CHAPTER I.

Produced by David Clarke, Stephen H. Sentoff and the Online

Distributed Proofreading Team at https://www.pgdp.net (This

file was produced from images generously made available

by The Internet Archive/Canadian Libraries)

A

SYSTEM OF LOGIC

RATIOCINATIVE AND INDUCTIVE

VOL. I.

A

SYSTEM OF LOGIC

RATIOCINATIVE AND INDUCTIVE

BEING A CONNECTED VIEW OF THE

PRINCIPLES OF EVIDENCE

AND THE

METHODS OF SCIENTIFIC INVESTIGATION

BY

JOHN STUART MILL

IN TWO VOLUMES

VOL. I.

SEVENTH EDITION

LONDON:

LONGMANS, GREEN, READER, AND DYER

MDCCCLXVIII

PREFACE TO THE FIRST EDITION.

This book makes no pretence of giving to the world a new theory of the

intellectual operations. Its claim to attention, if it possess any, is

grounded on the fact that it is an attempt not to supersede, but to

embody and systematize, the best ideas which have been either

promulgated on its subject by speculative writers, or conformed to by

accurate thinkers in their scientific inquiries.

To cement together the detached fragments of a subject, never yet

treated as a whole; to harmonize the true portions of discordant

theories, by supplying the links of thought necessary to connect them,

and by disentangling them from the errors with which they are always

more or less interwoven; must necessarily require a considerable amount

of original speculation. To other originality than this, the 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 effected a revolution in the theory of the

investigation of truth, or added any fundamentally new process to the

practice of it. The improvement which remains to be effected in the

methods of philosophizing (and the author believes that they have much

need of improvement) can only consist in performing, more systematically

and accurately, operations with which, at least in their elementary

form, the human intellect in some one or other of its employments is

already familiar.

In the portion of the work which treats of Ratiocination, the author has

not deemed it necessary to enter into technical details which may be

obtained in so perfect a shape from the existing treatises on what is

termed the Logic of the Schools. In the contempt entertained by many

modern philosophers for the syllogistic art, it will be seen that he by

no means participates; though the scientific theory on which its defence

is usually rested appears to him 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

distinctions which were contained in the old Logic, have been gradually

omitted from the writings of its later teachers; and it appeared

desirable both to revive these, and to reform and 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 Assertions, 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

generalizing the modes of investigating truth and estimating evidence,

by which so many important and recondite laws of nature have, in the

various sciences, been aggregated to the stock of human knowledge. That

this is not a task free from difficulty may be presumed from the fact,

that even at a very recent period, eminent writers (among whom it is

sufficient to name Archbishop Whately, and the author of a celebrated

article on Bacon in the _Edinburgh Review_) have not scrupled to

pronounce it impossible.[1] The author has endeavoured to combat their

theory in the manner in which Diogenes confuted the sceptical reasonings

against the possibility of motion; remembering that Diogenes' argument

would have been equally conclusive, though his individual perambulations

might not have extended beyond the circuit of his own tub.

Whatever may be the value of what the author has succeeded in effecting

on this branch of his 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 science, which have been published within the last few

years. To these treatises, and to their authors, he has endeavoured to

do justice in the body of the work. But as with one of these writers,

Dr. Whewell, he has occasion frequently to express differences of

opinion, it is more particularly incumbent on him in this place to

declare, that without the aid derived from the facts and ideas contained

in that gentleman's _History of the Inductive Sciences_, the

corresponding portion of this work would probably not have been written.

The concluding Book is an attempt to contribute towards the solution of

a question, which the decay of old opinions, and the agitation that

disturbs 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 social phenomena are really exceptions to the general

certainty and uniformity of the course of nature; and how far the

methods, by which so many of the laws of the physical world have been

numbered among truths irrevocably acquired and universally assented to,

can be made instrumental to the formation of a similar body of received

doctrine in moral and political science.

PREFACE TO THE THIRD AND FOURTH EDITIONS.

Several criticisms, of a more or less controversial character, on this

work, have appeared since the publication of the second edition; and Dr.

Whewell has lately published a reply to those parts of it in which some

of his opinions were controverted.[2]

I have carefully reconsidered all the points on which my conclusions

have been assailed. But I have not to announce a change of opinion on

any matter of importance. Such minor oversights as have been detected,

either by myself or by my critics, I have, in general silently,

corrected: but it is not to be inferred that I agree with the objections

which have been made to a passage, in every instance in which I have

altered or cancelled it. I have often done so, merely that it might not

remain a stumbling-block, when the amount of 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 favourable for

placing my own conclusions, and the grounds of them, more clearly and

completely before the reader. Truth, on these subjects, is militant, and

can only establish itself by means of conflict. The most opposite

opinions can make a plausible show of evidence while each has the

statement of its own case; and it is only possible to ascertain which of

them is in the right, after hearing and comparing what each can say

against the other, and what the other can urge in its defence.

Even the criticisms from which I most dissent have been of great service

to me, by showing in what places the exposition most needed to be

improved, or the argument strengthened. And I should have been well

pleased if the book had undergone a much greater amount of attack; as in

that case I should probably have been enabled to improve it still more

than I believe I have now done.

* * * * *

In the subsequent editions, the attempt to improve the work by additions

and corrections, suggested by criticism or by thought, has been

continued. In the present (seventh) edition, a few further corrections

have been made, but no material additions.

FOOTNOTES:

[1] In the later editions of Archbishop Whately's _Logic_, he states his

meaning to be, not that "rules" for the ascertainment of truths by

inductive investigation cannot be laid down, or that they may not be "of

eminent service," but that they "must always be comparatively vague and

general, and incapable of being built up into a regular demonstrative

theory like that of the Syllogism." (Book IV. ch. iv. § 3.) And he

observes, that to devise a system for this purpose, capable of being

"brought into a scientific form," would be an achievement which "he must

be more sanguine than scientific who expects." (Book IV. ch. ii. § 4.)

To effect this, 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.

[2] Now forming a chapter in his volume on _The Philosophy of

Discovery_.

CONTENTS

OF

THE FIRST VOLUME.

INTRODUCTION.

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

provisional 1

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

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

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

5. Relation of logic to the other sciences 8

6. Its utility, how shown 10

7. Definition of logic stated and illustrated 11

BOOK I.

OF NAMES AND PROPOSITIONS.

CHAPTER I. _Of the Necessity of commencing with an

Analysis of Language._

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

2. First step in the analysis of Propositions 18

3. Names must be studied before Things 21

CHAPTER II. _Of Names._

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

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

3. General and Singular names 26

4. Concrete and Abstract 29

5. Connotative and Non-connotative 31

6. Positive and Negative 42

7. Relative and Absolute 44

8. Univocal and Æquivocal 47

CHAPTER III. _Of the Things denoted by Names._

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

Categories of Aristotle 49

2. Ambiguity of the most general names 51

3. Feelings, or states of consciousness 54

4. Feelings must be distinguished from their physical

antecedents. Perceptions, what 56

5. Volitions, and Actions, what 58

6. Substance and Attribute 59

7. Body 61

8. Mind 67

9. Qualities 69

10. Relations 72

11. Resemblance 74

12. Quantity 78

13. All attributes of bodies are grounded on states of

consciousness 79

14. So also all attributes of mind 80

15. Recapitulation 81

CHAPTER IV. _Of Propositions._

§ 1. Nature and office of the copula 85

2. Affirmative and Negative propositions 87

3. Simple and Complex 89

4. Universal, Particular, and Singular 93

CHAPTER V. _Of the Import of Propositions._

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

between two ideas 96

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

meanings of two names 99

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

excluding something from, a class 103

4. What it really is 107

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

existence, a causation 110

6. --or a resemblance 112

7. Propositions of which the terms are abstract 115

CHAPTER VI. _Of Propositions merely Verbal._

§ 1. Essential and Accidental propositions 119

2. All essential propositions are identical propositions 120

3. Individuals have no essences 124

4. Real propositions, how distinguished from verbal 126

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

CHAPTER VII. _Of the Nature of Classification, and

the Five Predicables._

§ 1. Classification, how connected with Naming 129

2. The Predicables, what 131

3. Genus and Species 131

4. Kinds have a real existence in nature 134

5. Differentia 139

6. Differentiæ for general purposes, and differentiæ for

special or technical purposes 141

7. Proprium 144

8. Accidens 146

CHAPTER VIII. _Of Definition._

§ 1. A definition, what 148

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

of analysis 150

3. Complete, how distinguished from incomplete definitions 152

4. --and from descriptions 154

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

Names with an implied assumption of the existence of

Things corresponding to them 157

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

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

knowledge of the corresponding Things 167

BOOK II.

OF REASONING.

CHAPTER I. _Of Inference, or Reasoning, in general._

§ 1. Retrospect of the preceding book 175

2. Inferences improperly so called 177

3. Inferences proper, distinguished into inductions and

ratiocinations 181

CHAPTER II. _Of Ratiocination, or Syllogism._

§ 1. Analysis of the Syllogism 184

2. The _dictum de omni_ not the foundation of reasoning,

but a mere identical proposition 191

3. What is the really fundamental axiom of Ratiocination 196

4. The other form of the axiom 199

CHAPTER III. _Of the Functions, and Logical Value, of the

Syllogism._

§ 1. Is the syllogism a _petitio principii_? 202

2. Insufficiency of the common theory 203

3. All inference is from particulars to particulars 205

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

the rules of the syllogism are rules for the interpretation

of the record 214

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

6. The true type, what 222

7. Relation between Induction and Deduction 226

8. Objections answered 227

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

CHAPTER IV. _Of Trains of Reasoning, and Deductive

Sciences._

§ 1. For what purpose trains of reasoning exist 234

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

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

4. Why there are deductive sciences 240

5. Why other sciences still remain experimental 244

6. Experimental sciences may become deductive by the progress

of experiment 246

7. In what manner this usually takes place 247

CHAPTER V. _Of Demonstration, and Necessary Truths._

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

the sense of necessarily following from hypotheses 251

2. Those hypotheses are real facts with some of their

circumstances exaggerated or omitted 255

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

these are not hypothetical 256

4. --but are experimental truths 258

5. An objection answered 261

6. Dr. Whewell's opinions on axioms examined 264

CHAPTER VI. _The same Subject continued._

§ 1. All deductive sciences are inductive 281

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

but generalizations from experience 284

3. In what sense hypothetical 289

4. The characteristic property of demonstrative science is to

be hypothetical 290

5. Definition of demonstrative evidence 292

CHAPTER VII. _Examination of some Opinions opposed to

the preceding doctrines._

§ 1. Doctrine of the Universal Postulate 294

2. The test of inconceivability does not represent the

aggregate of past experience 296

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

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

Contradiction and Excluded Middle 306

BOOK III.

OF INDUCTION.

CHAPTER I. _Preliminary Observations on Induction in general._

§ 1. Importance of an Inductive Logic 313

2. The logic of science is also that of business and life 314

CHAPTER II. _Of Inductions improperly so called._

§ 1. Inductions distinguished from verbal transformations 319

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

3. --and from descriptions 323

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

5. Further illustration of the preceding remarks 336

CHAPTER III. _On the Ground of Induction._

§ 1. Axiom of the uniformity of the course of nature 341

2. Not true in every sense. Induction _per enumerationem

simplicem_ 346

3. The question of Inductive Logic stated 348

CHAPTER IV. _Of Laws of Nature._

§ 1. The general regularity in nature is a tissue of partial

regularities, called laws 351

2. Scientific induction must be grounded on previous

spontaneous inductions 355

3. Are there any inductions fitted to be a test of all others? 357

CHAPTER V. _Of the Law of Universal Causation._

§ 1. The universal law of successive phenomena is the Law of

Causation 360

2. --_i.e._ the law that every consequent has an invariable

antecedent 363

3. The cause of a phenomenon is the assemblage of its

conditions 365

4. The distinction of agent and patient illusory 373

5. The cause is not the invariable antecedent, but the

_unconditional_ invariable antecedent 375

6. Can a cause be simultaneous with its effect? 380

7. Idea of a Permanent Cause, or original natural agent 383

8. Uniformities of coexistence between effects of different

permanent causes, are not laws 386

9. Doctrine that volition is an efficient cause, examined 387

CHAPTER VI. _Of the Composition of Causes._

§ 1. Two modes of the conjunct action of causes, the mechanical

and the chemical 405

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

exceptional 408

3. Are effects proportional to their causes? 412

CHAPTER VII. _Of Observation and Experiment._

§ 1. The first step of inductive inquiry is a mental analysis of

complex phenomena into their elements 414

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

3. Advantages of experiment over observation 417

4. Advantages of observation over experiment 420

CHAPTER VIII. _Of the Four Methods of Experimental

Inquiry._

§ 1. Method of Agreement 425

2. Method of Difference 428

3. Mutual relation of these two methods 429

4. Joint Method of Agreement and Difference 433

5. Method of Residues 436

6. Method of Concomitant Variations 437

7. Limitations of this last method 443

CHAPTER IX. _Miscellaneous Examples of the Four Methods._

§ 1. Liebig's theory of metallic poisons 449

2. Theory of induced electricity 453

3. Dr. Wells' theory of dew 457

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

5. Examples of the Method of Residues 471

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

CHAPTER X. _Of Plurality of Causes; and of the Intermixture

of Effects._

§ 1. One effect may have several causes 482

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

the Method of Agreement 483

3. Plurality of Causes, how ascertained 487

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

5. Difficulties of the investigation, when causes compound

their effects 494

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

7. The method of simple observation inapplicable 500

8. The purely experimental method inapplicable 501

CHAPTER XI. _Of the Deductive Method._

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

causes by direct induction 507

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

complex cases 512

3. Third stage; verification by specific experience 514

CHAPTER XII. _Of the Explanation of Laws of Nature._

§ 1. Explanation defined 518

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 coexistence 518

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

the sequence 519

4. Laws are always resolved into laws more general than

themselves 520

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

a more general one 524

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

CHAPTER XIII. _Miscellaneous Examples of the Explanation of

Laws of Nature._

§ 1. The general theories of the sciences 529

2. Examples from chemical speculations 531

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

nervous system 533

4. Examples of following newly-discovered laws into their

complex manifestations 534

5. Examples of empirical generalizations, afterwards confirmed

and explained deductively 536

6. Example from mental science 538

7. Tendency of all the sciences to become deductive 539

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 common with logic. Almost every writer having taken a

different view of some of the particulars which these branches of

knowledge are usually understood to include; each has so framed his

definition as to indicate beforehand his own peculiar tenets, and

sometimes to beg the question in their favour.

This diversity is not so much an evil to be complained of, as an

inevitable and in some degree a proper result of the imperfect state of

those sciences. It is not to be expected that there should be agreement

about the definition of anything, until there is agreement about the

thing itself. To define, is to select from among all the properties of a

thing, those which shall be understood to be designated and declared by

its name; and the properties must be well known to us before we can be

competent to determine which of them are fittest to be chosen for this

purpose. Accordingly, in the case of so complex an aggregation of

particulars as are comprehended in anything which can be called a

science, the definition we set out with is seldom that which a more

extensive knowledge of the subject shows to be the most appropriate.

Until we know the particulars themselves, we cannot fix upon the most

correct and compact mode of circumscribing them by a general

description. It was not until after an extensive and accurate

acquaintance with the details of chemical phenomena, 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 these volumes.

§ 2. Logic has often been called the Art of Reasoning. A writer[1] who

has done more than any other person to restore this study to the rank

from which it had fallen in the estimation of the cultivated class in

our own country, has adopted the above definition with an amendment; he

has defined Logic to be the Science, as well as the Art, of reasoning;

meaning by the former term, the analysis of the mental process which

takes place whenever we reason, and by the latter, the rules, grounded

on that analysis, for conducting the process 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 every art does not bear the

name of a science, it is only because several sciences are often

necessary to form the groundwork of a single art. So complicated are the

conditions which govern our practical agency, that to enable one thing

to be _done_, it is often requisite to _know_ the nature and properties

of many things.

Logic, then, comprises the science of reasoning, as well as an art,

founded on that science. But the word Reasoning, again, like most other

scientific terms in popular use, abounds in ambiguities. In one of its

acceptations, it means syllogizing; or the mode of inference which may

be called (with sufficient accuracy for the present purpose) concluding

from generals to particulars. In another of its senses, to reason is

simply to infer any assertion, from assertions already admitted: and in

this sense induction is as much entitled to be called reasoning as the

demonstrations of geometry.

Writers on logic have generally preferred the former 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 sufficient reasons will, I believe, unfold themselves as we

advance, why this should be not only the provisional but the final

definition. It involves, at all events, no arbitrary change in the

meaning of the word; for, with the general usage of the English

language, the wider signification, I believe, accords better than the

more restricted one.

§ 3. But Reasoning, even in the widest sense of which the word is

susceptible, does not seem to 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 connexion with reasoning, and as a preparation for

the doctrine and rules of the syllogism. Yet they were treated with

greater minuteness, and dwelt on at greater length, than was required

for that purpose alone. More recent writers on logic have generally

understood the term as it was employed 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 classification: and we

perhaps oftener hear persons speak of a logical arrangement, or of

expressions logically defined, than of conclusions logically deduced

from premises. Again, a man is often called a great logician, or a man

of powerful logic, not for the 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

being ample, is well under his command for argumentative use. Whether,

therefore, we conform to the practice of those who have made the subject

their particular study, or to that of popular writers and common

discourse, the province of logic will include several operations of the

intellect not usually considered to fall within the meaning of the terms

Reasoning and Argumentation.

These various operations might be brought within the compass of the

science, and the additional advantage be obtained of a very simple

definition, if, by an extension of the term, sanctioned by high

authorities, we were to define logic as the science which treats of the

operations of the human understanding in the pursuit of truth. For to

this ultimate end, naming, classification, definition, and all other

operations over which logic has ever claimed jurisdiction, are

essentially subsidiary. They may all be regarded as contrivances for

enabling a person to know the truths which are needful to him, and to

know them at the precise moment at which they are needful. Other

purposes, indeed, are also served by these operations; for instance,

that of imparting our knowledge to others. But, viewed with regard to

this purpose, they have never been considered as within the province 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

conceived 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

little, that which is now suggested has the opposite fault of including

too much.

