions of the theorem.
4. From the considerations now adduced, the following conclusions
seem to be established. All inference is from particulars to particulars:
General propositions are merely registers of such inferences already made,
and short formula) for making more: The major premise of a syllogism,
consequently, is a formula of this description : and the conclusion is not an
inference drawn front 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 forgotten : but a record remains, not indeed descriptive of the facts
themselves, but showing how those cases may be distinguished, respecting
which, the facts, when known, were considered to warrant a given infer-
ence. According to the indications of this record we draw our conclusion :
which is, to all intents and purposes, a conclusion from the forgotten facts.
For this it is essential that we should read the record correctly: and the
rules of the syllogism are a set of precautions to insure our doing so.
This view of the functions of the syllogism is confirmed by the consid-
eration of precisely those cases which might be expected to be least favor-
able to it, namely, those in which ratiocination is independent of any pre-
vious induction. We have already observed that the syllogism, in the or-
dinary course of our reasoning, is only the latter half of the process of
traveling from premises to a conclusion. There are, however; some pecul-
FUNCTIONS AND VALUE OF THE SYLLOGISM. 147
iar 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 ac-
cepted as of an authoritative character : and the information thus commu-
nicated, 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 po-
litical 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 gen-
eral 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 ob-
serve, is general. The proposition asserts, not that all men are any thing,
but that all men shall do something.
In both these cases the generalities are the original data, and the partic-
ulars are elicited from them by a process which correctly resolves itself
into a series of syllogisms. The real nature, however, of the supposed de-
ductive process, is evident enough. The only point to be determined is,
whether the authority which declared the general proposition, intended to
include this case in it; and whether the legislator intended his command
to apply to the present case among others, or not. This is ascertained by
examining whether the case possesses the marks by which, as those author-
ities 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 witness's or
the legislator's intention, through the indication given by their words.
This is a question, as the Germans express it, of hermeneutics. The opera-
tion is not a process of infei'ence, 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 ascertain the testimony of a witness, or the will of a
legislator, by interpreting the signs in which the one has intimated his as-
sertion 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 w r e 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 Wel-
lington 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 proposi-
tion), concerning the inferences which that former experience would war-
rant.
148 REASONING.
( This view of the nature of the syllogism renders consistent and intel-
ligible what otherwise remains obscure and 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 prevent us from
assenting to any thing, the truth of which would contradict something to
which we had previously on good grounds given our assent. And they
tell us, that the sole ground which a syllogism affords for assenting to the
conclusion, is that the supposition of its being false, combined with the
supposition that the premises are true, would lead to a contradiction in
terms. Now this would be but a lame account of the real grounds which
we have for believing the facts which we learn from reasoning, in contra-
distinction 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 contemporary 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, notwithstanding, live forever. 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 conform-
able to the legislator's intention. The rules for this interpretation are the
rules of the syllogism : and its sole purpose is to maintain consistency be-
tween the conclusions we draw in every particular case, and the previous
general directions for drawing them; whether those general 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 tes-
timony), an inference from particulars to particulars ; authorized by a pre-
vious inference from particulars to generals, and substantially the same with
it ; of the nature, therefore, of Induction. But while these conclusions ap-
pear to me undeniable, I must yet enter a protest, as strong as that of Arch-
bishop Whately himself, against the doctrine that the syllogistic art is use-
less for the purposes of reasoning. The reasoning lies in the act of gener-
alization, not in interpreting the record of that act; but the syllogistic form
is an indispensable collateral security for the correctness of the generaliza-
tion itself.
It has already been seen, that if we have a collection of particulars suffi-
cient for grounding an induction, we need not frame a general proposition;
we may reason at once from those particulars to other particulars. But it
is to be remarked withal, that whenever, from a set of particular cases, we
can legitimately draw any inference, we may legitimately make our infer-
FUNCTIONS AND VALUE OF THE SYLLOGISM. 149
ence 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 sin-
gle 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 full
extent, the Avhole of what our evidence must prove if it proves any thing.
This throwing of the whole body of possible inferences from a given set
of particulars, into one general expression, operates as a security for their
being just inferences, in more ways than one. First, the general principle
presents a larger object to the imagination than any of the singular prop-
ositions which it contains. A process of thought which leads to a com-
prehensive generality, is felt as of greater importance than one which ter-
minates 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 un-
observed 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 insufficient evidence
as sufficient. But if, instead of concluding straight to the particular case,
we place before ourselves an entire class of facts the whole contents of a
general proposition, every tittle of which is legitimately inferable from our
premises, if that one particular conclusion is so ; there is then a considera-
ble likelihood that if the premises are insufficient, and the general inference
therefore, groundless, it will comprise within it some fact or facts the re-
verse 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 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 inference is legiti-
mate, of referring to a parallel case, is universally acknowledged. But by
ascending to the general proposition, we bring under our view not one par-
allel 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
150 REASONING.
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 process of interpreta-
tion, will be resolvable into a syllogism or a series of syllogisms, the majors
of which will be general propositions embracing whole classes of cases ;
every one of which propositions must be true in all its extent, if the argu-
ment 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
sutlicicnt to support it. And in proportion to the greater chance of our
detecting the inconclusiveness of our evidence, will be the increased reli-
ance 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 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 repre-
sented, and which is admirably calculated, if they are inconclusive, to bring
their inconclusiveness to light. An induction from particulars to generals,
followed by a syllogistic 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 rea-
son, and into which it is indispensable to throw our reasoning, when there
is any doubt of its validity : though when the case is familiar and little
complicated, and there is no suspicion of error, we may, and do, reason at
once from the known particular cases to unknown ones.*
/ These are the uses of syllogism, as a mode of verifying any given argu-
ment. Its ulterior uses, as respects the general course of our intellectual
operations, hardly require illustration, being in fact the acknowledged uses
of general language. They amount substantially to this, that the induc-
tions may be made once for all : a single careful interrogation of experi-
ence may suffice, and the result may be registered in the form of a general
proposition, which is committed to memory or to writing, and from which
afterward 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, 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 insuflicient evidence become consecrated, and,
as it were, hardened into general maxims; and the mind cleaves to them
* The language of ratiocination would, I think, be brought into closer agreement with the
real nature of the process, if the general propositions employed in reasoning, instead of being
in the form All men are mortal, or Every man is mortal, were expressed in the form Any
man is mortal. This mode of expression, exhibiting as the type of all reasoning from expe-
rience "The men A, B, C, etc., are so and so, therefore any man is so and so," would much
bettor manifest the true idea that inductive reasoning is always, at bottom, inference from
particulars to particulars, and that the whole function of general propositions in reasoning, is
to vouch for the legitimacy of such inferences.
FUNCTIONS AND VALUE OF THE SYLLOGISM. 151
from habit, after it has outgrown any liability to bo misled by similar falla-
cious appearances if they were now for the first time presented ; but hav-
ing forgotten the particulars, it does not think of revising its own forme!
decision. An inevitable drawback, which, however considerable in itself,
forms evidently but a small set-off against the immense benefits of general
language.
The use of the syllogism is in truth no other than the use of general
propositions in reasoning. We can reason without them ; in simple and
obvious cases we habitually do so; minds of great sagacity can do it in
cases not simple and obvious, provided their experience supplies them with
instances essentially similar to every combination of circumstances likely
to arise. But other minds, and the same minds where they have not the
same pre-eminent advantages of pei'sonal experience, are quite helpless
without the aid of general propositions, wherever the case presents the
smallest complication ; and if we made no general propositions, few per-
sons 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 reason-
ing. It is, therefore, natural and indispensable to separate the process of
investigation into two parts ; and obtain general formulae for determining
what inferences may be drawn, before the occasion arises for drawing the
inferences. The work of drawing them is then that of applying the for-
mula ; and the rules of syllogism are a system of securities for the correct-
ness of the application.
6. To complete the series of considerations connected with the philo-
sophical character of the syllogism, it is requisite to consider, since the syl-
logism 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 mi-
nor premise, and in what manner it contributes to establish the conclusion :
for as to the major, we now fully understand, that the place which it nom-
inally 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 de-
gree, for the correctness of the process. The minor, however, being an in-
dispensable part of the syllogistic expression of an argument, without
doubt either is, or corresponds to, an equally indispensable part of the ar-
gument 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 pene-
trating, was a very hasty thinker, and whose want of due circumspection
rendered him fully as remarkable for what he did not see, as for what he
saw. I allude to Dr. Thomas Brown, whose theory of ratiocination is pe-
culiar. 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 description. See-
ing this, Dr. Brown not only failed to see the immense advantage, in point
of security for correctness, which is gained by interposing this step be-
tween the real evidence and the conclusion ; but he thought it incumbent
on him to strike out the major altogether from the reasoning process, with-
Io2 REASONING.
out substituting any thing else, and maintained that our reasonings consist
only of the minor premise and the conclusion, Socrates is a man, therefore
Socrates is mortal : thus actually suppressing, as an unnecessary step in
the argument, the appeal to former experience. The absurdity of this was
disguised from him by the opinion he adopted, that reasoning is merely an-
alyzing our own general notions, or abstract ideas ; and that the proposi-
tion, Socrates is mortal, is evolved from the proposition, Socrates is a man,
simply by recognizing 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 proposi-
tions, much further discussion can not 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 docs 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
perceicintj the relation between the idea of man and the idea of mortal. If
the reasoner lias 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
docs not take place merely because the reasoner, for want of due analysis,
does not perceive that his idea of man includes the idea of mortality ; it
takes place, much more commonly, because in his mind that relation be-
tween the two ideas has never existed. And in truth it never does exist,
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 recog-
nized the radical incorrectness, namely, that the meaning of a proposition
relates to the ideas of the things spoken of, and not to the things them-
selves ; I must yet observe, that the idea of man, as a universal idea, the
common property of all rational creatures, can not involve any thing but
what is strictly implied in the name. If any one includes in his own pri-
vate 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 contrary, 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 conclu-
sion, except with the assistance of the major, or of that which the major
represents, namely, the various singular propositions expressive of the se-
ries of observations, of which the generalization called the major premise is
the result.
In the argument, then, which proves that Socrates is mortal, one indis-
FUNCTIONS AND VALUE OF THE SYLLOGISM. 153
pensable part of the premises will be as follows : " My father, and my fa-
ther's father, A, B, C, and an indefinite number of other persons, were mor-
tal;" 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
vrincipil, and cut down to as much as is really known by direct evidence.
In order to connect this proposition with the conclusion Socrates is mor-
tal, the additional link necessary is such a proposition as the following :
Socrates resembles my father, and my father's father, and the other indi-
viduals specified." This proposition we assert when we say that Socrates
is a man. By saying so we likewise assert in what respect he resembles
them, namely, in the attributes connoted by the word man. And we con-
clude that he further resembles them in the attribute mortality.
7. We have thus obtained what we were seeking, a universal type of
the reasoning process. We find it resolvable in all cases into the follow-
ing elements: Certain individuals 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 conclusive from the mere form of the
expression ; nor can it possibly be so. That one proposition does or does
not assert the very fact which was already asserted in another, may appear
from the form of the expression, that is, from a comparison of the lan-
guage; but when the two propositions assert facts which are bona fide
different, whether the one fact proves the other or not can never appear
from the language, but must depend on other considerations. Whether,
from the attributes in which Socrates resembles those men who have here-
tofore died, it is allowable to infer that he resembles them also in being
mortal, is a question of Induction ; and is to be decided by the principles
or canons which we shall hereafter recognize as tests of the correct per-
formance of that great mental operation.
Meanwhile, however, it is certain, as before remarked, that if this infer-
ence can be drawn as to Socrates, it can be drawn as to all others who re-
semble the observed individuals in the same attributes in which he resem-
bles 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 lib-
erty, 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 lay-
ing down the universal 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 opera-
tion into two steps ; first, that of ascertaining what attributes are marks
of mortality ; and, secondly, whether any given individuals possess those
marks. And it will generally be advisable, in our speculations on the rea-
soning process, to consider this double operation as in 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 prem-
ises are particulars, whether we conclude from particulars to a general for-
mula, or from particulars to other particulars according to that formula, are
equally Induction; we shall yet, conformably to usage, consider the name
Induction as more peculiarly belonging to the process of establishing the
general proposition, and the remaining operation, which is substantially
that of interpreting the general proposition, we shall call by its usual name,
154 REASONING.
Deduction. And we shall consider every process by which any thing is
inferred respecting an unobserved case, as consisting of an Induction fol-
lowed 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 de-
sired.
8. The theory of the syllogism laid down in the preceding pages, has
obtained, among other important adhesions, three of peculiar value : those
of Sir John Ilerschel,* Dr. Whewell,f and Mr. Bailey ;J Sir John Herschel
considering the doctrine, though not strictly " a discovery," having been
anticipated by Berkeley, to be " one of the greatest steps which have yet
been made in the philosophy of Logic." " When we consider" (to quote
the further words of the same authority) " the inveteracy of the habits and
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 estimate of it. Their principal objection can not be bet-
ter or more succinctly stated than by borrowing a sentence from Archbish-
op Whately.| "In every case where an inference is drawn from Induc-
tion (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 ad-
duced 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 sufficiency of the
evidence on which the conclusion rests. That it is so, is the very essence
of my own theory. And whoever admits that the major premise is only
this, adopts the theory in its essentials.
But I can not concede that this recognition of the sufficiency of the evi-
dence that is, of the correctness of the induction is a part of the induc-
tion itself; unless we ought to say that it is a part of every thing we do,
to satisfy ourselves that it has been done rightly. We conclude from
known instances to unknown by the impulse of the generalizing propensi-
ty; and (until after a considerable amount of practice and mental disci-
pline) the question of the sufficiency of the evidence is only raised by a re-
trospective act, turning back upon our own footsteps, and examining wheth-
er we were warranted in doing what we have provisionally done. To
speak of this reflex operation as part of the original one, requiring to be
expressed in words in order that the verbal formula may correctly repre-
sent the psychological process, appears to me false psychology.^ We re-
view our syllogistic as well as our inductive processes, and recognize that
* Review of Quctclct on Probabilities, Essays, p. 3G7.
f Philosophy of Discovery, p. 285).
J Theory of Reasoning, chap, iv., to which I may refer for an able statement and enforce-
ment of the grounds of the doctrine.
On a recent careful reperusal of Berkeley's whole works, I have been unable to find this
doctrine in them. Sir John Ilerschel probably meant that it is implied in Berkeley's argu-
ment against abstract ideas. But I can not find that Berkeley saw the implication, or had
ever asked himself what bearing his argument had on the theory of the syllogism. Still less
can I admit that the doctrine is (as lias been affirmed by one of my ablest and most candid
critics) '' among the standing marks of what is called the empirical philosophy."
|| Logic, book iv., chap, i., sect. 1.
If 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. 155
they have been correctly performed; 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 if no
error appears, he recognizes 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 toward me because I see him, and not because I rec-
ognize that my eyes are open, and that eyesight is a means of knowledge.
In all operations which require care, it is good to assure ourselves that
the process has been performed accurately; but the testing of the proc-
ess is not the process itself; and, besides, may have been omitted alto-
gether, and yet the process be correct. It is precisely because that opera-
tion is omitted in ordinary unscientific reasoning, that there is any thing
gained in certainty by throwing reasoning into the syllogistic form. To
make sure, as far as possible, that it shall not be omitted, we make the test-
ing operation a part of the reasoning process itself. We insist that the
inference from particulars to particulars shall pass through a general propo-
sition. But this is a security for good reasoning, not a condition of all rea-
soning ; and in some cases not even a security. Our most familiar infer-
ences are all made before we learn the use of general propositions; and a
person of untutored sagacity will skillfully 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. Xow, this is precisely what forms of reasoning
do for us. We do not need them to enable us to reason, but to enable us
to know whether we reason correctly.
In still further answer to the objection, it may be added that even when
the te^t has been applied, and the sufficiency of the evidence recognized
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 realized in the
cases A, B, C, would be as much justified in concluding directly to the
Duke of Wellington as in concluding to all men. The general conclusion
~ O ~
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 conclu-
sion at all from particular instances, there is ground for a general conclu-
sion ; but that this general conclusion should be actually drawn, however
useful, can not 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 le-
gality 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 Ileview" (August, 1840). in a review of this treatise,
endeavors to show that there is no petitio princijiii 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, without 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
156 REASONING.
9. The preceding considerations enable us to understand the true na-
ture of what is termed, by recent writers, Formal Logic, and the relation
was never denied. That we can and do draw conclusions concerning cases specifically un-
known to us, is the datum from which all who discuss this subject must set out. The ques-
tion 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 lan-
guage 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 tiling is the proof of itself. Who-
ever 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, lie 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 suc-
cess or failure of an attempt to remove the difficulty. That he had reflected very little on the
point when he wrote his remarks, is shown by his oversight respecting the dictum de omni et
nullo. He acknowledges that this maxim as commonly expressed ''Whatever is true of a
class, is true of every thing included in the class," is a mere identical proposition, since the
class is nothing but the things included in it. But he thinks this defect would he cured by
wording the maxim thus '' Whatever is true of a class, is true of every thing which can he
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 things included in the class, the
tilings 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 pub-
licly to take their place in it that so long, in fact, as Socrates is not known to be a man, he
is not a man, and any assertion which can be made concerning men does not at all regard
him, nor is affected as to its truth or falsity by any tiling 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 reaching beyond the sphere of
our knowledge of individual cases; and that when a new individual, Socrates, is brought with-
in 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 theorv, the
smaller assertion is proved by the larger : while I contend, that both assertions are proved to-
gether, by the same evidence, namely, the grounds of experience on which the general asser-
tion 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.
2f>!>) : "The whole objection tacitly assumes the superfluity of the minor; that is, tacitly as-
sumes we know Socrates* to be a man as soon as we know him to be Socrates." The objec-
tion would be well grounded if the 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 7ie\v individual with the marks; and to
show that this comparison has been made, is the office of the minor. But since, by supposi-
tion, the new individual has the marks, whether we have ascertained him to have them or
not ; if we have affirmed the major premise, we have asserted him to be mortal. Now my
position is that this assertion can not be a necessary part of the argument. It can not be a
necessary condition of reasoning that we should begin by making an assertion, which is after-
ward to be employed in proving a part of itself. I can conceive only one way out of this dif-
ficulty, viz., that what really forms the proof is the other part of the assertion : the portion of
it, the truth of which has been ascertained previously : and that the unproved part is bound
up in one 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 syllo-
gism, predicating of Socrates a definite class name. I readily admit that it is no more a neces-
sary part of reasoning than the major. When there is a major, doing its work bv 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 er-
roneous reasoning. The only minor premise necessary to reasoning in the example under
* Mr. De Morgan says "Plato," but to prevent confusion I have kept to my own exempt urn.
FUNCTIONS AND VALUE OF THE SYLLOGISM. 157
between it and Logic in the widest sense. Logic, as I conceive it, is the
entire theory of 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 represented as the whole of Logic
properly so called, is really a very subordinate part of it, not being direct-
ly concerned with the process of Reasoning or Inference in the sense in
which that process is a part of the Investigation of Truth. What, then,
is Formal Logic ? The name seems to be properly applied to all that por-
tion of doctrine which relates to the equivalence of different modes of ex-
pression ; the rules for determining when assertions in a given form imply
or suppose the truth or falsity of other assertions. This includes the theo-
ry of the Import of Propositions, and of their Conversion, ^Equipollence,
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 observance 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 infer-
ences or conclusions in complete consistency with our general formulas 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 can not be true, but also because truth can only
be successfully pursued by drawing inferences from experience, which, if
warrantable at all, admit of being generalized, and, to test their warrant-
ableness, require to be exhibited in a generalized form ; after which the
correctness of their application to particular cases is a question which spe-
cially concerns the Logic of Consistency. This Logic, not requiring any
preliminary knowledge of the processes or conclusions of the various sci-
ences, 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 any thing else, though the reasons assigned for the practice are in
general very far from philosophical, admits of philosophical justification.
consideration, is, Socrates is like A, B, C, and the other individuals who are known to have
died. And this is the only universal type of that step in the reasoning process which is rep-
resented by the minor. Experience, however, of the uncertainty of this loose mode of infer-
ence, teaches the expediency of determining beforehand what kind of likeness to the cases ob-
served, is necessaiy to bring an unobserved case within the same predicate ; and the answer
to this question is the major. The minor then identifies the precise kind of likeness possessed
by Socrates, as being the kind required by the formula. 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 syl-
logism 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 prem-
ises. 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.
* Infra, book iii., chap. ii.
158 REASONING.
CHAPTER IV.
OP TRAINS OF REASONING, AND DEDUCTIVE SCIENCES.
1. IN our analysis of the syllogism, it appeared that the minor premise
always affirms a resemblance between a new ease and some cases previous-
ly known ; while the major premise asserts something which, having been
found true of those known cases, we consider ourselves warranted in hold-
ing true of any other case resembling the former in certain given particu-
lars.
If all ratiocinations resembled, as to the minor premise, the examples
which were exclusively employed in the preceding chapter; if the resem-
blance, which that premise asserts, were obvious to the senses, as in the
proposition " Socrates is a man," or were at once ascertainable by direct
observation ; there would be no 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 can not di-
rectly observe the fact which is to be proved, but can not 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 conclu-
sion respecting the animal now present will be instantly 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 poisonous, the substance which is before me is arsenic, therefore it is poi-
sonous. The truth of the minor may not here be obvious at first sight;
it may not be intuitively evident, but may itself be known only by infer-
ence. 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 hypochloride of calcium, is arsenic ; the substance before me con-
forms 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 add-
ing induction to induction. Two separate inductions must have taken
place to render this chain of inference possible ; inductions founded, prob-
ably, 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 exam-
ined various objects which yielded under the given circumstances a dark
TRAINS OF REASONING. 159
spot with the given property, and found that they possessed the properties
connoted by the word arsenic ; they were metallic, volatile, their vapor had
a smell of garlic, and so forth. Next, we, or others for us, have examined
various specimens which possessed this metallic and volatile character,
whose vapor had this smell, etc., and have invariably found that they were
poisonous. The first observation we judge that we may extend to all sub-
stances whatever which yield that particular kind of dark spot; the second,
to all metallic and volatile substances resembling those we examined ; and
consequently, not to those only which are seen to be such, but to those
which are concluded to be such by the prior induction. The substance
before us is only seen to come within one of these inductions ; but by
means of this one, it is brought within the other. We are still, as before,
concluding from particulars to particulars ; but we are now concluding
from particulars observed, to other particulars which are not, as in the
simple case, seen to resemble them in 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 consider as a mark of the former re-
semblance.
This first example of a train of reasoning is still extremely simple, the
series consisting of only two syllogisms. The following is somewhat more
complicated : No government, which earnestly seeks the good of its sub-
jects, is likely to be overthrown ; some particular government earnestly seeks
the good of its subjects, therefore it is not likely to be overthrown. The ma-
jor premise in this argument we shall suppose not to be derived from con-
siderations a priori^ but to be a generalization from history, which, wheth-
er correct or erroneous, must have been founded on observation of govern-
ments concerning whose desire of the good of their subjects there was no
doubt. It has been found, or thought to be found, that these were not
easily overthrown, and it has been deemed that those 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 sub-
jects. But does the government in question thus resemble them? This
may be debated pro and con by many arguments, and must, in any case, be
pi'oved by another induction ; for we can not directly observe the senti-
ments and desires of the persons who carry on the government. To prove
the minor, therefore, we require an argument in this form : Every govern-
ment 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 in-
duction, as thus : What is asserted by intelligent and disinterested witness-
es, 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 of our senses
that the case of the government under consideration resembles a number
of former cases, in the circumstance of having something asserted respect-
ing it by intelligent 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 re-
semblance with those other governments or persons ; and since they were
known to desire the good of the people, it is thereupon, by a second indue-
160 REASONING.
tion, 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 revolution, and
thence, by a third induction, it is concluded that this particular govern-
ment is also likely to escape. This is still reasoning from particulars to
particulars, but we now reason to the new instance from three distinct sets
of former instances : to one only of those sets of instances do we directly
perceive the new one to be similar; but from that similarity we induc-
tively infer that it has the attribute by which it is assimilated to the next
set, and brought within the 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.
:i. Notwithstanding the superior complication of these examples, com-
pared 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 proposi-
tions are not steps in the reasoning, are not intermediate links in the chain
of inference, between the particulars observed and those to which we ap-
ply the observation. If we had sufficiently capacious memories, and a suf-
ficient power of maintaining order among a huge mass of details, the rea-
soning could go on without any general propositions ; they are mere for-
mula) for inferring particulars from particulars. The principle of gener-
al reasoning is (as before explained), that if, from observation of certain
known particulars, what was seen to be true of them can be inferred to be
true of any others, it may be inferred of all others which are of a certain
description. And in order that we may never fail to draw this conclusion
in a new case when it can be drawn correctly, and may avoid drawing it
when it can not, we determine once for all what are the distinguishing marks
by which such cases may be recognized. The subsequent process is mere-
ly 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 particu-
lars, from the observed instances to an unobserved one: but in drawing
this inference, 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 infer-
ence could, and when it could not, be drawn. The real premises are the in-
dividual observations, even though they may have been forgotten, or, being
the observations of others and not of ourselves, may, to iis, 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 recognize 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 recognized
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 ground-
ed on particulars its similarity to which is only ascertained in this indirect
manner.
Thus, in the preceding example, the ultimate inductive inference was,
that a certain government was not likely to be overthrown ; this inference
TRAINS OF REASONING. 161
was drawn according to a formula in which desire of the public good was
set down as a mark of not being likely to be overthrown ; a mark of this
mark was, acting in a particular manner; and a mark of acting in that
manner was, being asserted to do so by intelligent and disinterested wit-
nesses : this mark, the government under discussion was recognized by the
senses as possessing. Hence that government fell within the last induc-
tion, and by it was brought within all the others. The perceived resem-
blance of the case to one set of observed particular cases, brought it into
known resemblance with another set, and that with a third.
In the more complex branches of knowledge, the deductions seldom con-
sist, as in the examples hitherto exhibited, of a single chain, a a mark of b,
b of c, c of d, therefore a a mark of d. They consist (to carry on the same
metaphor) of several chains united at the extremity, as thus : a a mark of
d, b of e, c of f, d e f of ?i, therefore a b c a. mark of n. Suppose, for exam-
ple, the following combination of circumstances: 1st, rays of light impin-
ging on a reflecting surface ; 2d, that surface parabolic ; 3d, those rays
parallel to each other and to the axis of the surface. It is to be proved
that the concourse of these three circumstances is a mark that the reflected
rays will pass through the focus of the parabolic surface. Now, each of
the three circumstances is singly a mark of something material to the case.
Rays of light impinging on a reflecting surface are a mark that those rays
will be reflected at an angle equal to the angle of incidence. The parabol-
ic form of the surface, is a mark that, from any point of it, a line drawn to
the focus and a line parallel to the axis will make equal angles with the
surface. And finally, the parallelism of the rays to the axis is a mark that
their angle of incidence coincides with one of these equal angles. The
three marks taken together are therefore a mark of all these three things
united. But the three united are evidently a mark that the angle of re-
flection must coincide with the other of the two equal angles, that formed
by a line drawn to the focus ; and this again, by the fundamental axiom
concerning straight lines, is a mark that the 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
w r here the hypothesis includes numerous conditions: "Jfa 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," etc.
4. The considerations now stated remove a serious difficulty from the
view we have taken of reasoning ; which view might otherwise have
seemed not easily reconcilable with the fact that there are Deductive or
Ratiocinative Sciences. It might seem to follow, if all reasoning be induc-
tion, that the difficulties of philosophical investigation must lie in the in-
ductions exclusively, and that when these were easy, and susceptible of no
doubt or hesitation, there could be no science, or, at least, no difficulties in
science. The existence, for example, of an extensive Science of Mathemat-
ics, requiring the highest scientific genius in those who contributed to its
creation, and calling for a most continued and vigorous exertion of intel-
lect in order to appropriate it when created, may seem hard to be accounted
for on the foregoing theory. But the considerations 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
11
162 REASONING.
one within which the case evidently falls, to bring it within others in which
it can not 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 busi-
ness is ended. But new cases are continually arising, which do not obvi-
ously come within any formula whereby the question we want solved in
respect of them could be answered. Let us take an instance from geome-
try : and as it is taken only for illustration, let the reader concede to us
for the present, what we shall endeavor 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
formula} : 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 formu-
lae 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 differences of equal things and unequal things
are unequals. In all, eight formulae. The angles at the base of an isos-
celes triangle do not obviously come within any of these. The formula?
specify certain marks of equality and of inequality, but the angles can not
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 recognizing these angles as the differences of equal things'?
Because each of them is the difference not of one pair only, but of innu-
merable 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 exercise
of ingenuity, which, on the part of the first inventor, deserves to be re-
garded as considerable, two pairs of angles were hit upon, which united
these requisites. First, it could be perceived intuitively that their differ-
ences were the angles at the base ; and, secondly, they possessed one of the
marks of equality, namely, coincidence when applied to one another. This
coincidence, however, was not perceived intui-
tively, but inferred, in conformity to another
formula.