Truths are known to us in two ways: some are known directly, and of

themselves; some through the medium of other truths. The former are the

subject of Intuition, or Consciousness;[2] 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 which we know only by way of inference, are

occurrences which took place while we were absent, the events recorded

in history, or the theorems of mathematics. The two former we infer from

the testimony adduced, or from the traces of those past occurrences

which still exist; the latter, from the premises laid down in books of

geometry, under the title of definitions and axioms. Whatever we are

capable of knowing must belong to the one class or to 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, in the sense in which I conceive the science, nothing to do.

These questions are partly not a subject of science at all, partly that

of a very different science.

Whatever is known to us by consciousness, is known beyond possibility of

question. What one sees or feels, whether bodily or mentally, one cannot

but be sure that one sees or feels. No science is required for the

purpose of establishing such truths; no rules of art can render our

knowledge of them more certain than it is in itself. There is no logic

for this portion of our knowledge.

But we may fancy that we see or feel what we in reality infer. A truth,

or supposed truth, which is really the result of a very rapid inference,

may seem to be apprehended intuitively. It has long been agreed by

thinkers of the most opposite schools, that this mistake is actually

made in so familiar an instance as that of the eyesight. There is

nothing of which we appear to ourselves to be more directly conscious,

than the distance of an object from us. Yet it has long been

ascertained, that what is perceived by the eye, is at most nothing more

than a variously coloured surface; that when we fancy we see distance,

all we really see is certain variations of apparent size, and degrees of

faintness of colour; that our estimate of the object's distance from us

is the result partly of a rapid inference from the muscular sensations

accompanying the adjustment of the focal distance of the eye to objects

unequally remote from us, and partly of a comparison (made with so much

rapidity that we are unconscious of making it) between the size and

colour of the object as they appear at the time, and the size and colour

of the same or of similar objects as they appeared when close at hand,

or when their degree of remoteness was known by other evidence. The

perception of distance by the eye, which seems so like intuition, is

thus, in reality, an inference grounded on experience; an inference,

too, which we learn to make; and which we make with more and more

correctness as our 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

colour.[3]

Of the science, therefore, which expounds the operations of the human

understanding in the pursuit of truth, one essential part is the

inquiry: What are the facts which are the objects of intuition or

consciousness, and what are those which we merely infer? But this

inquiry has never been considered a portion of logic. Its place is in

another and a perfectly distinct department of science, to which the

name metaphysics more particularly belongs: that portion of mental

philosophy which attempts to determine what part of the furniture of the

mind belongs to it originally, and what part is constructed out of

materials furnished to it from without. To this science appertain the

great and much debated questions of the existence of matter; the

existence of spirit, and of a distinction between it and matter; the

reality of time and space, as things without the mind, and

distinguishable from the objects which are said to exist in them. For in

the present state of the discussion on these topics, it is almost

universally allowed that the existence of matter or of spirit, of space

or of time, is in its nature unsusceptible of being proved; and that if

anything is known of them, it must be by immediate intuition. To the

same science belong the inquiries into the nature of Conception,

Perception, Memory, and Belief; all of which are operations of the

understanding in the pursuit of truth; but with which, as phenomena of

the mind, or with the possibility which may or may not exist of

analysing any of them into simpler phenomena, the logician as such has

no concern. To this science must also be referred the following, and all

analogous questions: To what extent our intellectual faculties and our

emotions are innate--to what extent the result of association: Whether

God, and duty, are realities, the existence of which is manifest to us

_à priori_ by the constitution of our rational faculty; or whether our

ideas of them are acquired notions, the origin of which we are able to

trace and explain; and the reality of the objects themselves a question

not of consciousness or intuition, but of evidence and reasoning.

The province of logic must be restricted to that portion of our

knowledge which consists of inferences from truths previously known;

whether those antecedent data be general propositions, or particular

observations and perceptions. Logic is not the science of Belief, but

the science of Proof, or Evidence. In so far as belief professes to be

founded on proof, the office of logic is to supply a test for

ascertaining whether or not the belief is well grounded. With the claims

which any proposition has to belief on the evidence of consciousness,

that is, without evidence in the proper sense of the word, logic has

nothing to do.

§ 5. By far the greatest portion of our knowledge, whether of general

truths or of particular facts, being avowedly matter of inference,

nearly the whole, not only of science, but of human conduct, is amenable

to the authority of logic. To draw inferences has been said to be the

great business of life. Every one has daily, hourly, and momentary need

of 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 afterwards apply certain rules,

either devised by themselves, or prescribed for their guidance by

others; and as they do this well or ill, so they discharge well or ill

the duties of their several callings. It is the only occupation in

which the mind never ceases to be engaged; and is the subject, not of

logic, but of knowledge in general.

Logic, however, is not the same thing with knowledge, though the field

of logic is coextensive with the field of knowledge. Logic is the common

judge and arbiter of all particular investigations. It does not

undertake to find evidence, but to determine whether it has been found.

Logic neither observes, nor invents, nor discovers; but judges. It is no

part of the business of logic to inform the surgeon what appearances are

found to accompany a violent death. This he must learn from his own

experience and observation, or from that of others, his predecessors in

his peculiar pursuit. But logic sits in judgment on the sufficiency of

that observation and 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 decide whether any given fact fulfils

these conditions, or whether facts can be found which fulfil them in a

given case, belongs exclusively to the particular art or science, or to

our knowledge of the particular subject.

It is in this sense that logic is, what Bacon so expressively called it,

_ars artium_; the science of science itself. All science consists of

data and conclusions from those data, of proofs and what they prove: now

logic points out what relations must subsist between data and whatever

can be concluded from them, between proof and everything which it can

prove. If there be any such indispensable relations, and if these can be

precisely determined, every particular branch of science, as well as

every individual in the guidance of his conduct, is bound to conform to

those relations, under the penalty of making false inferences, of

drawing conclusions which are not grounded in the realities of things.

Whatever has at any time been concluded justly, whatever knowledge has

been acquired otherwise than by immediate intuition, depended on the

observance of the laws which it is the province of logic to investigate.

If the conclusions are just, and the knowledge real, those laws, whether

known or not, have been observed.

§ 6. We need not, therefore, seek any farther for a solution of the

question, so often agitated, respecting the utility of logic. If a

science of logic exists, or is capable of existing, it must be useful.

If there be rules to which every mind consciously or unconsciously

conforms in every 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 empirically in the course of their studies. Mankind judged of

evidence, and often correctly, before logic was a science, or they never

could have made it one. And they executed great mechanical works before

they understood the laws of mechanics. But there are limits both to what

mechanicians can do without principles of mechanics, and to what

thinkers can do without principles of logic. A few individuals, by

extraordinary genius, or by the accidental acquisition of a good set of

intellectual habits, may work without principles in the same way, or

nearly the same way, in which they would have worked if they had been in

possession of principles. But the bulk of mankind require either to

understand the theory of what they are doing, or to have rules laid down

for them by those who have understood the theory. In the progress of

science from its easiest to its more difficult problems, each great step

in advance has usually had either as its precursor, or as its

accompaniment and necessary condition, a corresponding improvement in

the notions and principles of logic received among the most advanced

thinkers. And if several of the more difficult sciences are still in so

defective a state; if not only so little is proved, but disputation has

not terminated even about the little which seemed to be so; the reason

perhaps is, that men's logical notions have not yet acquired the degree

of extension, or of accuracy, requisite for the estimation of the

evidence proper to those particular departments of knowledge.

§ 7. Logic, then, is the science of the operations of the understanding

which are subservient to the estimation of evidence: both the process

itself of advancing from known truths to unknown, and all other

intellectual operations in so far as auxiliary to this. It includes,

therefore, the operation of Naming; for language is an instrument of

thought, as well as a means of communicating our thoughts. It includes,

also, Definition, and Classification. For, the use of these operations

(putting all other minds than one's own out of consideration) is to

serve not only for keeping our evidences and the conclusions from them

permanent and readily accessible in the memory, but for so marshalling

the facts which we may at any time be engaged in investigating, as to

enable us to perceive more clearly what evidence there is, and to judge

with fewer chances of error whether it be sufficient. These, 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 connexion with

the problem of Evidence, further than that, like all other problems

addressed to the understanding, it presupposes them.

Our object, then, will be, to attempt a correct analysis of the

intellectual process called Reasoning or Inference, and of such other

mental operations as are intended to facilitate this; as well as, on the

foundation of this analysis, and _pari passu_ with it, to bring together

or frame a set of rules or canons for testing the sufficiency of any

given evidence to prove any given proposition.

With respect to the first part of this undertaking, I do not attempt to

decompose the mental operations in question into their ultimate

elements. It is enough if the analysis as far as it goes is correct,

and if it goes far enough for the practical purposes of logic considered

as an art. The separation of a complicated phenomenon into its component

parts is not like a connected and interdependent chain of proof. If one

link of an argument breaks, the whole drops to the ground; but one step

towards an analysis holds good and has an 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 elements themselves admit of decomposition, is an

important inquiry, but does not affect the certainty of the science up

to that point.

I shall, accordingly, attempt to analyse the process of inference, and

the processes subordinate to inference, so far only as may be requisite

for ascertaining the difference between a correct and an incorrect

performance of those processes. The reason for thus limiting our design,

is evident. It has been said by objectors to logic, that we do not learn

to use our muscles by studying their anatomy. The fact is not quite

fairly stated; for if the action of any of our muscles were vitiated by

local weakness, or other physical defect, a knowledge of their anatomy

might be very necessary for effecting a cure. But we should be justly

liable to the criticism involved in this objection, were we, in a

treatise on logic, to carry the analysis of the reasoning process beyond

the point at which any inaccuracy which may have crept into it must

become visible. In learning bodily exercises (to carry on the same

illustration) we do, and must, analyse the bodily motions so far as is

necessary for distinguishing those which ought to be performed from

those which ought not. To a similar extent, and no further, it is

necessary that the logician should analyse the mental processes with

which Logic is concerned. Logic has no interest in carrying the analysis

beyond the point at which it becomes apparent whether the operations

have in any individual case been rightly or wrongly performed: in the

same manner as the science of music teaches us to discriminate between

musical notes, and to know the combinations of which they are

susceptible, but not what number of vibrations in a second correspond to

each; which, though useful to be known, is useful for totally different

purposes. The extension of Logic as a Science is determined by its

necessities as an Art: whatever it does not need for its practical ends,

it leaves to the larger science which may be said to correspond, not to

any particular art, but to art in general; the science which deals with

the constitution of the human faculties; and to which, in the part of

our mental nature which concerns Logic, as well as in all other parts,

it belongs to decide what are ultimate facts, and what are resolvable

into other facts. And I believe it will be found that most of the

conclusions arrived at in this work have no necessary connexion with any

particular views 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 cannot, indeed, be pretended that logical principles can be

altogether irrelevant to those more abstruse discussions; nor is it

possible but that the view we are led to take of the problem which logic

proposes, must have a tendency favourable to the adoption of some one

opinion, on these controverted subjects, rather than another. For

metaphysics, in endeavouring to solve its own peculiar problem, must

employ means, the validity of which falls under the cognizance of logic.

It proceeds, no doubt, as far as possible, merely by a closer and more

attentive interrogation of our consciousness, or more properly speaking,

of our memory; and so far is not amenable to logic. But wherever this

method is insufficient to attain the end of its inquiries, it must

proceed, like other sciences, by means of evidence. Now, the moment this

science begins to draw inferences from evidence, logic becomes the

sovereign judge whether its inferences are well grounded, or what other

inferences would be so.

This, however, constitutes no nearer or other relation between logic

and metaphysics, than that which exists between logic and every other

science. And I can conscientiously affirm, that no one proposition laid

down in this work has been adopted for the sake of establishing, or with

any reference to its fitness for being employed in establishing,

preconceived opinions in any department of knowledge or of inquiry on

which the speculative world is still undecided.[4]

FOOTNOTES:

[1] Archbishop Whately.

[2] I use these terms indiscriminately, because, for the purpose in

view, there is no need for making any distinction between them. But

metaphysicians usually restrict the name Intuition to the direct

knowledge we are supposed to have of things external to our minds, and

Consciousness to our knowledge of our own mental phenomena.

[3] This important theory has of late been called in question by a

writer of deserved reputation, Mr. Samuel Bailey; but I do not conceive

that the grounds on which it has been admitted as an established

doctrine for a century past, have been at all shaken by that gentleman's

objections. I have elsewhere said what appeared to me necessary in reply

to his arguments. (_Westminster Review_ for October 1842; reprinted in

_Dissertations and Discussions_, vol. ii.)

[4] The view taken in the text, of the definition and purpose of Logic,

stands in marked opposition to that of the school of philosophy which,

in this country, is represented by the writings of Sir William Hamilton

and of his numerous pupils. Logic, as this school conceives it, is "the

Science of the Formal Laws of Thought;" a definition framed for the

express purpose of excluding, as 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 1865, and entitled _An Examination of

Sir William Hamilton's Philosophy, and of the Principal Philosophical

Questions discussed in his Writings_. For the purposes of the present

Treatise, I am content that the justification of the larger extension

which I give to the domain of the science, should rest on the sequel of

the Treatise itself. Some remarks on the relation which the Logic of

Consistency bears to the Logic of Truth, and on the place which that

particular part occupies in the whole to which it belongs, will be found

in the present volume (Book II. chap. iii. § 9).

BOOK I.

OF NAMES AND PROPOSITIONS.

'La scolastique, qui produisit dans la logique, comme dans la morale,

et dans une partie de la métaphysique, une subtilité, une précision

d'idées, dont l'habitude inconnue aux anciens, a contribué plus qu'on ne

croit au progrès de la bonne philosophie.'--CONDORCET, _Vie de Turgot_.

'To the schoolmen the vulgar languages are principally indebted for what

precision and analytic subtlety they possess.'--SIR W. HAMILTON,

_Discussions in Philosophy_.

CHAPTER I.

OF THE NECESSITY OF COMMENCING WITH AN ANALYSIS OF LANGUAGE.

§ 1. It is so much the established practice of writers on logic to

commence their treatises by a few general observations (in most cases,

it is true, rather meagre) on Terms and their varieties, that it will,

perhaps, scarcely be required from me in merely following the common

usage, to be as particular in assigning my reasons, as it is usually

expected that those should be who deviate from it.

The practice, indeed, is recommended by considerations far too obvious

to require a formal justification. Logic is a portion of the Art of

Thinking: Language is evidently, and by the admission of all

philosophers, one of the principal 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 attempt the study of methods of

philosophizing, would be as if some one should attempt to become an

astronomical observer, having never learned to adjust the focal distance

of his optical instruments so as to see distinctly.

Since Reasoning, or Inference, the principal subject of logic, is an

operation which usually takes place by means of words, and in

complicated cases can take place in no other way; those who have not a

thorough insight into the signification and purposes of words, will be

under chances, amounting almost to certainty, of reasoning or inferring

incorrectly. And logicians have generally felt that unless, in the very

first stage, they removed this source of error; unless they taught their

pupil to put away the glasses which distort the object, and to use

those which are adapted to his purpose in such a manner as to assist,

not perplex, his vision; he would not be in a condition to practise the

remaining part of their discipline with any prospect of advantage.

Therefore it is that an inquiry into language, so far as is needful to

guard against the errors to which it gives rise, has at all times been

deemed a necessary preliminary to the study of logic.

But there is another reason, of a still more fundamental nature, why the

import of words should be the earliest subject of the logician's

consideration: because without it he cannot examine into the import of

Propositions. Now this is a subject which stands on the very threshold

of the science of logic.

The object of logic, as defined in the Introductory Chapter, is to

ascertain how we come by that portion of our knowledge (much the

greatest portion) which is not intuitive: and by what criterion we can,

in matters not self-evident, distinguish between things proved and

things not proved, between what is worthy and what is unworthy of

belief. Of the various questions which present themselves to our

inquiring faculties, some receive an answer from direct consciousness,

others, if resolved at all, can only be resolved by means of evidence.

Logic is concerned with these last. But before inquiring into the mode

of resolving questions, it is necessary to inquire what are those which

offer themselves; what questions are conceivable; 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

believed or disbelieved. How many kinds of inquiries can be propounded;

how many kinds of judgments can be made; and how many kinds of

propositions it is possible to frame with a meaning; are but different

forms of one and the same question. Since, then, the objects of all

Belief and of all Inquiry express themselves in propositions; a

sufficient scrutiny of Propositions and of their varieties will apprize

us what questions mankind have actually asked of themselves, and what,

in the nature of answers to those questions, they have actually thought

they had grounds to believe.

Now the first glance at a proposition shows that it is formed by putting

together two names. A proposition, according to the common simple

definition, which is sufficient for our purpose, is, _discourse, in

which something is affirmed or denied of something_. Thus, in the

proposition, Gold is yellow, the quality _yellow_ is affirmed of the

substance _gold_. In the proposition, Franklin was not born in England,

the fact expressed by the words _born in England_ is denied of the man

Franklin.

Every proposition consists of three parts: the Subject, the Predicate,

and the Copula. The predicate is the name denoting that which is

affirmed or denied. The subject is the name denoting the person or thing

which something is affirmed or denied of. The copula is the sign

denoting that there is an affirmation or denial; and thereby enabling

the hearer or reader to distinguish a proposition from any other kind of

discourse. Thus, in the proposition, The earth is round, the Predicate

is the word _round_, which denotes the quality affirmed, or (as the

phrase is) predicated: _the earth_, words denoting the object which that

quality is affirmed of, compose the Subject; the word _is_, which serves

as the connecting mark between the subject and predicate, to show that

one of them is affirmed of the other, is called the Copula.

Dismissing, for the present, the copula, of which more will be said

hereafter, every proposition, then, consists of at least two names;

brings together two names, in a particular manner. This is already a

first step towards what we are in quest of. It appears from this, that

for an act of belief, _one_ object is not sufficient; the simplest act

of belief supposes, and has something to do with, _two_ objects: two

names, to say the least; and (since the names must be names of

something) two _nameable things_. A large class of thinkers would cut

the matter short by saying, two _ideas_. They would say, that the

subject and predicate are both of them names of ideas; the idea of gold,

for instance, and the idea of yellow; and that what takes place (or part

of what takes place) in the act of belief, consists in bringing (as it

is often expressed) one of these ideas under the other. But this we are

not yet in a condition to say: whether such be the correct mode of

describing the phenomenon, is an after consideration. The result with

which for the present we must be contented, is, that in every act of

belief _two_ objects are in some manner taken cognizance of; that there

can be no belief claimed, or question propounded, which does not embrace

two distinct (either material or intellectual) 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 suggests

that meaning to the mind of any one who is listening to me. But suppose

I ask him, Whether it is true: whether he believes it? He can give no

answer. There is as yet nothing to believe, or to disbelieve. Now,

however, let me make, of all possible assertions respecting the sun, the

one which involves the least of reference to any object besides itself;

let me say, "the sun exists." Here, at once, is something which a person

can say he believes. But here, instead of only one, we find two distinct

objects of conception: the sun is one object; existence is another. Let

it not be said that this second conception, existence, is involved in

the first; for the sun may be conceived as no longer existing. "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 cannot exist. When I say "the

sun," "my father," or a "round square," I do not call upon the hearer

for any belief or disbelief, nor can either the one or the other be

afforded me; but if I say, "the sun exists," "my father exists," or "a

round square exists," I call for belief; and should, in the first of the

three instances, meet with it; in the second, with belief or disbelief,

as the case might be; in the third, with disbelief.

§ 3. This first step in the analysis of the object of belief, which,

though so obvious, will be found to be not unimportant, is the only one

which we shall find it practicable to make without a preliminary survey

of language. If we attempt to proceed further in the same path, that is,

to analyse any further the import of Propositions; we find forced upon

us, as a subject of previous consideration, the import of Names. For

every proposition consists of two names; and every proposition affirms

or denies one of these names, of the other. Now what we do, what passes

in our mind, when we affirm or deny two names of one another, must

depend on what they are names of; since it is with reference to that,

and not to the mere names themselves, that we make the affirmation or

denial. Here, therefore, we find a new reason why the signification of

names, and the relation generally between names and the things signified

by them, must occupy the preliminary stage of the inquiry we are engaged

in.

It may be objected that the meaning of names can guide us at most only

to the opinions, possibly the foolish and groundless opinions, which

mankind have formed concerning things, and that as the object of

philosophy is truth, not opinion, the philosopher should dismiss words

and look into things themselves, to ascertain what questions can be

asked and answered in regard to them. This advice (which no one has it

in his power to follow) is in reality an exhortation to discard the

whole fruits of the labours of his predecessors, and conduct himself as

if he were the first person who had ever turned an inquiring eye upon

nature. What does any one's personal knowledge of Things amount to,

after subtracting all which he has acquired by means of the words of

other people? Even after he has learned as much as people usually do

learn from others, will the notions of things contained in his

individual mind afford as sufficient a basis for a _catalogue raisonné_

as the notions which are in the minds of all mankind?

In any enumeration and classification of Things, which does not set out

from their names, no varieties of things will of course be comprehended

but those recognised by the particular inquirer; and it will still

remain to be established, by a subsequent examination of names, that the

enumeration has omitted nothing which ought to have been included. But

if we begin with names, and use them as our clue to the things, we bring

at once before us all the distinctions which have been recognised, not

by a single inquirer, but by all inquirers taken together. It doubtless

may, and I believe it will, be found, that mankind have multiplied the

varieties unnecessarily, and have imagined distinctions among things,

where there were only distinctions in the manner of naming them. But we

are not entitled to assume this in the commencement. We must begin by

recognising the distinctions made by ordinary language. If some of these

appear, on a close examination, not to be fundamental, the enumeration

of the different kinds of realities may be abridged accordingly. But to

impose upon the facts in the first instance the yoke of a theory, while

the grounds of the theory are reserved for discussion in a subsequent

stage, is not a course which a logician can reasonably adopt.

CHAPTER II.

OF NAMES.

§ 1. "A name," says Hobbes,[1] "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 had[2] before in his mind." This simple

definition of a name, as a word (or set of words) serving the double

purpose of a mark to recall to ourselves the likeness of a former

thought, and a sign to make it known to others, appears unexceptionable.

Names, indeed, do much more than this; but whatever else they do, grows

out of, and is the result of this: as will appear in its proper place.

Are names more properly said to be the names of things, or of our ideas

of things? The first is the expression in common use; the last is that

of some metaphysicians, who conceived that in adopting it they were

introducing a highly important distinction. The eminent thinker, just

quoted, seems to countenance the latter opinion. "But seeing," he

continues, "names ordered in speech (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,

cannot be understood in any sense but this, that he that hears it

collects that he that pronounces it thinks of a stone."

If it be merely meant that the conception alone, and not the thing

itself, is recalled by the name, or imparted to the hearer, this of

course cannot be denied. Nevertheless, there seems good reason for

adhering to the common usage, and calling 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

proper to consider a word as the _name_ of that which we intend to be

understood by it when we use it; of that which any fact that we assert

of it is to be understood of; that, in short, concerning which, when we

employ the word, we intend to give information. Names, therefore, shall

always be spoken of in this work as the names of things themselves, and

not merely of our ideas of things.

But the question now arises, of what things? and to answer this it is

necessary to take into consideration the different kinds of names.

§ 2. It is usual, before examining the various classes into which names

are commonly divided, to begin by distinguishing from names of every

description, those words which are not names, but only parts of names.

Among such are reckoned particles, as _of_, _to_, _truly_, _often_; the

inflected cases of nouns substantive, as _me_, _him_, _John's_; and even

adjectives, as _large_, _heavy_. These words do not express things of

which anything can be affirmed or denied. We cannot say, Heavy fell, or

A heavy fell; Truly, or A truly, was asserted; Of, or An of, was in the

room. Unless, indeed, we are speaking of the mere words themselves, as

when we say, Truly is an English word, or, Heavy is an adjective. In

that case they are complete names, viz. names of those particular

sounds, or of those particular collections of written characters. This

employment of a word to denote the mere letters and syllables of which

it is composed, was termed by the schoolmen the _suppositio materialis_

of the word. In any other sense we cannot introduce one of these words

into the subject of a proposition, unless in combination with other

words; as, A heavy _body_ fell, A truly _important fact_ was asserted, A

_member_ of _parliament_ was in the room.

An adjective, however, is capable of standing by itself as the predicate

of a proposition; as when we say, Snow is white; and occasionally even

as the subject, for we may say, White is an agreeable colour. The

adjective is often said to be so used by a grammatical ellipsis: Snow is

white, instead of Snow is a white object; White is an agreeable colour,

instead of, A white colour, or, The colour white, is agreeable. The

Greeks and Romans were allowed, by the rules of their language, to

employ this ellipsis universally in the subject as well as in the

predicate of a proposition. In English this cannot, generally speaking,

be done. We may say, The earth is round; but we cannot say, Round is

easily moved; we must say, A round object. This distinction, however, is

rather grammatical than logical. Since there is no difference of meaning

between _round_, and _a round object_, it is only custom which

prescribes that on any given occasion one shall be used, and not the

other. We shall, therefore, without scruple, speak of adjectives as

names, whether in their own right, or as representative of the more

circuitous forms of expression above exemplified. The other classes of

subsidiary words have no title whatever to be considered as names. An

adverb, or an accusative case, cannot under any circumstances (except

when their mere letters and syllables are spoken of) figure as one of

the terms of a proposition.

Words which are not capable of being used as names, but only as parts of

names, were called by some of the schoolmen Syncategorematic terms: from

[Greek: syn], with, and [Greek: katêgoreô], 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 accompanied by any other word, was termed by the same

authorities a Categorematic 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 multiplication of technical expressions. A mixed term

is, in the only useful sense of the word, Categorematic. It belongs to

the class of what have been called many-worded names.

For, as one word is frequently not a name, but only part of a name, so a

number of words often compose one single name, and no more. These words,

"the place which the wisdom or policy of antiquity had destined for the

residence of the Abyssinian princes," form in the estimation of the

logician only one name; one Categorematic term. A mode of determining

whether any set of words makes only one name, or more than one, is by

predicating something of it, and observing whether, by this predication,

we make only one assertion or several. Thus, when we say, John Nokes,

who was the mayor of the town, died yesterday--by this 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 among names, not according to the words they are composed

of, but according to their signification.

§ 3. All names are names of something, real or 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 naming them, we do so by putting together several words, each of

which, by itself, might be and is used for an indefinite number of other

objects; as when I say, _this stone_: "this" and "stone" being, each of

them, names that may be used of many other objects besides the

particular one meant, though the only object of which they can both be

used at the given moment, consistently with their signification, may be

the one of which I wish to speak.

Were this the sole purpose for which names, that are common to more

things than one, could be employed; if they only served, by mutually

limiting each other, to afford a designation for such individual objects

as have no names of their own; they could only be ranked among

contrivances for economizing the use of language. But it is evident that

this is not their sole function. It is by their means that we are

enabled to assert _general_ propositions; to affirm or deny any

predicate of an indefinite number of things at once. The distinction,

therefore, between _general_ names, and _individual_ or _singular_

names, is fundamental; and may be 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 _John_ is only capable of being truly

affirmed of one single person, at least in the same sense. For though

there are many persons who bear that name, it is not conferred upon

them to indicate any qualities, or anything which belongs to them in

common; and cannot be said to be affirmed of them in any _sense_ at all,

consequently not in the same sense. "The king who succeeded William the

Conqueror," is also an individual name. For, that there cannot be more

than one person of whom it can be truly affirmed, is implied in the

meaning of the words. Even "_the_ king," when the occasion or the

context defines the individual of whom it is to be understood, may

justly be regarded as an individual name.

It is not unusual, by way of explaining what is meant by a 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 general name."

It is necessary to distinguish _general_ from _collective_ names. A

general name is one which can be predicated of _each_ individual of a

multitude; a collective name cannot be predicated of each separately,

but only of all taken together. "The 76th regiment of foot in the

British army," which is a collective name, is not a general but an

individual name; for though it can be predicated of a multitude of

individual soldiers taken jointly, it cannot be predicated of them

severally. We may say, Jones is a soldier, and Thompson is a soldier,

and Smith is a soldier, but we cannot say, Jones is the 76th regiment,

and Thompson is the 76th regiment, and Smith is the 76th regiment. We

can only say, Jones, and Thompson, and Smith, and Brown, and so forth

(enumerating all the soldiers), are the 76th regiment.

"The 76th regiment" is a collective name, but not a general one: "a

regiment" is both a collective and a general name. General with respect

to all individual regiments, of each of which separately it can be

affirmed; collective with respect to the individual soldiers of whom any

regiment is composed.

§ 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 attribute of those things. _Old_ is a name of

things; _old age_ is a name of one of their attributes.

I have used the words concrete and abstract in the sense annexed to them

by the schoolmen, who, notwithstanding the imperfections of their

philosophy, were unrivalled in the construction of technical language,

and whose definitions, in logic at least, though they never went more

than a little way into the subject, have seldom, I think, been altered

but to be spoiled. A practice, however, has grown up in more modern

times, which, if not introduced by Locke, has gained currency chiefly

from his example, of applying the expression "abstract name" to all

names which are the result of abstraction or generalization, and

consequently to all general names, instead of confining it to the names

of attributes. The metaphysicians of the Condillac school,--whose

admiration of Locke, passing over the profoundest speculations of that

truly original genius, usually fastens with peculiar eagerness upon his

weakest points,--have gone on imitating him in this abuse of language,

until there is now some difficulty in restoring the word to its original

signification. A more wanton alteration in the 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

already available for the purpose to which _abstract_ has been

misappropriated, while the misappropriation leaves that important class

of words, the names of attributes, without any compact distinctive

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, mean

the opposite of _concrete_: by an abstract name, the name of an

attribute; by a concrete name, the name of an object.

Do abstract names belong to the class of general, or to that of singular

names? Some of them are certainly general. I mean those which are names

not of one single and definite attribute, but of a class of attributes.

Such is the word _colour_, which is a name common to whiteness, redness,

&c. Such is even the word whiteness, in respect of the different shades

of whiteness to which it is applied in common; the word magnitude, in

respect of the various degrees of magnitude and the various dimensions

of space; the word weight, in respect of the various degrees of weight.

Such also is the word _attribute_ itself, the common name of all

particular attributes. But when only one attribute, neither variable in

degree nor in kind, is designated by the name; as visibleness;

tangibleness; equality; squareness; milkwhiteness; then the name can

hardly be considered general; for though it denotes an attribute of many

different objects, the attribute itself is always conceived as one, not

many.[3] To avoid needless logomachies, the best course would probably

be to consider these names as neither general nor individual, and to

place them in a class apart.

It may be objected to our definition of an abstract name, that not only

the names which we have called abstract, but adjectives, which we have

placed in the concrete class, are names of attributes; that _white_, for

example, is as much the name of the colour as _whiteness_ is. But (as

before remarked) a word ought to be considered as the name of that which

we intend to be understood by it when we put it to its principal use,

that is, when we employ it in predication. When we say snow is white,

milk is white, linen is white, we do not mean it to be understood that

snow, or linen, or milk, is a colour. We mean that they are things

having the colour. The reverse is the case with the word whiteness; what

we affirm to _be_ whiteness is not snow, but the colour of snow.

Whiteness, therefore, is the name of the colour exclusively: white is a

name of all things whatever having the colour; a name, not of the

quality whiteness, but of every white object. It is true, this name was

given to all those various objects on account of the quality; and we may

therefore say, without impropriety, that the quality forms part of its

signification; but a name can only be said to stand for, or to be a name

of, the things of which it can be predicated. We shall presently see

that all names which can be said to have any signification, all names by

applying which to an individual we give any information respecting that

individual, may be said to _imply_ an attribute of some sort; but they

are not names of the attribute; it has its own proper abstract name.

§ 5. This leads to the consideration of a third great division of names,

into _connotative_ and _non-connotative_, the latter sometimes, but

improperly, called _absolute_. This is one of the most important

distinctions which we shall have occasion to point out, and one of those

which go deepest into the nature of language.

A non-connotative term is one which signifies a subject only, or an

attribute only. A connotative term is one which denotes a subject, and

implies an attribute. By a subject is here meant anything which

possesses attributes. Thus John, or London, or England, are names which

signify a subject only. Whiteness, length, virtue, signify an attribute

only. None of these names, therefore, are connotative. But _white_,

_long_, _virtuous_, are connotative. The word white, denotes all white

things, as snow, paper, the foam of the sea, &c., and implies, or as it

was termed by the schoolmen, _connotes_[4], the attribute _whiteness_.

The word white is not predicated of the attribute, but of the subjects,

snow, &c.; but when we predicate it of them, we imply, or connote, that

the attribute whiteness belongs to them. The same may be said of the

other words above cited. Virtuous, for example, is the name of a class,

which includes Socrates, Howard, the 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 considered.

All concrete general names are connotative. The word _man_, for example,

denotes Peter, Jane, John, and an indefinite number of other

individuals, of whom, taken as a class, it is the name. But it is

applied to them, because they possess, and to signify that they possess,

certain attributes. These seem to be, corporeity, animal life,

rationality, and a certain external form, which for distinction we call

the human. Every existing thing, which possessed all these attributes,

would be called a man; and anything which possessed none of them, or

only one, or two, or even three of them without the fourth, would not be

so called. For example, if in the interior of Africa there were to be

discovered a race of animals possessing reason equal to that of human

beings, but with the form of an elephant, they would not be called men.

Swift's Houyhnhnms would not be so called. Or if such newly-discovered

beings possessed the form of man without any vestige of reason, it is

probable that some other name than that of man would be found for them.

How it happens that there can be any doubt about the matter, will appear

hereafter. The word _man_, therefore, signifies all these attributes,

and all subjects which possess these attributes. But it can be

predicated only of the subjects. What we call men, are the subjects, the

individual Stiles and Nokes; not the qualities by which their humanity

is constituted. The name, therefore, is said to signify the subjects

_directly_, the attributes _indirectly_; it _denotes_ the subjects, and

implies, or involves, or indicates, or as we shall say henceforth

_connotes_, the attributes. It is a connotative name.

Connotative names have hence been also called _denominative_, 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.[5]

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 connote an attribute of those attributes. Of this

description, for example, is such a word as _fault_; equivalent to _bad_

or _hurtful quality_. This word is a name common to many attributes, and

connotes hurtfulness, an attribute of those various attributes. When,

for example, we say that slowness, in a horse, is a fault, we do not

mean that the slow movement, the actual change of place of the slow

horse, is a bad thing, but that the property or peculiarity of the

horse, from which it derives that name, the quality of being a slow

mover, is an undesirable peculiarity.

In regard to those concrete names which are not general but individual,

a distinction must be made.

Proper names are not connotative: they denote the individuals who are

called by them; but they do not indicate or imply any attributes as

belonging to those individuals. When we name a child by the name Paul,

or a dog by the name Cæsar, 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 confessedly ceased to be true, no

one would any longer think of applying the name. Proper names are

attached to the objects themselves, and are not dependent on the

continuance of any attribute of the object.

But there is another kind of names, which, although they are individual

names, that is, predicable only of one object, are really connotative.

For, though we may give to an 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 anything 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 language, general, not individual

names: for, however they may be _in fact_ predicable only of one object,

there is nothing in the meaning of the words themselves which implies

this: and, accordingly, when we are imagining and not affirming, we may

speak of many suns; and the majority of mankind have believed, and still

believe, that there are many gods. But it is easy to produce words which

are real instances of connotative individual names. It may be part of

the meaning of the connotative name itself, that there can exist but

one individual possessing the attribute which it connotes: as, for

instance, "the _only_ son of John Stiles;" "the _first_ emperor of

Rome." Or the attribute connoted may be a connexion with some

determinate event, and the connexion may be of such a kind as only one

individual could have; or may at least be such as only one individual

actually had; and this may be implied in the form of the expression.