For greater clearness, I subjoin an analysis
of the demonstration. Euclid, it will be re-
membered, demonstrates his fifth proposition
by means of the fourth. This it is not allow-
able for us to do, because we are undertaking
to trace deductive truths not to prior deduc-
tions, but to their original inductive founda-
tion. 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. (\Ve must begin, as
TRAINS OF REASONING.
163
in Euclid, by prolonging 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. Having that mark
of equality, they are concluded by this formula to be equal.
SECOND FORMULA. Equal straight lines or angles, being applied to one
another, coincide.
AC, AB, are within this formula by supposition ; AD, AE, have been
brought within it by the preceding step. The angle at A considered as an
angle of the triangle ABE, and the same angle considered as an angle of
the triangle ACD, are of course within the formula. All these pairs, there-
fore, possess the property which, according to the second formula, is a
mark that when applied to one another they will coincide. Conceive
them, then, applied to one another, by turning over the triangle ABE, and
laying it on the triangle ACD in such a manner that AB of the one shall
lie upon AC of the other. Then, by the equality of the angles, AE will lie
on AD. But AB and AC, AE and AD are equals ; therefore they will co-
incide altogether, and of course at their extremities, D, E, and B, C.
THIRD FORMULA. Straight lines, having their extremities coincident,
coincide.
BE and CD have been brought within this formula by the preceding in-
duction ; they will, therefore, coincide.
FOURTH FORMULA. Angles, having their sides coincident, coincide.
The third induction having shown that BE and CD coincide, and the
second that AB, AC, coincide, the angles ABE and ACD are thereby
brought within the fourth formula, and accordingly coincide.
FIFTH FORMULA. Things which coincide are equal.
The angles ABE and ACD are brought within this formula by the in-
duction immediately preceding. This train of reasoning being also appli-
cable, 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 cut-
ting one pair of angles out of another, while each pair shall be correspond-
ing 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
combine a few simple inductions, as to bring within each of them innumer-
able cases which are not obviously included in it ; and how long, and nu-
104 REASONING.
morons, 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 inductions involved in all geometry are comprised in those
simple ones, the formula 1 of which are the Axioms, and a few of the so-call-
ed Definitions. The remainder of the science is made up of the processes
employed for bringing unforeseen cases within these inductions; or (in syl-
logistic language) for proving the minors necessary to complete the syllo-
gisms ; the majors being the definitions and axioms. In those definitions
and axioms are laid down the whole of the marks, by an artful combina-
tion 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 Reasoning,
forms the whole difficulty of the science, and, with a trifling exception, 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 Sci-
ence as possible ; for endeavoring to construct the science from the fewest
and the simplest possible inductions, and to make these, by any combina-
nations however complicated, suffice for proving even such truths, relating
to complex cases, as could be proved, if we chose, by inductions from spe-
cific experience. Every branch of natural philosophy was originally exper-
imental ; 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 consist of no more than one step,
and are expressed by single syllogisms, all these sciences have become to
some extent, and some of them in nearly the whole of their extent, sciences
of pure reasoning; whereby multitudes of truths, already known by induc-
tion from as many different sets of experiments, have come to be exhibited
as deductions or corollaries from inductive propositions of a simpler and
more universal character. Thus mechanics, hydrostatics, optics, acoustics,
thermology, have successively been rendered mathematical ; and astronomy
was brought by Xewton 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, therefore, 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 induction. 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
can not be observed to have the requisite marks, have, however, marks of
those marks.
We can now, therefore, perceive what is the generic distinction between
* Infra, book iii., ch. iv., 3, and elsewhere.
TRAINS OF REASONING. 165
sciences which can be made Deductive, and those which must as yet re-
main Experimental. The difference consists in our having been able, or
not yet able, to discover marks of marks. If by our various inductions we
have been able to 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 any thing 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 color 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 proposi-
tions, is purely experimental. Chemistry, in the present state of our
knowledge, has not yet thrown off this character. There are other sci-
ences, 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, etc. In these sciences we can mount the lad-
der 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 al-
though even d, our only direct mark of e, may not be perceptible in those
objects, but only inferable. Or, varying the first metaphor, we may be
said to get from a to e underground : the marks b, c, d, which indicate the
route, must all be possessed somewhere by the objects concerning which
we arc 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 experi-
mental science, the inductions, as we have said, lie detached, as, a a mark of
>, c a mark of d, e a mark off, and so on : now, a new set of instances, and
a consequent new induction, may at any time bridge over the interval be-
tween 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 induc-
tion may raise an arch high in the air, which bridges over hosts of them
at once; b, d,f, and all the rest, turning out to be marks of some one thing,
or of things between which a connection has already been traced. As
when 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 de-
gree merely experimental, into a deductive science.
Transformations of the same nature, but on a smaller scale, continually
take place in the less advanced branches of physical knowledge, without
enabling them to throw off the character of experimental sciences. Thus
with regard to the two unconnected propositions before cited, namely,
Acids redden vegetable blues, Alkalies make them green ; it is remarked by
Liebig, that all blue coloring matters which are reddened by acids (as well
as, reciprocally, all red coloring matters which are rendered blue by alka-
lies) contain nitrogen : and it is quite possible that this circumstance may
one day furnish a bond of connection between the two propositions in
question, by showing that the antagonistic action of acids and alkalies in
166 REASONING.
producing or destroying the color 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 generaliza-
tions are continually taking place, is still in the main an experimental sci-
ence ; 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 generali-
zation, which, though relating to one of the subordinate aspects of chemical
phenomena, possesses within its limited sphere this comprehensive charac-
ter; the principle of Dalton, called the atomic theory, or the doctrine of
chemical equivalents : which by enabling us to a certain extent to foresee
the proportions in which two substances will combine, before the experi-
ment has been tried, constitutes undoubtedly a source of new chemical
truths obtainable by deduction, as well as a connecting principle for all
truths of the same description previously obtained by experiment.
V. The discoveries which change the method of a science from experi-
mental to deductive, mostly consist in establishing, either by deduction or
by direct experiment, that the varieties of a particular phenomenon uni-
formly 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 ex-
periment that every variety of sound was consequent on, and therefore a
mark of, a distinct and definable variety of oscillatory motion among the
particles of the transmitting medium. When this was ascertained, it fol-
lowed that every relation of succession or co-existence which obtained be-
tween phenomena of the more known class, obtained also between the
phenomena which correspond to them in the other class. Every sound,
being a mark of a particular oscillatory motion, became a mark of every
thing which, by the laws of dynamics, was known to be inferable from
that motion ; and every thing which by those same laws was a mark of any
oscillatory motion among the particles of an elastic medium, became a mark
of the corresponding sound. And thus many truths, not before suspected,
concerning sound, become deducible from the known laws of the propaga-
tion of motion through an elastic medium; while facts already empirically
known respecting sound, become an indication of corresponding properties
of vibrating bodies, previously undiscovered.
But the grand agent for transforming experimental into deductive sci-
ences, is the science of number. The properties of number, alone among
all known phenomena, are, in the most rigorous sense, properties of all
things whatever. All things are not colored, or ponderable, or even ex-
tended ; 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
TRAINS OF REASONING. 167
to variations of quantity either in those same or in some other phenomena ;
every formula of mathematics applicable to quantities which vary in that
particular manner, becomes a mark of a corresponding general truth re-
specting the variations in quality which accompany them: and the sci-
ence 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 un-
paralleled extension given to the deductive 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 peculiar 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 re-
lating to quantity or quality, would be capable of being inferred. Hence
it followed that every geometrical question could be solved, if the corre-
sponding algebraical one could ; and geometry received an accession (act-
ual or potential) of new truths, corresponding to every property of num-
bers 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 va-
rieties 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 num-
ber do but fulfill the function proper to all propositions forming a train of
reasoning, viz., that of enabling us to arrive in an indirect method, by
marks of marks, at such of the properties of objects as we can not direct-
ly 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 concerned; while the fact sought
presupposes a certain relation between the quantities of some other ele-
ments : now, if these last quantities are dependent in some known manner
upon the former, or vic versa, we can argue from the numerical relation
between the one set of quantities, to determine that which subsists be-
tween the other set ; the theorems of the calculus affording the intermedi-
ate 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.
168 REASONING.
CHAPTER 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, deductive? Why are
they called the Exact Sciences ? Why are mathematical certainty, and the
evidence of demonstration, common phrases to express the very highest
degree of assurance attainable by reason ? Why are mathematics by al-
most all philosophers, and (by some) even those branches of natural phi-
losophy which, through the medium of mathematics, have been converted
into deductive sciences, considered to be independent of the evidence of
experience and observation, and characterized as systems of Necessary
Truth ?
The answer I conceive to be, that this character of necessity, ascribed to
the truths of mathematics, and (even with some reservations to be here-
after made) the peculiar certainty attributed to them, is an illusion ; in or-
der to sustain which, it is necessary to suppose that those truths relate to,
and express the properties of, purely imaginary objects. It is acknowl-
edged that the conclusions of geometry are deduced, partly at least, from
the so-called Definitions, and that those definitions are assumed to be cor-
rect 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 OIK- concerning the meaning of a word, can ever
follow ; and that what apparently follows from a definition, follows in real-
ity from an implied assumption that there exists a real thing conformable
thereto. This assumption, in the case of the definitions of geometry, is not
strictly true : 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, exist-
ence of such things. I answer that, according to any test we have of possi-
bility, they are not even possible. Their existence, so far as we can form
any judgment, would seem to be inconsistent with the physical constitu-
tion of our planet at least, if not of the universe. To get rid of this diffi-
culty, and at the same time to save the credit of the supposed system of
necessary truth, it is customary to say that the points, lines, circles, and
squares which are the subject of geometry, exist in our conceptions mere-
ly, and are part of our minds ; which minds, by working on their own ma-
terials, construct an a priori science, the evidence of which is purely men-
tal, and has nothing whatever to do with outward experience. By how-
soever high authorities this doctrine may have been sanctioned, it appears
DEMONSTRATION, AND NECESSARY TRUTHS. 169
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
cisibile, the smallest portion of surface which we can see. A line, as de-
fined 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, in-
stead of the whole. But we can not conceive a line without breadth ; we
can form no mental picture of such a line : all the lines which we have in
our minds are lines possessing breadth. If any one doubts this, we may
refer him to his own experience. I much question if any one who fancies
that 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 possible, mathematics could not exist as
a science : a supposition which there will be no difficulty in showing to be
entirely groundless.
Since, then, neither in nature, nor in the human mind, do there exist any
objects exactly corresponding to the definitions of geometry, while yet that
science can not be supposed to be conversant about nonentities ; 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 gener-
alizations, 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 impor-
tance in practice will be incurred by feigning it to be exactly true. When
we have occasion to extend these inductions, or their consequences, to cases
in which the error would be appreciable to lines of perceptible breadth
or thickness, parallels which deviate sensibly from equidistance, and the
like we correct our conclusions, by combining with them a fresh set of
propositions relating to the aberration; just as we also take in proposi-
tions 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 ex-
cept 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 : according-
ly, we formally announce in the definitions, that we intend to proceed on
this plan. But it is an error to suppose, because we resolve to confine our
attention to a certain number of the properties of an object, that we there-
fore conceive, or have an idea of, the object, denuded of its other proper-
ties. 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
properties, 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 princi-
1 TO REASONING.
pies 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 suppo-
sition. The opinion of Dugald Stewart respecting the foundations of ge-
ometry, 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 compel-
ling assent, on condition that those hypotheses are true.*
When, therefore, it is affirmed that the conclusions of geometry are nec-
essary truths, the necessity consists in reality only in this, that they cor-
rectly follow from the suppositions from which they are deduced. Those
suppositions are so far from being necessary, that they are not even true ;
they purposely depart, more or less widely, from the truth. The only sense
in which necessity can be ascribed to the conclusions of any scientific in-
vestigation, 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 derivative 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 sup-
posed certain for the purposes of the particular science. And therefore
the conclusions of all deductive sciences were said by the ancients to be
necessary propositions. We have observed already that to be predicated
necessarily was characteristic of the predicable Proprium, and that a pro-
prium was any property of a thing which could be deduced from its es-
sence, that is, from the properties included in its definition.
2. The important doctrine of Dugald Stewart, which I have endeav-
ored to enforce, has been contested by Dr. Whewell, both in the disserta-
tion appended to his excellent Meclianical Undid, and in his elaborate
work on the Pliilosophy 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. WhewelPs purpose ; for it is these very assumptions which arc as-
serted to be hypotheses, and which he, if he denies that geometry is founded
* It is justly remarked by Professor Bain (Logic, ii., 134) that the word Hypothesis is here
used in a somewhat peculiar sense. An hypothesis, in science, usually means n supposition
not proved to he true, hut surmised to he so, because if true it would account for certain
known facts ; and the final result of the speculation may be to prove its truth. The hypothe-
ses spoken of in the text are of a different character ; they are known not to he literally true,
while as much of them as is true is not hypothetical, but certain. The two cases, however,
resemble in the circumstance that in both we reason, not from a truth, but from an assump-
tion, and the truth therefore of the conclusions is conditional, not categorical. This suffices
to justify, in point of logical propriety, Stewart's use of the term. It is of course needful to
hear in mind that the hypothetical element in the definitions of geometry is the assumption
that what is very nearly true is exactly so. This unreal exactitude might be called a fiction,
as properly as an hypothesis; but that appellation, still more than the other, would fail to
point out the close relation which exists between the fictitious point or line and the points
and lines of which we have experience.
DEMONSTRATION, AND NECESSARY TRUTHS. Ifl
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 hypoth-
eses which have no relation whatever to fact. Since an hypothesis framed
for the purpose of scientific inquiry must relate to something which has
real existence (for there can be no science respecting nonentities), it fol-
lows that any hypothesis we make respecting an object, to facilitate our
study of it, must not involve any thing which is distinctly false, and repug-
nant 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 suppressing 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 conclusions. Of this na-
ture, accordingly, are the first principles involved in the definitions of ge-
ometry. 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 sup-
pose an imaginary animal, and work out by deduction, from the known
laws of physiology, its natural history ; or an imaginary commonwealth,
and from the elements composing it, might argue what would be its fate.
And the conclusions which we might thus draw from purely arbitrary hy-
potheses, might form a highly useful intellectual exercise : but as they could
only teach us what icould be the properties of objects which do not really
exist, they would not constitute any addition to our knowledge of nature :
while, on the contrary, if the hypothesis merely divests a real object of
some portion of its properties, without clothing it in false ones, the conclu-
sions 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 geom-
etry which are involved in the so-called definitions, he has, I conceive, great-
ly the advantage of Stewart on another important point in the theory of
geometrical reasoning; the necessity of admitting, among those first prin-
ciples, axioms as well as definitions. Some of the axioms of Euclid might,
no doubt, be exhibited in the form of definitions, or might be deduced, by
reasoning, from 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 ap-
plied to one another as to coincide ;" the three axioms which follow (Mag-
nitudes 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,
* Mechanical Euclid, pp. 149 et seqq.
172 REASONING.
the remainders are equal), may be proved by an imaginary superposition,
resembling that by which the fourth proposition of the first book of Euclid
is demonstrated. But though these and several others may be struck out
of the list of first principles, because, though not requiring demonstration,
they are susceptible of it; there will be found in the list of axioms two or
three fundamental truths, not capable of being demonstrated: among which
must be reckoned the proposition that two straight lines can not inclose a
space (or its equivalent, Straight lines which coincide in two points coin-
cide altogether), and some property of parallel lines, other than that which
constitutes their definition : one of the most suitable for the purpose being
that selected by Professor Playfair: "Two straight lines which intersect
each other can not both of them be parallel to a third straight line."*
The axioms, as well those which are indemonstrable as those which ad-
mit of being demonstrated, differ from that other class of fundamental
principles which are involved in the definitions, in this, that they are true
without any mixture of hypothesis. That things which are equal to the
same thing are equal to one another, is as true of the lines and figures in
nature, as it would be of the imaginary ones assumed in the definitions.
In this respect, however, mathematics arc 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 ap-
proximations 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 dim-
inution of one second in all that period. These arc 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 or-
der to use them for the further advancement of our knowledge, we must
feign that they are exactly true, though they really want something of be-
ing so.
ij 4. It remains to inquire, what is the ground of our belief in axioms
what is the evidence on which they rest? I answer, they are experi-
mental truths; generalizations from observation. The proposition, Two
straight lines can not 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 proposition enunciated in this
work for which a more unfavorable 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 eminent a cham-
* We might, it is true, insert this property into the definition of parallel linos, framing the
definition so as to require, both that when produced indefinitely they shall never meet, and
also that any straight line which intersects one of them shall, if prolonged, meet the other.
Hut l)v 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 in the same plane, other than those which an; parallel according to the
definition, had the property of never meeting although indefinitely produced, the demonstra-
tions of the subsequent portions of the theory of parallels could not be maintained.
DEMONSTRATION, AND NECESSARY TRUTHS. 173
pion of the contrary opinion as Dr. Whewell has found occasion for a most
elaborate treatment of the whole theory of axioms, in attempting to con-
struct 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 represented. If what is
said by Dr. Whewell, in support of an opinion which he has made the
foundation of a systematic work, can be shown not to be conclusive, enough
will have been done, without going elsewhere 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 can not 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 per-
ceived a priori, by the constitution of the mind itself, from the first mo-
ment 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.
They can not, however, but allow that the truth of the axiom, Two
straight lines can not inclose a space, even if evident independently of ex-
perience, is also evident from experience. Whether the axiom needs con-
firmation or not, it receives confirmation in almost every instant of our
lives ; since we can not look at any two straight lines which intersect one
another, without seeing that from that point they continue to diverge more
and more. Experimental proof crowds in upon us in such endless profu-
sion, 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 be-
lieving 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 be-
lieve it with an intensity of conviction far greater than we accord to any
ordinary physical truth : and this too at a time of life much earlier than
that from which we date almost any part of our acquired knowledge, and
much too early to admit of our retaining any recollection of the 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
~ o o
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 be-
lief 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 be-
lief 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 knowledge of nature is derived from
the same sources as every other part.*
* Some persons find themselves prevented from believing that the axiom, Two straight lines
can not inclose H 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 absolutely 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 present them-
selves 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
174 REASONING.
This, for instance, they would be able to do, if they could prove chrono-
logically that we had the conviction (at least practically) so early in infan-
cy as to be anterior to those impressions on the senses, upon which, on the
other theory, the conviction is founded. This, however, can not be proved:
the point being too far back to be within the reach of memory, and too ob-
scure for external observation. The advocates of the a priori theory are
obliged to have recourse to other arguments. These are reducible to two,
which I shall endeavor 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 can not 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 recognize
that two such lines can not inclose a space. Intuition is " imaginary look-
ing ;"* 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 can not 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 can not 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. How can this, in any
single case, be proved by actual observation ? We may follow the lines to
any distance we please ; but we can not 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 impossibility than observation
affords us, we should have no ground for believing the axiom at all.
To these arguments, which 1 trust I can not be accused of understating,
a satisfactory answer will, I conceive, be found, if we advert to one of the
characteristic properties of geometrical forms their capacity of being
painted in the imagination with a distinctness equal to reality : in other
words, the exact resemblance of our ideas of form to the sensations which
true, for two of them may, ami 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 can not be proved by
induction, show themselves unfamiliar with a common and perfectly valid mode of inductive
proof; proof by approximation. Though experience furnishes us with no lines so unim-
peachably straight that two of them are incapable 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 bad no breadth or flexure at all. they would inclose no
space at all, is a correct inductive 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.
* Whewell's History of Scientific Ideas, i., 140.
DEMONSTRATION, AND NECESSARY TRUTHS. 175
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 an-
gles, 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 ; inasmuch as pic-
tures, 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 therefore
be laid in direct experience, even if the experiments (which in this case
consist merely in attentive contemplation) were practiced 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 rep-
resentative of its class, are completely fulfilled by an object existing only
in our fancy. Without denying, therefore, the possibility of satisfying our-
selves that two straight lines can not inclose a space, by merely thinking
of straight lines without actually looking at them ; I contend, that we do
not believe this truth on the ground of the imaginary intuition simply, but
because we know that the imaginary lines exactly resemble real ones, and
that we may conclude from them to real ones with quite as much certainty
as we could conclude from one real line to another. The conclusion, there-
fore, is still an induction from observation. And we should not be author-
ized to substitute observation of the image in our mind, for observation
of the reality, if we had not learned by long-continued experience that the
properties of the reality are faithfully represented in the image; just as
we should be scientifically warranted in describing an animal which we
have never seen, from a picture made of it with a daguerreotype ; but not
until we had learned by ample experience, that observation of such a pic-
ture is precisely equivalent to observation of the original.
These considerations also remove the objection arising from the im-
possibility of ocularly following the lines in their prolongation to infinity.
For though, in order actually to see that two given lines never meet, it
would be necessary to follow them to infinity ; yet without doing so we
may know that if they ever do meet, or if, after diverging from one anoth-
er, they begin again to approach, this must take place not at an infinite,
but at a finite distance. Supposing, therefore, such to be the case, we can
transport 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 occasion to make from former ocular
observation, we learn by the evidence of experience, that a line which, after
diverging from another straight line, begins to approach to it, produces
the impression on our senses which we describe by the expression, " 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 ap-
pear," he says, "how we can compare our ideas with the realities, since we know the realities
only by our ideas." We know the realities by our sensations. Dr. Whewell surely does not
hold the " doctrine of perception by means of ideas," which Reid gave himself so much trou-
ble to refute.
176 REASONING.
The preceding argument, which is, to my mind unanswerable, merges,
however, in a still more comprehensive one, which is stated most clearly
and conclusively by Professor Bain. The psychological reason why ax-
ioms, and indeed many propositions not ordinarily classed as such, may be
learned from the idea only without referring to the fact, is that in the proc-
ess of acquiring the idea we have learned the fact. The proposition is
assented to as soon as the terms are understood, because in learning to un-
derstand the terms we have acquired the experience which proves the propo-
sition to be true. " We required," says Mr. Bain,* " concrete experience in
the first instance, to attain to the notion of whole and part; but the notion,
once arrived at, implies that the whole is greater. In fact, we could not
have the notion without an experience tantamount to this conclusion
When we have mastered the notion of straightness, we have also mastered
that aspect of it expressed by the affirmation that two straight lines can
not inclose a space. Xo intuitive or innate powers or perceptions are
needed in such cases We can not have the full meaning of Straight-
ness, without going through a comparison of straight objects among them-
selves, and with their opposites, bent or crooked objects. The result of
this comparison is, inter alia, that straightness in two lines is seen to be
incompatible with inclosing a space; the inclosure of space involves crook-
edness in at least one of the lines." And similarly, in the case of every
first principle,! " tne same knowledge that makes it understood, suffices to
verify it." The more this observation is considered the more (I am con-
vinced) it will be felt to go to the very root of the controversy.
6. 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)
If Dr. Whewell doubts whether \ve 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 sensa-
tions 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 recall in imagination a color or an odor with the same distinctness and ac-
curacy 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 colors
or of odors 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 color 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 colors ; that is, he might examine his
mental pictures, and find there a property of the outward objects. But in hardly any case
except that of simple geometrical forms, could this be done by mankind generally, with a de-
gree of assurance equal to that which is given by a contemplation of the objects themselves.
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 hardlv know
whether his nose is long or short. Hut every body has a perfectly distinct mental image of a
straight line, a circle, or a rectangle. 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 recol-
lections. " * Logic, i., I' 1 .'!.'. " f Jbid., 220.
DEMONSTRATION, AND NECESSARY TRUTHS. 177
are conceived by us not only as true, but as universally and necessarily
true. Now, experience can not possibly give to any proposition this char-
acter. I may have seen snow a hundred times, and may have seen that it
was white, but this can not give nuHBQtire assurance even that all snow is
white; much less that snow must be white. "However many instances
we may have observed of the truth of a proposition, there is nothing to
assure us that the next case shall not be an exception to the rule. If it
be strictly true that every ruminant animal yet known has cloven hoofs,
we still can not be sure that some creature will not hereafter be discov-
ered which has the first of these attributes, without having the other
Experience must always consist of a limited number of observations ; and,
however numerous these may be, they can show nothing with regard to
the infinite number of cases in which the experiment has riot been made."
Besides, Axioms are not only universal, they are also necessary. Now " ex-
perience can not offer the smallest ground for the necessity of a proposi-
tion. She can observe and record what has happened; but she can not
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 can not 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 can not detect any
internal bond, which indissolubly connects the future with the past, the pos-
sible with the real. To learn a proposition by experience, and to see it to
be necessarily true, are two altogether different processes of thought."*
And Dr. W he well adds, " If any one does not clearly comprehend this dis-
tinction of necessary and contingent truths, he will not be able to go along
with us in our researches into the foundations of human knowledge ; nor,
indeed, to pursue with success any speculation on the subject."f
In the following passage, we are told what the distinction is, the non-
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 the negation of the truth is not only false, but
impossible ; in which we can not, even by an effort of imagination, or in
a supposition, conceive the reverse of that which is asserted. That there
are such truths can not be doubted. We may take, for example, all rela-
tions of number. Three and Two added together make Five. We can
not conceive it to be otherwise. We can not, 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 can not figure to
ourselves as being false, must rest on evidence of a higher and more cogent
description than any which experience can afford.
Now I can not but wonder that so much stress should be laid on the cir-
cumstance of inconceivableness, when there is such ample experience to
* History of Scientific Ideas, I, 65-67. t Ibid., i., 60. J Ibid., 58, 59.
12
178 REASONING.
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 na-
ture, than the extreme difficulty at first felt in conceiving any thing as pos-
sible, 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 in-
stance either seen or thought of them separately, there is by the primary
law of association an increasing 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 sepa-
rate any two ideas which have once become firmly associated in their
minds ; and if persons of cultivated intellect have any advantage on the
point, it is only because, having seen and heard and read more, and being
more accustomed to exercise their imagination, they have experienced their
sensations and thoughts in more varied combinations, and have been pre-
vented from forming many of these inseparable associations. But this ad-
vantage has necessarily its limits. The most practiced intellect is not ex-
empt 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 lie is
not led during that period either by accident or by his voluntary mental
operations to think of them apart, lie will probably in time become incapa-
ble 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 re-
markable instances of this in the history of science : instances in which the
most instructed men rejected as impossible, because inconceivable, things
which their posterity, by earlier practice and longer perseverance in the at-
tempt, found it quite easy to conceive, and which every body 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 upward instead of downward.
The Cartesians long rejected the Newtonian doctrine of the gravitation of
all bodies toward one another, on the faith of a general proposition, the re-
verse of which seemed to them to be inconceivable the proposition that a
body can not act where it is not. All the cumbrous machinery of imagi-
nary vortices, assumed without the smallest particle of evidence, appeared
to these philosophers a more rational mode of explaining the heavenly mo-
tions, than one which involved what seemed to them so great an absurdity.f
* " If all mankind bad spoken one language, we can not doubt tbat tberc would have been
n powerful, perhaps a universal, school of philosophers, who would have believed in the in-
herent connection between names and tilings, 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, etc." De Morgan, Formal L<>gi<~, p. 2 Hi.
t It would be difficult to name a man more remarkable at once for the greatness 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 cou/il <// make a body re-
volve round a distant centre, unless either by some impelling mechanism, or by miracle:
"Tout ce (jiii n'est pas explicable," says he in a letter to the Abbe Conti. '* par la nature des
creatures, est miraculeux. II no sullit pas de dire: Dieu a fait une telle loi de nature ; done
la chose est uaturelle. II faut que la loi soil exe'cutable par les natures des cre'atures. Si
DEMONSTRATION, AND NECESSARY TRUTHS. 179
And they no doubt found it as impossible to conceive that a body should
act upon the earth from 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 gravita-
tion ; and his writings prove, that though he deemed the particular nature
of the intermediate agency a matter of conjecture, the necessity of some
such agency appeared to him indubitable.
If, then, it be so natural to the human mind, even in a high state of cul-
ture, to be incapable of conceiving, and on that ground to believe impossi-
ble, what is afterward not only found to be conceivable but proved to be
true ; what wonder if in cases where the association is still older, more con-
firmed, and more familiar, and in which nothing ever occurs to shake our
conviction, or even suggest to us any conception at variance with the asso-
ciation, the acquired incapacity should continue, and be mistaken for a nat-
ural incapacity ? It is true, our experience of the varieties in nature ena-
bles us, within certain limits, to conceive other varieties analogous to them.
We can conceive the sun or moon falling ; for though we never saw them
fall, nor ever, perhaps, imagined them falling, we have seen so many other
things fall, that we have innumerable familiar analogies to assist the con-
ception ; which, after all, we should probably have some difficulty in fram-
ing, were we not well accustomed to see the sun and moon move (or ap-
pear to move), so that we are only called upon to conceive a slight change
in the direction of motion, a circumstance 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 conceive the last point of space, we have
the idea irresistibly raised of other points beyond it. When we try to im-
agine the last instant of time, we can not help conceiving another instant
after it. Nor is there any necessity to assume, as is done by a modern
school of metaphysicians, a peculiar fundamental law of the mind to ac-
count 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 can not 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 inconceivable
to us ? What analogy have we, what similar order of facts in any other
branch of our experience, to facilitate to us the conception of two straight
lines inclosing a space ? Nor is even this all. I have already called atten-
tion to the peculiar property of our impressions of form, that the ideas or
mental images exactly resemble their prototypes, and adequately represent
them for the purposes of scientific observation. From this, and from the
intuitive character of the observation, which in this case reduces itself to
Dieu donnait cette loi, par exemple, k un corps libre, de tourner a 1'entour d'un certain centre,
ilfaudrait ou quil y joignit d'autres corps qui par lew impulsion Vobligeassent de rester tou-
jours dans son orbite circulaire, ou quil mit un ange a ses trousses, ou en/in ilfaudrait quil y
concourut extraordinairement ; car naturellement il s'e'cartera par la tangente." Works of
Leibnitz, ed. Dutens, iii., 446.
ISO REASONING.
simple inspection, we can not so much as call up in our imagination two
straight lines, in order to attempt to conceive them inclosing a space, with-
out 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 circumstances, proves any thing against the experimental or-
igin 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 recognizing the distinc-
tion held by him between necessary and contingent truths, to study geom-
etry a condition 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 convinced that nothing more
is requisite than a moderate familiarity with those laws, to dispel the illu-
sion which ascribes a peculiar necessity to our earliest inductions from ex-
perience, and measures the possibility of things in themselves, by the hu-
man capacity of conceiving them.
I hope to be pardoned for adding, that Dr. Whewell himself has both
confirmed by his testimony the effect of habitual association in giving to
an experimental truth the appearance of a necessary one, and afforded a
striking instance of that remarkable law in his own person. In his Philos-
ophy of the Inductive Sciences he continually asserts, that propositions
which not only are not self-evident, but which we know to have been dis-
covered 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 impossible to conceive that they had not been recognized
from the 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 something absurd in Newton's doctrine of the different refrangibility
of differently colored rays; or those who imagined that when elements
combine, their sensible qualities must be manifest in the compound ; or
those who were reluctant to give up the distinction of vegetables into herbs,
shrubs, and trees. We can not 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 re-
ality such a persuasion is a mere delusion. The persons Avho, in such in-
stances 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
* Novum Oryanum Renvvatum, pp. 32, 33.
DEMONSTRATION, AND NECESSARY TRUTHS. 181
evidence of axioms. For what is that theory? That the truth of axioms
can not have been learned from experience, because their falsity is incon-
ceivable. But Dr. Whewell himself says, that we are continually led, by
the natural progi-ess of thought, to regard as inconceivable what our fore-
fathers not only conceived but believed, nay even (he might have added)
were unable to conceive the reverse of. He can not intend to justify this
mode of thought : he can not mean to say, that we can be right in regard-
ing as inconceivable what others have conceived, and as self-evident what
to others did not appear evident at all. After so complete an admis-
sion that inconceivableness is an accidental thing, not inherent in the phe-
nomenon 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 paradoxes. The first law was especially so. That
a body, once in motion, would continue forever 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 w r as 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 be-
gan to believe that laws, thus contradictory to first appearances, and which,
even after full proof had been obtained, it had required generations to ren-
der familiar to the minds of the scientific world, were under " a demonstra-
ble necessity, compelling them to be such as they are and no 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,"f does actually so think of the law just mentioned ; of which he
says: "Though the discovery of the first law of motion was made, histor-
ically 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 experience.''^ Can there be a more striking exemplifi-
cation than is here afforded, of the effect of association which we have de-
scribed? Philosophers, for generations, have the most extraordinary diffi-
culty in putting certain ideas together; they at last succeed in doing so;
and after a sufficient repetition 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 impossibility, of sev-
ering them from one another. If such be the pvogress 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
* History of Scientific Ideas, i., 264. t Ibid., i., 263. J Ibid., 240.
182 REASONING.
appearances familiar from the first dawn of intelligence, and of the conclu-
siveness of which, from the earliest records of human thought, no skeptic
has suggested even a momentary doubt?
The other instance which I shall quote is a truly astonishing one, and
may be called the re duct to adabsurdum of the theory of inconceivableness.
Speaking of the laws of chemical composition, Dr. YVhewell 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 experiment. For how in fact can we conceive combi-
nations, otherwise than as definite in kind and quality? If we were to
suppose eacli element ready to combine with any other indifferently, and
indifferently in any quantity, we should have a world in which all would be
confusion and indetiniteness. 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 u-e can not conceive a world in which this
should not be the case, it would appear that we can not 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 can not conceive a world in which the simple elements should com-
bine in other than definite proportions; that by dint of meditating on a
scientific truth, the original discoverer of which was still living, he should
have rendered the association in his own mind between the idea of combi-
nation and that of constant proportions so familiar and intimate as to be
unable to conceive the o;ie fact without the other.; is so signal an instance
of the mental law for which I am contending, that one word more in illus-
tration must be superfluous.
In the latest and most complete elaboration of his metaphysical system
(the Philosophy of Discovery), us well as in the earlier discourse on the
Fundamental Antithesis of Philosophy, 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 com-
bination to be a necessary truth. All lie 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 dif-
ficult attainment.'''! And he explains that the inconceivableness which, ac-
cording to his theory, is the test of axioms, " depends entirely upon the
clearness of the Ideas which the axioms involve. So long as those ideas
are vague and indistinct, the contrary of an axiom may be assented to,
though it can not be distinctly conceived. It may be assented to, not be-
cause it is possible, but because we do not see clearly what is possible. To
a person who is only beginning to think geometrically, there may appear
nothing absurd in the assertion that two straight lines may 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 proc-
esses, Keaction should be greater or less than Action ; and so, again, to a
* Hist. Scientific Ideas, ii., 25, 2G. + Phil, of Disc., p. 339.
DEMONSTRATION, AND NECESSARY TRUTHS. 183
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 can not conceive, but "those of which we can not
distinctly conceive, the contrary."! So long as our ideas are indistinct al-
together, 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 learned from experience, we can not,
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 repre-
senting to themselves the phenomena of nature in the character which that
law assigns to them. The habit which constitutes the scientific cast of
mind, that of conceiving facts of all descriptions conformably to the laws
which regulate them phenomena of all descriptions according to the re-
lations which have been ascertained really to exist between them ; this hab-
it, in the case of newly-discovered relations, comes only by degrees. So
long as it is not thoroughly formed, no necessary character is ascribed to
the new truth. But in time, the philosopher attains a state of mind in
which his mental picture of nature spontaneously represents 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 arranging phenomena in certain groups, and ex-
plaining them by means of certain principles, makes any other arrangement
or explanation of these facts be felt as unnatural : and it may at last be-
come as difficult to him to represent the facts to himself in any other mode,
as it often was, originally, to represent them in that mode.
But, further (if the theory is true, as we are supposing it to be), any
other mode in which he tries, or in which he was formerly accustomed,
to represent the phenomena, will be seen by him to be inconsistent with
the facts that suggested the new theory facts which now form a part of
his mental picture of nature. And since a contradiction is always incon-
ceivable, his imagination rejects these false theories, and declares itself in-
capable of conceiving them. Their inconceivableness to him does not, how-
ever, result from any thing in the theories themselves, intrinsically and a
priori repugnant to the human faculties ; it results from the repugnance
between them and a portion of the 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 inconceiv-
able, merely from the fact that contradictory elements can not be combined
in the same conception. Although, then, his real reason for rejecting theo-
ries 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 it is self-evi-
dent, and does not need the evidence of experience at all.
* Phil, of Disc., p. 338. t Ibid., p. 463.
184 REASONING.
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 :i scientifically
cultivated mind is actually, in virtue of that cultivation, unable to conceive
suppositions which a common man conceives without the smallest difficul-
ty. For there is nothing inconceivable in the suppositions themselves; the
impossibility is in combining them with facts inconsistent witli them, as
part of the same mental picture ; an obstacle of course only felt by those
who know the facts, and are able to perceive the inconsistency. As far as
the suppositions themselves are concerned, in the case of many of Dr. Whc-
well's necessary truths, the negative of the axiom is, and probably will be
as long as the human race lasts, as easily conceivable as the affirmative.
There is no axiom (for example) to which Dr. Whewell ascribes a more
thorough character of necessity and self-evidence, than that of the inde-
structibility 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 distin-
guishable 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 :ire ready to combine with one another " indifferently 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 sol-
id, liquid, or aeriform, exhibit to our daily observation the very phenomenon
declared to be inconceivable.
According to Dr. Whewell, these and similar laws of nature can not be
drawn from experience, inasmuch as they are, on the contrary, assumed in
the interpretation of experience. Our inability to "add to or diminish the
quantity of matter in the world," is 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 chem-
ical analysis, they did not prove by trial, but took for granted, as self-evi-
dent, 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 hy-
pothesis, which is to be finally held true or not, according as the experi-
ments decide. The hypothesis chosen for this purpose will naturally be
one which groups together some considerable 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 na-
ture or art, had many appearances in its favor 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 a
universal law of nature, at first doubtful. Because it was doubtful, exper-
iments were devised to verify it. Men assumed its truth hypothetically,
and proceeded to try whether, on more careful examination, the phenomena
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
* Phil. "/Disc., pp. 472, 473.
DEMONSTRATION, AND NECESSARY TRUTHS. 185
the doctrine took its place as a 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-evident, and did not
need proof. Otherwise all the true theories in the sciences are necessary
and self-evident; for no one knows better than Dr. Whewell that they all
began by being assumed, for the purpose of connecting them by deduc-
tions with those facts of experience on which, as evidence, they now con-
fessedly rest.*
* The Quarterly Review for June, 1841, contained an article of great ability on Dr. Whe-
well'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 supports that opinion by a line of argument strikingly
coinciding with mine. When I state that the whole of the present chapter (except the last
four pages, added in the fifth edition) was written before I had seen the article (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 por-
tion 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 mag-
nitude in the abstract, which are equally true of space, time, force, number, and every other
magnitude susceptible of aggregation and subdivision. Such propositions, where they are
not mere definitions, as some of them are, carry their inductive origin on the face of their
enunciation Those which declare that two straight lines can not inclose a space, and
that two straight lines which cut one another can not 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 uniform-
ity 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 ex-
perience, 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 can not even propose the proposition in an intelligible form to
any one whose experience ever since he was born has not assured him of the fact. The unity
of direction, or that we can not 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 can not attempt mentally to exemplify the conditions of the assertion
in an imaginary case opposed to it, without violating our habitual recollection of this experi-
ence, 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 re-
gards 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 a/ ways, 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 simplicity 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 propositions, other than
as truths inductively collected from observation, even in geometry itself, it can hardly be ex-
pected that, in a science of obviously contingent 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 bal-
ance 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
186 REASONING.
it has even a paradoxical appearance, which is only to be removed by giving our lever thick-
ness, 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 pos-
sibly assure us that they do act under precisely similar circumstances ? that points which dif-
fer 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 ma-
terial universe may not be such as to place that portion of space occupied by it in such rela-
tions to the forces exerted in it, as may invalidate the absolute similarity of circumstances as-
sumed? 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 destruction of force by force. Now
how is this destruction effected? Assuredly by the counter-pressure which supports the ful-
crum. But would not this destruction equally arise, and by the same amount of counteract-
ing 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 lilt-
ing 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. "\Vlie\vell justly remarks,
' Xo one probably ever made a trial for the purpose of showing that the pressure on the sup-
port is equal to the sum of the weights.' But it is precisely because in every action
of his lite 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 for the 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 propositions of axiomatic simplicity
and obviousness, and having for their subject-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 necessary, 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 par-
adoxical, but the reverse, in our being led by observation to a recognition of such truths, as
general propositions, co-extensive at least with all human experience. That they pervade all
the objects of experience, must insure their continual suggestion by experience ; that they are
true, must insure that consistency of suggestion, that iteration of uncontradicted 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 it-
self 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
can not, 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 ire may on any occa-
sion summon before our imagination AH 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 fur-
nishes might seem intuitive." Sir John Leslie, quoted by Sir William Hamilton, Discourses,
etc., p. 272.
DEMONSTRATION, AND NECESSARY TRUTHS. 187
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 com-
monly represented to be systems of necessary truth, we have been led to
the following conclusions. The results of those sciences are indeed nec-
essary, 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 favor of the definitions
and axioms themselves. With regard to axioms, we found that, consid--
ered as experimental truths, they rest on superabundant and obvious ev-
idence. We inquired, 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 experimental origin. We de-
cided, that the burden of proof lies w r ith those who maintain the affirma-
tive, and we examined, at considerable length, such arguments as they have
produced. The examination having led to the rejection of those arguments,
we have thought ourselves warranted in concluding that axioms are but a
class, the most universal class, of inductions from experience; the simplest
and easiest cases of generalization from the facts furnished to us by our
senses or by our internal consciousness.
While the axioms of demonstrative sciences thus appeared to be exper-
imental truths, the definitions, as they are incorrectly called, in those sci-
ences, 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 ob-
servation 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 individ-
ual instance accompany, and in almost all instances modify, the property
thus exclusively predicated. The denial, therefore, is a mere fiction, or sup-
position, made for the purpose of excluding the consideration of those mod-
ifying 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 Demon-
strative Sciences are all, without exception, Inductive Sciences ; that then-
evidence is that of experience ; but that they are also, in virtue of the pe-
culiar character of one indispensable portion of the general formulae ac-
cording 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.
188 REASONING.
What wo have now asserted, however, can not be received as universally
true of Deductive or Demonstrative Sciences, until verified by being ap-
plied to the most remarkable of all those sciences, that of Numbers ; the
theory of the Calculus; Arithmetic and Algebra. It is harder to believe
of the doctrines of this science than of any other, either that they are not
truths a priori, but experimental truths, or that their peculiar certainty is
owing to their being not absolute but only conditional truths. This, there-
fore, 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 generally received, and is
still far from being altogether exploded, among metaphysicians.
2. This theory attempts to solve the difficulty apparently inherent in
the case, by representing the propositions of the science of numbers as
merely verbal, and its processes as simple transformations of language, sub-
stitutions of one expression for another. The proposition, Two and one is
equal to three, according to these writers, is not a truth, is not the assertion
of a really existing fact, but a definition of the word three ; a statement
that mankind have agreed to use the name three as a sign exactly equiva-
lent 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 terminology, by which equiva-
lent 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 de-
monstrate a new geometrical theorem by algebra), they have not explain-
ed ; 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 Nominal-
ism. The doctrine that we can discover facts, detect the hidden processes
of nature, by an artful manipulation of language, is so contrary to common
sense, that a person must have made some advances in philosophy to be-
lieve 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 reconcilable with the nature of the Science of Numbers. P"or we
do not carry any ideas along with us when we use the symbols of arithme-
tic or of algebra. In a geometrical demonstration we have a mental dia-
gram, if not one on paper ; AB, AC, are present to our imagination as lines,
intersecting other lines, forming an angle with one another, and the like ;
but not so a and b. These may represent lines or any other magnitudes,
but those magnitudes are never thought of; nothing is realized in our im-
agination but a and b. The ideas which, on the particular occasion, they
happen to represent, are banished from the mind during every intermediate
part of the process, between the beginning, when the premises are trans-
lated from things into signs, and the end, when the conclusion is translated
back from signs into things. Nothing, then, being in the reasoner's mind
but the symbols, what can seem more inadmissible than to contend that the
reasoning process has to do with any thing more? We seem to have come
to one of Bacon's Prerogative Instances ; an experimentum crucis on the
nature of reasoning itself.
DEMONSTRATION, AND NECESSARY TRUTHS. 189
Nevertheless, it will appear on consideration, that this apparently so de-
cisive instance is no instance at all ; that there is in every step of an arith-
metical or algebraical calculation a real induction, a real inference of facts
from facts; and that what disguises the induction is simply its compre-
hensive nature, and the consequent extreme generality of the language.
All numbers must be numbers of something: there are no such things as
numbers in the abstract. Ten must mean ten bodies, or ten sounds, or ten
beatings of the pulse. But though numbers must be numbers of some-
thing, they may be numbers of any thing. Propositions, therefore, con-
cerning numbers, have the remarkable peculiarity that they are proposi-
tions concerning all things whatever; all objects, all existences of every
kind, known to our experience. All things possess quantity ; consist of
parts which can be numbered ; and in that character possess all the prop-
erties 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 arith-
metical proposition in which the number four stands on one side of the
equation. Algebra extends the generalization still farther: every number
represents that particular number of all things without distinction, but ev-
ery algebraical symbol does more, it represents all numbers without dis-
tinction. 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 -j- b) =. 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 of angles only, it is no wonder that
the symbols should not excite in our minds ideas of any things in particu-
lar. When we demonstrate the forty-seventh proposition of Euclid, it is
not necessary that the words should raise in us an image of all right-angled
triangles, but only of some one right-angled triangle : so in algebra we
need not, under the symbol a, picture to ourselves all things whatever, but
only some one thing; why not, then, the letter itself? The mere written
characters, a, b, x, y, z, serve as well for representatives of Things in general,
as any more complex and apparently more concrete conception. That we
are conscious of them, however, in their character of things, and not of mere
signs, is evident from the fact that our whole process of reasoning is car-
ried 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 , b, and #, 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,-qr of signs as such,
but of magnitudes, which is as much as to say, of all things. The infer-
ences, therefore, which are successively drawn, are inferences concerning
things, not symbols; though as any Things whatever will serve the turn,
there is no necessity for keeping the idea of the Thing at all distinct, and
consequently the process of thought may, in this case, be allowed without
danger to do what all processes of thought, when they have been performed
often, will do if permitted, namely, to become entirely mechanical. Hence
the general language of algebra comes to be used familiarly without excit-
ing ideas, as all other general language is prone to do from mere habit,
though in no other case than this can it be done with complete safety.
190 REASONING.
Hut 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 our-
selves to be thinking and talking of the things, and not the mere symbols,
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 respecting Things, they all have the appearance of being
identical propositions. The assertion, Two and one is equal to three, con-
sidered as an assertion respecting objects, as for instance, "Two pebbles
and one pebble are equal to three pebbles," does not affirm equality be-
tween two collections of pebbles, but absolute identity. It affirms that if
we put one pebble to two pebbles, those very pebbles are three. The ob-
jects, therefore, being the very same, and the mere assertion that "objects
are themselves" being insignificant, it seems but natural to consider the
proposition, Two and one is equal to three, as asserting mere identity of
signification between the two names.
This, however, though it looks so plausible, will not bear examination.
The expression " two pebbles and one pebble," and the expression " three
pebbles," stand indeed for the same aggregation of objects, but they by no
means stand for the same physical fact. They are names of the same ob-
jects, but of those objects in two different states : though they denote 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 al-
teration of place and arrangement be made to produce either the one set of
sensations or the other, though a very familiar proposition, is not an iden-
tical 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 Num-
ber. The fundamental truths of that science all rest on the evidence of
sense; they are proved by showing to our eyes and our fingers that any
given number of objects ten balls, for example may by separation and
re-arrangement exhibit to our senses all the different sets of numbers the
sums 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 ev-
idence 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. Hut they are
definitions in the geometrical sense, not the logical; asserting not the mean-
ing of a term only, but along with it an observed matter of fact. The
proposition, "A circle is a figure bounded by a line which has all its points
equally distant from a point within it," is called the definition of a circle;
but the proposition from which so many consequences follow, and which
is really a first principle in geometry, is, that figures answering to this de-
scription exist. And thus we may call "Three is two and one "a defini-
tion of three ; but the calculations which depend on that proposition do
not follow from the definition itself, but from an arithmetical theorem lire-
supposed in it, namely, that collections of objects exist, which while they
impress the senses thus, V, may be separated into two parts, thus, co -
This proposition being granted, we term all such parcels Threes, after
DEMONSTRATION, AND NECESSARY TRUTHS. 191
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 conclusion we pre-
viously arrived at, that the processes even of deductive sciences are alto-
gether inductive, and that their first principles are generalizations from ex-
perience. It remains to be examined whether this science resembles geom-
etry in the further circumstance, that some of its inductions are not exactly
true ; and that the peculiar certainty ascribed to it, on account of which its
propositions are called Necessary Truths, is fictitious and hypothetical, be-
ing true in no other sense than that those propositions legitimately follow
from the hypothesis of the truth of premises which are avowedly mere ap-
proximations 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,
etc., which may be called the definitions of the various numbers, in the im-
proper or geometrical sense of the word Definition ; and secondly, the two
following axioms : The sums of equals are equal, The differences of equals
are equal. These two are sufficient ; for the corresponding propositions re-
specting 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 objects whatever, and, as it may
seem, exactly true, without the hypothetical assumption of unqualified truth
where an approximation 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 demonstrations is independent of all
hypothesis.
On more accurate investigation, however, it will be found that, even in
this case, there is one hypothetical element in the ratiocination. In all
propositions concerning numbers, a condition is implied, without which
none of them would be true; and that condition is an assumption which
may be false. The condition is, that 1 = 1 ; that all the numbers are num-
bers 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 cer-
tain 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 equiv-
alent in any other respect, is all that is material, the conclusions of arith-
metic, so far as they go to that alone, are true without mixture of hypoth-
esis. There are such cases in statistics ; as, for instance, an inquiry into
the amount of the population of any country. It is indifferent to that in-
quiry whether they are grown people or children, strong or weak, tall or
short; the only thing we want to ascertain is their number. But when-
ever, from equality or inequality of number, equality or inequality in any
other respect is to be inferred, arithmetic carried into such inquiries be-
comes as hypothetical a science as geometry.- All units must be assumed
to be equal in that other respect ; and this is never accurately true, for one
actual pound weight is not exactly equal to another, nor one measured mile's
length to another ; a nicer balance, or more accurate measuring instruments,
would ahvavs detect some difference.
192 REASONING.
What is commonly called mathematical certainty, therefore, which com-
prises the twofold conception of unconditional truth and perfect accuracy,
is not an attribute of all mathematical truths, but of those only which re-
late to pure Number, as distinguished from Quantity in the more enlarged
sense ; and only so long as we abstain from supposing that the numbers
are a precise index to actual quantities. The certainty usually ascribed to
the conclusions of geometry, and even to those of mechanics, is nothing
whatever but certainty of inference. We can have full assurance of par-
ticular results under particular suppositions, but we can not 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 Deductive Sciences is
hypothetical. They proceed by tracing the consequences of certain -as-
sumptions ; leaving for separate consideration Avhether the assumptions
are true or not, and if not exactly true, whether they arc a sufficiently near
approximation to the truth. The reason is obvious. Since it is only in
questions of pure number that the assumptions are exactly true, and even
there only so long as no conclusions except purely 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
assumptions to be true may be performed once for all, and the results
held ready to be employed as the occasions turn up for use. We thus do
all beforehand that can be so done, and leave the least possible work to be
performed when cases arise and press for a decision. This inquiry into the
inferences which can be drawn from assumptions, is what properly consti-
tutes Demonstrative Science.
It is of course quite as practicable to arrive at new conclusions from
facts assumed, as from facts observed; from fictitious, as from real, induc-
tions. Deduction, as we have seen, consists of a series of inferences in this
form a is a mark of b, b of c, c of d, therefore a is a mark of </, 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 r, 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 syn-
thetically 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. Some-
times the same thing is knowingly done, for the purpose of showing the
falsity of the assumption ; which is called a reductio ad absurdum. In
such cases, the reasoning is as follows : a is a mark of i, 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.
THEORIES CONCERNING AXIOMS. lOii
5. It has even been held by some writers, that all ratiocination rests
in the last resort on a reductio ad absurdum; since the way to enforce as-
sent to it, in case of obscurity, would be to show that if the conclusion be
denied we must deny some one at least of the premises, which, as they are
all supposed true, would be a contradiction. And in accordance with this,
many have thought that the peculiar nature of the evidence of ratiocina-
tion consisted in the impossibility 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 ratiocination itself
rests. If any one denies the conclusion notwithstanding his admission of
the premises, he is not involved in any direct and express contradiction un-
til 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, there-
fore, no one is ever forced to a contradiction in terms : he can only be
forced to a contradiction (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 any thing, 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 syllogis-
tic form, it is evident without the aid of any other syllogism, that he who,
admitting the premises, fails to draw the conclusion, does not conform to
the above axiom.
We have now proceeded as far in the theory of Deduction as we can ad-
vance in the present stage of our inquiry. Any further insight into the
subject requires that the foundation shall have been laid of the philosophic
theory of Induction itself; in which theory that of Deduction, as a mode
of Induction, which we have now shown it to be, will assume spontaneous-
ly 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 illustration, can often receive it most
effectually, and least tediously, in the form of a defense 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 ineonceiva-
* Principles of Psychology.
13
194 REASONING.
bleness." He tliinks 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 any thing, than that the belief of it " invariably exists."
Whenever any fact or proposition is invariably believed ; that is, if I un-
derstand Mr. Spencer rightly, believed by all persons, and by one's self at all
times ; it is entitled to be received as one of the primitive truths, or orig-
inal premises of our knowledge. Secondly, the criterion by which we de-
cide whether any thing 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 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." lie
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 can not 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 con-
sider 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 inconceiva-
bleness of their negatives. We can not, he says, by any effort, conceive
these objects of thought as mere states of our mind ; as not having an ex-
istence external to us. Their real existence is, therefore, as certain as our
sensations themselves. The truths which are the subject of direct knowl-
edge, being, according to this doctrine, known to be truths only by the in-
conceivability 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 can not conceive them not to follow ; inconceivability is thus the ulti-
mate 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 inconceivable things, some
things which were not inconceivable." And he himself, in this very book,
denies not a few propositions usually regarded as among the most marked
examples of truths whose negations are inconceivable. But occasional fail-
ure, he says, is incident to all tests. If such failure vitiates " the test of in-
conceivableness," it " must similarly vitiate all tests whatever. We con-
sider 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 consider
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 ns such, until better instructed. Similarly, though men may have
thought some things inconceivable which were not so, there may still be in-
THEORIES CONCERNING AXIOMS. 195
conceivable things ; and the inability to conceive the negation of a thing,
may still be out- best warrant for believing it Though occasional-
ly it may prove an imperfect test, yet, as our most certain beliefs are capa-
ble of no better, to doubt any one belief because we have no higher guar-
antee for it, is really to doubt all beliefs." Mr. Spencer's doctrine, there-
fore, 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 inconceivable-
ness of its negation to invariably exist, is true," Mr. Spencer enforces by
two arguments, one of which may be distinguished as positive, and the
other as negative.
The positive argument is, that every such belief represents the aggregate
of all past experience. "Conceding the entire truth of" the "position,
that during any phase of human progress, the ability or inability to form
a specific conception wholly depends on the experiences men have had;
and that, by a widening of their experiences, they may, by and by, be en-
abled 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 per-
fect agreement of all pre-existing experience in support of it, it follows that,
at any time, the inconceivableness of its negation is the deepest test any
belief admits of Objective facts are ever impressing themselves upon
us ; our experience is a register of these objective facts ; and the incon-
ceivableuess of a thing implies that it is wholly at variance with the regis-
ter. Even were this all, it is not clear how, if every truth is primarily in-
ductive, any better test of truth could exist. But it must be remembered
that while many of these facts, impressing themselves upon us, are occa-
sional; while others again are very general; some are universal and un-
changing. These universal and unchanging facts are, by the hypothesis,
certain to establish beliefs of which the negations are inconceivable ; while
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 experi-
ences, 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 uniform-
ities produce, as they must, absolute uniformities in our experience ; and
if .... these absolute uniformities in our experience disable us from con-
ceiving the negations of them ; then answering to each absolute \miformi-
ty 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 ulti-
mately complete. In nearly all cases this test of inconceivableness must be
valid now " (I wish I could think we were so nearly arrived at omnis-
cience) ; " and where it is not, it still expresses the net result of our experi-
ence up to the present time ; which is the most that any test can do."
To this I answer, first, that it is by no means true that the inconceivabili-
ty, by us, of the negative of a proposition proves all, or even any, " pre-exist-
ing experience " to be in favor of the affirmative. There may have been
no such pre-existing experiences, but only a mistaken supposition of expe-
rience. How did the inconceivability of antipodes prove that experience
had given any testimony against their possibility ? How did the incapaci-
190 REASONING.
ty men felt of conceiving sunset otherwise than as a motion of the sun,
represent any " net result " of experience in support of its being the sun
and not the earth that moves ? It is not experience that is represented, it
is only a superficial semblance of experience. The only thing proved with
regard to real experience, is the negative fact, that men have not had it
of the kind which would have made the inconceivable proposition conceiv-
able.
Next : Even if it were true that inconceivableness represents the net re-
sult of all past experience, why should we stop at the representative when
we can get at the thing represented ? If our incapacity to conceive the
negation of a given supposition is proof of its truth, because proving that
our experience has hitherto been uniform in its favor, the real evidence for
the supposition is not the inconceivableness, but the uniformity of experi-
ence. Now this, which is the substantial and only proof, is directly access-
ible. We are not obliged to presume it from an incidental consequence.