"The father of Socrates" is an example of the one kind (since Socrates

could not have had two fathers); "the author of the Iliad," "the

murderer of Henri Quatre," of the second. For, though it is conceivable

that more persons than one might have participated in the authorship of

the Iliad, or in the murder of Henri Quatre, the employment of the

article _the_ implies that, in fact, this was not the case. What is here

done by the word _the_, is done in other cases by the context: thus,

"Cæsar's army" is an individual name, if it appears from the context

that the army meant is that which Cæsar commanded in a particular

battle. The still more general expressions, "the Roman army," or "the

Christian army," may be individualized in a similar manner. Another case

of frequent occurrence has already been noticed; it is the following.

The name, being a many-worded one, may consist, in the first place, of a

_general_ name, capable therefore in itself of being affirmed of more

things than one, but which is, in the second place, so limited by other

words joined with it, that the entire expression can only be predicated

of one object, 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 afterwards limited by the article and the word _present_, to

such individuals as possess the attributes at one indivisible point of

time, it becomes applicable only to one individual. And as this appears

from the meaning of the name, without any extrinsic proof, it is

strictly an individual name.

From the preceding observations it will easily be collected, that

whenever the names given to objects convey any information, that is,

whenever they have properly any meaning, the meaning resides not in what

they _denote_, but in what they _connote_. The only names of objects

which connote nothing are _proper_ names; and these have, strictly

speaking, no signification.[6]

If, like the robber in the Arabian Nights, we make a mark with chalk on

a house to enable us to know it again, the mark has a purpose, but it

has not properly any meaning. The chalk does not declare anything about

the house; it does not mean, This is such a person's house, or This is a

house which contains booty. The object of making the mark is merely

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 hereafter know, when I see the mark--not indeed any

attribute of the house--but simply that it is the same house which I am

now looking at. Morgiana chalked all the other houses in a similar

manner, and defeated the scheme: how? simply by obliterating the

difference of appearance between that house and the others. The chalk

was still there, but it no longer served the purpose of a distinctive

mark.

When we impose a proper name, we perform an operation in some degree

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 enables 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 individual thing with which we were

previously acquainted.

When we predicate of anything its proper name; when we say, pointing to

a man, this is Brown or Smith, or pointing to a city, that it is York,

we do not, merely by so doing, convey to the hearer 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 Minster. But this is in virtue of what he has

previously heard concerning York; not by anything implied in the name.

It is otherwise when objects are spoken of by connotative names. When we

say, The town is built of marble, we give the hearer what may be

entirely new 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 recognised as possessing it. They are not mere marks, but

more, that is to say, significant marks; and the connotation is what

constitutes their significance.

As a proper name is said to be the name of the one 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 Sophroniscus: 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 Greek, an Athenian, a sculptor, an old man, an

honest man, a brave man. All these are, or may be, names of

Sophroniscus, not indeed of him alone, but of him and each of an

indefinite number of other human beings. Each of these names is applied

to Sophroniscus for a different reason, and by each whoever understands

its meaning is apprised of a distinct fact or number of facts concerning

him; but those who knew nothing about the names except that they were

applicable to Sophroniscus, would be 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

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 unsettled and vague; mankind

have not come to any positive agreement about the matter. When we come

to treat of Classification, we shall have occasion to show under what

conditions this vagueness may exist without practical inconvenience; and

cases will appear in which the ends of language are better promoted by

it than by complete precision; in order that, in natural history for

instance, 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 precise notion of their meaning than can be loosely collected

from observing what objects they are used to denote. It is in this

manner that we all acquire, and inevitably so, our first knowledge of

our vernacular language. A child learns the meaning of the words _man_,

or _white_, by hearing them applied to a variety of individual objects,

and finding out, by a process of 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

possession of which in common by them all, their general resemblance

depends. When this is the case, people use the name without any

recognised connotation, 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 competent to solve all doubts. But a similar

resource does not exist in the generality of cases; and new objects are

continually presenting themselves to men, women, and children, which

they are called upon to class _proprio motu_. They, accordingly, do this

on no other principle than that of superficial similarity, giving to

each new object the name of that familiar object, the idea of which it

most readily recalls, or which, on a cursory inspection, it seems to

them most to resemble: as an unknown substance found in the ground will

be called, according to its texture, earth, sand, or a stone. In this

manner, names creep on from subject to subject, until all traces of a

common meaning sometimes 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

meditated on the present condition of those branches of knowledge.

Since, however, the introduction of a new technical language as the

vehicle of speculations on subjects belonging to the domain of daily

discussion, is extremely difficult 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 attributes, when we call

an object by that name, we really mean to predicate of the object. And

the question of most nicety is, how to give this fixed connotation to a

name, with the least possible change in the objects which the name is

habitually employed to denote; with the least possible disarrangement,

either by adding or subtraction, of the group of objects which, in

however imperfect a manner, it serves to circumscribe and hold together;

and with the least vitiation of the truth of any propositions which are

commonly received as true.

This desirable purpose, of giving a fixed connotation where it is

wanting, is the end aimed at whenever any one attempts to give a

definition of a general name already in use; every definition of a

connotative name being an attempt either merely to declare, or to

declare and analyse, the connotation of the name. And the fact, that no

questions which have arisen in the moral sciences have been subjects of

keener controversy than the definitions of almost all the leading

expressions, is a proof how great an extent the evil to which we have

adverted has attained.

Names with indeterminate connotation are not to be confounded with names

which have more than one connotation, that is to say, ambiguous words. A

word may have several meanings, but all of them fixed and recognised

ones; as the word _post_, for example, or the word _box_, the various

senses of which it would be endless to enumerate. And the paucity of

existing names, in comparison with the demand for them, may often render

it advisable and even necessary to retain a name in this multiplicity

of acceptations, distinguishing these so clearly as to prevent their

being confounded with one another. Such a word may be considered as two

or more names, accidentally written and spoken alike.[7]

§ 6. The fourth principal division of names, is into _positive_ and

_negative_. Positive, as _man_, _tree_, _good_; negative, as _not-man_,

_not-tree_, _not-good_. To every positive concrete name, a corresponding

negative one might 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 connotative, the corresponding

negative name is connotative likewise; but in a peculiar way, connoting

not the presence but the absence of an attribute. Thus, _not-white_

denotes all things whatever except white things; and connotes the

attribute of not 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

others are really positive though their form is negative. The word

_inconvenient_, for example, does not express the mere absence of

convenience; it expresses a positive attribute, that of being the cause

of discomfort or annoyance. So the word _unpleasant_, notwithstanding

its negative form, does not connote the mere absence of pleasantness,

but a less degree of what is signified by the word _painful_, which, it

is hardly necessary to say, is positive. _Idle_, on the other hand, is a

word which, though positive in form, expresses nothing but what would be

signified either by the phrase _not working_, or by the phrase _not

disposed to work_; and _sober_, either by _not drunk_ or by _not

drunken_.

There is a class of names called _privative_. A privative name is

equivalent in its signification to a positive and a negative name taken

together; being the name of something which has once had a particular

attribute, or for some other reason might have been expected to have it,

but which has it not. Such is the word _blind_, which is not equivalent

to _not seeing_, or to _not capable of seeing_, for it would not, except

by a poetical or rhetorical figure, be applied to stocks and stones. A

thing is not usually said to be blind, unless the class to which it is

most familiarly referred, or to which it is referred on the particular

occasion, be chiefly composed of things which can see, as in the case of

a blind man, or a blind horse; or unless it is supposed for any reason

that it ought to see; as in saying of a man, that he rushed blindly into

an abyss, or of philosophers or the clergy that the greater part of them

are blind guides. The names called privative, therefore, connote two

things: the absence of certain attributes, and the presence of others,

from which the presence also of the former might naturally have been

expected.

§ 7. The fifth leading division of names is into _relative_ and

_absolute_, or let us rather say, _relative_ and _non-relative_; for the

word absolute is put upon much too hard duty in metaphysics, not to be

willingly spared when its services can be dispensed with. It resembles

the word _civil_ in the language of jurisprudence, which stands for the

opposite of criminal, the opposite of ecclesiastical, the opposite of

military, the opposite of political--in short, the opposite of any

positive word which wants a negative.

Relative names are such as father, son; ruler, subject; like; equal;

unlike; unequal; longer, shorter; cause, effect. Their characteristic

property is, that they are always given in pairs. Every relative name

which is predicated of an object, supposes another object (or objects),

of which we may predicate either that same name or another relative name

which is said to be the _correlative_ of the former. Thus, when we call

any person a son, we suppose other persons who must be called parents.

When we call any event a cause, we suppose another event which is an

effect. When we say of any distance that it is longer, we suppose

another distance which is shorter. 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

attribute; and each of them has or might have a corresponding abstract

name, to denote the attribute connoted by the concrete. Thus the

concrete _like_ has its abstract _likeness_; the concretes, father and

son, have, or might have, the abstracts, paternity, and filiety, or

sonship. The concrete name connotes an attribute, and the abstract name

which answers to it denotes that attribute. But of what nature is the

attribute? Wherein consists the peculiarity in the connotation of a

relative name?

The attribute signified by a relative name, say some, is a relation; and

this they give, if not as a sufficient explanation, at least as the only

one attainable. If they are asked, What then is a relation? they do not

profess to be able to tell. It is generally regarded as something

peculiarly recondite and mysterious. I cannot, however, perceive in what

respect it is more so than any other attribute; indeed, it appears to me

to be so in a somewhat less degree. I conceive, rather, that it is by

examining into the signification of relative names, or, in other words,

into the nature of the attribute which they 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 _de_noted by the

names are different, they both, in a certain sense, connote the same

thing. They cannot, indeed, be said to connote the same _attribute_: to

be a father, is not the same thing as to be a son. But when we call one

man a father, another a son, what we mean to affirm is a set of facts,

which are exactly the same in both cases. To predicate of A that he is

the father of B, and of B that he is the son of A, is to assert one and

the same fact in different words. The two propositions are exactly

equivalent: neither of them asserts more or asserts less than the

other. The paternity of A and the filiety of B are not two facts, but

two modes of expressing the same fact. That fact, when analysed,

consists of a series of physical events or phenomena, in which both A

and B are parties concerned, and from which they both derive names. What

those names really connote, is this series of events: that is the

meaning, and the whole meaning, which either of them is intended to

convey. The series of events may be said to _constitute_ the relation;

the schoolmen called it the foundation of the relation, _fundamentum

relationis_.

In this manner any fact, or series of facts, in which two different

objects are implicated, and which is therefore 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 aspect, 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 evidently be regarded with equal

propriety in either light. And all that appears necessary to account for

the existence of relative names, is, that whenever there is a fact in

which two individuals are concerned, an attribute grounded on that fact

may be ascribed to either of these individuals.

A name, therefore, is said to be relative, when, over and above the

object which it denotes, it implies in its signification the existence

of another object, also deriving a denomination from the same fact which

is the ground of the first name. Or (to express the same meaning in

other words) a name is relative, when, being the name of one thing, its

signification cannot be explained but by mentioning another. Or we may

state it thus--when the name cannot be employed in discourse so as to

have a meaning, unless the name of some other thing than what it is

itself the name of, be either expressed or understood. These definitions

are all, at bottom, equivalent, being modes of variously expressing this

one distinctive circumstance--that every other attribute of an object

might, without any contradiction, be conceived still to exist if no

object besides that one had ever existed;[8] 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

_æquivocal_: these, however, are not two kinds of names, but two

different modes of employing names. A name is univocal, or applied

univocally, with respect to all things of which it can be predicated _in

the same sense_: it is æquivocal, or applied æquivocally, as respects

those things of which it is predicated in different senses. It is

scarcely necessary to give instances of a fact so familiar as the double

meaning of a word. In reality, as has been already observed, an

æquivocal or ambiguous word is not one name, but two names, accidentally

coinciding in sound. _File_ meaning a steel instrument, and _file_

meaning a line of soldiers, have no more title to be considered one

word, because written alike, than _grease_ and _Greece_ have, because

they are pronounced alike. They are one sound, appropriated to form two

different words.

An intermediate case is that of a name used _analogically_ or

metaphorically; that is, a name which is predicated of two things, not

univocally, or exactly in the same signification, but in significations

somewhat similar, and which being derived one from the other, one of

them may be considered the primary, and the other a secondary

signification. As when we speak of a brilliant light and a brilliant

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 perfect 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.

CHAPTER III.

OF THE THINGS DENOTED BY NAMES.

§ 1. Looking back now to the commencement of our inquiry, let us attempt

to measure how far it has advanced. Logic, we found, is the Theory of

Proof. But proof supposes something provable, which must be a

Proposition or Assertion; since nothing but a Proposition can be an

object of belief, or therefore of proof. A Proposition is, discourse

which affirms or denies something of some other thing. This is one step:

there must, it seems, be two things concerned in every act of belief.

But what are these Things? They can be no other than those signified by

the two names, which being joined together by a copula constitute the

Proposition. If, therefore, we knew what all names signify, we should

know everything which in the existing state of human knowledge, is

capable either of being made a subject of affirmation or denial, or of

being itself affirmed or denied of a subject. We have accordingly, in

the preceding chapter, reviewed the various kinds of Names, in order to

ascertain what is signified by each of them. And we have now carried

this survey far enough to be able to take an account of its results, and

to exhibit an enumeration of all kinds of Things which are capable of

being made predicates, or of having anything 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 philosophers. The Categories, or Predicaments--the former a

Greek word, the latter its literal translation in the Latin

language--were intended by him and his followers as an enumeration of

all things capable 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 nameable thing whatsoever. The following are the classes into

which, according to this school of philosophy, Things in general might

be reduced:--

[Greek: Ousia], Substantia.

[Greek: Poson], Quantitas.

[Greek: Poion], Qualitas.

[Greek: Pros ti], Relatio.

[Greek: Poiein], Actio.

[Greek: Paschein], Passio.

[Greek: Pou], Ubi.

[Greek: Pote], Quando.

[Greek: Keisthai], Situs.

[Greek: Echein], 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 superficially conducted, would have shown the

enumeration to be both redundant and defective. Some objects are

omitted, and others repeated several times under different heads. It is

like a division of animals into men, quadrupeds, horses, asses, and

ponies. That, for instance, could not be a very comprehensive view of

the nature of Relation which could exclude 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 genus_ the class which forms the

tenth category is manifest. On the other hand, the enumeration takes no

notice of anything besides substances and attributes. In what category

are we to place sensations, or any other feelings and states of mind; as

hope, joy, fear; sound, smell, taste; pain, pleasure; thought, 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. Feelings, or states of consciousness, are assuredly to be

counted among realities, but they cannot be reckoned either among

substances or attributes.

§ 2. Before recommencing, under better auspices, the attempt made with

such imperfect success by the great founder of the science of logic, we

must take notice of an unfortunate ambiguity in all the concrete names

which correspond to the most general of all abstract terms, the word

Existence. When we have occasion for a name which shall be capable of

denoting whatever exists, as contradistinguished from non-entity or

Nothing, there is hardly a word applicable to the purpose which is not

also, and even more familiarly, taken in a sense in which it denotes

only substances. But substances are not all that exists; attributes, if

such things are to be spoken of, must be said to exist; feelings

certainly exist. Yet when we speak of an _object_, or of a _thing_, we

are almost always 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 Classification

of Things would, I believe, prepare most readers for an enumeration like

those in natural history, beginning with the great divisions of animal,

vegetable, and mineral, and subdividing them into classes and orders.

If, rejecting the word Thing, we endeavour to find another of a more

general import, or at least more exclusively confined to that general

import, a word denoting all that exists, and connoting only simple

existence; no word might be presumed fitter for such a purpose than

_being_: originally the present participle of a verb which in one of its

meanings is exactly equivalent to the verb _exists_; and therefore

suitable, even by its grammatical formation, to be the concrete of the

abstract _existence_. But this 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 applied 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. Attributes are never

called Beings; nor are feelings. A Being is that which excites feelings,

and which possesses attributes. The soul is called a Being; God and

angels are called Beings; but if we were to say, extension, colour,

wisdom, virtue, are beings, we should perhaps be suspected of thinking

with some of the ancients, that the cardinal virtues are animals; or, at

the least, of holding with the Platonic school the doctrine of

self-existent Ideas, or with the followers of Epicurus that of Sensible

Forms, which detach themselves in every direction from bodies, and by

coming in contact with our organs, cause our perceptions. We should be

supposed, in short, to believe that Attributes are Substances.

In consequence of this perversion of the word Being, philosophers

looking about for something to supply its place, laid their hands upon

the word Entity, a piece of barbarous Latin, invented by the schoolmen

to be used as an abstract name, in which class its grammatical form

would seem to place it; but being seized by logicians in distress to

stop a leak in their terminology, it has ever since been used as a

concrete name. The kindred word _essence_, born at the same time and of

the same parents, scarcely underwent a more complete transformation

when, from being the abstract of the verb _to be_, it came to denote

something sufficiently concrete to be enclosed in a glass bottle. The

word Entity, since it settled down into a concrete name, has retained

its universality of signification somewhat less impaired than any of the

names before 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 suspicion.

Every word which was originally intended to connote mere existence,

seems, after a long time, to enlarge its connotation to _separate_

existence, or existence freed from the condition of belonging to a

substance; which condition being precisely what constitutes an

attribute, attributes are gradually shut out; and along with them

feelings, which in ninety-nine cases out of a hundred have no other name

than that of the attribute which is grounded on them. Strange that when

the greatest embarrassment felt by all who have any considerable number

of thoughts to express, is to find a sufficient variety of precise words

fitted to express them, there should be no practice to which even

scientific thinkers are more addicted than that of taking valuable words

to express ideas which are sufficiently expressed by other words already

appropriated to them.