If all past experience is in favor of a belief, let this be stated, and the be-
lief openly rested on that ground: after which the question arises, what
that fact may be worth as evidence of its truth? For uniformity of expe-
rience is evidence in very different degrees : in some cases it is strong evi-
dence, in others weak, in others it scarcely amounts to evidence at all.
That all metals sink in water, was a uniform experience, from the origin
of the human race to the discovery of potassium in the present century
by Sir Humphry Davy. That all swans are white, was a uniform experi-
ence down to the discovery of Australia. In the few cases in which uni-
formity of experience does amount to the strongest possible proof, as with
such propositions as these, Two straight lines can not inclose a space, Ev-
ery 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 further 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 com-
monest. The mere familiarity of one mode of production of a phenome-
non often suffices to make every other mode appear inconceivable. What-
ever 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 recognizes. It was not for want of ex-
perience that the Cartesians were unable to conceive that one body could
produce motion in another without contact. They had as much experience
of other modes of producing motion as they had of that mode. The plan-
ets 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 inconceivableness, instead of representing their
experience, dominated and overrode their experience. Without dwelling
further on what I have termed the positive argument of Mr. Spencer in
support of his criterion of truth, I pass to his negative argument, on which
he lays more stress.
THEORIES CONCERNING AXIOMS. 197
3. The negative argument is, that, whether inconceivability be good
evidence or bad, no stronger evidence is to be obtained. That what is in-
conceivable can not be true, is postulated 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 demon-
stration. Logic is simply a systematization of the process by which we in-
directly obtain this warrant for beliefs that do not directly possess it. To
gain the strongest conviction possible respecting any complex fact, we ei-
ther analytically descend from it by successive steps, each of which we un-
consciously 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
intermediate beliefs which invariably exist." The following passage sums
up the theory : " When we perceive that the negation of the belief is in-
conceivable, we have all possible warrant for asserting the invariability of
its existence: and in asserting this, we express alike our logical justifica-
tion of it, and the inexorable necessity we are under of holding it
We have seen that this is the assumption on which every conclusion what-
ever ultimately rests. We have no other guarantee for the reality of con-
sciousness, of sensations, of personal existence ; we have no other guaran-
tee for any axiom ; we have no other guarantee for any step in a demon-
stration. Hence, as being 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 inconceivable-
ness of their negations 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 recognized as valid except because we can not conceive the conclu-
sion not to follow from the premises.
It will be convenient to take the last part of this argument first. In ev-
ery 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 can not conceive it not to follow. Consequently if the postulate is fal-
lible, the conclusions of reasoning are more vitiated by that uncertainty
than direct intuitions ; and the disproportion 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 argu-
ment does rest on an assumption, and we have seen in the preceding chap-
ters what the assumption is. It is, that whatever has a mark, has what it
is a mark of. The evidence of this axiom I shall not consider at present ;*
* Mr. Spencer is mistaken in supposing me to claim any peculiar " necessity " for this ax-
iom as compared with others. I have corrected the expressions which led him into that mis-
apprehension of my meaning.
198 REASONING.
let us suppose it (with Mr. Spencer) to be the inconceivableness of its re-
verse.
Let us now add a second step to the argument : we require, what ? An-
other 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 repetition of the assumption at all weakens the force of the
argument. If it were necessary the second time to assume some other ax-
iom, 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. Hut 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 assumptions would make but one chance of
error among them all. It is satisfactory that AVC are not obliged to sup-
pose the deductions of pure mathematics to be among the most uncertain
of argumentative processes, which on Mr. Spencer's theory they could
hardly fail to be, since they are the longest. Hut the number of steps in
an argument does not subtract from its reliableness, if no new premises, oi
an uncertain character, are taken up by the way.*
To speak next of the premises. Our assurance of their truth, whether
tlu-y !><> generalities or individual facts, is grounded, in Mr. Spencer's opin-
ion, 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
* Mr. Spencer, ii> recently returning to the subject (Principles of Psychology, new edition,
chap, xii. : " The Test of Relative Validity"}, makes two answers to the preceding remarks.
One is :
' Were an argument formed by repeating the same proposition over and over again, it
would l>e true that any intrinsic fallibility of the postulate would not make the conclusion
more untrustworthy than the first step. But an argument consists of unlike propositions.
Now. since Mr. Mill's criticism on the Universal Postulate is that in some cases, which he
naiads, it has proved to be an untrustworthy test ; it follows that in any argument consisting
of heterogeneous propositions, there is a risk, increasing as the number of propositions in-
creases, that some one of them belongs to this class of cases, and is wrongly accepted because
of the inconceivableness of its negation."
No doubt: but this supposes new premises to be taken in. The point we are discussing is
the fallibility not of the premises, but of the reasoning, as distinguished from the premises.
Now the validity of the reasoning depends always upon the same axiom, repeated (in thought)
"over and over again,'' vi/., that whatever has a mark, has what it is a mark of. Even,
therefore, on the assumption that this axiom rests ultimately on the Universal Postulate, and
that, the Postulate not being wholly trustworthy, the axiom mav be one of the cases of its
failure; all the risk there is of this is incurred at the verv first step of the reasoning, and is
not added to. however long may be the series of subsequent steps.
I am here arguing, of course, from Mr. Spencer's point of view. From my own the case is
still clearer ; for, in my view, the truth that whatever has a mark has what it is a mark of, is
wholly trustworthy, and derives none of its evidence from so very untrustworthy a test as the
inconceivability of the negative.
Mr. Spencer's second answer is valid up to a certain point : it is, that every prolongation of
the process involves additional chances of casual error, from carelessness in the reasoning
operation. This is an important consideration in the private speculations of an individual
reasoner: and even with respect to mankind at large, it must be admitted that, though mere
oversights in the syllogistic process, like errors of addition in an account, are special to the
individual, and seldom escape detection, confusion of thought produced (for example) by am-
biguous terms has led whole nations or ages to accept fallacious reasoning as valid. But this
very fact points to causes of error so much more dangerous than the mere length of the proc-
ess, as quite to vitiate the doctrine that the ''test of the relative validities of conflicting con-
clusions" is the number of times the fundamental postulate is involved. On the contrary, the
subjects on which the trains of reasoning are longest, and the assumption, therefore, oftenest
repeated, are in general those which are best fortified against the really formidable causes of
fallacy ; as in the example already given of mathematics.
THEORIES CONCERNING AXIOMS. 199
of, and would sincerely disclaim founding an argument upon, but from
which his case derives no little advantage notwithstanding. By inconceiv-
ableness is sometimes meant, inability to form or get rid of an idea some-
times, inability to form or get rid of a belief. The former meaning is the
most conformable to the analogy of language; for a conception always
means an idea, and never a belief. The wrong meaning of " inconceivable"
is, however, fully as frequent in philosophical discussion as the right mean-
ing, 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 in-
conceivable. But antipodes were not inconceivable in the primitive sense
of the word. An idea of them could be formed without difficulty : they
could be completely pictured to the mental eye. What was difficult, and,
as it then seemed, impossible, was to apprehend them as believable. The
idea could be put together, of men sticking on by their feet to the under
side of the earth ; but the belief would follow, that they must fall off. An-
tipodes were not unimaginable, but they were unbelievable.
On the other hand, when I endeavor 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 inconceivablencss almost
always turns on the alternate substitution of each of those meanings for
the other.
In which of these two senses does Mr. Spencer employ the term, when
he makes it a test of the truth of a proposition that its negation is incon-
ceivable ? Until Mr. Spencer expressly stated the contrary, I inferred from
the course of his argument, that he meant unbelievable. lie has, however,
in a paper published in the fifth number of the Fortnightly Review, dis-
claimed this meaning, and declared that by an inconceivable proposition
he means, now and always, " one of which the terms can not, by any effort,
be brought before consciousness in that relation which the proposition as-
serts between them a proposition of which the subject and predicate offer
an insurmountable resistance to union in thought." We now, therefore,
know positively that Mr. Spencer always endeavors to use the word incon-
ceivable in this, its proper, sense : but it may yet be questioned whether
his endeavor is 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 can not conceive that I am not
feeling cold, this expression can not be translated into "I can not con-
ceive myself not feeling cold," for it is evident that I can : the word
conceive, therefore, is here used to express the recognition of a matter of
fact the perception of truth or falsehood ; which I apprehend to be ex-
actly the meaning of an act of belief, as distinguished from simple con-
ception. 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 inconceivability, in
Mr. Spencer's theory, is only a test of truth, inasmuch as it is a test of
200 REASONING.
believubility. The inconceivablencss of a supposition is the extreme case
of its unbelievability. This is the very foundation of Mr. Spencer's doc-
trine. The invariability of the belief is with him the real guarantee.
The attempt to conceive the negative is made in order to test the inevita-
bleness of the belief. It should be called, an attempt to believe the nega-
tive. When Mr. Spencer says that while looking at the sun a man can not
conceive that lie is looking into darkness, he should have said that a man
can not believe that he is doing so. For it is surely possible, in broad day-
light, to imagine one's self looking into darkness.* As Mr. Spencer him-
self 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," /. e., to believe. So that the statement resolves it-
self into this : That I exist, and that I have sensations, I believe, because I
can not believe otherwise. And in this case every one will admit that the
impossibility is real. Any one's present sensations, or other states of sub-
jective 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 believ-
ing 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 guar-
antee which are, in a similar manner, invariable and necessary. With re-
gard to these other beliefs, they can not be necessary, since they do not al-
ways 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 independent 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 maintained, without ob-
vious error, that we can not imagine tangible objects as mere states of our
own and other people's consciousness; that the perception of them irresist-
ibly 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 material objects, are mere modifications of con-
sciousness ; complex 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 persistence of an idea, and that
what we can succeed in imagining we can not at the moment help appre-
hending 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 an infant by stories
of ghosts, though he disbelieves them in after years (and perhaps never be-
lieved them), may be unable all his life to be in a dark place, in circum-
stances stimulating to the imagination, without mental discomposure. The
idea of ghosts, with all its attendant terrors, is irresistibly called up in his
mind by the outward circumstances. Mr. Spencer may say, that while he
* Mr. Spencer makes a distinction between conceiving myself looking into darkness, and
conceiving that I inn then and there looking into darkness. To me it seems that this change
of the- expression to the form / am, just marks the transition from conception to belief, and
that the phrase ''to conceive that I rim," or "that any thing is," is not consistent with using
the word conceive in its rigorous sense.
THEORIES CONCERNING AXIOMS. 201
is under the influence of this terror he does not disbelieve in ghosts, but
has a temporary and uncontrollable belief in them. Be it so ; but allowing
it to be so, which would it be truest to say of this man on the whole that
he believes in ghosts, or that he does not believe in them ? Assuredly that
he does not believe in them. The case is similar with those who disbelieve
a material world. Though they can not get rid of the idea ; though while
looking at a solid object they can not help having the conception, and there-
fore, 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
doctrine. The belief therefore is not invariable ; and the test of inconceiv-
ableness 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 phenomenon 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 Coper-
nicus. Mr. Spencer does not say, " In looking at sunrise it is impossible
not to conceive that it is the sun which moves, therefore this is what every
body believes, and we have all the evidence for it that we can have for any
truth." Yet this would be an exact parallel to his doctrine about the belief
in matter.
The existence of matter, and other Noumena, as distinguished from the
phenomenal world, remains a question of argument, as it was before ; and
the very general, but neither necessary nor universal, belief in them, 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 believed, so general and apparently spontaneous a belief can have
originated. And its opponents have never hesitated to accept this chal-
lenge.* The amount of their success in meeting it will probably deter-
mine the ultimate verdict of philosophers on the question.
4. In the revision, or rather reconstruction, of his " Principles of Psy-
chology," as one of the stages or platforms in the imposing structure of
his System of Philosophy, Mr. Spencer has resumed what he justly termsf
the " amicable controversy that has been long pending between us ;" ex-
pressing at the same time a regret, which I cordially share, that " this
lengthened exposition of a single point of difference, unaccompanied by
an exposition of the numerous points of concurrence, unavoidably produces
an appearance of dissent very far greater than that which exists." I be-
lieve, with Mr. Spencer, that the difference between us, if measured by our
conclusions, is " superficial rather than substantial ;" and the value I attach
to so great an amount of agreement, in the field of analytic psychology,
* I have myself accepted the contest, and foughf it out on this battle-ground, in the eleventh
chapter of An Examination of Sir William Hamilton's Philosophy.
t Chap. xi.
202 REASONING.
with a thinker of his force and depth, is such as I can hardly overstate.
l>ut I also agree with him that the difference which exists in our premises
is one of "profound importance, philosophically considered;" and not to
be dismissed while any part of the case of either of us has not been fully
examined and discussed.
In his present statement of the Universal Postulate, Mr. Spencer has ex-
changed his former expression, " beliefs which invariably exist," for the
following: "cognitions of which the predicates invariably exist along with
their subjects." And he says that "an abortive effort to conceive the ne-
gation of a proposition, shows that the cognition expressed is one of which
the predicate invariably exists along with its subject ; and the discovery
that the predicate invariably exists along with its subject, is the discovery
that this cognition is one we are compelled to accept." Both these prem-
ises of Mr. Spencer's syllogism I am able to assent to, but in different senses
of the middle term. If the invariable existence of the predicate along
with its subject, is to be understood in the most obvious meaning, as an
existence in actual Nature, or in other words, in our objective, or sensa
tional, experience, I of course admit that this, once ascertained, compels us
to accept the proposition : but then I do not admit that the failure of an at-
tempt to conceive the negative, proves the predicate to be always co-exist-
ent with the subject in actual Nature. If, on the other hand (which I believe
to be Mr. Spencer's meaning) the invariable existence of the predicate along
with the subject is to be understood only of our conceptive faculty, /. e.,
that the one is inseparable from the other in our thoughts ; then, indeed,
the inability to separate the two ideas proves their inseparable conjunc-
tion, here and now, in the mind which has failed in the attempt ; but this
inseparability in thought does not prove a corresponding inseparability in
fact ; nor even in the thoughts of other people, or of the same person in a
possible future.
" That some propositions have been wrongly accepted as true, because
their negations were supposed inconceivable when they were not," does
not, in Mr. Spencer's opinion, "disprove the validity of the test;" not only
because any test whatever " is liable to yield untrue results, either from in-
capacity or from carelessness in those who use it," but because the propo-
sitions in question " were complex propositions, not to be established by a
test applicable to propositions no further decomposable." "A test legiti-
mately applicable to a simple proposition, the subject and predicate of which
are in direct relation, can not be legitimately applied to a complex proposi-
tion, the subject and predicate of which are indirectly related through the
many simple propositions implied." " That things which are equal to the
same thing are equal to one another, is a fact which can be known by di-
rect comparison of actual or ideal relations But that the square of
the hypothenuse of a right-angled triangle equals the sum of the squares
of the other two sides, can not be known immediately by comparison of
two states of consciousness : here the truth can be reached only mediately,
through a series of simple judgments respecting the likenesses or unlike-
nesses of certain relations." Moreover, even when the proposition admits
of being tested by immediate consciousness, people often neglect to do it.
A school-boy, in adding up a column of figures, will say " 35 and 9 are 46,"
though this is contrary to the verdict which consciousness gives when 35
* ~
and 9 are really called up before it; but this is not done. And not only
school-boys, but men and thinkers, do not always " distinctly translate into
their equivalent states of consciousness the words they use."
THEORIES CONCERNING AXIOMS. 203
It is but just to give Mr. Spencer's doctrine the benefit of the limitation
he claims viz., that it is only applicable to propositions which are assented
to on simple inspection, without any intervening media of proof. But this
limitation does not exclude some of the most marked instances of proposi-
tions now known to be false or groundless, but whose negative was once
found inconceivable : such as, that in sunrise and sunset it is the sun which
moves; that gravitation may exist without an intervening medium; and
even the case of antipodes. The distinction drawn by Mr. Spencer is real ;
but, in the case of the propositions classed by him as complex, conscious-
ness, until the media of proof are supplied, gives no verdict at all: it nei-
ther declares the equality of the square of the hypothenuse with the sum
of the squares of the sides to be inconceivable, nor their inequality to be
inconceivable. But in all the three cases which I have just cited, the in-
conceivability seems to be apprehended directly ; no train of argument was
needed, as in the case of the square of the hypothenuse, to obtain the ver-
dict of consciousness on the point. Neither is any of the three a case like
that of the school-boy's mistake, in which the mind was never really brought
into contact with the proposition. They are cases in which one of two op-
posite predicates, mero adspectu, seemed to be incompatible with the sub-
ject, and the other, therefore, to be proved always to exist with it.*
As now limited by Mr. Spencer, the ultimate cognitions fit to be submit-
ted to his test are only those of so universal and elementary a character as
to be represented in the earliest and most unvarying experience, or appar-
ent experience, of all mankind. In such cases the inconceivability of the
negative, if real, is accounted for by the experience : and why (I have ask-
ed) should the truth be tested by the inconceivability, when we can go fur-
ther back for proof namely, to the experience itself ? To this Mr. Spen-
cer answers, that the experiences can not be all recalled to mind, and if re-
called, would be of unmanageable multitude. To test a proposition by ex-
perience seems to him to mean that "before accepting as certain the prop-
osition that any rectilineal figure must have as many angles as it has sides,"
I have " to think of every triangle, square, pentagon, hexagon, etc., which I
have ever seen, and to verify the asserted relation in each case." I can
only say, with surprise, that I do not understand this to be the meaning of
an appeal to experience. It is enough to know that one has been seeing
the fact all one's life, and has never remarked any instance to the contrary,
and that other people, with every opportunity of observation, unanimously
declare the same thing. It is true, even this experience may be insufficient,
and so it might be even if I could recall to mind every instance of it; but
* In one of the three cases, Mr. Spencer, to my no small surprise, thinks that the belief of
mankind "can not be rightly said to have undergone" the change I allege. Mr. Spencer
himself still thinks we are unable to conceive gravitation acting through empty space. "If
an astronomer, avowed that he could conceive gravitative force as 'exercised through space ab-
solutely void, my private opinion would be that he mistook the nature of conception. Con-
ception implies representation. Here the elements of the representation are the two bodies
and an agency by which either affects the other. To conceive this agency is to represent it
in some terms derived from our experiences that is, from our sensations. As this agency
gives us no sensations, we are obliged (if we try to conceive it) to use symbols idealized from
our sensations imponderable units forming a medium."
If Mr. Spencer means that the action of gravitation gives us no sensations, the assertion is
one than which I have not seen, in the writings of philosophers, many more startling. What
other sensation do we need than the sensation of one body moving toward another? "The
elements of the representation" are not two bodies and an "agency," but two bodies and an
effect ; viz., the fact of their approaching one another. If we are able to conceive a vacuum,
is there any difficulty in conceiving a body falling to the earth through it ?
204 REASONING.
its insufficiency, instead of being brought to light, is disguised, if instead of
sifting the experience itself, I appeal to a test which bears no relation to
the sufficiency of the experience, but, at the most, only to its familiarity.
These remarks do not lose their force even if we believe, with Mr. Spencer,
that mental tendencies originally derived from experience impress them-
selves permanently on the cerebral structure and are transmitted by inher-
itance, so that modes of thinking which arc acquired by the race become
innate and a priori in the individual, thus representing, in Mr. Spencer's
opinion, the experience of his progenitors, in addition to his own. All that
would follow from this is, that a conviction might be really innate, i. c., prior
to individual experience, and yet not be true, since the inherited tendency
to accept it may have been originally the result of other causes than its
truth.
Mr. Spencer would have a much stronger case, if he could really show
that the evidence of Reasoning rests on the Postulate, or, in other words,
that we believe that a conclusion follows from premises only because we
can not conceive it not to follow. But this statement seems to me to be
of the same kind as one I have previously commented on, viz., that I believe
I see light, because I can not, while the sensation remains, conceive that I
am looking into darkness. Both these statements seem to me incompatible
with the meaning (as very rightly limited by Mr. Spencer) of the verb to
conceive. To say that when I apprehend that A is B and that B is C, I
can not conceive that A is not C, is to my mind merely to say that I am
compelled to believe that A is C. If to conceive be taken in its proper
meaning, vix., to form a mental representation, I may be able to conceive A
as not being C. After assenting, with full understanding, to the Coperni-
cau proof that it is the earth and not the sun that moves, I not only can
conceive, or represent to myself, sunset as a motion of the sun, but almost
every one finds this conception of sunset easier to form, than that which
they nevertheless know to be the true one.
5. Sir William Hamilton holds as I do, that inconceivability is no criteri-
on 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."* Sir William Hamil-
ton 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 Xoumena 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 us from behind the curtain
which veils from us the mysterious world of Things in themselves are
the two principles, which he terms, after the school-men, the Principle of
Contradiction, and the Principle of Excluded Middle: the first, that two
contradictory propositions can not both be true; the second, that they can
not both be false. Armed with these logical weapons, we may boldly face
Things in themselves, and tender to them the double alternative, sure that
* Uiscussions, etc., 2d cd., p. 024.
THEORIES CONCERNING AXIOMS. 205
they must absolutely elect one or the other side, though we may be forever
precluded from discovering which. To take his favorite example, we can
not conceive the infinite divisibility of matter, and we can not conceive a
minimum, or end to divisibility : yet one or the other must be true.
As I have hitherto said nothing of the two axioms in question, those of
Contradiction and of Excluded Middle, it is not unseasonable to consider
them here. The former asserts that an affirmative proposition and the cor-
responding negative proposition can not both be true ; which has generally
been held to be intuitively evident. Sir William Hamilton and the Ger-
mans consider it to be the statement in words of a form or law of our
thinking faculty. Other philosophers, not less deserving of consideration,
deem it to be an identical proposition ; an assertion involved in the mean-
ing 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 prop-
osition asserts nothing but the falsity of the affirmative, and has no other
sense or meaning whatever. The Principium Contradictionis should there-
fore put off the ambitious phraseology which gives it the air of a funda-
mental antithesis pervading nature, and should be enunciated in the simpler
form, that the same proposition can not at the same time be false and true.
But I can go no further with the Nominalists ; for I can not 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 foundation of it I take to be, that Belief and Disbelief are two dif-
ferent mental states, excluding one anothei'. This we know by the simplest
observation of our own minds. And if we carry our observation outward,
we also find that light and darkness, sound and silence, motion and quies-
cence, equality and inequality, preceding and following, succession and si-
multaneousness, 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 generaliza-
tion from all these facts.
In like manner as the Principle of Contradiction (that one of two contra-
dictories must be false) means that an assertion can not be both true and
false, so the Principle of Excluded Middle, or that one of two contradic-
tories must be true, means that an assertion must be either true or false :
either the affirmative is true, or otherwise the negative is true, which means
that the affirmative is false. I can not help thinking this principle a sur-
prising specimen of a so-called necessity of Thought, since it is not even
true, unless with a large qualification. 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. Be-
tween 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 max-
im 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 nonentity must be either infinite-
ly or finitely divisible. In the second place, though matter, considered as
206 REASONING.
the occult cause of our sensations, do really exist, yet what we call divisi-
bility may be an attribute only of our sensations of sight and touch, and
not of their (incognizable cause. Divisibility may not be predicable at all,
in any intelligible sense, of Things in themselves, nor therefore of Matter
in itself ; and the assumed necessity of being either infinitely or finitely di-
visible, 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 Iteview I extract the follow-
ing passage. The germ of an idea identical with that of Mr. Spencer may
be found in the present chapter, on a preceding page ; 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-ex-
istence 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 colorless, we think of its having color, the change consists in the
addition to the concept of an element that was before absent from it the
object can not 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 uni-
versal experience that some mental states are directly destructive of other
states. It formulates a certain absolutely constant law, that the appearance
of any positive mode of consciousness can not occur without excluding a
correlative negative mode ; and that the negative mode can not occur with-
out excluding the correlative positive mode : the antithesis of positive and
negative being, indeed, merely an expression of this experience. Hence it
follows that if consciousness is not in one of the two modes it must be in
the other."*
I must here close this supplementary chapter, and with it the Second
Book. The theory of Induction, in the most comprehensive sense of the
term, will form the subject of the Third.
* Professor Bain (Logic, i., 10) identifies the Principle of Contradiction with his Law of
Relativity, viz., that ''every thing that can be thought of, every affirmation that can be made,
has an opposite or counter notion or affirmation ;" a proposition which is one of the general
results of the whole body of human experience. For further considerations respecting the
axioms of Contradiction and Excluded Middle, see the twenty-first chapter of An Examina-
tion of iSir William Hamilton'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 successive 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.
"In such cases the inductive and deductive methods of inquiry may be said to go hand in
hand, the one verifying the conclusions deduced by the other ; and the combination of experi-
ment and theory, which may thus be brought to bear in such cases, forms an engine of dis-
covery infinitely more powerful than either taken separately. This state of any department
of science is perhaps of all others the most interesting, and. that which promises the most to
research." SIR J. HERSCHEL, Discourse on the Study of Natural Philosophy.
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 M'hich the investiga-
tion of nature essentially consists. We have found that all Inference, con-
sequently all Proof, and all discovery of truths not self-evident, consists of
inductions, and the interpretation of inductions : that all our knowledge,
not intuitive, conies to us exclusively from that source. What Induction
is, therefor/;, and what conditions render it legitimate, can not but be deem-
ed the main question of the science of logic the question which includes
all others. It is, however, one which professed writers on logic have al-
most entirely passed over. The generalities of the subject have not been
altogether neglected by metaphysicians ; but, for want of sufficient ac-
quaintance with the processes by which science has actually succeeded in
establishing general truths, their analysis of the inductive operation, even
when unexceptionable as to correctness, has not been specific enough to be
made the foundation of practical rules, which might be 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 meth-
ods which they themselves employed in their habitual pursuits never un-
til very lately made any serious attempt to philosophize on the subject, nor
regarded the mode in which they arrived at their conclusions as deserving
of study, independently of the conclusions themselves.
208 INDUCTION.
2. For the purposes of the present inquiry, Induction may be 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,
definite 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 de-
finable respects, resemble those we have observed.
If these remarks are just; if the principles and rules of inference are the
same whether we infer general propositions or individual facts; it follows
that a complete logic of the sciences would be also a complete logic of prac-
tical business and common life. Since there is no case of legitimate infer-
ence 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 induction whatever. Whether we
are inquiring into a scientific principle or into an individual fact, and wheth-
er we proceed by experiment or by ratiocination, every step in the train of
inferences is essentially inductive, and the legitimacy of the induction de-
pends in both cases on the same conditions.
True it is that in the case of the practical inquirer, who is endeavoring
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
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 ap-
peals are mostly, in themselves, sufficiently trite, and assented to as soon as
stated : his skill lies in bringing his case under those propositions or princi-
ples ; in calling to mind such of the known or received maxims of probabil-
ity 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 nat-
ural or acquired sagacity, aided by knowledge of the particular subject, and
of subjects allied with it. Invention, though it can be cultivated, can not
be reduced to rule; there is no science which will enable a man to bethink
himself of that which will suit his purpose.
But when he Jins 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 knowledge and sagacity in the choice
of the inductions out of which he will construct his argument. But the
validity of the argument when constructed, depends on principles, and must
be tried by tests which are the same for all descriptions of inquiries,
whether the result be to give A an estate, or to enrich science with a new
general truth. In the one case and in the other, the senses, or testimony,
must decide on the individual facts; the rules of the syllogism will deter-
mine whether, those facts being supposed correct, the case really falls with-
in the formulae of the different inductions under which it has been succes-
INDUCTION IN GENERAL. 209
sively brought; and finally, the legitimacy of the inductions themselves
must be decided by other rules, and these it is now our purpose to investi-
gate. 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 sci-
ence ; in all those which are principally deductive, and most of all in math-
ematics ; where the inductions themselves are few in number, and so obvi-
ous and elementary that they seem to stand in no need of the evidence of
experience, while to combine them so as to prove a given theorem or solve
a problem, may call for the utmost powers of invention and contrivance
with which our species is gifted.
If the identity of the logical processes which prove particular facts and
those which establish general scientific truths, required any additional con-
firmation, it would be sufficient to consider that in many branches of sci-
ence, single facts have to be proved, as well as principles ; facts as com-
pletely 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 with-
out disturbing in any degree the homogeneity of its method. A remark-
able example of this is afforded by astronomy. The individual facts on
which that science grounds its most important 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 deter-
mined by a very circuitous process. The share which direct observation
had in the work consisted in ascertaining, at one and the same instant, the
zenith distances of the moon, as seen from two points very remote from
one another on the earth's surface. The ascertainment of these angular
distances ascertained their supplements ; and since the angle at the earth's
centre subtended by the distance between the two places of observation
was deducible by spherical trigonometry from the latitude and longi-
tude 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 as-
certained, at least in terms of the earth's radius, from elementary theo-
rems of geometry. At each step in this demonstration a new induction
is taken in, represented in the aggregate of its results by a general propo-
sition.