When it is impossible to obtain good tools, the next best thing is to

understand thoroughly the defects of those we have. I have therefore

warned the reader of the ambiguity of the names which, for want of

better, I am necessitated to employ. It must now be the writer's

endeavour so to employ them as in no case to leave the meaning doubtful

or obscure. No one of the above terms being altogether unambiguous, I

shall not confine myself to any one, but shall employ on each occasion

the word which seems least likely in the particular case to lead to

misunderstanding; nor do I pretend to use either these or any other

words with a rigorous adherence to one single sense. To do so would

often leave us without a word to express what is signified by a known

word in some one or other of its senses: unless authors had an unlimited

licence to coin new words, together with (what it would be more

difficult to assume) unlimited power of making readers understand them.

Nor would it be wise in a writer, on a subject involving so much of

abstraction, to deny himself the advantage derived from even an improper

use of a term, when, by means of it, some familiar association is called

up which brings the meaning home to the mind, as it were by a flash.

The difficulty both to the writer and reader, of the attempt which must

be made to use vague words so as to convey a precise meaning, is not

wholly a matter of regret. It is not unfitting that logical treatises

should afford an example of that, to facilitate which is among the most

important uses of logic. Philosophical language will for a long time,

and popular language still longer, retain so much of vagueness and

ambiguity, that logic would be of little value if it did not, among its

other advantages, exercise the understanding in doing its work neatly

and correctly with these imperfect tools.

After this preamble it is time to proceed to our enumeration. We shall

commence with Feelings, the simplest class of nameable things; the term

Feeling being of course understood in its most enlarged sense.

I. FEELINGS, OR STATES OF CONSCIOUSNESS.

§ 3. A Feeling and a State of Consciousness are, in the language of

philosophy, equivalent expressions: everything is a feeling of which the

mind is conscious; everything which it _feels_, or, in other words,

which forms a part of its own sentient existence. In popular language

Feeling is not always synonymous with State of Consciousness; being

often taken more peculiarly for those states which are conceived as

belonging to the sensitive, or to the emotional, phasis of our nature,

and sometimes, with a still narrower restriction, to the emotional

alone, as distinguished from what are conceived as belonging to the

percipient or to the intellectual phasis. But this is an admitted

departure from correctness of language; just as, by a popular perversion

the exact converse of this, the word Mind is withdrawn from its rightful

generality of signification, and restricted to the intellect. The still

greater perversion by which Feeling is sometimes confined not only to

bodily 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 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 colour 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 may think of the loaf

which was eaten yesterday, or of the flower which will bloom to-morrow.

But the hobgoblin which never existed is not the same thing with my idea

of a hobgoblin, any more than the loaf which once existed is the same

thing with my idea of a loaf, or the flower which does not yet exist,

but which will exist, is the same with my idea of a flower. They are

all, not thoughts, but objects of thought; though at the present time

all the objects are alike non-existent.

In like manner, a Sensation is to be carefully distinguished from the

object which causes the sensation; our sensation of white from a white

object: nor is it less to be distinguished from the attribute whiteness,

which we ascribe to the object in consequence of its exciting the

sensation. Unfortunately 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 sensation: the name _whiteness_. But

when we speak of the sensation itself (as we have not occasion to do

this often except in our scientific speculations), language, which

adapts itself for the most part only to the common uses of life, has

provided us with no single-worded or immediate designation; we must

employ a circumlocution, and say, The sensation of white, or The

sensation of whiteness; we must denominate the sensation either from the

object, or from the attribute, by which it is excited. Yet the

sensation, though it never _does_, might very well be _conceived_ to

exist, without anything whatever to excite it. We can conceive it as

arising spontaneously in the mind. But if it so arose, we should have no

name to denote it which would not be a misnomer. In the case of our

sensations of hearing we are better provided; we have the word Sound,

and a whole vocabulary of words to denote the various kinds of sounds.

For as we are often conscious of these sensations in the absence of any

perceptible object, we can more easily conceive having them in the

absence of any object whatever. We need only shut our eyes and listen to

music, to have a conception of an 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 indiscriminately the sensation and the attribute.

Thus, _colour_ stands for the sensations of white, red, &c., but also

for the quality in the coloured object. We talk of the colours of things

as among their _properties_.

§ 4. In the case of sensations, another distinction has also to be kept

in view, which is often confounded, and never without mischievous

consequences. This is, the distinction between the sensation itself, and

the state of the bodily organs which precedes the sensation, and which

constitutes the physical agency by which it is produced. One of the

sources of confusion on this subject is the division commonly made of

feelings into Bodily and Mental. Philosophically speaking, there is no

foundation at all for this distinction: even sensations are states of

the sentient mind, not states of the body, as distinguished from it.

What I am conscious of when I see the colour blue, is a feeling of blue

colour, which is one thing; the picture on my retina, or the phenomenon

of hitherto mysterious nature which takes place in my optic nerve or in

my brain, is another thing, of which I am not at all conscious, and

which scientific investigation alone could have apprised me of. These

are states of my body; but the sensation of blue, which is the

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

feelings, thoughts, for instance, or emotions, are immediately excited

not by anything acting upon the bodily organs, but by sensations, or by

previous thoughts. This, however, is a distinction not in our feelings,

but in the agency which produces our feelings: all of them when actually

produced are states of mind.

Besides the affection of our bodily organs from without, and the

sensation thereby produced in our minds, many writers admit a third link

in the chain of phenomena, which they call a Perception, and which

consists in the recognition of an 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 merely acted upon by the outward object. And

according to some metaphysicians, it is by an act of the mind, similar

to perception, except in not being preceded by any sensation, that the

existence of God, the soul, and other hyper-physical objects is

recognised.

These acts of what is termed perception, whatever be the conclusion

ultimately come to respecting their nature, must, I conceive, take their

place among the varieties of feelings or states of mind. In so classing

them, I have not the smallest intention of declaring or insinuating any

theory as to the law of mind in which these mental processes may be

supposed to originate, or the conditions under which they may be

legitimate or the reverse. Far less do I mean (as Dr. Whewell seems to

suppose must be meant in an analogous case[9]) 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, whether physical or spiritual,

which are external to itself, I can see only cases of belief; but of

belief which claims to be intuitive, or independent of external

evidence. When a stone lies before me, I am conscious of certain

sensations which I receive from it; but if I say that these 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.

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 between 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 be said once more, I mean to

imply nothing of passivity, but simply that they are psychological

facts, facts which take place in the mind, and are to be carefully

distinguished from the external or physical facts with which they may be

connected either as effects or as causes.

§ 5. Among active states of mind, there is, however, one species which

merits particular attention, because it forms a principal part of the

connotation of some important classes of names. I mean _volitions_, or

acts of the will. When we speak of sentient beings by relative names, a

large portion of the connotation of the name usually consists of the

actions of those beings; actions past, present, and possible or probable

future. Take, for instance, the words Sovereign and Subject. What

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 connotation of names consists of

actions. Now what is an action? Not one thing, but a series of two

things: the state of mind called a volition, 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 moving

my arm; that is a state of my mind: my arm (not being tied or paralytic)

moves in obedience to my purpose; that is a physical fact, consequent on

a state of mind. The intention, followed by the fact, or (if we prefer

the expression) the fact when preceded and caused by the intention, is

called the action of moving my arm.

§ 6. Of the first leading division of nameable things, viz. Feelings or

States of Consciousness, we began by recognising three subdivisions;

Sensations, Thoughts, and Emotions. The first two of these we have

illustrated at considerable length; the third, Emotions, not being

perplexed by similar ambiguities, does not require similar

exemplification. And, finally, we have found it necessary to add to

these three a fourth species, commonly known by the name Volitions.

Without seeking to prejudge the metaphysical question whether any mental

state or phenomenon can be found which is not included in one or other

of these four species, it appears to me that the amount of illustration

bestowed upon these may, so far as we are concerned, suffice for the

whole genus. We shall, therefore, proceed to the two remaining classes

of nameable things; all things which are external to the mind being

considered as belonging either to the class of Substances or to that of

Attributes.

II. SUBSTANCES.

Logicians have endeavoured to define Substance and Attribute; but their

definitions are not so much attempts to draw a distinction between the

things themselves, as instructions what difference it is customary to

make in the grammatical structure of the sentence, according as we are

speaking of substances or of attributes. Such definitions are rather

lessons of English, or of Greek, Latin, or German, than of mental

philosophy. An attribute, say the school logicians, must be the

attribute _of_ something; colour, for example, must be the colour _of_

something; goodness must be the goodness _of_ something: and if this

something should cease to exist, or should cease to be connected with

the attribute, the existence of the attribute would be at an end. A

substance, on the contrary, is self-existent; in speaking about it, we

need not put _of_ after its name. A stone is not the stone _of_

anything; the moon is not the moon _of_ anything, but simply the moon.

Unless, indeed, the name which we choose to give to the substance be a

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 subsist. Thus, a father must be the father _of_

something, and so far resembles an attribute, in being referred to

something besides himself: if there were no child, there would be no

father: but this, when we look into the matter, only means that we

should not call him father. The man called father might still exist

though there were no child, as he existed before there was a child: and

there would be no contradiction in supposing him to exist, though the

whole universe except himself were destroyed. But destroy all white

substances, and where would be the attribute whiteness? Whiteness,

without any white thing, is a contradiction in terms.

This is the nearest approach to a solution of the difficulty, that will

be found in the common treatises on logic. It will scarcely be thought

to be a satisfactory one. If an attribute is distinguished from a

substance by being the attribute _of_ something, it seems highly

necessary to understand what is meant by _of_; a particle which needs

explanation too much itself, to be placed in front of the explanation of

anything else. And as for the self-existence of substance, it is very

true that a substance may be conceived to exist without any other

substance, but so also may an attribute without any other attribute: and

we can no more imagine a substance without attributes than we can

imagine attributes without a substance.

Metaphysicians, however, have probed the question deeper, and given an

account of Substance considerably more satisfactory than this.

Substances are usually distinguished as Bodies or Minds. Of each of

these, philosophers have at length provided us with a definition which

seems unexceptionable.

§ 7. A Body, according to the received doctrine of modern

metaphysicians, may be defined, the external cause to which we ascribe

our sensations. When I see and touch a piece of gold, I am conscious of

a sensation of yellow colour, and sensations of hardness and weight; and

by varying the mode of handling, I may add to these sensations many

others completely distinct from them. The sensations are all of which I

am directly conscious; but I consider them as produced by something not

only existing independently of my will, but external to my bodily organs

and to my mind. This external something I call a body.

It may be asked, how come we to ascribe our sensations to any external

cause? And is there sufficient ground for so ascribing them? It is

known, that there are metaphysicians who have raised a controversy on

the point; maintaining that we are not warranted in referring our

sensations to a cause such as we understand by the word Body, or to any

external cause whatever. Though we have no concern here with this

controversy, nor with the metaphysical niceties on which it turns, one

of the best ways of showing what is meant by Substance is, to consider

what position it is necessary to take up, in order to maintain its

existence against opponents.

It is certain, then, that a part of our notion of a body consists of the

notion of a number of sensations of our own, or of other sentient

beings, habitually occurring simultaneously. My conception of the table

at which I am writing is compounded of its visible form and size, which

are complex 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

colour, which is a sensation of sight; its hardness, which is a

sensation of the muscles; its composition, which is another word for all

the varieties of sensation which we receive under various circumstances

from the wood of which it is made, and so forth. All or most of these

various sensations frequently are, and, as we learn by experience,

always might be, 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 conceive

an orange to be divested of its natural colour without acquiring any new

one; to lose its softness without becoming hard, its roundness without

becoming square or pentagonal, or of any other regular or irregular

figure 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 connexion, making the sensations

occur together, does not, say these philosophers, necessarily require

what is called a substratum to support them. The conception of a

substratum is but one of many possible forms in which that connexion

presents itself to our imagination; a mode of, as it were, realizing the

idea. If there be such a substratum, suppose it this instant

miraculously annihilated, and let the sensations continue to occur in

the same order, and how would the substratum be missed? By what signs

should we be able to discover that its existence had terminated? Should

we not have as much reason to believe that it still existed as we now

have? And if we should not then be warranted in believing it, how can we

be so now? A body, therefore, according to these metaphysicians, is not

anything intrinsically different from the sensations which the body is

said to produce in us; it is, in short, a set of sensations, or rather,

of possibilities of 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 connexion, but a

cause external to our mind, which cause, by its own laws, determines the

laws according to which the sensations are connected and experienced.

The schoolmen used to call this external cause by the name we have

already employed, a _substratum_; and its attributes (as they expressed

themselves) _inhered_, literally _stuck_, in it. To this substratum the

name Matter is usually given in philosophical discussions. It was soon,

however, acknowledged by all who reflected on the subject, that the

existence of matter cannot be proved by extrinsic evidence. The answer,

therefore, now usually made to Berkeley and his followers, is, that the

belief is intuitive; that mankind, in all ages, have felt themselves

compelled, by a necessity of their nature, to refer their sensations to

an external cause: that even those who deny it in theory, yield to the

necessity in practice, and both in speech, thought, and feeling, do,

equally with the vulgar, acknowledge their sensations to be the effects

of something external to them: this knowledge, therefore, it is

affirmed, is as evidently intuitive as our knowledge of our sensations

themselves is intuitive. And here the question merges in the fundamental

problem of metaphysics properly so called; to which science we leave it.

But although the extreme doctrine of the Idealist 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

generally considered to have made out their case: viz., that _all we

know_ of objects is the sensations which they give us, and the order of

the occurrence of those sensations. Kant himself, on this point, is as

explicit as Berkeley or Locke. However firmly convinced that there

exists an universe of "Things in 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 (_Noumenon_) to

denote what the thing is in itself, as contrasted with the

_representation_ of it in our minds; he allows that this representation

(the matter of which, he says, consists of our sensations, though the

form is given by the laws of the mind itself) is all we know of the

object: and that the real nature of the Thing is, and by the

constitution of our faculties ever must remain, at least in the present

state of existence, an impenetrable mystery to us. "Of things absolutely

or in themselves," says Sir William Hamilton,[10] "be they external, be

they internal, we know nothing, or know them only as incognisable; and

become aware of their incomprehensible existence, only as this is

indirectly and accidentally revealed to us, through certain qualities

related to our faculties of knowledge, and which qualities, again, we

cannot think as unconditioned, irrelative, existent in and of

themselves. All that we know is therefore phænomenal,--phænomenal of the

unknown."[11] 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.[12]

There is not the slightest reason for believing that what we call the

sensible qualities of the object are a type of anything inherent in

itself, or bear any affinity to its own nature. A cause does not, as

such, resemble its effects; an east wind is not like the feeling of

cold, nor heat like the steam of boiling water. Why then should matter

resemble our sensations? Why should the inmost nature of fire or water

resemble the impressions made by those objects upon our senses?[13] Or

on what principle are we authorized to deduce from the effects, anything

concerning the cause, except that it is a cause adequate to produce

those effects? It may, therefore, safely be laid down as a truth both

obvious in itself, and admitted by all whom it is at present necessary

to take into consideration, that, of the outward world, we know and can

know absolutely nothing, except the sensations which we experience from

it.[14]

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

the more reasonable opinion) the unknown external cause, to which we

refer our sensations; it remains to frame a definition of Mind. Nor,

after the preceding observations, will this be difficult. For, as our

conception of a body is that of an unknown exciting cause of sensations,

so our conception of a mind is that of an unknown recipient, or

percipient, of them; and not of them alone, but of all our other

feelings. As body is understood to be the mysterious something which

excites the mind to feel, so mind is the mysterious something which

feels and thinks. It is unnecessary to give in the case of mind, as we

gave in the case of matter, a particular statement of the sceptical

system by which its existence as a Thing in itself, distinct from the

series of what are denominated its states, is called in question. But it

is necessary to remark, that on the inmost nature (whatever be meant by

inmost nature) of the thinking principle, as well as on the inmost

nature of matter, we are, and with our faculties must always remain,

entirely in the dark. All which we are aware of, even in our own minds,

is (in the words of Mr. James Mill) a certain "thread of consciousness;"

a series of feelings, that is, of sensations, thoughts, emotions, and

volitions, more or less numerous and complicated. There is a something I

call Myself, or, by another form of expression, my mind, which I

consider as distinct from these sensations, thoughts, &c.; a something

which I conceive to be not the thoughts, but the being that has the

thoughts, and which I can conceive as existing for ever in a state of

quiescence, without any thoughts at all. But what this being is, though

it is myself, I have no knowledge, other than the series of its states

of consciousness. As bodies manifest themselves to me only through the

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 conscious (including, of course,

thinking and willing): and were I to learn anything new concerning my

own nature, I cannot with my present faculties conceive this new

information to be anything else, than that I have some additional

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

described as the sentient _subject_ (in the scholastic sense of the

term) of all feelings; that which has or feels them. But of the nature

of either body or mind, further than the feelings which the former

excites, and which the latter experiences, we do not, according to the

best existing doctrine, know anything; and if anything, logic has

nothing to do with it, or with the manner in which the knowledge is

acquired. With this result we may conclude this portion of our subject,

and pass to the third and only remaining class or division of Nameable

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 cannot 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 attributes; and the distinction which we verbally make between the

properties of things and the sensations we receive from them, must

originate in the convenience of discourse rather than in the nature of

what is signified by the terms.

Attributes are usually distributed under the three heads of Quality,

Quantity, and Relation. We shall come to the two latter presently: in

the first place we shall confine 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 colour is one.

This is one view which may be taken of the subject. But there is also

another and a different view. It may be said, that it is true we _know_

nothing of sensible objects, except the sensations they excite in us;

that the fact of our receiving from snow the particular sensation which

is called a sensation of white, is the _ground_ on which we ascribe to

that substance the quality whiteness; the sole proof of its possessing

that quality. But because one thing may be the sole evidence of the

existence of another thing, it does not follow that the two are one and

the same. The attribute whiteness (it may be said) is not the fact of

receiving the sensation, but something in the object itself; a _power_

inherent in it; 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 presence of snow produces in

us that sensation, but that it does so through, and by reason of, that

power or quality.