Not only is the process by which an individual astronomical fact was
thus ascertained, exactly similar to those by which the same science estab-
lishes its general truths, but also (as we have shown to be the case in all
legitimate reasoning) a general proposition might have been concluded in-
stead 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 al-
most the only heavenly body the distance of which from the earth can real-
ly be thus ascertained, this is merely owing to the accidental circumstances
of the other heavenly bodies, which render them incapable of affording such
14
210 INDUCTION.
data as the application of the theorem requires ; for the theorem itself is
as true of them as it is of the moon.*
"VVe shall fall into no error, then, if in treating of Induction, we limit our
attention to the establishment of general propositions. The principles and
rules of Induction as directed to this end, are the principles and rules of
all Induction ; and the logic of Science is the universal Logic, applicable to
all inquiries in which man can engage.
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 individuals of a class 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 Induction, 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
* Dr. Whewell thinks it improper to apply the term Induction to any operation not termi-
nating in the establishment of a general truth. Induction, he says (Philosophy of Discovery,
p. 24.">), "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
onlv to the cases in which the general induction is consciously applied to a particular in-
stance, 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 im-
pulse, 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 precau-
tions required by scientific propriety. To the idea of Science, an express recognition and
distinct apprehension 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 n case supposed to he similar. I have endeav-
ored to show that this is not only as legitimate an operation, but substantially the same oper-
ation, 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 instantaneous use. But the in-
ferences drawn for the guidance of practical attairs. by persons who would often be quite in-
capable of expressing in unexceptionable terms the corresponding generalizations, may and
frequently do exhibit intellectual powers quite equal to any which have ever been displayed
in science; and if these inferences are not inductive, what are they? The limitation imposed
on the term by Dr. Whewell seems perfectly 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 Keid and Stewart, the principal legislators (as far as the English
language is concerned) of modern metaphysical terminology.
INDUCTIONS IMPROPERLY SO CALLED. 211
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 gen-
eral expression which admits of being stated in the form, "This and that
A are B, therefore every A is B " is called an induction, whether any
thing be really concluded or not: and the induction is asserted 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 ascertained to be true of every individual in it, so that the
nominal conclusion is not really a conclusion, but a mere re-assertion of the
premises. If we were to say, All the planets shine by the sun's light, from
observation of each separate planet, or All the Apostles were Jews, because
this is true of Peter, Paul, John, and every other apostle these, and such
as these, would, in the phraseology in question, be called perfect, and the
only perfect, Inductions. This, however, is a totally different kind of in-
duction 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 sim-
ulated arguments which we have quoted, are not generalizations ; the prop-
ositions purporting to be conclusions from them, are not really general
propositions. A general proposition is one in which the predicate is af-
firmed or denied of an unlimited number of individuals; namely, all, wheth-
er few or many, existing or capable of existing, which possess the proper-
ties 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 description, but only
for each of a number of individuals, designated as such, and as it were
counted off individually, the proposition, 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 " \.iaged notation are; but it is no part of the in-
vestigation of truth, though often bearing an important part in the prepa-
ration of the materials for that investigation.
As we may sum up a definite number of singular propositions 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 induc-
tion applied to every distinct species of animals, it has been established
that each possesses a nervous system, and we affirm thereupon that all an-
imals 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, how-
ever, must be made. If in concluding that all animals have a nervous sys-
tem, 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 ar-
rived at is not induction. But if our meaning is that the observations
made of the various species of animals have discovered to us a law of an-
imal 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 induc-
tion ; but in this case the general proposition contains more than the sum
of the special propositions from which it is inferred. The distinction is
still more forcibly brought out when we consider, that if this real general-
ization be legitimate at all, its legitimacy probably does not require that
212 INDUCTION.
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, can not 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 reflect-
ed 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 can
not 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 a universal property of the sections of the cone. The
distinction drawn in the two previous examples can have no place here,
there being no difference between all known sections of the cone and all
sections, since a cone dcmonstrably can not be intersected by a plane ex-
cept in one of these four lines. It would be difficult, therefore, to refuse
to the proposition arrived at, the name of a generalization, since there is
no room for any generalization beyond it. But there is no induction, be-
cause 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 theo-
rem by means of a diagram. Whether the diagram be on paper or only
in the imagination, the demonstration (as formerly observed*) does not
prove directly the general theorem ; it proves only that the conclusion,
which the theorem asserts generally, is true of the particular triangle or
circle 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 a uni-
versal proposition. Having shown that the three angles of the triangle
ABC are together equal to two right angles, we conclude that this is true
of every other triangle, not because it is true of ABC, but for the same
reason which proved it to be true of ABC. If this were to be called In-
duction, an appropriate name for it would be, induction by parity of rea-
soning. But the term can not 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 particular 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
conviction in the particular instances.
There are nevertheless, in mathematics, some examples of so-called In
duction, in which the conclusion does bear the appearance of a generaliza-
tion grounded on some of the particular cases included in it. A mathe-
matician, when he has calculated a sufficient number of the terms of an al-
* Supra, p. 145.
INDUCTIONS IMPROPERLY SO CALLED. 213
gebraical 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 improbable :
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 a priori ground of the law; since
any one who understands sufficiently the nature of multiplication to ven-
ture upon multiplying several lines of symbols at one operation, can not
but perceive that in raising a binomial to a power, the co-efficients must
depend on the laws of permutation and combination : and as soon as this
is recognized, the theorem is demonstrated. Indeed, when once it was seen
that the law prevailed in a few of the lower powers, its identity with the
law of permutation would at once suggest the considerations which prove
it to obtain universally. Even, therefore, such cases as these, are but ex-
amples 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 Induction, which it
is of real importance to clear up, because the theory of Induction has been,
in no ordinary degree, confused by it, and because the confusion is exem-
plified in the most recent and elaborate treatise on the inductive philosophy
which exists in our language. The error in question is that of confound-
ing 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 phe-
nomenon as a whole, by combining, or as we may say, piecing these de-
tached fragments together. A navigator sailing in the midst of the ocean
discovers land : he can not 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 pro-
nounces it an island. Now there was no particular time or place of ob-
servation 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 any thing of the
nature of an induction in this process ? Did he infei % any thing that had
not been observed, from something else which had ? Certainly not. He
214 INDUCTION.
had observed the whole of what the proposition 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 op-
eration, 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.
The object of Kepler was to determine the real path described by each
of the planets, or let us say by the planet Mars (since it was of that body
that lie 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 ap-
parent 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 lind what sort of a curve these different points would make, supposing
them to be all joined together. He expressed the whole series of the ob-
served places of Mars by what Dr. Whewell calls the general conception of
an ellipse. This operation was far from being as easy as that of the navi-
gator who expressed the series of his observations on successive points of
the coast by the general conception of an island. But it is the very same
sort of operation ; and if the one is not an induction but a description, this
must also be true of the other.
The only real induction concerned in the case, consisted in inferring that
because the observed places of Mars were correctly represented by points
in an imaginary ellipse, therefore Mars Avould continue to revolve in that
same ellipse; and in concluding (before the gap had been filled up by fur-
ther observations) that the positions of the planet during the time which
intervened between two observations, must have coincided with the inter-
mediate points of the curve. For these were facts which had not been di-
rectly observed. They were inferences from the observations; facts in-
ferred, as distinguished from facts seen. But these inferences were so far
from being a part of Kepler's philosophical operation, that they had been
drawn long before he was born. Astronomers had long known that the
planets periodically returned to the same places. When this had been as-
certained, there was no induction left for Kepler to make, nor did he make
any further induction. He merely applied his new conception to the facts
inferred, as he did to the facts observed. Knowing already that the plan-
ets 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,
lie found one for the other : but he found the expression only, not the in-
ference ; nor did he (which is the true test of a general truth) add any
thing to the power of prediction already possessed.
4. The descriptive operation which enables a number of details to be
summed up in a single proposition, Dr. Whewell, by an aptly chosen ex-
pression, has termed the Colligation of Facts. In most of his observations
INDUCTIONS IMPROPERLY SO CALLED. 215
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 gener-
ally ; and laying down, throughout his work, as principles of induction, the
principles of mere colligation.
Dr. Whewell maintains that the general proposition which binds togeth-
er the particular facts, and makes them, as it were, one fact, is not the mere
sum of those facts, but something more, since there is introduced a concep-
tion of the mind, which did not exist in the facts themselves. " The par-
ticular facts," says he,* " arc 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 mo-
tions of the planets, saw that these motions might be rightly considered as
produced 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 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 tho 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 sup-
plies from his own store a principle of connection. 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,
iudiscriminately, examples of both the processes which I am endeavoring
to distinguish from one another. When the Greeks abandoned the suppo-
sition that the planetary motions were produced by the revolution of mate-
rial wheels, and fell back upon the idea of " mere geometrical spheres or
circles," there was more in this change of opinion than the mere substitu-
tion of an ideal curve for a physical one. There was the abandonment of
a theory, and the replacement of it by a mere description. No one would
think of calling the doctrine of material wheels a mere description. That
doctrine was an attempt to point out the force by which the planets were
acted upon, and compelled to move in their orbits. But when, by a great
step in philosophy, the materiality of the wheels was discarded, and the ge-
ometrical 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 re-
volving in the inside of other wheels, gave place to the proposition, that
they moved in the same lines which would be traced by bodies so carried :
which was a mere mode of representing the sum of the observed facts ; as
Kepler's was another and a better mode of representing the same observa-
tions.
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 con-
ception of an ellipse must have presented itself to Kepler's mind, before he
could identify the planetary orbits with it. According to Dr. Whewell,
the conception was 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 recognized it; just as the island was an island before it had been
* Novum Organum Renovatum, pp. 72, 73.
216 INDUCTION.
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 con-
ception 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 ap-
propriate 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 suc-
cession, 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
navigator 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 can not see why any difference should be
made by its not being directly an object of sense, when every point in it is
as exactly ascertained as if it were so.
Subject to the indispensable condition which has just been stated, I do
not conceive that the part which conceptions have in the operation of
studying facts, has ever been overlooked or undervalued. No one ever dis-
puted that in order to reason about any thing we must have a conception
of it; or that when we include a multitude of things under a general ex-
pression, there is implied in the expression a conception of something com-
mon to those things. But it by no means follows that the conception is
necessarily pre-existent, or constructed by the mind out of its own mate-
rials. 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 can not directly perceive, it is because of the lim-
ited 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 afterward called in to connect.
This he himself admits, when he observes (which he does on several occa-
sions), how great a service would be rendered to the science of physiology
by the philosopher " who should establish a precise, tenable, and consistent
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 abstraction from the observations
themselves ; the mind had to supply hypothetically, from among the con-
ceptions it had obtained from other portions of its experience, some one
which would correctly represent the series of the observed facts. It had
* Novurn Oryanum Rvnovatum. p. 32.
INDUCTIONS IMPROPERLY SO CALLED. 217
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 compare these with the details actually observed. If they agreed,
the hypothesis would serve for a description of the phenomenon : if not, it
\\-as necessarily abandoned, and another tried. It is such a case as this
which gives rise to the doctrine that 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 posi-
tion. Not having these advantages, but possessing the conception of an el-
lipse, 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, consequent-
ly, 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, name-
ly, that it occupied in succession the various points in the circumference of
a given ellipse, was the very fact, the separate parts of which had been sep-
arately 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 reject-
ed, until one at last occurs tit to be chosen. We know from Kepler him-
self that before hitting upon the " conception " of an ellipse, he tried nine-
teen other imaginary paths, which, finding them inconsistent with the ob-
servations, he was obliged to reject. But as Dr. Whewell truly says, the
successful hypothesis, though a guess, ought generally to be called, not a
lucky, but a skillful guess. The guesses which serve to give mental unity
and wholeness to a chaos of scattered particulars, are accidents which rare-
ly occur to any minds but those abounding in knowledge and disciplined in
intellectual combinations.
How far this tentative method, so indispensable as a means to the colli-
gation of facts for purposes of description, admits of application to Induc-
tion itself, and what functions belong to it in that department, will be con-
sidered in the chapter of the present Book which relates to Hypotheses.
On the present occasion we have chiefly to distinguish this process of Col-'
ligation 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 unequivo-
cally false of the latter.
In different stages of the progress of knowledge, philosophers have em-
ployed, for the colligation of the same order of facts, different conceptions.
The early rude observations of the heavenly bodies, in which minute pre-
cision was neither attained nor sought, presented nothing inconsistent with
the representation of the path of a planet as an exact circle, having the earth
for its centre. As observations increased in accuracy, facts were disclosed
which were not reconcilable with this simple supposition : for the colliga-
tion of those additional facts, the supposition was varied ; and varied again
and again as facts became more numerous and precise. The earth was re-
moved 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 im-
aginary point which revolved in a circle round the earth : in proportion as
o i s INDUCTION.
observation elicited fresh facts contradictory to these representations, other
epicycles and other eccentrics 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.
AVhewell has remarked that these successive general expressions, though
apparently so conflicting, were all correct: they all answered the purpose
of colligation ; they all enabled the mind to represent to itself with facility,
and by a simultaneous glance, the whole body of facts at the time ascer-
tained : each in its turn served as a correct description of the phenomena,
so far as the senses had up to that time taken cognizance of them. If a
necessity afterward 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 positions, 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 correctness
of the former expression, considered as a general statement of the only facts
which it was intended to represent. And so true is this, that, as is well re-
marked 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 employed by
astronomers when only a rough approximation to correctness is required.
" L'astronomie moderne, en detruisant sans retour les hypotheses primi-
tives, envisagees comme lois reelles du monde, a soigneusement maintcnu
leur valeur positive et pennanente, la propriete de representer commode-
ment les phenomenes quand il s'agit d'une premiere ebauche. Nos res-
sources a cet egard sont memo bien plus etendues, precisement ii cause
quo nous ne nous faisons aucune illusion sur la realite des hypotheses ; ce
qui nous permet d'employer sans scrupule, en chaque cas, cello quo 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, succes-
sive descriptions of a phenomenon as a whole, which has been observed
only in parts, may, though conflicting, be all correct as far as they go. But
it would surely be absurd to assert this of conflicting inductions.
The scientific study of facts may be undertaken for three different pur-
poses : the simple description of the facts ; their explanation; or their pre-
diction : 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. Xow, Dr. Whewell's observation is true of the first
alone. Considered as a mere description, the circular theory of the heaven-
ly motions represents perfectly well their general features: and by adding
epicycles without limit, those motions, even as now known to us, might be
expressed with any degree of accuracy that might be required. The ellip-
tical 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
* Cours de Philosophic Positive, vol. ii., p. 202.
INDUCTIONS IMPROPERLY SO CALLED. 219
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 Xewtonian 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? Assur-
edly the one is true, and the other absolutely false.*
* Dr. \Vhe\vell, in his reply, contests the distinction here drawn, and maintains, 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 Dis-
covery, p. 231): " Undoubtedly 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 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 doc-
trine, 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 refer-
ence 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 in-
dicates, 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 distinction which Mr. Mill attempts to
draw between descriptions like Kepler's law of elliptical orbits, and other examples of induc-
tion."
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 Description ; it would, no doubt, have been reconcilable with the Newtonian
theory. The vortices, however, were not a mere aid to conceiving the motions of the plan-
ets, but a supposed physical agent, actively impelling them ; a material fact, which might be
true or not true, but could not be both true and not true. According to Descartes's theory it
was true, according to Newton's it was not true. Dr. AVhewell probably means that since the
phrases, centripetal and projectile force, do not declare the nature but only the direction of
the forces, the Newtonian theory does not absolutely contradict any hypothesis which may be
framed respecting the mode of 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 consist? In ascribing those motions to a
general law which obtains between all particles of matter, and in identifying this with the law
by which bodies fall to the ground. If the planets are kept in their orbits by a force which
draws the particles composing them toward 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 im-
220 INDUCTION.
In every way, therefore, it is evident that to explain induction as the
colligation of facts by means of appropriate conceptions, that is, concep-
tions which will really express 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.
There is, however, between Colligation and Induction, a real correlation,
which it is important to conceive correctly. Colligation is not always in-
duction ; but induction is always colligation. The assertion that the plan-
ets 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, toward
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 connection for those facts ; a
new principle for their classification.
Further, the descriptions which are improperly confounded with induc-
tion, are nevertheless a necessary preparation for induction ; no less neces-
sary than correct observation of the facts themselves. Without the pre-
vious colligation of detached observations by means of one general concep-
tion, 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
possible that both opinions can be true. As well might it be said that there is no contradic-
tion 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 celestial nature, is
incompatible with either of the two others : either that of their being moved by vortices, or
that which regards them as moving by a property which they have in common with the earth
and all terrestrial bodies. Dr. Whewell says that the theory of an inherent virtue agrees with
Newton's when the word inherent is left out, which of course it would be (he says) if " found
to be untenable." But leave that out, and where is the theory? The word inherent is the
theory. When that is omitted, there remains nothing except that the heavenly bodies move
" by a virtue,'' i. e., by a power of some sort; or by virtue of their celestial nature, which di-
rectly 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 doc-
trine. 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 reconcilable; 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 can not l>oth be true, still less, surely, can differ-
ent 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 suf-
ficient answer to a theory. Examples not liable to his objection are easily found, if the prop-
osition that conflicting predictions can not both be true, can be made clearer by any examples.
Suppose the phenomenon to be a newly-discovered comet, and that one astronomer predicts
its return once in every 3(X) 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 traiu 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
'.he latter.
INDUCTIONS IMPROPERLY SO CALLED. 221
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 subjects. Induction, therefore, always presup-
poses, not only that the necessary observations are made with the necessary
accuracy, but also that the results of these observations are, so far as prac-
ticable, connected together by general descriptions, enabling the mind to
represent to itself as wholes whatever phenomena are capable of being so
represented.
5. Dr. "Whewell has replied at some length to the preceding observa-
tions, restating his opinions, but without (as far as I can perceive) adding
any thing 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 difference of
opinion consists, as well as, in some measure, to account for it.
Nearly all the definitions of induction, by writers of authority, make it
consist in drawing inferences from known cases to unknown ; affirming of
a class, a predicate which has been found true of some cases belonging to
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. Nei-
ther was it an extension to all time, of what had been found true at some
particular time. The whole amount of generalization which the case ad-
mitted 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 uninterrupted
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 proposi-
tion 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 statement, as Dr. Whewell says,
was not the sum of the observations merely ; it was the sum of the obser-
vations 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 known cases to imknown, which constitutes Induc-
tion in the original and acknowledged meaning of the term.
Old definitions, it is true, can not prevail against new knowledge: and if
the Keplerian operation, as a logical process, be really identical with what
takes place in acknowledged induction, the definition of induction ought to
be so widened as to take it in ; since scientific language ought to adapt it-
self 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
* Phil, of Discov., p. 256.
222 INDUCTION.
docs think the operations identical. He allows of no logical process in any
case of induction, other than what there was in Kepler's case, namely,
guessing until a guess is found which tallies with the facts ; and accord-
ingly, as we shall see hereafter, lie 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. Whe-
well's phraseology, connect them by means of a new conception ; if the
conception does serve to connect the observations, we have all we want.
As the proposition in which it is 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 ad-
mits of proof ; though it may serve to prove other things, inasmuch as, by
placing the facts in mental connection with other facts, not previously seen
to resemble them, it assimilates the case to another class of phenomena,
concerning which real Inductions have already been made. Thus Kepler's
so-called law brought the orbit of Mars into the class ellipse, and by doing
so, proved all the properties of an ellipse to be true of the orbit : but in this
proof Kepler's law supplied the minor premise, and not (as is the case with
real Inductions) the major.
Dr. "NVhewell calls nothing Induction where there is not a new mental
conception introduced, and every thing induction where there is. But this
is to confound two very different things, Invention and Proof. The intro-
duction of a new conception belongs to Invention : and invention may be
required in any operation, but is the essence of none. A new conception
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 conceptions 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
inerely a necessary part of all induction, but the whole of it.
*The mental operation which extracts from a number of detached obser-
vations certain general characters in which the observed phenomena resem-
ble one another, or resemble other known facts, is what Bacon, Locke, and
.most subsequent metaphysicians, have understood by the word Abstrac-
tion. A general expression obtained by abstraction, connecting known
facts by means of common characters, but without concluding from them
to unknown, may, I think, with strict logical correctness, be termed a De-
scription ; nor do I know in what other way things can ever be described.
My position, however, does not depend on the employment of that partic-
ular word ; I am quite content to use Dr. Whewell's term Colligation, or
the more general phrases, " mode of representing, or of expressing, phe-
nomena :" provided it be clearly seen that the process is not Induction, but
something radically different.
GROUND OF INDUCTION. 223
What more may usefully be said on the subject of Colligation, or of the
correlative expression invented by Dr. Whewell, the Explication of Con-
ceptions, and generally on the subject of ideas and mental representations
as connected with the study of facts, will find a more appropriate place in
the Fourth Book, on the Operations Subsidiary to Induction : to which I
must refer the reader for the removal of any difficulty which the present
discussion may have left.
CHAPTER III.
OF THE GROUND OF INDUCTION.
1. INDUCTION properly so called, as distinguished from those mental
operations, sometimes, though improperly, designated by the name, which I
have attempted in the preceding chapter to characterize, may, then, be sum-
marily defined as Generalization from Experience. It consists in inferring
from some individual instances in which a phenomenon is observed to oc-
cur, that it occurs in all instances of a certain class ; namely, in all which
resemble the former, in what are regarded as the material circumstances.
In what way the material circumstances are to be distinguished from
those which are immaterial, or why some of the circumstances are material
and others not so, we are not yet ready to point out. We must first ob-
serve, that there is a principle implied in the very statement of what Induc-
tion 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 experi-
ence, has been described by different philosophers in different forms of lan-
guage : that the course of nature is uniform ; that the universe is governed
by ge'neral laws; and the like. One of the most usual of these modes of
expression, but also one of the most inadequate, is that which has been
brought into familiar use by the metaphysicians of the school of Reid
and Stewart. The disposition of the human mind to generalize from ex-
perience a propensity considered by these philosophers as an instinct of
our nature they usually describe under some such name as " our intuitive
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 orig-
inal 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 past and future, that we
* Essays on the Pursuit of Truth.
224 INDUCTION.
infer, but from the known to the unknown ; from facts observed to facts
unobserved ; from what we have perceived, or been directly conscious of,
to what has not come within our experience. In this last predicament is
the whole region of the future ; but also the vastly greater portion of the
present and of the past.
Whatever be the most proper mode of _expressmgjt, the .propositiuii that
yjjjhjq fiQui's'fTfTi7iruro"is titiifoTm, is the fundamental principle,, or jjjjj&jj&&*~
ioiu^ of Induction. It would yet be a great error to offer this large gener-
ali/ation as any explanation 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 arc 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. The obscurer laws of nature
were discovered by means of it, but the more obvious ones must have
been understood and assented to as general truths before it was ever heard
of. We 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 knowledge of the laws themselves ;
which could be done no otherwise than by induction. In what sense, then,
can a principle, which is so far from being our earliest induction, be re-
garded 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 contrib-
ute to their validity. As Archbishop 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 supply-
ing a major premise. If this be actually done, the principle which we are
now considering, that of the uniformity of the course of nature, will appear
as the ultimate major premise of all inductions, and will, therefore, stand to
all inductions in the relation in which, as has been shown at so much length,
the major proposition of a syllogism always stands to the conclusion ; not
contributing at all to prove it, but being a necessary condition of its being
proved ; since no conclusion is proved, for which there can not be found a
true major premise.*
* In the first edition a note was appended at this place, containing some criticism on Arch-
bishop 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 edi-
tion, the Archbishop observes in a tone of something like disapprobation, that the objections,
"doubtless from their being fully answered and found untenable, were silently suppressed,"
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 uneasiness. 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 objections ought not to
have been made "silently." I now break that silence, and state exactly what it is that I sup-
pressed, and why. I suppressed that alone which might be regarded as personal criticism on
the Archbishop. I had imputed to him the having omitted to ask himself a particular ques-
tion. I found that he had asked himself the question, and could give it an answer consistent
with his own theory. I had also, within the compass of a parenthesis, hazarded some re-
marks on certain general characteristics of Archbishop Whately as a philosopher. These re-
marks, though their tone. I hope, was neither disrespectful nor arrogant, I felt, on reconsider-
ation, that I was hardly entitled to make ; least of all, when the instance which I had re-
GROUND OF INDUCTION. 225
Th.p stnfprr^njij t^ 1Qt f ^ Q uniformity of the course of nature is the ulti-
mate major pvemiau in all cases of induction, may be thought to require
some explanation. The immediate major premise in every inductive argu-
ment, it certainly is not. Of that, Archbishop Whately's must be held to
be the correct account. The induction, " John, Peter, etc., are mortal, there-
fore all mankind are mortal," may, as he justly says, be thrown into a syl-
logism by prefixing as a major premise (what is at any rate a necessary
condition of the validity of the argument), namely, that what is true of
John, Peter, etc., is true of all mankind. But how came we by this ma-
jor premise? It is not self-evident; nay, in all cases of unwarranted gen-
eralization, it is not true. How, then, is it arrived at ? Necessarily either
by induction or ratiocination; and if by induction, the process, like all oth-
er inductive arguments, may be thrown into the form of a syllogism. This
previous syllogism it is, therefore, necessary to construct. There is, in the
long run, only one possible construction. The real proof that what is true
of John, Peter, etc., is true of all mankind, can only be, that a different sup-
position would be inconsistent with the uniformity which we know 7 to exist
in the course of nature. Whether there would be this inconsistency or not,
may be a matter of long and delicate inquiry ; but unless there would, we
have no sufficient ground for the major of the inductive syllogism. It
hence appears, that if we throw the whole course of any inductive argu-
ment 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. Othei's hold it
to be a principle which, antecedently to any verification by experience, we
garded 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 prem-
ise, remains exactly where it was ; and so far was I from thinking that my opinion had
been fullv "answered'' and was "untenable," that in the same edition in which I canceled
the note, I not only enforced the opinion by further arguments, but answered (though without
naming him) those of the Archbishop.
For not having made this statement before, I do not think it needful to apologize. It would
be attaching very great importance to one's smallest sayings, to think a formal retractation req-
uisite every time that one falls into an error. Nor is Archbishop Whately's well-earned fame
of so tender a quality as to require that in withdrawing a slight criticism on him I should have
been bound to offer a public amende for having made it.
* 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 necessaiy condition that the uniformity should pervade all na-
ture. It is enough that it pervades the particular class of phenomena to which the induction
relates. An induction concerning the motions of the planets, or the properties of the magnet.
would not be vitiated though we were to suppose that wind and weather are the sport of
chance, provided it be assumed that astronomical and 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 phe-
nomena 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 con-
cerned. 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, 13, and
0, implies either that we have already concluded all men to be mortal, or that we are now en-
titled to do so from the same evidence. A vast amount of confusion and paralogism respect-
ing the grounds of Induction would be dispelled by keeping in view these simple consider-
ations.
15
226 INDUCTION.
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 mathematics, 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.* At present it
is of more importance to understand thoroughly the import of the axiom
itself. For the proposition, that the course of nature is uniform, possesses
rather the brevity suitable to popular, than the precision requisite in phil-
osophical 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 tint the succession of rain and fine weather will be
the same in every future year as in the present. Nobody expects to have
the same dreams repeated every night. On the contrary, every body men-
tions it as something extraordinary, if the course of nature is constant, and
resembles itself, in these particulars. To look for constancy where con-
stancy 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 va-
rious. Some phenomena are always seen to recur in the very same combi-
nations in which we met with them at first; others seem altogether capri-
cious ; while some, which we had been accustomed to regard as bound
down exclusively to a particular set of 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, mankind believed in a 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 " In-
ductio per enunierationem simplicem, ubi non reperitur instantia contradic-
toria." It consists in ascribing the character of general truths to all prop-
ositions 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,
* Infra, chap. xxi.
GROUND OF INDUCTION. 227
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 conflicting character conies unsought. The notion
of seeking it, of experimenting for it, of interrogating nature (to use Ba-
con's expression) is of much later growth. The observation of nature, by
uncultivated intellects, is purely passive: they accept the facts which pre-
sent themselves, without taking the trouble of searching for more : it is a
superior mind only which asks itself what facts are needed to enable it to
come to a safe conclusion, and then looks out for these.
But though we have always a propensity to generalize from unvarying
experience, we are not always warranted in doing so. Before we can be
at liberty to conclude that something is universally true because we have
never known an instance to the 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 hav-
ing it, is the foundation 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 in-
duction 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 Inductive Philosophy. The value of his own con-
tributions 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 princi-
ples 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 experience
which we hear so confidently appealed to by all sects, parties, and interests,
is still, in his own emphatic words, mera palpatio.
3. In order to a better understanding of the problem which the logi-
cian must solve if he would establish a scientific theory of Induction, let us
compare a few cases of incorrect inductions with others which are acknowl-
edged to be legitimate. Some, we know, which, were believed for centuries
to be correct, were nevertheless incorrect. That all swans are white, can
not have been a good induction, since the conclusion has turned out errone-
ous. The experience, however, on which the conclusion restedj was genu-
* Infra, chap, xxi., xxii.