For the purposes of logic it is not of material importance which of

these opinions we adopt. The full discussion of the subject belongs to

the other department of scientific inquiry, so often alluded to under

the name of metaphysics; but it may be said here, that for the doctrine

of the existence of a peculiar species of entities called qualities, I

can see no foundation except in a tendency of the human mind which is

the cause of many delusions. I mean, the disposition, wherever we meet

with two names which are not precisely synonymous, to 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_ cannot be put indiscriminately one for the

other, it is supposed that they cannot both signify the same thing,

namely, the impression or feeling with which we are affected through our

senses by the presence of an object; though there is at least no

absurdity in supposing that this identical impression or feeling may be

called a sensation when considered merely in itself, and a quality when

looked at in relation to any one of the numerous objects, the presence

of which to our organs excites in our minds that among various other

sensations or feelings. And if this be admissible as a supposition, it

rests with those who contend for an entity _per se_ called a quality, to

show that their opinion is preferable, or is anything in fact but a

lingering remnant of the scholastic doctrine of occult causes; the very

absurdity which Molière so happily ridiculed when he made one of his

pedantic physicians account for the fact that "l'opium endormit," by the

maxim "parcequ'il a une vertu soporifique."

It is evident that when the physician stated that opium had "une vertu

soporifique," he did not account for, but merely asserted over again,

the fact that it _endormit_. In like manner, when we say that snow is

white because it has the quality of whiteness, we are only re-asserting

in more technical language the fact that it excites in us the sensation

of white. If it be said that the sensation must have some cause, I

answer, its cause is the presence of the assemblage of phenomena which

is termed the object. When we have asserted that as often as the object

is present, and our organs in their normal state, the sensation takes

place, we have stated all that we know about the matter. There is no

need, after assigning a certain and intelligible cause, to suppose an

occult cause besides, for the purpose of enabling the real cause to

produce its effect. If I am asked, why does the presence of the object

cause this sensation in me, I cannot tell: I can only say that such is

my nature, and the nature of the object; that the fact forms a part of

the constitution of things. And to this we must at last come, even after

interpolating the imaginary entity. Whatever number of links the chain

of causes and effects may consist of, how any one link produces the one

which is next to it, remains equally inexplicable to us. It is as easy

to comprehend that the object should produce the sensation directly and

at once, as that it should produce the same sensation by the aid of

something else called the _power_ of producing it.

But, as the difficulties which may be felt in adopting this view of the

subject cannot be removed without discussions transcending the bounds of

our science, I content myself with a passing indication, and shall, for

the purposes of logic, adopt a language compatible with either view of

the nature of qualities. I shall say,--what at least admits of no

dispute,--that the quality of whiteness ascribed to the object snow, is

_grounded_ on its exciting in us the sensation of white; and adopting

the language already used by the school logicians in the case of the

kind of attributes called Relations, I shall term the sensation of

white the foundation of the quality whiteness. For logical purposes the

sensation is the only essential part of what is meant by the word; the

only part which we ever can be concerned in proving. When that is

proved, the quality is proved; if an object excites 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 attribute called a Relation, the foundation of the attribute

must be something in which other objects are concerned besides itself

and the percipient.

As there may with propriety be said to be a relation between any two

things to which two correlative names are or may be given, we may expect

to discover what constitutes a relation in general, if we enumerate the

principal cases in which mankind have imposed correlative names, and

observe what these cases have in common.

What, then, is the character which 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 with_ 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

requires to be considered separately,) there seems to be one thing

common to all these cases, and only one; that in each of them there

exists or occurs, or has existed or occurred, or may be expected to

exist or occur, some fact or phenomenon, into which the two things which

are said to be related to each other, both enter as parties concerned.

This fact, or phenomenon, is what the Aristotelian logicians called the

_fundamentum relationis_. Thus in the relation of greater and less

between two magnitudes, the _fundamentum relationis_ is the fact that

one of the two magnitudes could, under certain conditions, be included

in, without entirely filling, the space occupied by the other magnitude.

In the relation of master and servant, the _fundamentum relationis_ is

the fact that the one has undertaken, or is compelled, to perform

certain services for the benefit and at the bidding of the other.

Examples might be indefinitely multiplied; but it is already obvious

that whenever two things are said to be related, there is some fact, or

series of facts, into which they both enter; and that whenever any two

things are involved in some one fact, or series of facts, we may ascribe

to those two things a mutual relation grounded on the fact. Even if they

have nothing in common but what is common to all things, that they are

members of the universe, we call that a relation, and denominate them

fellow-creatures, fellow-beings, or fellow-denizens of the universe. But

in proportion as the fact into which the two objects enter as parts is

of a more special and peculiar, or of a more complicated nature, so also

is the relation grounded upon it. And there are as many conceivable

relations as there are conceivable kinds of fact in which two things can

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

_fundamentum 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)

another word for intentions followed by an effect, and that effect being

but another word for sensations, or some other feelings, occasioned

either to the agent himself or to somebody else. There is no part of

what the names expressive of the relation imply, that is not resolvable

into states of consciousness; outward objects being, no doubt, supposed

throughout as the causes by which some of those states of consciousness

are excited, and minds as the subjects by which all of them are

experienced, but neither the external objects nor the minds making their

existence known otherwise than by the states of consciousness.

Cases of relation are not always so complicated as those to which we

last alluded. The simplest of all cases of relation are those expressed

by the words antecedent and consequent, and by the word simultaneous. If

we say, for instance, that dawn preceded sunrise, the fact in which the

two things, dawn and sunrise, were jointly concerned, consisted only of

the two things themselves; no third thing entered into the fact or

phenomenon at all. Unless, indeed, we choose to call the succession of

the two objects a third thing; but their succession is not something

added to the things themselves; it is something involved in them. Dawn

and sunrise announce themselves to our consciousness by two successive

sensations. Our consciousness of the succession of these sensations is

not a third sensation or feeling added to them; we have not first the

two feelings, and then a feeling of their succession. To have two

feelings at all, implies having them either successively, or else

simultaneously. Sensations, or other feelings, being given, succession

and simultaneousness are the two conditions, to the alternative of which

they are subjected by the nature of our faculties; and no one has been

able, or needs expect, to analyse the matter any farther.

§ 11. In a somewhat similar position are two other sorts of relations,

Likeness and 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 _fundamentum_

of this relation? The two sensations first, and then what we call a

feeling of resemblance, or of want of resemblance. Let us confine

ourselves to the former case. Resemblance is evidently a feeling; a

state of the consciousness of the observer. Whether the feeling of the

resemblance of the two colours be a third state of consciousness, which

I have _after_ having the two sensations of colour, 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 analyse any of our other feelings.

Likeness and unlikeness, therefore, as well as antecedence, sequence,

and simultaneousness, must stand apart among relations, as things _sui

generis_. They are attributes grounded on facts, that is, on states of

consciousness, but on states which are peculiar, unresolvable, and

inexplicable.

But, though likeness or unlikeness cannot be resolved into anything

else, complex cases of likeness or unlikeness can be resolved into

simpler ones. When we say of two things which consist of parts, that

they are like one another, the likeness of the wholes does admit of

analysis; it is compounded of 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 complex likeness be compounded:

likeness in a succession of bodily postures; likeness in voice, or in

the accents and intonations of the voice; likeness in the choice of

words, and in the thoughts or sentiments expressed, whether by word,

countenance, or gesture.

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

attributes except the sensations or states of feeling on which they are

grounded,) we mean really that those sensations, or states of feeling,

resemble each other. We may also say that two relations are alike. The

fact of resemblance between relations is sometimes called _analogy_,

forming one of the numerous meanings of that word. The relation in which

Priam stood to Hector, namely, that of father and son, 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 resembles the relation in which Napoleon stood to

France, though not so closely as to be called the same relation. The

meaning in both these instances must be, that a resemblance existed

between the facts which constituted the _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 things similar to itself. And as,

whenever two objects are jointly concerned 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 admit of its

being said that the two relations resemble; provided, of course, the

points of resemblance are found in those portions of the two phenomena

respectively which are connoted by the relative names.

While speaking of resemblance, it is necessary to take notice of an

ambiguity of language, against which scarcely any one is sufficiently on

his guard. Resemblance, when it exists in the highest degree of all,

amounting to 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 person. This is evidently an incorrect

application of the word _same_; for the feeling which I had yesterday is

gone, never to return; what I have to-day is another feeling, exactly

like the former perhaps, but distinct from it; and it is evident that

two different persons cannot be experiencing the same feeling, in the

sense in which we say that they are both sitting at the same table. By a

similar ambiguity we say, that two persons are ill of the _same_

disease; that two persons hold the _same_ office; not in the sense in

which we say that they are engaged in the same adventure, or sailing in

the same ship, but in the sense that they fill offices exactly similar,

though, perhaps, in distant places. Great confusion of ideas is often

produced, and many fallacies engendered, in otherwise enlightened

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 identity and undistinguishable resemblance.

Among modern writers, Archbishop Whately stands almost alone in having

drawn attention to this distinction, and to the ambiguity connected with

it.

Several relations, generally called by other names, are really cases of

resemblance. As, for example, equality; which is but another word for

the exact resemblance commonly called identity, considered as subsisting

between things in respect of their _quantity_. And this example forms a

suitable transition to the third and last of the three heads under

which, as already remarked, Attributes are commonly arranged.

V. QUANTITY.

§ 12. Let us imagine two things, between which there is no difference

(that is, no dissimilarity), except in quantity alone: for instance, a

gallon of water, and more than a gallon of water. A gallon of water,

like any other external object, makes its presence known to us by a set

of sensations which it excites. Ten gallons of water are also an

external object, making its presence known to us in a similar manner;

and as we do not mistake ten gallons of water for a gallon of water, it

is plain that the set of sensations is more or less different in the two

cases. In like manner, a gallon of water, and a gallon of wine, are two

external objects, making their presence known by two sets of sensations,

which sensations are different from each other. In the first case,

however, we say that the difference is in quantity; in the last there is

a difference in quality, while the quantity of the water and of the wine

is the same. What is the real distinction between the two cases? It is

not the province of Logic to analyse it; nor to decide whether it is

susceptible of analysis or not. For us the following considerations are

sufficient. It is evident that the sensations I receive from the gallon

of water, and those I receive from the gallon of wine, are not the same,

that is, not precisely alike; neither are they altogether unlike: they

are partly similar, partly dissimilar; and that in which they resemble

is precisely that in which alone the gallon of water and the ten gallons

do not resemble. That in which the gallon of water and the gallon of

wine are like each other, and in which the gallon and the ten gallons of

water are unlike each other, is called their quantity. This 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

drinking one gallon; or that to see or handle a foot-rule, and to see or

handle a yard-measure made exactly like it, are the same sensations. I

do not undertake to say what the difference in the sensations is.

Everybody knows, and nobody can tell; no more than any one could tell

what white is to a person who had never had the sensation. But the

difference, so far as cognizable by our faculties, lies in the

sensations. Whatever difference we say there is in the things

themselves, is, in this as in all other cases, grounded, and grounded

exclusively, on a difference in the sensations excited by them.

VI. ATTRIBUTES CONCLUDED.

§ 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 exciting those sensations. And the same general explanation has been

found to apply to most of the attributes usually classed under the head

of Relation. They, too, are grounded on some fact or phenomenon into

which the related objects enter as parts; that fact or phenomenon having

no meaning and no existence to us, except the series of sensations or

other states of 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 sensations or states of consciousness. We have been

obliged, indeed, to recognise 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 cannot, without transgressing the bounds of our

science, discuss it here), at least our knowledge of these relations,

and even our possibility of knowledge, is confined to those which

subsist between sensations, or other states of consciousness; for,

though we ascribe resemblance, or succession, or simultaneity, to

objects and to attributes, it is always in virtue of resemblance or

succession or simultaneity in the sensations or states of consciousness

which those objects excite, and on which those attributes are grounded.

§ 14. In the preceding investigation we have, for the sake of

simplicity, considered bodies only, and omitted minds. But what we have

said, is applicable, _mutatis mutandis_, to the latter. The attributes

of minds, as well as those of bodies, are grounded on states of feeling

or consciousness. But in the case of a 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 superstitious,

or meditative, or cheerful, we mean that the ideas, emotions, or

volitions implied in those words, form a frequently recurring part of

the series of feelings, or states of consciousness, which fill up the

sentient existence of that mind.

In addition, however, to those attributes of a mind which are grounded

on its own states of feeling, attributes may also be ascribed to it, in

the same manner as to a body, grounded on the feelings which it excites

in other minds. A mind does not, indeed, like a body, excite

sensations, but it may excite thoughts or emotions. The most important

example of attributes 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 contemplation of it excites the sentiment of admiration;

and indeed somewhat more, for the word implies that we not only feel

admiration, but approve that sentiment in ourselves. In some cases,

under the semblance of a single attribute, two are really predicated:

one of them, a state of the mind itself; the other, a state with which

other minds are affected by thinking of it. As when we say of any one

that he is generous. The word generosity 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 following purport:

Certain feelings form habitually a part of this person's sentient

existence; and the idea of those feelings of his, excites the sentiment

of approbation in ourselves or others.

As we thus ascribe attributes to minds on the ground of ideas and

emotions, so may we to bodies on similar grounds, and not solely on the

ground of sensations: as in speaking of the beauty of a statue; since

this attribute is grounded on the peculiar feeling of pleasure which the

statue produces in our minds; which is not a sensation, but an emotion.

VII. GENERAL RESULTS.

§ 15. Our survey of the varieties of Things which have been, or which

are capable of being, named--which have been, or are capable of being,

either predicated of other Things, or themselves made the subject of

predications--is now concluded.

Our enumeration commenced with Feelings. These we scrupulously

distinguished from the objects which excite them, and from the organs by

which they are, or may be supposed 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 merely volitions followed by an effect.

If there be any other kind of mental state not included under these

subdivisions, we did not think it necessary or proper in this place to

discuss its existence, or the rank which ought to be assigned to it.

After Feelings we proceeded to Substances. These are either Bodies or

Minds. Without entering into the grounds of the metaphysical doubts

which have been raised concerning the existence of Matter and Mind as

objective realities, we stated as sufficient for us the conclusion in

which the best thinkers are now for the most part agreed, that all we

can know of Matter is the sensations which it gives us, and the order of

occurrence of those sensations; and that while the substance Body is the

unknown cause of our sensations, the substance Mind is the unknown

recipient.

The only remaining class of Nameable Things is Attributes; and these are

of three kinds, Quality, Relation, and Quantity. Qualities, like

substances, are known to us no otherwise than by the sensations or other

states of consciousness which they excite: and while, in compliance with

common usage, we have continued to speak of them as a distinct class of

Things, we showed that in predicating them no one means to predicate

anything but those sensations or states of consciousness, on which they

may be said to be grounded, and by which alone they can be defined or

described. 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 involved

therein; and to this even the peculiar and simple relations just

adverted to are not exceptions. Those peculiar relations, however, are

so important, and, even if they might in strictness be classed among

states of consciousness, are so fundamentally distinct from any other of

those states, that it would be a vain subtlety to bring them under that

common description, and it is necessary that they should be classed

apart.

As the result, therefore, of our analysis, we obtain the following as an

enumeration and classification of all Nameable Things:--

1st. Feelings, or States of Consciousness.

2nd. The Minds which experience those feelings.

3rd. The Bodies, or external objects, which excite certain of those

feelings, together with the powers or properties whereby they excite

them; these last being included rather in compliance with common

opinion, and because their existence is taken for granted in the common

language from which I cannot prudently deviate, than because the

recognition of such powers or properties as real existences appears to

be warranted by a sound philosophy.

4th, and last. The Successions and Co-existences, the Likenesses and

Unlikenesses, between feelings or states of consciousness. Those

relations, when considered as 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.

This, until a better can be suggested, may serve as a substitute for the

abortive Classification of Existences, termed the Categories of

Aristotle. The practical application of it will appear when we commence

the inquiry into the Import of Propositions; in other words, when we

inquire what it is which the mind actually believes, when it gives what

is called its assent to a proposition.

These four classes comprising, if the classification be correct, all

Nameable Things, these or some of them must of course compose the

signification of all names; and of these, or some of them, is made up

whatever we call a fact.

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

or states of consciousness considered as such, is often called a

Psychological or Subjective fact; while every fact which is composed,

either wholly or in part, of something different from these, that is, of

substances and attributes, is called an Objective fact. We may say,

then, that every 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

cannot conclude from merely seeing two names put together, that they are

a predicate and a subject, that is, that one of them is intended to be

affirmed or denied of the other, it is necessary that there should be

some mode or form of indicating that such is the intention; some sign to

distinguish a predication from any other kind of 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 _is_, when an affirmation is intended, _is not_, when a negation;

or by some other part of the verb _to be_. The word which thus serves

the purpose of a sign of predication is called, as we formerly observed,

the _copula_. It is important that there should be no indistinctness in

our conception of the nature and office of the copula; for confused

notions respecting it are among the causes which have spread mysticism

over the field of logic, and perverted its speculations into

logomachies.

It is apt to be supposed that the copula is something more than a mere

sign of predication; that it also signifies existence. In the

proposition, Socrates is just, it may seem to be implied not only that

the quality _just_ can be affirmed of Socrates, but moreover that

Socrates _is_, that is to say, exists. This, however, only shows that

there is an ambiguity in the word _is_; a word which not only performs

the function of the copula in affirmations, but has also a meaning of

its own, in virtue of which it may itself be made the predicate of a

proposition. That the employment of it as a copula does not necessarily

include the affirmation of existence, appears from such a proposition as

this, A centaur is a fiction of the poets; where it cannot possibly be

implied that a centaur exists, since the proposition itself expressly

asserts that the thing has no real existence.