2-28 INDUCTION.
inc. 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 concluding 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 natu-
ralist Pliny ? As there were black swans, though civilized people had exist-
ed for three thousand years on the earth without meeting with them, may
there not also be " men whose heads do grow beneath their shoulders," not-
withstanding a rather less perfect unanimity of negative testimony from
observers? Most persons would answer Xo; it was more credible that a
bird should vary in its color, than that men should vary in the relative po-
sition 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 confi-
dence 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 a very feeble presumption that
the like result will hold in all other cases. That a straight line is the short-
est distance between two points, wo do not doubt to be true even in the re-
gion 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 conclusions he has arrived at will hold universally,
though the induction be founded but on a single instance. We do not
withhold our assent, waiting for a repetition of the experiment; or if we
do, it is from a doubt whether the one experiment 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 ; a uni-
versal proposition from a singular one. Now mark another case, and con-
trast 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 explored, he
had caught and examined a crow, and had found it to be gray.
Why is a single instance, in some cases, sufficient for a complete induc-
tion, while in others, myriads of concurring instances, without a single ex-
ception known or presumed, go such a very little way toward establishing
a universal proposition ? 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.
* In strictness, wherever the present constitution of space exists ; which we have ample
reason to believe that it does in the region of the fixed stars.
LAWS OF NATURE. 229
CHAPTER IV.
OF LAWS OF NATUKE.
1. Ix the contemplation of that uniformity in the course of nature,
which is assumed in every inference from experience, one of the first ob-
servations that present themselves is, that the uniformity in question is not
properly uniformity, but uniformities. The general regularity results from
the co-existence of partial regularities. The course of nature in general is
constant, because the course of each of the various phenomena that com-
pose it is so. A certain fact invariably occurs whenever certain circum-
stances are present, and does riot occur when they are absent ; the like is
true of another fact ; and so on. From these separate threads of connec-
tion between parts of the great whole which we term nature, a general tis-
sue of connection unavoidably weaves itself, by which the whole is held to-
gether. 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 produced,
which, along with and in the midst of infinite diversity, pervades all nature.
The first point, therefore, to be noted in regard to what is called the uni-
formity of the course of nature, is, that it is itself a complex fact, com-
pounded of all the separate uniformities which exist in respect to single
phenomena. These various uniformities, when ascertained by what is re-
garded as a sufficient induction, we call, in common parlance, Laws of Na-
ture. Scientifically speaking, that title is employed in a more restricted
sense, to designate the uniformities when reduced to their most simple ex-
pression. Thus in the illustration already employed, there were seven uni-
formities; all of which, if considered sufficiently certain, would, in the more
lax application of the term, be called laws of nature. But of the seven,
three alone are properly distinct and independent: these bping presup-
posed, the others follow of course. The first three, therefor" 5 ! 36 . I'ding to
the stricter acceptation, are called laws of nature ; the remailfuer not ; be-
cause they are in truth mere cases of the first three ; virtually included in
them ; said, therefore, to result, from them : whoever affirms those three has
already affirmed all the rest.
To substitute real examples for symbolical ones, the following are three
uniformities, or call them laws of nature: the law that air has weight, the
law that pressui'e 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 equilibrium
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 sustained at such
a height that the column of mercury were equal in weight to a column of
the atmosphere of the same diameter ; here would be a case, either of the
230 INDUCTION.
;iir not pressing upon the surface of the mercury with the force winch is
called its weight, or of the downward pressure on the mercury not being
propagated equally in an upward direction, or of a body pressed in one di-
rection 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 Torricel-
lian experiment, we might deduce its result from those laws. The known
weight of the air, combined with the position of the apparatus, would
bring the mercury within the first of the three inductions; the first induc-
tion 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, independently of specific
experience, through our knowledge of the simpler ones from which it results;
though, for reasons which will appear hereafter, verification by specific ex-
perience 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 laics, but can scarcely, in the strictness of scientific
speech, be termed Laws of Xature. 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 la\v ; as when, in mathematics,
we speak of the law of decrease of the successive terms of a converging
series. But the expression l<nr of nature has generally been employed
with a sort- of tacit reference to the original sense of the word law, namely,
the e:;j;r->sion of the will of a superior. When, therefore, it appeared that
any o*' 'he uniformities which were observed in nature, would result spon-
taneou^ly from certain other uniformities, no separate act of creative will
being vipposed necessary for the production of the derivative uniformities,
these have not usually been spoken of as laws of nature. According to
one r-ode of expression, the question, What are the laws of nature? may
be sti.ted thr,: : What are the fewest and simplest assumptions, which be-
ing g ted, the whole existing order of nature would T'csult? Another
mode ')f stating it would be thus: What are the fewest general proposi-
tions f; om \\hich all the uniformities which exist in the universe might be
deduc '...Inferred?
Kv coposit-, advance which marks an epoch in the progress of science,
has c< a step made toward the solution of this problem. Even a
simple colligation of inductions already made, without any fresh extension
of the inductive inference, is already an advance in that direction. When
Kepler expressed the regularity which exists in the observed motions of
the heavenly bodies, by the three general propositions called his laws, he,
in so doing, pointed out three simple suppositions which, instead of a much
greater number, would suffice to construct the whole scheme of the heav-
enly motions, so far as it was known up to that time. A similar and still
greater step was made when these laws, which at first did not seem to be
included in any more general truths, were discovered to be cases of the
three laws of motion, as obtaining among bodies which mutually tend to-
ward one another with a certain force, and have had a certain instantaneous
impulse originally impressed upon them. After this great discovery, Kep-
ler's three propositions, though still called laws, would hardly, by any per-
son accustomed to use language with precision, be termed laws of nature:
tii at phrase would be reserved for the simpler and more general laws into
which Newton is said to have resolved them.
LAWS OF NATURE. 231
According to this language, every well-grounded inductive generaliza-
tion 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 In-
ductive 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 im-
agine that this mode of statement amounts to a real analysis, or to any
thing but a mere verbal transformation 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 re-
duced to their simplest expression. It is, however, something to have ad-
vanced so far, as to see that the study of nature is the study of laws, not a
law ; of uniformities, in the plural number : that the different natural phe-
nomena 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 composed of distinct threads, and only to
be understood by tracing each of the threads separately; for which pur-
pose it is often necessary to unravel some portion of the web, and exhibit
the fibres apart. The rules of experimental inquiry are the contrivances
for unraveling the web.
2. In thus attempting to ascertain the general order of nature by as-
certaining the particular order of the occurrence of each one of the phe-
nomena of nature, the most scientific proceeding can be no more than an im-
proved form of that which was primitively pursued by the human under-
standing, 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 spontaneously adopted, they did
not, conformably to the well-meant but impracticable precept of Descartes,
set out from tlie 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 oth-
ers, that mankind learned, 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 connection between
those phenomena. No science was needed to teach that food nourishes,
that water drowns, or quenches thirst, that the sun gives light and heat,
that bodies fall to the ground. The first scientific inquirers assumed these
and the like as known truths, and set out from them to discover others
which were unknown: nor were they wrong in so doing, subject, however,
as they afterward began to see, to an ulterior 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 circum-
stance not originally attended to. It will appear, I think, from the subse-
quent 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 im-
practicable : since it is impossible to frame any scientific method of induc-
tion, 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 illustrations, and con-
sider why it is that, with exactly the same amount of evidence, both nega-
232 INDUCTION.
live and positive, we did not reject the assertion that there arc 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;* Ap-
parently because there is less constancy in the colors of animals, than in
the general structure of their anatomy. But how do we know this?
Doubtless, from experience. It appears, then, that we need experience to
inform us, in what degree, and in what cases, or sorts of cases, experience
is to be re-lied on. Experience 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 ex-
perience its own test. Experience testifies, that among the uniformities
which it exhibits or seems to exhibit, some arc more to be relied on than
others; and uniformity, therefore, may be presumed, from any given num-
ber of instances, 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 nar-
rower 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 va-
rieties of cases, without any essential alteration in its principle.
There are of course no means of applying such a test as that above de-
scribed, unless we already possess a general knowledge of the prevalent
character of the uniformities existing throughout nature. The indispen-
sable foundation, therefore, of a scientific formula of induction, must be a
survey of the inductions to which mankind have been conducted in unsci-
entific practice ; with the special purpose of ascertaining what kinds of
uniformities have been found perfectly invariable, pervading all nature,
and what are those which have been found to vary with difference of time,
place, or other changeable circumstances.
-L The necessity of such a survey is confirmed by the consideration,
that the stronger inductions are the touch-stone to which we always en-
deavor to bring the weaker. If we find any means of deducing one of
the less strong inductions from stronger ones, it acquires, at once, all the
strength of those from which it is deduced ; and even adds to that strength ;
since the independent experience on which the weaker induction previously
rested, becomes additional evidence of the truth of the better established
law in which it is now found to be included. We may have inferred, from
historical evidence, that the uncontrolled power of a monarch, of an aris-
tocracy, 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
practiced, in maintaining the predominance of reason and conscience over
the selfish propensities. It is at the same time obvious that ever, these
more general facts derive an accession of evidence from the testimony
which history bears to the effects of despotism. The strong induction be-
comes still stronger when a weaker one has been bound up with it.
On the other hand, if an induction conflicts with stronger inductions,
LAWS OF NATURE. 233
or with conclusions capable of being correctly deduced from them, then,
unless on reconsideration it should appear that some of the stronger induc-
tions have been expressed with greater universality than their evidence
warrants, 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 reli-
ance on astrology, or on the weather-prophecies in almanacs, were doubt-
less inductions supposed to be grounded on experience:* and faith in such
delusions seems quite capable of holding out against a great multitude of
failures, provided it be nourished by a reasonable number of casual coinci-
dences between the prediction and the event. What has really put an end
to these insufficient inductions, is their inconsistency with the stronger in-
ductions 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 inductions, whether
strong or weak, which can be connected by ratiocination, are confirmatory
of one another ; while any which lead deductively to consequences that are
incompatible, become mutually each other's test, showing that one or other
must be given up, or at least more guardedly expressed. In the case of
inductions which confirm each other, the one which becomes a conclusion
from ratiocination rises to at least the level of certainty of the weakest of
those from which it is deduced ; while in general all are more or less in-
creased in certainty. Thus the Torricellian experiment, though a mere
case of three more general law r s, not only strengthened greatly the evidence
on which those laws rested, but converted one of them (the weight of the
atmosphere) from a still doubtful generalization into a completely estab-
lished doctrine.
If, then, a survey of the uniformities which have been ascertained to ex-
ist in nature, should point out some which, as far as any human purpose re-
quires certainty, may be considered 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 re-
* Dr. Whewell (Phil, of Discov., p. 24G) will not allow these and similar erroneous judg-
ments 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 question to be, not in what manner these notions were at first suggested, but
by what evidence they have, from time to time, been supposed to be substantiated. If the be-
lievers in these erroneous opinions had been put on their defense, they would have referred
to experience : to the comet which preceded the assassination of Julius Csesar, or to oracles
and other prophecies known to have been fulfilled. It is by such appeals to facts that all
analogous superstitions, even in our day, attempt to justify themselves ; the supposed evi-
dence 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 a priori
prejudice does not prevent the erroneous opinion from being sincerely regarded as a legiti-
mate conclusion from experience ; though it improperly predisposes the mind to that inter-
pretation of experience.
Thus much in defense of the sort of examples objected to. But it would be easy to pro-
duce instances, equally adapted to the purpose, and in which no antecedent prejudice is at all
concerned. "For many ages," says Archbishop Whately, "all farmers 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.
234 INDUCTION.
spect 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 relations to one an-
other ; that of simultaneity, and that of succession. Every phenomenon is
related, in a uniform manner, to some phenomena that co-exist with it, and
to some that have preceded and will follow it.
Of the uniformities which exist among synchronous phenomena, the most
important, on every account, are the law r s 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, co-exist ; and the unvarying laws
which are the subject of the science of geometry, are an expression of the
mode of their co-existence.
This is a class of laws, or in other words, of uniformities, for the com-
prehension and proof of which it is not necessary to suppose any lapse of
time, any variety of facts or events succeeding one another. The proposi-
tions of geometry are independent of the succession of events. All things
which possess extension, or, in other words, which fill space, are subject to
geometrical laws. Possessing extension, they possess figure ; possessing
figure, they must possess some figure in particular, and have all the proper-
ties which geometry assigns to that figure. If one body be a sphere and
another a cylinder, of equal height and diameter, the one will be exactly
two-thirds of the other, let the nature and quality of the material be what
it will. Again, each body, and each point of a body, must occupy some
place or position among other bodies ; and the position of two bodies rela-
tively to each other, of whatever nature the bodies be, may be unerringly
inferred from the position of each of them relatively to any third body.
In the laws of number, then, and in those of space, we recognize in the
most unqualified manner, the rigorous universality of which we are in
quest. Those laws have been in all ages the type of certainty, the standard
of comparison for all inferior degrees of evidence. Their invariability is so
perfect, that it renders us unable even to conceive any exception to them ;
and philosophers have been led, though (as I have endeavored to show) er-
roneously, 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,
LAW OF CAUSATION. 235
this would be conclusive evidence to us that those other uniformities pos-
sessed the same rigorous certainty. But this we can not 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 our 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 in-
ferred. 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 and space are important elements in the
ascertainment of uniformities of succession, they can do nothing toward it
when taken by themselves. They can only be made instrumental 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 continuous 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 repi'esent the direction and quan-
tity of those forces ; we may by combining these truths with propositions
relating to the properties of straight lines and of parallelograms (as that a
triangle is half a parallelogram of the same base and altitude), deduce an-
other important uniformity of 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 dem-
onstrations 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 phenomenon, 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
endeavor 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 fun-
damental law must resemble the truths of geometry in their most remark-
able peculiarity, that of never being, in any instance whatever, defeated or
suspended by any change of circumstances.
Now among all those uniformities in the succession of phenomena, which
common observation is sufficient to bring to light, there are very few which
have any, even apparent, pretension to this rigorous indefeasibility : and of
those few, one only has been found capable of completely sustaining it. In
that one, however, we recognize a law which is universal also in another
sense ; it is co-extensive with the entire field of successive phenomena, all
instances whatever of succession being examples of it. This law is the
236 INDUCTION.
Law of Causation. The truth that every fact which has a beginning has a
cause, is co-extensive 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 every thing." 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 Induc-
tion, it is indispensable that this idea should, at the very outset of our in-
quiry, be, with the utmost practicable degree of precision, fixed and deter-
mined. If, indeed, it were necessary for the purpose of inductive logic
that the strife should be quelled, which has so long raged among the differ-
ent 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.
]>ut the science of the Investigation of Truth by means of Evidence, is
happily independent of many of the controversies which perplex the sci-
ence of the ultimate constitution of the human mind, and is under no ne-
cessity of pushing the analysis of mental phenomenon 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 phe-
nomenon ; I make no research into the ultimate or ontological cause of
any thing. To adopt a distinction familiar in the writings of the Scotch
metaphysicians, 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 deem-
ed, by the schools of metaphysics most in vogue at the present moment, to
imply a mysterious and most powerful tie, such as can not, 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 es-
sences 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,
which the theory of induction requires, is such a notion as can 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 na-
ture and some other fact which has preceded it; independently of all con-
siderations 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 phe-
nomena 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
(nurse 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 be-
LAW OF CAUSATION. 237
lieve, will continue to, succeed. The invariable antecedent is termed the
cause ; the invariable consequent, the effect. And the universality of the
law of causation consists in this, that every consequent is connected in this
manner with some particular antecedent, or set of antecedents. 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 invariably connected. For every event there ex-
ists some combination of objects or events, some given concurrence of cir-
cumstances, positive and negative, the occurrence of which is always fol-
lowed by that phenomenon. We may not have found out what this con-
currence 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 as-
surance we have that there is a law to be found if we only knew how to
find it, will be seen presently to be the source from which the canons of
the Inductive Logic derive their validity.
3. It is seldom, if ever, between a consequent and a single antecedent,
that this invariable sequence subsists. It is usually between a consequent
and the sum of several antecedents ; the concurrence of all of them being
requisite to produce, that is, to be certain of being followed by, the conse-
quent. In such cases it is very common to single out one only of the an-
tecedents under the denomination of Cause, calling the others merely Con-
ditions. 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 connection 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 bod-
ily constitution, a particular state of present health, and perhaps even a
certain state of the atmosphere ; the whole of which circumstances per-
haps 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
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 conditions, 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 permanency ; and
might therefore have preceded the effect by an indefinite length of dura-
tion, for want of the event which was requisite to complete the required
concurrence of conditions : while as soon as that event, eating the food,
occurs, no other cause is waited for, but the effect begins immediately to
take place : and hence the appearance is presented of a more immediate
and close connection between the effect and that one antecedent, than be-
tween the effect and the remaining conditions. But though we may think
proper to give the name of cause to that one condition, the fulfillment of
which completes the tale, and brings about the effect without further de-
lay; this condition has really no closer- relation to the effect than any of
the other conditions has. All the conditions were equally indispensable to
the production of the consequent ; and the statement of the cause is inconi-
238 INDUCTION.
plete, unless in some shape or other we introduce them all. A man takes
mercury, goes out-of-doors, and catches cold. We say, perhaps, that the
cause of his taking cold was exposure to the air. It is clear, however,
that his having taken mercury may have been a necessary condition of
his catching cold ; and though it might consist with usage to say that the
cause of his attack was exposure to the air, to be accurate we ought to
say that the cause was exposure to the air while under the effect of mer-
cury.
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 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 as-
sent, 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 principal
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 re-
sult than that of any other person who voted in the affirmative ; but, for
the purpose we have in view, which is to insist on his individual responsi-
bility, the part which any other person had in the transaction is not ma-
terial.
In all these instances the fact which was dignified with the name of
cause, was the one condition which came last into existence. But it must
not be supposed that in the employment of the term this or any other rule
is always adhered to. Nothing can better show the absence of any scien-
tific ground for the distinction between the cause of a phenomenon and its
conditions, than the capricious manner in which we select from among the
conditions that which we choose to denominate the cause. However nu-
merous 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 analyzing the conditions of some one
familiar phenomenon. For example, a stone thrown into water falls to the
bottom. What are the conditions 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 tautol-
ogy ; and this class of conditions, therefore, have never received the name
of cause from any but the Aristotelians, by whom they were called the ma-
terial cause, 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 by
the earth ; or by a power or property of the earth, or a force exerted by the
earth, all of which are merely roundabout ways of saying 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 par-
ticularity that the motion is toward 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 dis-
tance from it, in which the earth's attraction preponderates over that of any
LAW OF CAUSATION. 239
other body. Accordingly we may say, and the expression would be con-
fessedly correct, that the cause of the stone's falling is its being icithin 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 surrounding fluid, or in
other words that it surpass in weight an equal volume of water. Accord-
ingly 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 phenomenon may be
taken in its turn, and, with equal propriety in common parlance, but with
equal impropriety in scientific discourse, may be spoken of as if it were the
entire cause. And in practice, that particular condition is usually styled
the cause, whose share in the matter is superficially the most conspicuous,
or whose requisiteness to the production of the effect we happen to be in-
sisting 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 conditions. We say, for example, The army was surprised be-
cause the sentinel was off his post. But since the sentinel's absence was
not what created the enemy, or put the soldiers asleep, how did it cause
them to be surprised ? All that is really meant is, that the event would
not have happened if he had been at his duty. His being off his post was
no producing cause, but the mere absence of a preventing cause : it was
simply equivalent to his non-existence. From nothing, from a mere nega-
tion, no consequences can proceed. All effects are connected, by the law
of causation, with some set of^osi^'ye conditions; negative ones, it is true,
being almost always required in addition. In other Mjords, every fact or
phenomenon which has a beginning, invariably arises when some certain
combination of positive facts exists, provided certain other positive facts
do not exist.
There is, no doubt, a tendency (which our first example, that of death
from taking a particular food, sufficiently illustrates) to associate the idea
of causation with the pi'oximate 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 condi-
tions 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 any thing 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 a 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 constituting at each successive instant a fresh
fact, simultaneous with, or only immediately preceding, the effect. Inas-
much as the coming of the circumstance which completes the assemblage
of conditions, is a change or event, it thence happens that an event is al-
ways the antecedent in closest apparent proximity to the consequent : and
this may account for the illusion which disposes us to look upon the prox-
imate 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 prox-
imity 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
240 INDUCTION.
which notion, on the contrary, any one of the conditions, either positive or
negative, is found, on occasion, completely to accord.*
* The assertion, that any and every one of the conditions of a phenomenon may he and is, on
some occasions and for some purposes, spoken of as the cause, has been disputed by an intel-
ligent reviewer of this work in the Pn>spvctire Review (the predecessor of the justly esteemed
National Review}, who maintains that ''we always apply the word cause rather to that ele-
ment in the antecedents which exercises force, and which would tend at all times to produce
the same or a similar effect to that which, under certain conditions, it would actually pro-
duce.'' And he says, that "every one would feel" the expression, that the cause of a surprise
was the sentinel's being 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
which would have prevented the surprise." 1 can not think that it would be wrong to say,
that the event took place because the sentinel was absent, and yet right to say that it took
place 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 occasion could never arise for so speaking of it ; for
when in the inaccuracy of common 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 possi-
ble that the hearer may require to be informed of. The possession of bodily organs is a
known condition, and to give that as the answer, when asked the cause of a person's death,
would not supply the information sought. Once conceive that a doubt could exist as to his
having bodily organs, or 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, and 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 hook, that
a man lias time for it, which is a necessary condition." These conditions (besides that they
are antecedent states, and not proximate antecedent events, and are therefore never the con-
ditions in closest apparent proximity to the effect) are all of them so obviously implied, that it
is hardly possible there should exist that necessity for insisting on them, which alone gives
occasion for speaking of a single condition as if it were the cause. Wherever this necessity
exists 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 condition. If the only condition which can be supposed to be unknown is
a negative 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, un-
less the person was already understood to be ill, and in order to indicate that this negative cir-
cumstance 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 im-
plied in the word drowned. And here let 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 oth-
er negative, it would be felt that neither of them was sufficient, without the other, to produce
death.
With regard to the assertion that nothing is termed the cause, except the element which
exerts active force ; I waive the question as to the meaning of active force, and accepting the
phrase in its popular sense, I revert to a former example, and I ask, would it be more agree-
able 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 suf-
ficiently careful : but few people, I suppose, would say, that he stumbled because he walked.
Yet the only active force concerned was that which he exerted in walking : the others were
LAW OF CAUSATION. 241
The cause, then, philosophically speaking, is the sum total of the condi-
tions, positive and negative taken together ; the whole of the contingencies
of every description, which being realized, the consequent invariably fol-
lows. The negative 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 counteracting
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 (as mathe-
maticians know) the same quantity of effect, as it does in its ordinary op-
eration of causing the fall of bodies when simply deprived of their support.
If an alkaline solution mixed with an acid destroys its sourness, and pre-
vents 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 the general axiom that all causes are liable to be counteracted
in their effects by one another, to dispense with the consideration of nega-
tive conditions entirely, and limit the notion of cause to the assemblage of
the positive conditions of the phenomenon : one negative condition invaria-
bly understood, and the same in all instances (namely, the absence of coun-
teracting causes) being sufficient, along with the sum of the positive condi-
tions, to make up the whole set of circumstances on which the phenomenon
is dependent.
4. Among the positive conditions, as we have seen that there are some
mere negative conditions ; but they happened to be the only ones which there could be any
necessity to state; for he walked, most likely, in exactly his usual manner, and the nega-
tive 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 Air.
Baden Powell, the opening of flood-gates is said to be the cause of the flow of water ; yet the
active force is exerted by the water itself, and opening the flood-gates merely supplies a nega-
tive 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 condi-
tion 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 propo-
sition 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 agen-
cies were of this description, there would be no purpose served by employing the formula.
16
242 INDUCTION.
to which, in common parlance, the term cause is more readily and frequent-
ly awarded, so there are others to which it is, in ordinary circumstances,
refused. In most cases of causation a distinction is commonly drawn be-
tween something which acts, and some other thing which is acted upon ;
between an cujent and a patient. Both of these, it would be universally al-
lowed, 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 ob-
ject 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 ef-
fect is spoken of, so that if it were also reckoned as part of the cause, the
seeming incongruity would 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, an occult quality of the earth) is represented
as the agent or cause. But that there is nothing fundamental in the dis-
tinction may be 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 the mere verbal incongruity. We might say that the stone moves
toward the earth by the properties of the matter composing it; and ac-
cording to this mode of presenting the phenomenon, the stone itself might
without impropriety be called the agent ; though, to save the established
doctrine of the inactivity of matter, men usually prefer here also to ascribe
the effect to an occult quality, and say that the cause is not the stone itself,
but the weight or gravitation of the stone.
Those who have contended for a radical distinction between agent and
patient, have generally conceived the agent as that which causes some state
of, or some change in the state of, another object which is called the pa-
tient. But a little reflection will show that the license we assume of speak-
ing 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 apparent explanation of phenomena), is sim-
ply 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 sen-
sible qualities, its color, hardness, shape, and the like, are in reality (as no
one lias pointed out more clearly than Brown himself) phenomena of cau-
sation, 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 arc never more active
than in the production of those phenomena in which they arc 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 pro-
duced, as the laws of the outward object. Though we call prussic acid
LAW OF CAUSATION. 243
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 ef-
fects which so rapidly terminates his sentient existence. In the process of
education, we may call the teacher the agent, and the scholar only the ma-
terial acted upon ; yet in truth all the facts which pre-existed in the schol-
ar'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 proportion, 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 contribute, in the same manner as any of the other conditions, to the
production of the effect of which they are vulgarly treated as the mere the-
atre. All the positive conditions of a phenomenon are alike agents, alike
active ; and in any expression of the cause which professes to be complete,
none of them can with reason be excluded, except such as have already
been implied in the words used for describing the effect; nor by including
even these would there be incurred any but a merely verbal impropriety.
5. There is a case of causation which calls for separate notice, as it
possesses a peculiar feature, and presents a greater degree of complexity
than the common case. It often happens that the effect, or one of the ef-
fects, of a cause, is, not to produce of itself a certain phenomenon, but to
fit something else for producing it. In other words, there is a case of cau-
sation in which the effect is to invest an object with a certain property.
When sulphur, charcoal, and nitre are put together in certain proportions
and in a certain manner, the effect is, not an explosion, but that the mixture
acquires a property by which, in given circumstances, it will explode. The
various causes, natural and artificial, which educate the human body or the
human mind, have for their principal effect, not to make the body or mind
immediately do any thing, but to endow it with certain properties in oth-
er words, to give assurance that in given circumstances certain results will
take place in it, or as consequences of it. Physiological agencies often
have for the chief part of their operation to predispose the constitution to
some mode of action. To take a simpler instance than all these : putting
a coat of white paint upon a wall does not merely produce in those who
see it done, the sensation of white ; it confers on the wall the permanent
property of giving that kind of sensation. Regarded in reference to the
sensation, the putting on of the paint is a condition of a condition ; it is a
condition of the wall's causing that particular fact. The wall may have
been painted years ago, but it has acquired a property which has lasted till
now, and will last longer; the antecedent condition necessary to enable the
wall to become in its turn a condition, has been fulfilled once for all. In a
case like this, where the immediate consequent in the sequence is a proper-
ty produced in an object, no one now supposes the property to be a sub-
stantive entity " inherent " in the object. What has been produced is what,
in other language, may be called a state of preparation in an object for pro-
ducing an effect. The ingredients of the gunpowder have been brought into
a state of preparation for exploding as soon as the other conditions of an
explosion shall have occurred. In the case of the gunpowder, this state of
preparation consists in a certain collocation of its particles relatively to one
another. In the example of the wall, it consists in a new collocation of two
>44 INDUCTION.
things relatively to each other the wall and the paint. In the example of
the molding influences on the human mind, its being a collocation at all is
only conjectural; for, even on the materialistic hypothesis, it would remain
to be proved that the increased facility with which the brain sums up a
column of figures when it has been long trained to calculation, is the result
of a permanent new arrangement of some of its material particles. We
must, therefore, content ourselves with what we know, and must include
among the effects of causes, the capacities given to objects of being causes
of other effects. This capacity is not a real thing existing in the objects ;
it is but a name for our conviction that they will act in a particular man-
ner when certain new circumstances arise. We may invest this assurance
of future events with a fictitious objective existence, by calling it a state of
the object. But unless the state consists, as in the case of the gunpowder
it does, in a collocation of particles, it expresses no present fact; it is but
the contingent future fact brought back under another name.