Many volumes might be filled with the frivolous speculations concerning

the nature of Being, ([Greek: to on, ousia], 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 exist_, and when

it signifies to _be_ some specified thing, as to _be_ a man, to _be_

Socrates, to _be_ seen or spoken of, to _be_ a phantom, even to _be_ a

nonentity, it must still, at bottom, answer to the same idea; and that a

meaning must be found for it which shall suit all these cases. The fog

which rose from this narrow spot diffused itself at an early period over

the whole surface of metaphysics. Yet it becomes us not to triumph over

the great intellects of Plato and 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

languages which eminent thinkers have used as the vehicle of their

thoughts, is the practical lesson we learn respecting the ambiguities of

words, by finding that the same word in one language corresponds, on

different occasions, to different words in another. When not thus

exercised, even the strongest understandings find it difficult to

believe that things which have a common name, have not in some respect

or other a common nature; and often expend much labour very unprofitably

(as was frequently done by the two philosophers just mentioned) in vain

attempts to discover in what this common nature consists. But, the habit

once formed, intellects much inferior are capable of detecting even

ambiguities which are common to many languages: and it is surprising

that the one now under consideration, though it exists in the modern

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[15] 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 affirmative and negative. An affirmative proposition is that in

which the predicate is _affirmed_ of the subject; as, Cæsar is dead. A

negative proposition is that in which the predicate is _denied_ of the

subject; as, Cæsar is not dead. The copula, in this last species of

proposition, consists of the words _is not_, which are the sign of

negation; _is_ being the sign of affirmation.

Some logicians, among whom may be mentioned Hobbes, state this

distinction differently; they recognise only one form of copula, _is_,

and attach the negative sign to the predicate. "Cæsar is dead," and

"Cæsar is not dead," according to these writers, are propositions

agreeing not in the subject 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 accordingly define a negative proposition

to be one in which the predicate is a negative name. The point, though

not of much practical moment, deserves notice as an example (not

unfrequent in logic) where by means of an apparent simplification, but

which is merely verbal, matters are made more complex than before. The

notion of these writers was, that they could get rid of the 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 attribute. So that when we affirm

a negative name, what we are really predicating is absence and not

presence; we are asserting not that anything is, but that something is

not; to express which operation no word seems so proper as the word

denying. The fundamental distinction is between a fact and the

non-existence of that fact; between seeing something and not seeing it,

between Cæsar's being dead and his not being dead; and if this were a

merely verbal distinction, the generalization which brings both within

the same form of assertion would be a real simplification: the

distinction, however, being real, and in the facts, it is the

generalization confounding the distinction that is merely verbal; and

tends to obscure the subject, by treating the difference between two

kinds of truths as if it were only a difference between two kinds of

words. To put things together, and to put them or keep them asunder,

will remain different operations, whatever tricks we may play with

language.

A remark of a similar nature may be applied to most of those

distinctions among propositions which are said to have reference to

their _modality_; as, difference of tense or time; the sun _did_ rise,

the sun _is_ rising, the sun _will_ rise. These differences, like that

between affirmation and negation, might be glossed over by considering

the incident of time as a mere modification of the predicate: thus, The

sun is _an object having risen_, The sun is _an object now rising_, The

sun is _an object to rise hereafter_. But the simplification would be

merely verbal. Past, present, and future, do not constitute so many

different kinds of rising; they are designations belonging to the event

asserted, to the _sun's_ rising to-day. They affect, not the predicate,

but the applicability of the predicate to the particular subject. That

which we affirm to be past, present, or future, is not what the subject

signifies, nor what the 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 circumstance of time is properly considered as attaching to the

copula, which is the sign of predication, and not to the predicate. If

the same cannot be said of such modifications as these, Cæsar _may_ be

dead; Cæsar is _perhaps_ dead; it is _possible_ that Cæsar is dead; it

is only because these fall altogether under another head, being properly

assertions not of anything relating to the fact itself, but of the state

of our own mind in regard to it; namely, our absence of disbelief of it.

Thus "Cæsar may be dead" means "I am not sure that Cæsar is alive."

§ 3. The next division of propositions is into Simple and Complex. A

simple proposition is that in which one predicate is affirmed or denied

of one subject. A complex proposition is that in which there is more

than one predicate, or more than one subject, or both.

At first sight this division has the air of an absurdity; a solemn

distinction of things into one and more than one; as if we were to

divide horses into single horses and teams of horses. And it is true

that what is called a complex proposition is often not a proposition at

all, but several propositions, held together by a conjunction. Such, for

example, is this: Cæsar is dead, and Brutus is alive: or even this,

Cæsar 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 abbreviations, and generally

abbreviations of propositions; a kind of short-hand, whereby something

which, to be expressed fully, would have required a proposition or a

series of propositions, is suggested to the mind at once. Thus the

words, Cæsar is dead and Brutus is alive, are equivalent to these: Cæsar

is dead; Brutus is alive; it is desired that the two preceding

propositions should be thought of together. If the words were, Cæsar is

dead _but_ Brutus is alive, the sense would be equivalent to the same

three propositions together with a fourth; "between the two preceding

propositions there exists a contrast:" viz. either between the two facts

themselves, or between the feelings with which it is desired that they

should be regarded.

In the instances cited the two propositions are kept visibly distinct,

each subject having its separate predicate, and each predicate its

separate subject. For brevity, however, and to avoid repetition, the

propositions are often blended together: as in this, "Peter and James

preached at Jerusalem and in Galilee," which contains four propositions:

Peter preached at Jerusalem, Peter preached in Galilee, James preached

at Jerusalem, James preached in Galilee.

We have seen that when the two or more propositions comprised in what is

called a complex proposition are stated absolutely, and not under any

condition or proviso, it is not a proposition at all, but a plurality of

propositions; since what it expresses is not a single assertion, but

several 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 subjects and of predicates, and may be said in one sense

of the word to consist of several propositions, contains but one

assertion; and its truth does not at all imply that of the simple

propositions which compose it. An example of this is, when the simple

propositions are connected by the particle _or_; as, Either A is B or C

is D; or by the particle _if_; as, A is B if C is D. In the former case,

the proposition is called _disjunctive_, in the latter, _conditional_:

the name _hypothetical_ was originally common to both. As has been well

remarked by Archbishop Whately and others, the disjunctive form is

resolvable into the conditional; every disjunctive proposition 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

conditional in meaning; and the words hypothetical and conditional may

be, as indeed they generally are, used synonymously. Propositions in

which the assertion is not dependent on a condition, are said, in the

language of logicians, to be _categorical_.

An hypothetical proposition is not, like the pretended complex

propositions which we previously considered, a mere aggregation of

simple propositions. The simple propositions which form part of the

words in which it is couched, form no part of the assertion which it

conveys. When we say, If the Koran comes from God, Mahomet is the

prophet of God, we do not intend to affirm either that the Koran does

come from God, or that Mahomet is really his prophet. Neither of these

simple propositions may be true, and yet the truth of the hypothetical

proposition may be indisputable. What is asserted is not the truth of

either of the propositions, but the inferribility of the one from the

other. What, then, is the subject, and what the predicate of the

hypothetical proposition? "The Koran" is not the subject of it, nor is

"Mahomet:" for nothing is affirmed or denied either of the Koran or of

Mahomet. The real subject of the predication is the entire proposition,

"Mahomet is the prophet of God;" and the affirmation is, that this is a

legitimate inference from the proposition, "The Koran comes from God."

The subject and predicate, therefore, of an hypothetical 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 following: "The proposition

C is D, is a legitimate inference from the proposition A is B."

The distinction, therefore, between hypothetical and categorical

propositions, 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 an hypothetical

proposition, is that of being an inference from a certain other

proposition. But this is only one of many attributes that might be

predicated. We may say, That the whole is greater than its part, is an

axiom in mathematics: That the Holy Ghost proceeds from the Father

alone, is a tenet of the Greek Church: The doctrine of the divine right

of kings was renounced by Parliament at the Revolution: The

infallibility of the Pope has no countenance from Scripture. In all

these cases the subject of the predication is an entire proposition.

That which these different predicates are affirmed of, is _the

proposition_, "the whole is greater than its part;" _the proposition_,

"the Holy Ghost proceeds from the Father alone;" _the proposition_,

"kings have a divine right;" _the proposition_, "the Pope is

infallible."

Seeing, then, that there is much less difference between hypothetical

propositions and any others, than one might be led to imagine from their

form, we should be at a loss to account for the conspicuous position

which they have been selected to fill in treatises on logic, if we did

not remember that what they predicate of a proposition, namely, its

being an inference from something else, is precisely that one of its

attributes with which most of all a logician is concerned.

§ 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 Cæsar_ 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 universal propositions. No man is immortal, is also an universal

proposition, since the predicate, immortal, is denied of each and every

individual denoted by the term man; the negative proposition being

exactly equivalent to the following, Every man is not-immortal. But

"some men are wise," "some men are not wise," are particular

propositions; the predicate _wise_ being in the one case affirmed and in

the other denied not of each and every individual denoted by the term

man, but only of each and every one of some portion of those

individuals, without specifying what portion; for if this were

specified, the proposition would be changed either into a singular

proposition, or into an universal proposition with a different subject;

as, for instance, "all _properly instructed_ men are wise." There are

other forms of particular propositions; as, "_Most_ men are imperfectly

educated:" it being immaterial how large a portion of the subject the

predicate is asserted of, as long as it is left uncertain how that

portion is to be distinguished 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 observes, is a solecism, of the same nature as that

committed by some grammarians when in their list of genders they

enumerate the _doubtful_ gender. The speaker must mean to assert the

proposition either as an universal or as a particular proposition,

though he has failed to declare which: and it often happens that though

the words do not show which of the two he intends, the context, or the

custom of speech, supplies the deficiency. Thus, when it is affirmed

that "Man is mortal," nobody doubts that the assertion is intended of

all human beings; and the word indicative of universality is commonly

omitted, only because the meaning is evident without it. In the

proposition, "Wine is good," it is understood with equal readiness,

though for somewhat different reasons, that the assertion is not

intended to be universal, but particular.[16]

When a general name stands for each and every individual which it is a

name of, or in other words, which it denotes, it is said by logicians to

be _distributed_, or taken distributively. Thus, in the proposition, All

men are mortal, the subject, Man, is distributed, because mortality is

affirmed of each and every man. The predicate, Mortal, is not

distributed, because the only mortals who are spoken of in the

proposition are those who happen to be men; while the word may, for

aught that appears, and in fact does, comprehend within it an indefinite

number of objects besides men. In the proposition, Some men are mortal,

both the predicate and the subject are undistributed. In the following,

No men have wings, both the predicate and the subject are distributed.

Not only is the attribute of having wings denied of the entire class

Man, but that class is severed and cast out from the whole of the class

Winged, and not merely from some part of that class.

This phraseology, which is of great service in stating and

demonstrating the rules of the syllogism, enables us to express very

concisely the definitions of an universal and a particular proposition.

An universal proposition is that of which the 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

explaining and illustrating these, more suitable opportunities will

occur in the sequel.

CHAPTER V.

OF THE IMPORT OF PROPOSITIONS.

§ 1. An inquiry into the nature of propositions must have one of two

objects: to analyse the state of mind called Belief, or to analyse what

is believed. All language recognises a difference between a doctrine or

opinion, and the fact of entertaining the opinion; between assent, and

what is assented to.

Logic, according to the conception here formed of it, has no concern

with the nature of the act of judging or believing; the consideration of

that act, as a phenomenon of the mind, belongs to another science.

Philosophers, however, from Descartes downwards, and especially from the

era of Leibnitz and Locke, have by no means observed this distinction;

and would have treated with great disrespect any attempt to analyse the

import of Propositions, unless founded on an analysis of the act of

Judgment. A proposition, they would have said, is but the expression in

words of a Judgment. The thing expressed, not the mere verbal

expression, is the important matter. When the mind assents to a

proposition, it judges. Let us find out what the mind does when it

judges, and we shall know what propositions mean, and not otherwise.

Conformably to these views, almost all the writers on Logic in the last

two centuries, whether English, German, or French, have made their

theory of Propositions, from one end to the other, a theory of

Judgments. They considered a Proposition, or a Judgment, for they used

the two words indiscriminately, to consist in affirming or denying one

_idea_ of another. To judge, was to put two ideas together, or to bring

one idea under another, or to compare two ideas, or to perceive the

agreement or disagreement between two ideas: and the whole doctrine of

Propositions, together with the theory of Reasoning, (always necessarily

founded on the theory of Propositions,) was stated as if Ideas, or

Conceptions, or whatever other term the writer preferred as a name for

mental representations generally, constituted essentially the subject

matter and substance of those operations.

It is, of course, true, that in any case of judgment, as for instance

when we judge that gold is yellow, a process takes place in our minds,

of which some one or other of these theories is a partially correct

account. We must have the idea of gold and the idea of yellow, and these

two ideas must be brought together in our mind. But in the first place,

it is evident that this is only a part of what takes place; for we may

put two ideas together without any act of belief; as when we merely

imagine something, such as a golden mountain; or when we actually

disbelieve: for in order even to disbelieve that Mahomet was an apostle

of God, we must put the idea of Mahomet and that of an apostle of God

together. To determine what it is that happens in the case of assent or

dissent besides putting two ideas together, is one of the most intricate

of metaphysical problems. But whatever the solution may be, we may

venture to assert that it can have nothing whatever to do with the

import of propositions; for this reason, that propositions (except

sometimes when the mind itself is the subject treated of) are not

assertions respecting our ideas of things, but assertions respecting the

things themselves. In order to believe that gold is yellow, I must,

indeed, have the idea of gold, and the idea of yellow, and something

having 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

everything else that I do. I cannot dig the ground unless I have the

idea of the ground, and of a spade, and of all the other things I am

operating upon, and unless I put those ideas together.[17] But it would

be a very ridiculous description of digging the ground to say that it is

putting one idea into another. Digging is an operation which is

performed upon the things themselves, though it cannot be performed

unless I have in my mind the ideas of them. And in like manner,

believing is an act which has for its subject the facts themselves,

though a previous mental conception of the facts is an indispensable

condition. When I say that fire causes heat, do I mean that my idea of

fire causes my idea of heat? No: I mean that the natural phenomenon,

fire, causes the natural phenomenon, heat. When I mean to assert

anything respecting the ideas, I give them their proper name, I call

them ideas: as when I say, that a child's idea of a battle is unlike the

reality, or that the ideas 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

proposition, is the relation between the two _ideas_ corresponding to

the subject and predicate, (instead of the relation between the two

_phenomena_ which they respectively express,) seems to me one of the

most fatal errors ever 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 Philosophy connected with Logic,

which have been produced since the intrusion of this cardinal error,

though sometimes written by men of extraordinary abilities and

attainments, almost always tacitly imply a theory that the investigation

of truth consists in contemplating and handling our ideas, or

conceptions of things, instead of the things themselves: a doctrine

tantamount to the assertion, that the only mode of acquiring knowledge

of nature is to study it at second hand, as represented in our own

minds. Meanwhile, inquiries into every kind of natural phenomena were

incessantly establishing great and fruitful truths on most important

subjects, by processes upon which these views of the nature of Judgment

and Reasoning threw no light, and in which they afforded no assistance

whatever. No wonder that those who knew by practical experience how

truths are arrived at, should deem a science futile, which consisted

chiefly of such speculations. What has been done for the advancement of

Logic since these doctrines came into vogue, has been done not by

professed logicians, but by discoverers in the other sciences; in whose

methods of investigation many principles of logic, not previously

thought of, have 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 purpose respecting it.

We have to inquire, then, on the present occasion, not into Judgment,

but judgments; not into the act of believing, but into the thing

believed. What is the immediate object of belief in a Proposition? What

is the matter of fact signified by it? What is it to which, when I

assert the proposition, I give my assent, and call upon others to give

theirs? What is that which is expressed by the form of discourse called

a Proposition, and the conformity of which to fact constitutes the truth

of the proposition?

§ 2. One of the clearest and most consecutive thinkers whom this country

or the world has produced, I mean Hobbes, has given the following answer

to this question. In every proposition (says he) 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 everything of which _man_

is a name. All men are six feet high, is not true, because _six feet

high_ is not a name of everything (though it is of some things) of which

_man_ is a name.

What is stated in this theory as the definition of a true proposition,

must be allowed to be a property which all true propositions possess.

The subject and predicate being both of them names of things, if they

were names of quite different things the one name could not,

consistently with its signification, be predicated of the other. If it

be true that some men are copper-coloured, it must be true--and the

proposition does really assert--that among the individuals denoted by

the name man, there are some who are also among those denoted by the

name copper-coloured. If it be true that all oxen ruminate, it must be

true that all the individuals denoted by the name ox are also among

those denoted by the name ruminating; and whoever asserts that all oxen

ruminate, undoubtedly does assert that this relation subsists between

the two names.

The assertion, therefore, which, according to Hobbes, is the only one

made in any proposition, really is made in every proposition: and his

analysis has consequently one of the requisites for being the true one.

We may go a step farther; it is the only analysis that is rigorously

true of all propositions without exception. What he gives as the meaning

of propositions, 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 warrant us in putting together two words with a copula

between them, it is really enough that the thing or things denoted by

one of the names should be capable, without violation of usage, of being

called by the other name also. If, then, this be all the 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 meaning, that

same collocation combined with other circumstances, that _form_

combined with other _matter_, does convey more, and much more.

The only propositions of which Hobbes' principle is a 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 objects: and when a proper name is predicated of another

proper name, all the signification conveyed is, that both the names are

marks for the same object. But this is precisely what Hobbes produces as

a theory of predication in general. His doctrine is a full explanation

of such predications as these: Hyde was Clarendon, or, Tully is Cicero.

It exhausts the meaning of those propositions. But it is a sadly

inadequate theory of any others. That it should ever have been thought

of as such, can be accounted for only by the fact, that Hobbes, in

common with the other Nominalists, bestowed little or no attention upon

the _connotation_ of words; and sought for their meaning exclusively in

what they _denote_: as if all names had been (what none but proper names

really are) marks put upon 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

connotative, resides in the connotation. When, therefore, we are

analysing the meaning of any proposition in which the predicate and the

subject, or either of them, are connotative names, it is to the

connotation of those terms that we must exclusively look, and not to

what they _denote_, or in the language of Hobbes (language so far

correct) are names of.

In asserting that the truth of a proposition depends on the conformity

of import between its terms, as, for instance, that the proposition,

Socrates is wise, is a true proposition, because Socrates and wise are

names applicable to, or, as he expresses it, names of, the same person;

it is very 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 fixed the meaning of the word wise, they were not

thinking of Socrates, nor, when his parents gave him the name of

Socrates, were they thinking of wisdom. The names _happen_ to fit the

same person because of a certain _fact_, which fact was not known, nor

in being, when the names were invented. If we want to know what the fact

is, we shall find the clue to it in the _connotation_ of the names.