It may be thought that this form of causation requires us to admit an
exception to the doctrine that the conditions of a phenomenon the ante-
cedents required for calling it into existence must all be found among the
facts immediately, not remotely, preceding its commencement. But what
we have arrived at is not a correction, it is only an explanation, of that doc-
trine. In the enumeration of the conditions required for the occurrence of
any phenomenon, it always has to be included that objects must be present,
possessed of given properties. It is a condition of the phenomenon explo-
sion that an object should be present, of one or other of certain kinds,
which for that reason are called explosive. The presence of one of these
objects is a condition immediately precedent to the explosion. The condi-
tion which is not immediately precedent is the cause which produced, not
the explosion, but the explosive property. The conditions of the explosion
itself were all present immediately before it took place, and the general law,
therefore, remains intact.
6. It now remains to advert to a distinction which is of first-rate im-
portance both for clearing up the notion of cause, and for obviating a very
specious objection often made against the view which we have taken of the
subject.
When we define the cause of any thing (in the only sense in which the
present inquiry has any concern with causes) to be "the antecedent which
it invariably follows," we do not use this phrase as exactly synonymous
with " the antecedent which it invariably Jins followed in our past expe-
rience." Such a mode of conceiving causation would be liable to the ob-
jection very plausibly urged by Dr. Reid, namely, that according to this
doctrine night must be the cause of day, and day the cause of night; since
these phenomena have invariably succeeded one another from the begin-
ning of the world. But it is necessary to our using the word cause, that
we should believe not only that the antecedent always Juts been followed by
the consequent, but that, as long as the present constitution of things* en-
dures, 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 imaginable
circumstances, but only that it will be so provided the sun rises above the
* I mean by this expression, the ultimate laws of nature (whatever they may be) as distin-
guished from the derivative laws and from the collocations. The diurnal revolution of the
earth (for example) is not a part of the constitution of things, because nothing can be so called
which might possibly be terminated or altered by natural causes.
LAW OF CAUSATION. 245
horizon. If the sun ceased to rise, which, for aught we know, may be per-
fectly 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 properties of matter, this combination of
antecedents will be followed by the consequent, day ; that if the combina-
tion 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 line* 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
involves the idea of necessity. If there be any meaning which confessedly
belongs to the term necessity, it is unconditionalness. That which is nec-
essary, 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 oc-
currence 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 phe-
nomenon took place without it.
Invariable sequence, therefore, is not synonymous with causation, unless
the sequence, besides being invariable, is unconditional. There are se-
quences, as uniform in past experience as any others whatever, which yet
we do not regard as cases of causation, but as conjunctions in some sort
accidental. Such, to an accurate thinker, is that of day and night. The one
might have existed for any length of time, and the other not have followed
the sooner for its existence ; it follows only if certain other 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 gen-
eral 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 ante-
cedent, 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 "unconditional-
ly," 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 ex-
perience can give in any case, for recognizing the two phenomena as cause
and effect ; and that to say that more is necessary to require a belief that
the succession is unconditional, or, in other words, that it would be invari-
able under all changes of circumstances, is to acknowledge in causation an
* I use the words "straight line" for brevity and simplicity. In reality the line in question
is not exactly straight, for, from the eft'ect 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.
240 INDUCTION.
element of belief not derived from experience. The answer to this is, that
it is experience itself which teaches us that one uniformity of sequence is
conditional and another unconditional. When we judge that the succes-
sion of night and day is a derivative sequence, depending on something
else, we proceed on grounds of experience. It is the evidence of experi-
ence which convinces us that day could equally exist without being fol-
lowed by night, and that night could equally exist without being followed
by day. To say that these beliefs are "not generated by our mere ob-
servation of sequence,"* is to forget that twice in every twenty-four hours,
when the sky is clear, we have an experimentum crucia 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 antecedent which is only conditionally invariable, is not the in-
variable 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 cor-
rectly represent all possible cases, the hitherto invariable antecedent is not
accounted the cause; but why? Because we are not sure that it is the in-
variable antecedent.
Such cases of sequence as that of day and night not only do not contra-
dict the doctrine which resolves causation into invariable sequence, but are
necessarily implied in that doctrine. It is evident, that from a limited
number of unconditional sequences, there will result a much greater num-
ber of conditional ones. Certain causes being given, that is, certain ante-
cedents which are unconditionally followed by certain consequents; the
mere co-existence of these causes will give rise to an unlimited number
of additional uniformities. If two causes exist together, the effects of both
will exist together; and if many causes co-exist, these causes (by what we
shall term hereafter the intermixture of their laws) will give rise to new ef-
fects, accompanying or succeeding one another in some particular order,
which order will be invariable while the causes continue to co-exist, but no
longer. The motion of the earth in a given orbit round the sun, is a scries
of changes which follow one another as antecedents and consequents, and
will continue to do so while the sun's attraction, and the force with which
the earth tends to advance in a direct line through space, continue to co-
exist in the same 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 invari-
able within the limits of human experience, is not a case of causation. It
is not unconditional.
This distinction between the relations of succession which, so far as we
know, are unconditional, and those relations, whether of succession or of
co-existence, which, like the earth's motions, or the succession of day and
night, depend on the existence or on the co-existence of other antecedent
facts corresponds to the great division which Dr. Whewell and other
writers have made of the field of science, into the investigation of what
* Second Burnett Prize Essay, by I'rincipul Tulloch. p. 25.
LAW OF CAUSATION. 247
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 M. Comte, limit the sphere of scientific investigation to Laws of Phe-
nomena, and speak of the inquiry into causes as vain and futile. The
causes which M. Comte designates as inaccessible, 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 desig-
nate 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 involves, or needs involve, no particular theory." To
which it may be added, that by rejecting this form of expression, M. Comte
leaves himself without any term for marking a distinction which, however
incorrectly expressed, is not only real, but is one of the fundamental dis-
tinctions 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 de-
scription is not one of the many benefits which the philosophy of Induction
has received from M. Comte's great powers.
7. Does a cause always stand with its effect in the relation of anteced-
ent 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 produced, the two
things do very generally co-exist; 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 causd
cessat et effectus, has been a dogma of the schools : the necessity for the
continued existence of the cause in order to the continuance of the effect,
seems to have been once a generally received doctrine. Kepler's numerous
attempts to account for the motions of the heavenly bodies on mechanical
principles, were rendered abortive by his always supposing that the agency
which set those bodies in motion must continue to operate in order to keep
up the motion which it at first produced. Yet there were at all times
many familiar instances of the continuance of effects, long after their causes
had ceased. A coup de soleil gives a person brain-fever : will the fever go
off as soon as he is moved out of the sunshine ? A sword is run through
his body : must the sword remain in his body in order that he may con-
tinue dead ? A plowshare once made, remains a plowshare, without any
continuance of heating and hammering, and even after the man who heat-
ed and hammered it has been gathered to his fathers. On the other hand,
the pressure which forces up the merqury in an exhausted tube must be
* Letters on the Philosophy of the Human Mind, First Series, p. 219.
JIS INDUCTION.
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 illumination which
the sun diffuses over the earth ceases when the sun goes down.
There is, therefore, a distinction to be drawn. The conditions which are
necessary for the tirst production of a phenomenon, are occasionally also
necessary for its continuance ; though more commonly its continuance re-
quires no condition except negative ones. Most things, once produced, con-
tinue as they are, until something changes or destroys them ; but some re-
quire the permanent presence of the agencies which produced them at first.
These may, if we please, be considered as instantaneous phenomena, re-
quiring to be renewed at each instant by the cause by which they were at
first generated. Accordingly, the illumination of any given point of space
has always been looked upon as an instantaneous fact, which perishes and
is perpetually renewed as long as the necessary conditions subsist. If we
adopt this language we avoid the necessity of admitting that the continu-
ance 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 coun-
teract 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 those 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 in-
stant, the production of the effect (a question raised and argued with much
ingenuity by Sir John Herschcl 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 perceptible by our faculties ;
and when there is an interval, we can not tell by how many intermediate
links imperceptible to us that inverval may really be tilled 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. Wheth-
er the cause and its effect be necessarily successive or not, the begin-
ning of a phenomenon is what implies a cause, and causation is the law of
the succession of phenomena. 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 phenom-
enon invariably commences, or has its origin. Whether the effect coin-
cides 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 d9tibt, between two co-existent phenomena, which is cause and
which effect, we rightly deem the question solved if we can ascertain which
of them preceded the other.
8. It continually happens that several different phenomena, 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
* Essays, pp. 200-208.
LAW OF CAUSATION. 249
sorts of effects quite heterogeneous, but which go on simultaneously one
with another ; provided, of course, that all other conditions requisite for
each of them also exist. Thus, the sun produces the celestial motions ; it
produces daylight, and it produces heat. The earth causes the fall of heavy
bodies, and it also, in its capacity of a great magnet, causes the phenomena
of the magnetic needle. A crystal of galena causes the sensations of hard-
ness, of weight, of cubical form, of gray color, and many others between
which we can trace no interdependence. The purpose to which the phrase-
ology of Properties and Powers is specially adapted, is the expression of
this sort of cases. When the same phenomenon is followed (either sub-
ject 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 pro-
duced by a different property of the cause. Thus we distinguish the at-
tractive or gravitative property of the earth, and its magnetic property :
the gravitative, lurniniferous, and calorific properties of the sun : the color,
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 connection between the differ-
ent effects produced and the object which produces them, they are a very
powerful instrument of abridgment, and of that acceleration of the proc-
ess 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 in-
definite and probably an enormous length of time previous. The sun, the
earth, and planets, with their various constituents, air, water, and other dis-
tinguishable substances, whether simple or 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 begin-
ning of our experience. But we can give no account of the origin of the
Permanent Causes themselves. Why these particular natural agents ex-
isted 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 can not answer. More than this : we can discover
nothing regular in the distribution itself; we can reduce it to no xiniformi-
ty, 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 simi-
lar distribution prevails in another. The co-existence, therefore, of Prime-
val Causes ranks, to us, among merely casual concurrences : and all those
sequences or co-existences among the effects of several such causes, which,
though invariable while those causes co-exist, would, if the co-existence ter-
minated, terminate along with it, we do not class as cases of causation, or
laws of nature : we can only calculate on finding these sequences or co-ex-
istences Avhere 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 some-
times 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 sue-
250 INDUCTION.
cession of clay and night, the ebb and flow of the sea, and many other ef-
fects, while, as we can assign no cause (except conjecturally) for the rota-
tion itself, it is entitled to be ranked as a primeval cause. It is, however,
only the oriyiu of the rotation which is mysterious to us : once begun, its
continuance is accounted for by the first law of motion (that of the perma-
nence of rectilinear motion once impressed) combined with the gravitation
of the parts of the earth toward one another.
All phenomena- without exception which begin to exist, that is, all except
the primeval causes, arc effects either immediate or remote of those primi-
tive facts, or of some combination of them. There is no Thing produced,
no event happening, in the known universe, which is not connected by a
uniformity, or invariable sequence, with some one or more of the phenom-
ena- 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 counteracting cause shall co-exist. These antecedent phe-
nomena, again, were connected in a similar manner with some that pre-
ceded 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 neces-
sary, or, in other words, the unconditional, consequences of some former col-
location of the Permanent Causes.
The state of the whole universe at any instant, we believe to be the con-
sequence of its state at the previous instant; insomuch that one who knew
all the agents which exist at the present moment, their collocation in space,
and all their properties, in other words, the laws of their agency, could pre-
dict the whole subsequent history of the universe, at least unless some new
volition of a power capable of controlling the universe should supervene.*
And if any particular state of the entire universe could ever recur a second
time, all subsequent states would return too, and history would, like a cir-
culating decimal of many figures, periodically repeat itself:
Jam reclit et virgo. redeunt Sat urn ia regna
Alter erit turn Tiphys, et altera qua: vehat Argo
Delectos lieroas ; erunt quoque altera bella,
Atque iterum ad Trojam magnus rnittetur 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
* 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 (Hook vi. , chap. -). In the mean time, I may
remark that these metaphysicians, who, it must he observed, ground the main part of their ob-
jection on the supposed repugnance of the doctrine in question to our consciousness, seem to
me to mistake the fact which consciousness testifies against. What is really in contradiction
to consciousness, they would, I think, on strict self-examination, find to be, the application to
human actions and volitions of the ideas involved in the 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 docs act in conformity to his
character, and that anv one who thoroughly knew his character could certainly predict how he
would act in anv 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
anv one but an Asiatic titalist.
LAW OF CAUSATION. 251
whom we can suppose acquainted with the original distribution of all nat-
ural agents, and with the whole of their properties, that is, the laws of suc-
cession 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.
9. Since every thing which occurs is determined by laws of causation
and collocations of the original causes, it follows that the co-existences
which are observable among effects can not be themselves the subject of
any similar set of laws, distinct from laws of causation. Uniformities
there are, as well of co-existence as of succession, among effects ; but these
must in all cases be a mere result either of the identity or of the co-exist-
ence of their causes : if the causes did not co-exist, neither could the ef-
fects. 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 same cause) the co-existences of phenomena can in no case be univers-
al, unless the co-existences of the primeval causes to which the effects are
ultimately traceable can be reduced to a universal law : but we have seen
that they can not. There are, accordingly, no original and independent, in
other words no unconditional, uniformities of co-existence, between effects
of different causes ; if they co-exist, it is only because the causes have cas-
ually co-existed. The only independent and unconditional co- existences
which are sufficiently invariable to have any claim to the character of
laws, are between different and mutually 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 lat-
ter part of the present Book, under the name of the Specific Properties of
Kinds.
10. Since the first publication of the present treatise, the sciences of
physical nature have made a great advance in generalization, through the
doctrine known as the Conservation or Persistence of Force. This impo-
sing edifice of theory, the building and laying out of which has for some
time been the principal occupation of the most systematic minds among
physical inquirers, consists of two stages : one, of ascertained fact, the oth-
er containing a large element of hypothesis.
To begin with the first. It is proved by numerous facts, both natural
and of artificial production, that agencies which had been regarded as dis-
tinct and independent sources of force heat, electricity, chemical action,
nervous and muscular action, momentum of moving bodies are inter-
changeable, in definite and fixed quantities, with one another. It had long
been known that these dissimilar phenomena had the power, under certain
conditions, of producing one another: what is new in the theory is a more
accurate estimation of what this production consists in. What happens is,
that the whole or part of the one kind of phenomena disappears, and is re-
placed by phenomena of one of the other descriptions, and that there is an
equivalence in quantity between the phenomena that have disappeared and
those which have been produced, insomuch that if the process be reversed,
the very same quantity which had disappeared will re-appear, without in-
crease or diminution. Thus the amoimt of heat which will raise the tem-
perature of a pound of water one degree of the thermometer, will, if ex-
pended, say in the expansion of steam, lift a weight of 772 pounds one
252 INDUCTION.
foot, or a weight of one pound 772 feet: and the same exact quantity of
heat can, by certain means, be recovered, through the expenditure of exact-
ly that amount of mechanical motion.
The establishment of this comprehensive law has led to a change in the
language in which the scientific world had been accustomed to speak of
what are called the Forces of nature. Before this correlation between phe-
nomena most unlike one another had been ascertained, their unlikeness had
caused them to be referred to so many distinct forces. Now that they are
known to be convertible into one another without loss, they are spoken of
as all of them results of one and the same force, manifesting itself in dif-
ferent modes. This force (it is said) can only produce a limited and defi-
nite quantity of effect, but always does produce that definite quantity; and
produces it, according to circumstances, in one or another of the forms, or
divides it among several, but so as (according to a scale of numerical
equivalents established by experiment) always to make up the same sum;
and no one of the manifestations can be produced, save by the disappear-
ance of the equivalent quantity of another, which in its turn, in appropriate
circumstances, will re-appear undiminished. This mutual interchangeabil-
ity of the forces of nature, according to fixed numerical equivalents, is the
part of the new doctrine which rests on irrefragable fact.
To make the statement true, however, it is necessary to add, that an in-
definite and perhaps immense interval of time may elapse between the dis-
appearance of the force in one form and its re-appearance in another. A
stone thrown up into the air with a given force, and falling back immedi-
ately, will, by the time it reaches the earth, recover the exact amount of me-
chanical momentum which was expended in throwing it up, deduction be-
ing made of a small portion of motion which has been communicated to
the air. But if the stone has lodged on a height, it may not fall back for
years, or perhaps ages, and until it does, the force expended in raising it is
temporarily lost, being represented only by what, in the language of the
new theory, is called potential energy. The coal imbedded in the earth is
considered by the theory as a vast reservoir of force, which has remained
dormant for many geological periods, and will so remain until, by being
burned, it gives out the stored-up force in the form of heat. Yet it is
not supposed that this force is a material thing which can be confined by
bounds, as used to be thought of latent heat when that important phenom-
enon was first discovered. What is meant is that when the coal does at
last, by combustion, generate a quantity of heat (transformable like all oth-
er heat into mechanical momentum, and the other forms of force), this ex-
trication of heat is the re-appearance of a force derived from the sun's rays,
expended myriads of ages ago in the vegetation of the organic substances
which were the material of the coal.
Let us now pass to the higher stage of the theory of Conservation of
Force; the part which is no longer a generalization of proved fact, but a
combination of fact and hypothesis. Stated in few words, it is as follows:
That the Conservation of Force is really the Conservation of Motion ; that
in the various interchanges between the forms of force, it is always motion
that is transformed into motion. To establish this, it is necessary to as-
sume motions which are hypothetical. The supposition is, that there are
motions which manifest themselves to our senses only as heat, electricity,
etc., being molecular motions; oscillations, invisible to us, among the mi-
nute particles of bodies ; and that these molecular motions are transmutable
into molar motions (motions of masses), and molar motions into molecular.
LAW OF CAUSATION. 253
Now there is a real basis of fact for this supposition : we have positive evi-
dence of the existence of molecular motion in these manifestations of force.
In the case of chemical action, for instance, the particles separate and form
new combinations, often with a great visible disturbance of the mass. In
the case of heat, the evidence is equally conclusive, since heat expands bod-
ies (thit is, causes their particles to move from one another) ; and if of
sufficient amount, changes their mode of aggregation from solid to liquid,
or from liquid to gaseous. Again, the mechanical actions which produce
heat friction, and the collision of bodies must from the nature of the
case produce a shock, that is, an internal motion of particles, which indeed,
we find, is often so violent as to break them permanently asunder. Such
facts are thought to warrant the inference, that it is not, as was supposed,
heat that causes the motion of particles, but the motion of particles that
causes heat; the original cause of both being the previous motion (whether
molar or molecular collision of bodies or combustion of fuel) which form-
ed the heating agency. This inference already contains hypothesis ; but at
least the supposed cause, the intestine motion of molecules, is a vera causa.
But in order to reduce the Conservation of Force to Conservation of Mo-
tion, it was necessary to attribute to motion the heat propagated, through
apparently empty space, from the sun. This required the supposition
(already made for the explanation of the laws of light) of a subtle ether
pervading space, which, though impalpable to us, must have the property
which constitutes matter, that of resistance, since waves are propagated
through it by an impulse from a given point. The ether must be supposed
(a supposition not required by the theory of light) to penetrate into the
minute interstices of all bodies. The vibratory motion supposed to be tak-
ing place in the heated mass of the sun, is considered as imparted from
that mass to the particles of the surrounding ether, and through them to
the particles of the same ether in the interstices of terrestrial bodies ; and
this, too, with a sufficient mechanical force to throw the particles of those
bodies into a state of similar vibration, producing the expansion of their
mass, and the sensation of heat in sentient creatures. All this is hypothe-
sis, though, of its legitimacy as hypothesis, I do not mean to express any
doubt. It would seem to follow as a consequence from this theory, that
Force may and should be defined, matter in motion. This definition, how-
ever, will not stand, for, as has already been seen, the matter needs not be
in actual motion. It is not necessary to suppose that the motion after-
ward manifested, is actually taking place among the molecules of the coal
during its sojourn in the earth ;* certainly not in the stone which is at rest
on the eminence to which it has been raised. The true definition of Force
must be, not motion, but Potentiality of Motion ; and what the doctrine,
if established, amounts to, is, not that there is at all times the same quan-
tity of actual motion in the universe ; but that the possibilities of motion
are limited to a definite quantity, which can not be added to, but which
can not be exhausted ; and that all actual motion which takes place in Na-
ture is a draft upon this limited stock. It needs not all of it have ever ex-
isted as actual motion. There is a vast amount of potential motion in the
universe in the form of gravitation, which it would be a great abuse of
* I believe, however, the accredited authorities do suppose that molecular motion, equiva-
lent in amount to that which will be manifested in the combustion of the coal, is actually tak-
ing place during the whole of the long interval, if not in the coal, yet in the oxygen which
will then combine with it. But how purely hypothetical this supposition is, need hardly be
remarked ; I venture to say, unnecessarily and extravagantly hypothetical.
254 INDUCTION.
hypothesis to suppose to have been stored up by the expenditure of an
equal amount of actual motion in some former state of the universe. Xor
does the motion produced by gravity take place, so far as we kno\v, at the
expense of any other motion, either molar or molecular.
It is proper to consider whether the adoption of this theory as a scien-
tific truth, involving as it does a change in the conception hitherto enter-
tained of the most general physical agencies, requires any modification in
the view I have taken of Causation as a law of nature. As it appears to
me, none whatever. The manifestations which the theory regards as
modes of motion, are as much distinct and separate phenomena when re-
ferred to a single force, as when attributed to several. Whether the phe-
nomenon is called a transformation of force or the generation of one, it has
its own set or sets of antecedents, with which it is connected by invariable
and unconditional sequence; and that set, or those sets, of antecedents are
its cause. The relation of the Conservation theory to the principle of
Causation is discussed in much detail, and very instructively, by Professor
Bain, in the second volume of his Logic. The chief practical conclusion
drawn by him, bearing on Causation, is, that we must distinguish in the
assemblage of conditions which constitutes the Cause of a phenomenon,
two elements : one, the presence of a force ; the other, the collocation or
position of objects which is required in order that the force may undergo
the particular transmutation which constitutes the phenomenon. Now, it
might always have been said with acknowledged correctness, that a force
and a collocation were both of them necessary to produce any phenomenon.
The law of causation is, that change can only be produced by change.
Along with any number of stationary antecedents, which are collocations,
there must be at least one changing antecedent, which is a force. To pro-
duce a bonfire, there must not only be fuel, and air, and a spark, which are
collocations, but chemical action between the air and the materials, which
is a force. To grind corn, there must be a certain collocation of the parts
composing a mill, relatively to one another and to the corn ; but there must
also be the gravitation of water, or the motion of wind, to supply a force.
But as the force in these cases was regarded as a property of the objects
in which it is embodied, it seemed tautology to say that there must be the
collocation and the force. As the collocation must be a collocation of ob-
jects possessing the force-giving property, the collocation, so understood,
included the force.
How, then, shall we have to express these facts, if the theory be finally
substantiated that all Force is reducible to a previous Motion ? We shall
have to say, that one of the conditions of every phenomenon is an ante-
cedent Motion. But it will have to be explained that this needs not be
actual motion. The coal which supplies the force exerted in combustion
is not shown to have been exerting that force in the form of molecular
motion in the pit; it was not even exerting pressure. The stone on the
eminence is exerting a pressure, but only equivalent to its weight, not to
the additional momentum it would acquire by falling. The antecedent,
therefore, is not a force in action ; and we can still only call it a property
of the objects, by which they would exert a force on the occurrence of a
fresh collocation. The collocation, therefore, still includes the force. The
force said to be stored up, is simply a particular property which the object
has acquired. The cause we are in search of, is a collocation of objects
possessing that particular property. When, indeed, we inquire further into
the cause from which they derive that property, the new conception iutro-
LAW OF CAUSATION. 255
duced by the Conservation theory comes in : the property is itself an ef-
fect, and its cause, according to the theory, is a former motion of exactly
equivalent amount, which has been impressed on the particles of the body,
perhaps at some very distant period. But the case is simply one of those
we have already considered, in which the efficacy of a cause consists in its
investing an object with a property. The force said to be laid up, and
merely potential, is no more a really existing thing than any other proper-
ties of objects are really existing things. The expression is a mere arti-
fice of language, convenient for describing the phenomena: it is unneces-
sary to suppose that any thing has been in continuous existence except an
abstract potentiality. A force suspended in its operation, neither mani-
festing itself by motion nor by pressure, is not an existing fact, but a name
for our conviction that in appropriate circumstances a fact would take
place. We know that a pound weight, were it to fall from the earth into
the sun, would acquire in falling a momentum equal to millions of pounds ;
but we do not credit the pound weight with more of actually existing force
than is equal to the pressure it is now exerting on the earth, and that is
exactly a pound. We might as well say that a force of millions of pounds
exists in a pound, as that the force which will manifest itself when the
coal is burned is a real thing existing in the coal. What is fixed in the coal
is only a certain property : it has become fit to be the antecedent of an ef-
fect called combustion, which partly consists in giving out, under certain
conditions, a given definite quantity of heat.
We thus see that no new general conception of Causation is introduced
by the Conservation theory. The indestructibility of Force no more in-
terferes with the theory of Causation than the indestructibility of Matter,
meaning by matter the element of resistance in the sensible world. It
only enables us to understand better than before the nature and laws of
some of the sequences.
This better understanding, however, enables us, with Mr. Bain, to admit,
as one of the tests for distinguishing causation from mere concomitance,
the expenditure or transfer of energy. If the effect, or any part of the
effect, to be accounted for, consists in putting matter in motion, then any
of the objects present which has lost motion has contributed to the effect;
and this is the true meaning of the proposition that the cause is that one
of the antecedents which exerts active force.
11. It is proper in this place to advert to a rather ancient doctrine re-
specting causation, which has been revived during the last few years in
many quarters, and at present gives more signs of life than any other the-
ory of causation at variance Avith 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 causa-
tion. We know that we can move our bodies. Respecting the phenom-
ena 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 ai % e conscious of power before we have experience of re-
sults. An act of volition, whether followed by an effect or not, is ac-
companied by a consciousness of effort, "of force exerted, of power in ac-
tion, which is necessarily causal, or causative." This feeling of energy or
force, inherent in an act of will, is knowledge a priori; assurance, prior to
256 INDUCTION.
experience, that we have the power of causing effects. Volition, therefore,
it is asserted, is something more than an unconditional antecedent; 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 doctrine, that Volition is the sole Efficient Cause of all
phenomena. " It is inconceivable that dead force could continue unsup-
ported for a moment beyond its creation. We can not even conceive of
change or phenomena without the energy of a mind." "The word act ion"
itself, says another writer of the same school, " has no real significance ex-
cept when applied to the doings of an intelligent agent. Let any one con-
ceive, if he can, of any power, energy, or force inherent in a lump of mat-
ter." Phenomena may have the semblance of being produced by phys-
ical causes, but they are in reality produced, say these writers, by the im-
mediate 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 pro-
jectile 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 Ef-
ficient 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 phenom-
enal causes, belongs as much to Logic as to metaphysics, and is a fit sub-
ject for discussion here.
To my apprehension, a volition is not an efficient, but simply a physical
cause. Our will causes our bodily actions in the same sense, and in no
other, in which cold causes ice, or a spark causes an explosion of gunpow-
der. 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 intend-
ed by the theory. The antecedent, indeed, and the consequent, are sub-
jects of consciousness. But the connection between them is a subject of
experience. I can not admit that our consciousness of the volition con-
tains in itself any a priori knowledge that the muscular motion will fol-
low. If our nerves of motion were paralyzed, or our muscles stiff and in-
flexible, and had been so all our lives, I do not see the slightest ground for
supposing that we should ever (unless by information from other people)
have known any thing of volition as a physical power, or been conscious of
any tendency in feelings of our mind to produce 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 begin-
ning 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,
LAW OF CAUSATION. 257
that it " is refuted by the consideration that between the overt fact of cor-
poreal movement of which we are cognizant, and the internal act of mental
determination of which we are also cognizant, there intervenes a numerous
series of intermediate agencies of which we have no knowledge ; and, con-
sequently, that we can have no consciousness of any causal connection be-
tween the extreme links of this chain, the volition to move and the limb
moving, as this hypothesis asserts. Xo one is immediately conscious, for
example, of moving his arm through his volition. Previously to this ulti-
mate 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 conscious-
ness, absolutely nothing. A person struck with paralysis is conscious of
no inability in his limb to fulfill the determinations of his will ; and it is
only after having willed, and finding that his limbs do not obey his volition,
that he learns by this experience, that the external movement does not fol-
low the internal act. But as the paralytic learns after the volition that his
limbs do not obey his mind ; so it is only after volition that the man in
health learns, that his limbs do obey the mandates of his will."*
Those against whom I am contending have never produced, 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" 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 con-
ceptive faculty; mistaking, as I apprehend, for the laws of that faculty its
acquired habits, grounded on the spontaneous tendencies of its uncultured
state. The succession between the will to move a limb and the actual mo-
tion 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 ex-
* Lectures on Metaphysics, vol. ii., Lect. xxxix., pp. 391-2.
I regret that I can not invoke the authority of Sir William Hamilton in favor 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 com-
plete 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 contro-
verted in the sixteenth chapter of An Examination of Sir William Hamilton's Philosophy.)
t Unless we are to consider as such the following statement, by one of the writers quoted
in the text : "In the case of mental exertion, the result to be accomplished is preconsicfered
or meditated, and is therefore known a priori, or before experience." (Bowen's Lou-ell Lec-
tures on the Application of Metaphysical and Ethical Science to the Evidence of Religion..
Boston, 1849.) This is merely saying that when we will a thing we have an idea of it. But
to have an idea of what we wish to happen, does not imply a prophetic knowledge that it will,
happen. Perhaps it will be said that the first time we exerted our will, when we had of
course no experience of any of the powers residing in us, we nevertheless must already have'
known that we possessed them, since we can not will that which we do not believe to be in
our power. But the impossibility is perhaps in the words only, 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 compli-
cated 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 anv thing more than antecedence and consequence..
17
258 INDUCTION.
terior to our bodies, and especially more so than any other case of the ap-
parent origination (as distinguished from the mere communication) of mo-
tion. Now, it is the natural tendency of the mind to be always attempting
to facilitate its conception of unfamiliar facts by assimilating them to oth-
ers which are familiar. Accordingly, our voluntary acts, being the most
familiar to us of all cases of causation, are, in the infancy and early youth
of the human race, 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 oilier 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 liaynal, ' wherever they sec motion which they can not ac-
count for, there they suppose a soul.' All men may be considered as sav-
ages in this respect, until they are capable of instruction, and of using their
faculties in a more perfect manner than savages do.
"The Abbe RaynaFs 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 favor, 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 origi-
nally intended to distinguish what is really active from what is merely pas-
sive ; and in all languages, we find active verbs applied to those objects, in
which, according to the 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 mo-
tions and changes by active verbs.
" There is no surer way of tracing the sentiments of nations before they
have records, than by the structure of their language, which, 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 specula-
tion, they begin to philosophize, and soon discover, that many of those ob-
jects 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
discoveries of the same kind.
LAW OF CAUSATION. 259
"As philosophy advances, life and activity in natural 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 turn-
ed by another, that by a third ; and how far this necessary succession may
reach, the philosopher does not know."*
There is, then, a spontaneous tendency of the intellect to account to it-
self 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 voluntary agency slowly gives
way before it. The suggestions, however, of daily life continuing to be
more powerful than those of scientific thought, the original instinctive phi-
losophy maintains its ground in the mind, underneath the growths obtain-
ed by cultivation, and keeps up a constant resistance to their throwing
their roots deep into the soil. The theory against which I am contend-
ing derives its nourishment from that substratum. Its strength does not
lie in argument, but in its affinity to an obstinate tendency of the infancy
of the human mind.
That this tendency, however, is not the result of an inherent mental law,
is proved by superabundant evidence. The history of science, from its
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 affording it to
others, and even of serving as the ultimate explanation of things in gen-
eral.
One of the ablest recent supporters of the Volitional theory has furnish-
ed an explanation, at once historically true and philosophically acute, of
the failure of the Greek philosophers in physical inquiry, in Avhich, as I
conceive, he unconsciously depicts his own state of mind. " Their stum-
bling-block was one as to the nature of the evidence they had to expect
for their conviction They had not seized the idea that they must not
expect to understand the processes of outward causes, but only their re-
sults ; 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 connection, where they meant by natural
that which would per se carry some presumption to their own mind.
.... They wanted to see some reason why the physical antecedent should
produce this particular consequent, and their only attempts were in direc-
tions 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
* Reid's Essays on the Active Powers, Essay iv. , chap. 3.
t Prospective Review for February, 1850.
200 INDUCTION.
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 clear-
ly pointed out their error, thinks that lie perceives in the nature of the
phenomenon Volition. And to complete the statement of the case, lie
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 effi-
ciency, 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 persistency 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 word explanation, and which the reviewer would have us think can
only be found in referring phenomena to a will. When Thales and Hippo
held that moisture was the universal cause, and external element, of which
all other things were but the infinitely various sensible manifestations;
when Anaximenes predicated the same thing of air, Pythagoras of numbers,
and the like, they all thought that they had found a real explanation ; and
were content to rest in this explanation as ultimate. The ordinary se-
quences of the external universe appeared to them, no less than to their
critic, to be inconceivable without the supposition of some universal agen-
cy 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 in-
conceivable, and gave the same full satisfaction to the demands of their
conceptive faculty.
It was not the Greeks alone, who " wanted to see some reason why the
physical antecedent should produce this particular consequent," some con-
nection "which would per se carry some presumption to their own mind."
Among modern philosophers, Leibnitz laid it down as a self-evident prin-
ciple 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 pow-
er, and as the real bond of connection between physical antecedents and
their consequents, he demanded some naturally and per se efficient physic-
al antecedent as the bond of connection between Volition itself and its ef-
fects, lie distinctly refused to admit the will of God as a sufficient ex-
planation of, any thing except miracles; and insisted upon finding some-
thing that would account better for the phenomena of nature than a mere
reference to divine volition.*
Again, and conversely, the action of mind upon matter (which, we are
now told, not only needs no explanation itself, but is the explanation of all
other effects), has appeared to some thinkers to be itself the grand incon-
ceivability. It was to get over this very difficulty that the Cartesians in-
vented 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 couuec-
* Vide supra, p. 178, note.
LAW OF CAUSATION. 261
tion, 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 ma-
terial and a mental fact could be causes one of another. They regarded
them as mere Occasions on which the real agent, God, thought fit to exert
his power as a Cause. When a man wills to move his foot, it is not his
will that moves it, but God (they said) moves it on the occasion of his
will. God, according to this system, is the only efficient cause, not qua
mind, or qua endowed with volition, but qua omnipotent. This hypoth-
esis was, as I said, originally suggested by the supposed inconceivability
of any real mutual action between Mind and Matter ; but it was afterward
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 ultimately 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 gen-
eral, not to be satisfied with knowing that one fact is invariably anteced-
ent 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 com-
pletely satisfied by an agency purely physical, provided it be much more
familiar than that which it is invoked to explain. To Thales and Anaxim-
cnes, it appeared inconceivable that the antecedents which \ve see in nature
should produce the consequents ; but perfectly natural that water, or air,
should produce them. The writers whom I oppose declare this inconceiv-
able, but can conceive that mind, or volition, is per se an efficient cause :
while the Cartesians could not conceive even that, but peremptorily de-
clared 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 sci-
ence: that both what persons can, and what they can not, 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 inconceiv-
able 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, determine
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 ex-
planation.
By what rule is any one to decide between one theory of this descrip-
tion and another ? The theorists do not direct us- to any external evidence ;
they appeal each to his own subjective feelings. One says, the succession
C B appears to me more natural, conceivable, and credible per se, than the
succession A B ; you are therefore mistaken in thinking that B depends
upon A ; I am certain, though I can give no other evidence of it, that C
comes in between A and B, and is the real and only cause of B. The oth-
er 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
26'J INDUCTION.
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 I) theory to the C theory. It is plain that there is no universal
law operating here, except the la\v that each person's conceptions are gov-
erned and limited by his individual experiences and habits of thought.
We are warranted in saying of all three, what each of them already be-
lieves of the other two, namely, that they exalt into an original law of the
human intellect and of outward nature one particular sequence of phe-
nomena, which appears to them more natural and more conceivable than
other sequences, only because it is more familiar. And from this judg-
ment 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, and the
direct agent in producing even what is apparently produced by something
else. Volitions are not known to produce any thing directly except nerv-
ous 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 phenomenal cause, and that volition, in the case of the pe-
culiar 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 if 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 efficient 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 conclud-
ing 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 by the recently revived controversy on the old subject of Plural-
ity of Worlds, in which the contending parties have been so conspicuously
successful in overthrowing one another. Here also we have experience
only of a single case, that of the world in which we live, but that this is in-
habited we know absolutely, and without possibility of doubt. Now if on
this evidence any one were to infer that every heavenly body without ex-
ception, sun. planet, satellite, comet, fixed star or nebula, is inhabited, and
must be so from the inherent constitution of things, his inference would
exactly resemble that of the writers who conclude that because volition is
the efficient cause of our own bodily motions, it must be the efficient cause
of every thing 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 assur-
ance, 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
LAW OF CAUSATION. 263
phenomena and mine conform to tbe 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 Voli-
tion Theory ask us to infer that volition causes every thing, for no reason
except that it causes one particular thing ; although that one phenomenon,
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.
o o
NOTE SUPPLEMENTARY TO THE PRECEDING CHAPTER.
The author of the Second Burnett Prize Essay (Dr. Tulloch), who has employed a consid-
erable number of pages in controverting the doctrines of the preceding chapter, has somewhat
surprised me by denying a fact, which I imagined too well known to require proof that there
have been philosophers who found in physical explanations of phenomena the same complete
mental satisfaction which we are told is only given by volitional explanation, and others who
denied 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 counter-statement
as to the first of these cases the author shows what we believe now hardly admits of doubt
that the Greek philosophers distinctly recognized as beyond and above their priniiil material
source, the volf, or Divine Intelligence, as the efficient and originating Source of all ; and as
to the second, by proof that it was the mode, not l\\efact, 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 vovg rests on a passage of Cicero de Naturd Deorum ; and whoever will refer to any of
the accurate historians of philosophy, will find that they treat this as a mere fancy of Cicero,
resting on no authority, opposed to all the evidence ; and make surmises as to the manner in
which Cicero may have been led into the error. (See Hitter, vol. i., p. 211, 2d ed. ; Brandis,
vol. i., pp. 118-9, 1st ed. ; Preller, Historia Philosophic Grieco-RomancE, p. 10. "Schiefe
Ansicht, durchaus zu venverfen;" "augenscheinlich folgernd statt zu berichten ;" " quibus
vera sententia Thaletis plane detorquetur," are the expressions of these writers.) As for An-
nximenes, 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 a era deum statuit ;" or, ac-
cording 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 fa-
miliar with the metaphysical terminology of antiquity, must not be misled by finding it stated
that Anaximenes attributed i/w/Y') (translated soul, or life) to his universal element, the air.
The Greek philosophers acknowledged several kinds of YW;^/), the nutritive, the sensitive, and
the intellective.! Even the moderns, with admitted 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 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 contemporaries, had held the doctrine that
voi'c 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 enu-
merating 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
* Westminster Review for October, 1855.
t See the whole doctrine in Aristotle de A'nimd, where the dpex-iK?) tjjvxij IS treated as
exactly equivalent to Openrmy
264 INDUCTION.
Final Cause, he proceeds to say, that most of the early philosophers recognized only the sec-
ond kind of Cause, the Matter of a thing, rilr iv r'/.rjf eltifi fiorar <l>r/0r]aav (ipxuc eirai irurruv.
As his first example he specifies Thules, whom he describes as taking the lead in this view of
the subject, u r;/c roiairtjc upxV/" <?i/ncrooiar. and goes on to Ilippon, Anaxinienes, Dioge-
nes (of Apollonia), Hippasus of Metapontum, Ileraclitus, and Ernj)edocles. Anaxagoras.
however (he proceeds to say), taught a different doctrine, as we know, and it is a/lcyi'd that
Herinotimus of Clazomenrc taught it before him. Anaxagoras represented, that even if these
various theories of the universal material were true, there would be need of some other cause
to account for the transformations of the materials, since the material can not originate its
own changes: ov ]up <5;) TO }e vironeiftevov ai'To TTOIKI f^era3d/./.fiv iavTO' l.tyu iV oior or re
TO i-i'/.ov of'Te o \a7.Kof ahiof TOV /UEra/3a?,?.Civ inu-epov ai'Ttir, oi'(5e TTOIE'L TO fit.v fi'/or K/.ii'tji-
>'> r5t : \a/.Kbf di'dpiiii'Ta, uA/J erepov TL r/;c fiera^o/.^f O.ITIOV, viz., the other kind of cause, <>tfer
>'/ up\f/ -//<; Ktrr'/aeuf an Efficient Cause. Aristotle ex]>resses great approbation of this doc-
trine (which he says made its author appear the only sober man among persons raving, oioi>
rrjttxji' fpiivr/ Trap' eiKij /U'} 01 '~ rt f ~ou vrportpop) ; but while describing tlie influence which it ex-
ercised 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 : ovutv idvaxepuvav
tv tavTotr. It is surelv unnecessary to say more in proof of the matter of fact which Dr. Tul-
loch and his reviewer disbelieve.
Having pointed out what lie thinks the error of these early speculators in not recognizing
the need of an efficient cause, Aristotle goes on to mention two other efficient causes to which
they might have had recourse, instead of intelligence: TI'%TI, chance, and TO UVTO/LIUTOV, spon-
taneity. He indeed puts these aside as not sufficiently worthy causes for the order in the uni-
verse, ui'iV av T(I> avro/JuTCf) Kal TIJ TV^IJ Toaoi'Toi' t'~t~pK<^ai, Trpujfia K.a?M el^ev ; but he does
not reject them as incapable of producing a/n/ effect, but only as incapable of producing that
effect. He himself recognizes TI\\TJ and TO ai'TO/j.u.Tov as co-ordinate agents with Mind in pro-
ducing the phenomena of the universe; the department allotted to them being composed of
all the classes of phenomena which are not supposed to follow any uniform law. Jiy thus in-
cluding Chance among efficient causes, Aristotle fell into an error which philosophy has now
outgrown, but which is by no means so alien to the spirit even of modern 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 the results of abstraction.
Chance could make out as good a title to that dignity as many other of the mind's abstract
creations: it had had a name given to it, and why should it not be a reality? As for T<> ar-
rouuTnr, it is recognized 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 com-
pelled by its constitution to conceive volition as the origin of all force, and the efficient cause
of all phenomena.*
* It deserves notice that the parts of nature which Aristotle regards as representing evi-
dence of design, are the Uniformities : the phenomena in so far as. reducible to law. Tr\;/
and TO ai'TouuTov 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 In-
telligent Will. The common, or what may be called the instinctive, religious interpretation
of nature, is the reverse of this. The events in which men spontaneously see the hand of a
supernatural being, are those which can not, as they think, be reduced to a physical law.
What they can distinctly connect with physical causes, and especially what they can predict,
though of course ascribed to an Author of Nature, if they already recognize 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 counte-
nanced 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 /(iws of nature but in the collocations, ?. c., 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 kimU of'
matter have been so placed as to promote beneficent ends, is what lie regards at the proof of
a Divine 1'rovidcnce. Mr. Baden I'owell, in his Essay entitled "Philosophy of Creation,' 1
lias returned to the point of view of Aristotle and the ancients, and vigorously re-asserts the
doctrine that the indication of design in the universe is not special adaptations, but Uniformi-
ty and Law, these being the evidences of mind, and not what appears to us to be a provision
LAW OF CAUSATION. 265
With regard to the modem philosophers (Leibnihz and the Cartesians) whom I had cited as
having maintained that the action of mind upon matter, so far from being the only conceiva-
ble 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 read-
ing 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 Pre-established 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 a
priori; the proof and explanation in the case of contingent facts being derived from the na-
ture of their causes ; which could not be the causes unless there was something in their nature
showing them to be capable of producing those particular effects. And this "something"
which accounts for the production of phy>ical 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 producing any physical effects whatever. " On ne saurait concevoir," he says,
" une action re'ciproque dc la matiere et de 1'intelligence 1'une sur Fautre," and there is there-
fore (he contends) no choice but between the Occasional Causes of the Cartesians and his
own Pre-established Harmony, according to which there is no more connection betAveen 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 ; I did not make that mistake, though the re-
viewer 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 sys-
tem of Occasional Causes, is its principal expositor. In Part II., chap, iii., of his Sixth Book,
having first said that matter can not have the power of moving itself, he proceeds to argue
that neither can mind have the power of moving it. " Quand on examine 1'idee que Ton a de
tons les esprits finis, on ne voit point de liaison necessaire entre ler.r volonte' et le mouvement
de quelque corps que ce soit, on voit au contraire qu'il n'y en a point, et qu'il n'y en peut avoir"
(there is nothing in the idea of finite mind which can account for its causing the motion of a
body) ; "on doit aussi conclure, si on vent raisonner selon ses lumieres, qu'il n'y a aucun esprit
cre'e' qui puisse remuer quelque corps qne ce soit comme cause veritable on principale, de
meme que Ton a dit qu'aucim 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 omnipotence ; and the idea of omnipotence does con-
tain the idea of being able to move bodies. Thus it is the nature of omnipotence which ren-
ders 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 incredible. If
Malebranche had not believed in an omnipotent Being, he would have held all action of mind
on body to be a demonstrated impossibility.*
A doctrine more precisely the reverse of the Volitional theory of causation can not well be
imagined. The Volitional theory is, that we know by intuition or by direct experience the
action of our own mental volitions on matter ; that we may hence infer all other action upon
matter to be that of volition, and might thus know, without any other evidence, that matter
is under the government of a Divine Mind. Leibnitz and the Cartesians, on the contrary,
maintain that our volitions do not and can not act upon matter, and that it is only the ex-
istence of an all-governing Being, and that Being omnipotent, which can account for the se-
quence 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
for our uses. While I decline to express any opinion here on this vexata qufestio, 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 honorable contrast with the other dissertations, so far as
they have come under my notice, which have appeared on either side of that controversy.
* In the words of Fonteuelle, another celebrated Cartesian, "les philosophes anssi bien que
le peuple avaient crti que Tame et le corps agissaient reellement et physiquement l'nn sur
Fautre. Descartes vint, qui prouva que leur nature ne permettait point cette sorte de com-
munication veritable, et qu'ils n'en pouvaient avoir qu'une appareute, dont Dieu e'tait le Me'di-
ateur." ((Eurres de Fontenelle, ed. 1767, torn, v., p. 534.)
206 INDUCTION.
from one another, invokes not only as its evidence, hut as its sole evidence, the absolute in-
conceivability of any theory but itself, we are enabled to measure the worth of this kind of
evidence: and when we find the Volitional theory entirely built upon the assertion that by
our mental constitution \ve are compelled to recognize our volitions as efficient causes, and
then find other thinkers maintaining that we know that they are not and can not be such
causes, and can not conceive them to be so, I think we have a right to say that this supposed
law of our mental constitution does not exist.
Dr. Tulloch (pp. 4.">-47) thinks it a sufficient answer to this, that Leibnitz and the Cartesians
were Tlieists, 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.
Tulloch mistakes the nature of the question. I was not writing on Theism, as Dr. Tulloch
is, but against a particular theory of causation, which, if it be unfounded, can give no effect-
ive support to Theism or to any thing else. I found it asserted that volition is the only ef-
ficient cause, on the ground that no other efficient cause is conceivable. To this assertion I
oppose the instances of Leibnitz and of the Cartesians, who affirmed with equal positiveness
that volition as an efficient cause is itself not conceivable, and that omnipotence, which ren-
ders all things conceivable, can alone take away the impossibility. This 1 thought, and think,
a conclusive answer to the argument on which this theory of causation avowedly depends.
But 1 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
thev held the theorv.
CHAPTER VI.
OX 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 dis-
tinction still remains to be pointed out: a distinction so radical, and of so
much importance, as to require a chapter to itself.
The preceding discussions have rendered us familiar with the case in
which several agents, or causes, concur as conditions 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 followed, 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 a priori, at a correct pre-
diction of what will arise from their conjunct agency. To render this pos-
sible, 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 call-
ed mechanical, namely the phenomena of the communication 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 speak-
ing, defeats or 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 exact-
ly 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
COMPOSITION OF CAUSES. 267
upon first by one of the two forces, and afterward 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 combination of two substances produces, as
is well known, a third substance, with properties different from those of
either of the two substances separately, or of 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 color of blue vitriol a mixture of the colors of sulphuric
acid and copper. This explains why mechanics is a deductive or demon-
strative science, and chemistry not. In the one, we can compute the ef-
fects of combinations of causes, whether real or hypothetical, from the
laws which we know to govern those causes when acting separately, be-
cause they continue to observe the same laws when in combination which
they observe when separate : whatever would have happened in conse-
quence 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 conform 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 from any new com-
bination 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 extraordinary 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 themselves 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 AVC
might imagine our knowledge of the properties of the severaTingredients
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, fibrine, 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, un-
less gelatine or fibrine 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 gunpowder tends to project a bullet
toward the sky, while its gravity tends to make it fall to the ground. A
268 INDUCTION.
stream running into a reservoir at one end tends to -fill it higher and high-
er, while a drain at the other extremity tends to empty it. Now, in such
cases as these, even if the t\vo causes which are in joint action exactly an-
nul one another, still the laws of both are fulfilled; the effect is the same
as if the drain had been open for half an hour first,* and the stream had
flowed in for as long afterward. Each agent produces 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 operations an effect
which at first seems quite dissimilar to those which they produce separate-
ly, but which on examination proves to be really the sum of those separate
effects. It will be noticed that we here enlarge the idea of the sum of two
effects, so as to include what is commonly called their difference, but which
is in reality the result of the addition of opposites; a conception to which
mankind are indebted for that admirable extension of the algebraical cal-
culus, which has so vastly increased its powers as an instrument of discov-
ery, by introducing into its reasonings (with the sign of subtraction pre-
fixed, and under the name of Negative Quantities) every description what-
ever of positive phenomena, provided they are of such a quality in reference
to those previously introduced, that to add the one is equivalent to sub-
tracting an equal quantity of the other.
There is, then, one mode of the mutual interference of laws of nature, in
which, even when the concurrent causes annihilate each other's effects, each
exerts its full efficacy according to its own law its law as a separate agent.
But in the other description of cases, the agencies which are brought to-
gether cease entirely, and a totally different set of phenomena arise : as in
the experiment of two liquids which, when mixed in certain proportions,
instantly become, not a larger amount of liquid, but a solid mass.
2. This difference between the case in which the joint effect of causes
is the sum of their separate effects, and the case in which it is heteroge-
neous to them between laws which work together without alteration, and
laws which, when called upon to work together, cease and give place to oth-
ers is one of the fundamental distinctions in nature. The former case,
that of the Composition of Causes, is the general one; the other is always
special and exceptional. There are no objects which do not, as to some of
their phenomena, obey the principle of the Composition of Causes; none
that have not some laws which are rigidly fulfilled in every 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 elements or of the compound will vary, if they be carried far-
ther from their centre of attraction, or brought nearer to it ; but whatever
effects the one effects 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 physi-
ological or vital properties in addition. Those bodies continue, as before,
* 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
ihu conditions of that diminution of pressure do not arise.
COMPOSITION OF CAUSES. 26&
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 sepa-
rate operation of the causes, the new laws, while they supersede one portion
of the previous laws, may co-exist with another portion, and may even com-
pound 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 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 commence when these elementary
agents are brought together into some moderate number of not very com-
plex combinations. 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 combi-
nations, 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 innu-
merable 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 circumstances to encourage
the hope that such general laws will hereafter be discovered. The differ-
ent 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 en-
able us to foresee the sort of compound which will result from a new com-
bination before we have actually tried it, and to judge of what sort of el-
ements some new substance is compounded before we have analyzed 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 second-
ary aspect, that of quantity; and in. respect to quality, we have already
some partial generalizations, sufficient to indicate the possibility of ulti-
mately proceeding 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
270 INDUCTION.
which result produce nn 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 substances 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 ; and in chemis-
try, 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 per-
haps destined one day to be rendered deductive.
It would seem, therefore, that there is no class of phenomena in which
the Composition of Causes does not obtain: that as a general rule, causes
in combination produce exactly the same effects as when acting singly : but
that this rule, though general, is not universal: that in some instances, at
some particular points in the 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 composition, to an
indefinite extent, like the laws which they superseded.
3. That effects are proportional to their causes is laid down by some
writers as an axiom in the theory of causation; and great use is sometimes
made of this principle in reasonings respecting the laws of nature, though it
is encumbered with many difficulties and apparent exceptions, which much
ingenuity has been expended in showing not to be real ones. This propo-
sition, 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 in-
clined plane, a force equal to two hundred weight will raise two bodies ex-
actly 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 sepa-
rately raise the two bodies in question? The fact, therefore, that when ex-
erted jointly they raise both bodies at once, results from the Composition
of Causes, and is a mere instance of the general fact that mechanical forces
are subject to the law of Composition. And so in every other case which
can be supposed. For the doctrine of the proportionality of effects to their
causes can not of course be applicable to cases in which the augmentation
of the cause alters the kind of effect; that is, in which the surplus quanti-
ty 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, and a triple quantity decomposes it:
these three effects being heterogeneous, no ratio, whether corresponding
* Professor Bain adds several other well-established chemical generalizations: "The laws
that simple substances exhibit the strongest affinities; that compounds arc more fusible than
their elements; that combination tends to a lower state of matter from gas down to solid;"
and some general propositions concerning the circumstances which facilitate or resist chem-
ical combination. (Logic, ii., 2,">4.)
COMPOSITION OF CAUSES. 271
or not to that of the quantities of heat applied, can be established between
them. Thus the supposed axiom of the proportionality of effects to their
causes fails at the precise point where the principle of the Composition of
Causes also fails; viz., where the concurrence of causes is such as to deter-
mine a change in the properties of the body generally, and render it sub-
ject to new laws, more or less dissimilar to those to which it conformed in
its previous state. The recognition, therefore, of any such law of propor-
tionality is superseded by the more comprehensive principle, in which as
much of it as is true is implicitly asserted.*
The general remarks on causation, which seemed necessary as an intro-
duction to the theory of the inductive process, may here terminate. That
process is essentially an inquiry into cases of causation. All the uniformi-
ties which exist in the succession of phenomena, and most of the uniformi-
ties in their co-existence, 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 determine what causes are correct-
ly assigned to what effects, and what effects to what causes, we should be
virtually acquainted with the whole course of nature. All those uniformi-
ties which are mere results of causation might then be explained and ac-
counted for; and every individual fact or event might be predicted, pro-
vided we had the requisite data, that is, the requisite knowledge of the cir-
cumstances which, in the particular instance, preceded it.
To ascertain, therefore, what are the laws of causation which exist in na-
ture ; 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.
* Professor Bain (Logic, ii., 39) points out a class of cases, other than that spoken of in
the text, which he thinks must be regarded as an exception to the Composition of Causes.
"Causes that merely make good the collocation for bringing a prime mover into action, or
that release a potential force, do not follow any such rule. One man may direct a gun upon
a fort as well as three : two sparks are not more effectual than one in exploding a barrel of
gunpowder. In medicine there is a certain dose that answers the end ; and adding to it does
no more good."
I am not sure that these cases are really exceptions. The law of Composition of Causes, I
think, is really fulfilled, and the appearance to the contrary is produced by attending to the
-remote instead of the immediate effect of the causes. In the cases mentioned, the immedi-
ate effect of the causes in action is a collocation, and the duplication of the cause does double
the quantity of collocation. Two men could raise the gun to the required angle twice as
quickly as one, though one is enough. Two sparks put two sets of particles of the gunpow-
der into the state of intestine motion which makes them explode, though one is sufficient. It
is the collocation itself that does not, by being doubled, always double the effect ; because in
many cases a certain collocation, once obtained, is all that is required for the production of
the whole amount of effect which can be produced at all at the given time and place. Dou-
bling the collocation with difference of time and place, as by pointing two guns, or exploding
a second barrel after the first, does double the effect. This remark applies still more to Mr.
Bain's third example, that of a double dose of medicine ; for a double dose of an aperient
does purge more violently, and a double dose of laudanum does produce longer and sounder
sleep. But a double purging, or a double amount of narcotism, may have remote effects dif-
ferent in kind from the effect of the smaller amount, reducing the case to that of heteropathic
laws, discussed in the text.
272 INDUCTION.
CHAPTER vii.
CF OBSERVATION" AXD EXPERIMENT.
1. IT results from the preceding exposition, that the process of ascer-
taining what consequents, in nature, are invariably 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
in some fact or concourse of facts which immediately preceded the occur-
rence, 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 :v great sequence,
which we know to be uniform. If the whole prior state of the entire uni-
verse 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 an-
tecedent 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 indispensa-
ble lirst 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 choas into single facts. We must learn to see in the chaotic ante-
cedent a multitude of distinct antecedents, in the chaotic consequent a mul-
titude of distinct consequents. This, supposing it done, will not of itself
tell us on which of the antecedents each consequent is invariably attendant.
To determine that point, we must endeavor to effect a separation of the
facts from one another, not in our minds only, but in nature. The mental
analysis, however, must take place first. And every one knows that in the
mode of performing it, one intellect differs immensely from another. It is
the essence of the act of observing ; for the observer is not he who merely
sees the thing which is before his 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, confounding it with what
he imagines, or with what he infers ; another takes note of the kind of all
the circumstances, but being inexpert in estimating their degree, leaves the
quantity of eacli 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 separating 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 men-
tal culture, fit a person for being a good observer: that, however, is a
question not of Logic, but of the Theory of Education, in the most en-
larged sense of the term. There is not properly an Art of Observing.
OBSERVATION AND EXPERIMENT. 073
There may be rules for observing. 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 strength-
ening the limbs, not an art of using them.
The extent and minuteness of observation which may be 