A bird or a stone, a man, or a wise man, means simply, an object having

such and such attributes. The real meaning of the word man, is those

attributes, and not Smith, Brown, and the remainder of the individuals.

The word _mortal_, in like manner connotes a certain attribute or

attributes; and when we say, All men are mortal, the meaning of the

proposition is, that all beings which possess the one set of attributes,

possess also the other. If, in our experience, the attributes connoted

by _man_ are always accompanied by the attribute connoted by _mortal_,

it will follow as a consequence, that the class _man_ will be wholly

included in the class _mortal_, and that _mortal_ will be a name of all

things of which _man_ is a name: but why? Those objects are brought

under the name, by possessing the attributes connoted by it: but their

possession of the attributes is the real condition on which the truth of

the proposition depends; not their being called by the name. Connotative

names do not precede, but follow, the attributes which they connote. If

one attribute happens to be always found in conjunction with another

attribute, the concrete names which answer to those attributes will of

course be predicable of the same subjects, and may be said, in Hobbes'

language, (in the propriety of which on this occasion I fully concur,)

to be two names for the same things. But the possibility of a concurrent

application of the two names, is a mere consequence of the conjunction

between the two attributes, and was, in most cases, never thought of

when the names were introduced and their signification fixed. That the

diamond is combustible, was a proposition certainly not dreamt of when

the words Diamond and Combustible first received their meaning; and

could not have been discovered by the most ingenious and refined

analysis of the signification of those words. It was found out by a very

different process, namely, by exerting the senses, and learning from

them, that the attribute of combustibility existed in the diamonds upon

which the experiment was tried; the number or character of the

experiments being such, that what was true of those individuals might be

concluded to be true of all substances "called by the name," that is, of

all substances possessing the attributes which the name connotes. The

assertion, therefore, when analysed, is, that wherever we find certain

attributes, there will be found a certain other attribute: which is not

a question of the signification of names, but of laws of nature; the

order existing among phenomena.

§ 3. Although Hobbes' theory of Predication has not, in the terms in

which he stated it, met with a very favourable reception from subsequent

thinkers, a theory virtually identical with it, and not by any means so

perspicuously expressed, may almost be said to have taken the rank of an

established opinion. The most generally received notion of Predication

decidedly is that it consists in referring something to a class, _i.e._,

either placing an individual under a class, or placing one class under

another class. Thus, the proposition, Man is mortal, asserts, according

to this view of it, that the class man is included in the class mortal.

"Plato is a philosopher," asserts that the individual Plato is one of

those who compose the class philosopher. If the proposition is negative,

then instead of placing something in a class, it is said to exclude

something from a class. Thus, if the following be the 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 nothing but an

indefinite number of individuals denoted by a general name. The name

given to them in common, is what makes them a class. To refer anything

to a class, therefore, is to look upon it as one of the things which are

to be called by that common name. To exclude it from a class, is to say

that the common name is not applicable to it.

How widely these views of predication have prevailed, is evident from

this, that they are the basis of the celebrated _dictum de omni et

nullo_. When the syllogism is resolved, by all who treat of it, into an

inference that what is true of a class is true of all things whatever

that belong to the class; and when this is laid down by almost all

professed logicians as the ultimate principle to which all reasoning

owes its validity; it is clear that in the general estimation of

logicians, the propositions of which reasonings are composed can be the

expression of nothing but the process of dividing things into classes,

and referring everything to its proper class.

This theory appears to me a signal example of a logical error very often

committed in logic, that of [Greek: hysteron proteron], or explaining a

thing by something which presupposes it. When I say that snow is white,

I may and ought to be thinking of snow as a class, because I am

asserting a proposition as true of all snow: but I am certainly not

thinking of white objects as a class; I am thinking of no white object

whatever except snow, but only of that, and of the sensation of white

which it gives me. When, indeed, I have judged, or assented to the

propositions, that snow is white, and that several other things are also

white, I gradually begin to think of white objects as a class, including

snow and those other things. But this is a conception which followed,

not preceded, those judgments, and therefore cannot be given as an

explanation of them. Instead of explaining the effect by the cause, this

doctrine explains the cause by the effect, and is, I conceive, founded

on a latent misconception of the nature of classification.

There is a sort of language very generally prevalent in these

discussions, which seems to suppose that classification is an

arrangement and grouping of definite and known individuals: that when

names were imposed, mankind took into consideration all the individual

objects in the universe, distributed them into parcels or lists, and

gave to the objects of each list a common name, repeating this operation

_toties quoties_ until they had invented all the general names of which

language consists; which having been once done, if a question

subsequently arises whether a certain general name can be truly

predicated of a certain particular object, we have only (as it were) to

read the roll of the objects upon which that name was conferred, and see

whether the object about which the question arises is to be found among

them. The framers of language (it would seem to be supposed) have

predetermined all the objects that are to compose each class, and we

have only to refer to the record of an antecedent decision.

So absurd a doctrine will be owned by nobody when thus nakedly stated;

but if the commonly received explanations of classification and naming

do not imply this theory, it requires to be shown how they admit of

being reconciled with any other.

General names are not marks put upon definite objects; classes are not

made by drawing a line round a given number of assignable individuals.

The objects which compose any given class are perpetually fluctuating.

We may frame a class without knowing the individuals, or even any of the

individuals, of which it may be composed; we may do so while believing

that no such individuals exist. If by the _meaning_ of a general name

are to be understood the things which it is the name of, no general

name, except by accident, has a fixed meaning at all, or ever long

retains the same meaning. The only mode in which any general name has a

definite meaning, is by being a name of an indefinite variety of things;

namely, of all things, known or unknown, past, present, or future, which

possess certain definite attributes. When, by studying not the meaning

of words, but the phenomena of nature, we 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 individual in the class because the proposition is true; the

proposition is not true because the object is placed in the class.

It will appear hereafter, in treating of reasoning, how much the theory

of that intellectual process has been vitiated by the influence of these

erroneous notions, and by the habit which they exemplify of assimilating

all the operations of the human understanding which have truth for their

object, to 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' theory of Predication, according to the

well-known remark of Leibnitz, and the avowal of Hobbes himself,[18]

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 bottom, 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 admission

cannot be made in stronger terms than it is by Hobbes himself;[19]

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 says that general names are given to things on account of

their attributes, and that abstract names are the names of those

attributes. "Abstract is that which in any subject denotes the cause of

the concrete name.... And these causes of names are the same with the

causes of our conceptions, namely, some power of action, or affection,

of the thing conceived, which some call the manner by which anything

works upon our senses, but by most men they are called _accidents_."[20]

It is strange that having gone so far, he should not have gone one step

farther, and seen that what he calls the cause of the concrete name, is

in reality the meaning of it; and that when we predicate of any subject

a name which is given _because_ of an attribute (or, as he calls it, an

accident), our object is not to affirm the name, but, by means of the

name, to affirm the attribute.

§ 4. Let the predicate be, as we have said, a connotative term; and to

take the simplest case first, let the subject be a proper name: "The

summit of Chimborazo is white." The word white connotes an attribute

which is possessed by the individual object designated by the words

"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 information 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 subject, has the attributes connoted by

the predicate.

If we now suppose the subject also to be a connotative name, the meaning

expressed by the proposition has advanced a step farther in

complication. Let us first suppose the proposition to be universal, as

well as affirmative: "All men are mortal." In this case, as in the last,

what the proposition asserts (or expresses a belief of) is, of course,

that the objects denoted by the subject (man) possess the attributes

connoted by the predicate (mortal). But the characteristic of this case

is, that the objects are no longer _individually_ designated. They are

pointed out only by some of their attributes: they are the objects

called men, that is, possessing the attributes connoted by the name man;

and the only thing known of them may be those attributes: indeed, as the

proposition is general, and the objects denoted by the subject are

therefore indefinite in number, most of them are not known individually

at all. The assertion, therefore, is not, as before, that the attributes

which the predicate connotes are possessed by any given individual, or

by any number of individuals previously known as John, Thomas, &c., but

that those attributes are possessed by each and every individual

possessing certain other attributes; that whatever has the attributes

connoted by the subject, has also those connoted by the predicate; that

the latter set of attributes _constantly accompany_ the former set.

Whatever has the attributes of man has the attribute of mortality;

mortality constantly accompanies the attributes of man.[21]

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

forming part of, the fact or phenomenon upon which the attribute is

grounded; we may add one more step to complete the analysis. The

proposition which asserts that one attribute always accompanies another

attribute, really asserts thereby no other thing than this, that one

phenomenon always accompanies another phenomenon; insomuch that where we

find the one, we have assurance of the existence of the other. Thus, in

the proposition, All men are mortal, the word man connotes the

attributes which we ascribe to a certain kind of living creatures, on

the ground of certain phenomena which they exhibit, and which are partly

physical phenomena, namely the impressions made on our senses by their

bodily form and structure, and partly mental phenomena, namely the

sentient and intellectual life which they have of their own. All this is

understood when we utter the word man, by any one to whom the meaning of

the word is known. Now, when we say, Man is mortal, we mean that

wherever these various physical and mental phenomena are all found,

there we have assurance that the other physical and mental phenomenon,

called death, will not fail to take place. The proposition does not

affirm _when_; for the connotation of the word _mortal_ goes no farther

than to the occurrence of the phenomenon at some time or other, leaving

the precise time undecided.

§ 5. We have already proceeded far enough, not only to demonstrate the

error of Hobbes, but to ascertain the real import of by far the most

numerous class of propositions. The object of belief in a proposition,

when it asserts anything more than the meaning of words, is generally,

as in the cases which we have examined, either the co-existence or the

sequence of two phenomena. At the very commencement of our inquiry, we

found that every act of belief implied two Things: we have now

ascertained what, in the most frequent case, these two things are,

namely two Phenomena, in other words, two states of consciousness; and

what it is which the proposition affirms (or denies) to subsist between

them, namely either succession or co-existence. And this case includes

innumerable instances which no one, previous to reflection, would think

of referring to it. Take the following example: A generous person is

worthy of honour. Who would expect to recognise here a case of

co-existence between phenomena? But so it is. The attribute which causes

a person to be termed generous, is ascribed to him on the ground of

states of his mind, and particulars of his conduct: both are phenomena:

the former are facts of internal consciousness; the latter, so far as

distinct from the former, are physical facts, or perceptions of the

senses. Worthy of honour admits of a similar analysis. Honour, as here

used, means a state of approving and admiring emotion, followed on

occasion by corresponding outward acts. "Worthy of honour" connotes all

this, together with our approval of the act of showing honour. All these

are phenomena; states of internal consciousness, accompanied or followed

by physical facts. When we say, A generous person is worthy of honour,

we affirm co-existence between the two complicated 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, honour, would be followed in our minds by another inward

feeling, approval.

After the analysis, in a former chapter, of the import of names, many

examples are not needed to illustrate the import of propositions. When

there is any obscurity, or 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 connoted by a name. But where it is seen what the phenomenon

is, there is seldom any difficulty in seeing that the assertion conveyed

by the proposition is, the co-existence of one such phenomenon with

another; or the succession of one such phenomenon to another: their

_conjunction_, in short, so that where the one is found, we may

calculate on finding both.

This, however, though the most common, is not the only meaning which

propositions are ever intended to convey. In the first place, sequences

and co-existences are not only asserted respecting Phenomena; we make

propositions also respecting those hidden causes of phenomena, which are

named substances and attributes. A substance, however, being to us

nothing but either that which causes, or that which is 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 entities, except in virtue of the Phenomena by

which alone they manifest themselves to our faculties. When we say,

Socrates was cotemporary 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 does not assert that alone; it

asserts that the Thing in itself, the _noumenon_ Socrates, was existing,

and doing or experiencing those various facts during the same time.

Co-existence and sequence, therefore, may be affirmed or denied not only

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

Coexistence, there are some which assert simple Existence; and others

assert Causation, which, subject to the explanations which will follow

in the Third Book, must be considered provisionally as a 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 analyse; for which no _fundamentum_, distinct from the

objects themselves, could be assigned. Besides propositions which assert

a sequence or co-existence between two phenomena, there are therefore

also propositions which assert resemblance between them: as, This colour

is like that colour;--The heat of to-day is _equal_ to the heat of

yesterday. It is true that such an assertion might with some

plausibility be brought within the description of an affirmation of

sequence, by considering it as an assertion that the simultaneous

contemplation of the two colours is _followed_ by a specific feeling

termed the feeling of resemblance. But there would be nothing gained by

encumbering ourselves, especially in this place, with a generalization

which may be looked upon as strained. Logic does not undertake to

analyse mental facts into their ultimate elements. Resemblance 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

predicate is a general name, do, in point of fact, affirm or deny

resemblance. All such propositions affirm that a thing belongs to a

class; but things being classed together according to their resemblance,

everything is of course classed with the things which it is supposed to

resemble most; and thence, it may be said, when we affirm that Gold is a

metal, or that Socrates is a man, the affirmation intended is, that

gold resembles other metals, and Socrates other men, more nearly than

they resemble the objects contained in any other of the classes

co-ordinate with these.

There is some slight degree of foundation for this remark, but no more

than a slight degree. The arrangement of things into classes, such as

the class _metal_, or the class _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 assert; 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, therefore, in which

objects are referred to a class because they possess the attributes

constituting the class, are so far from asserting nothing but

resemblance, that they do not, 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[22]) that there is

sometimes a convenience in extending the boundaries of a class so as to

include things which possess in a very inferior degree, if in any, some

of the characteristic properties of the class,--provided they resemble

that class more than any other, insomuch that the general propositions

which are true of the class, will be nearer to being true of those

things than any other equally general propositions. For instance, there

are substances called metals which have very few of the properties by

which metals are commonly recognised; and almost every great family of

plants or animals has a few anomalous genera or species on its borders,

which are admitted into it by a sort of courtesy, and concerning which

it has been matter of discussion to what family they properly belonged.

Now when the class-name is predicated of any object of this description,

we do, by so predicating it, affirm resemblance and nothing more. And in

order to be scrupulously correct it ought to be said, that in every case

in which we predicate a general name, we affirm, not absolutely that the

object possesses the properties designated by the name, but that it

_either_ possesses those properties, or if it does not, at any rate

resembles the things which do so, more than it resembles any other

things. In most cases, however, it is unnecessary to suppose any such

alternative, the latter of the two grounds being very seldom that on

which the assertion is made: and when it is, there is generally some

slight difference in the form of the expression, as, This species (or

genus) is _considered_, or _may be ranked_, as belonging to such and

such a family: we should hardly say positively that it does belong to

it, unless it possessed unequivocally the properties of which the

class-name is scientifically 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 unanalysable resemblance. The classes in

question are those into which our simple sensations, or other simple

feelings, are divided. Sensations of white, for instance, are classed

together, not because we can take them to pieces, and say they are alike

in this, and not alike in that, but because we feel them to be alike

altogether, though in different degrees. When, therefore, I say, The

colour I saw yesterday was a white colour, or, The sensation I feel is

one of tightness, in both cases the attribute I affirm of the colour or

of the other sensation is mere resemblance--simple _likeness_ to

sensations which I have had before, and which have had those names

bestowed upon them. The names of feelings, like other concrete general

names, are connotative; but they connote a mere resemblance. When

predicated of any individual feeling, the information they convey is

that of its likeness to the other feelings which we have been accustomed

to call by the same name. Thus much may suffice in illustration of the

kind of propositions in which the matter-of-fact asserted (or denied) is

simple Resemblance.

Existence, Coexistence, 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 matters-of-fact; of all things that can be believed, or tendered for

belief; of all questions that can be propounded, and all answers that

can be returned to them. Instead of Coexistence and Sequence, we shall

sometimes say, for greater particularity, Order in Place, and Order in

Time: Order in Place being the specific mode of coexistence, not

necessary to be more particularly analysed here; while the mere fact of

coexistence, or simultaneousness, may be classed, together with

Sequence, under the head of Order in Time.

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

thought it necessary to analyse directly those alone, in which the terms

of the proposition (or the predicate at least) are concrete terms. But,

in doing so, we have indirectly analysed those in which the terms are

abstract. The distinction between an abstract term and its corresponding

concrete, does not turn upon any difference in what they are appointed

to signify; for the real signification of a concrete general name is, as

we have so often said, its connotation; and what the concrete term

connotes, forms the entire meaning of the abstract name. Since there is

nothing in the import of an abstract name which is not in the import of

the corresponding concrete, it is natural to suppose that neither can

there be anything in the import of a proposition of which the terms are

abstract, but what there is in some proposition which can be framed of

concrete terms.

And this presumption a closer examination will confirm. An abstract name

is the name of an attribute, or combination of attributes. The

corresponding concrete is a name given to things, because of, and in

order to express, their possessing that attribute, or that combination

of attributes. When, therefore, we predicate of anything a concrete

name, the attribute is what we in reality predicate of it. But it has

now been shown that in all propositions of which the predicate is a

concrete name, what is really predicated is one of five things:

Existence, Coexistence, Causation, Sequence, or Resemblance. An

attribute, therefore, is necessarily either an existence, a coexistence,

a causation, a sequence, or a resemblance. When a proposition consists

of a subject and predicate which are abstract terms, it consists of

terms which must necessarily signify one or other of these things. When

we predicate of anything an abstract name, we affirm of the thing that

it is one or other of these five things; that it is a case of Existence,

or of Coexistence, or of Causation, or of Sequence, or of Resemblance.

It is impossible to imagine any proposition expressed in abstract terms,

which cannot be transformed into a precisely equivalent proposition in

which the terms are concrete; namely, either the concrete names which

connote the attributes themselves, or the names of the _fundamenta_ of

those attributes; the facts or phenomena on which they are grounded. To

illustrate the latter case, let us take this proposition, of which the

subject only is an abstract name, "Thoughtlessness is dangerous."

Thoughtlessness is an attribute, grounded on the facts which we call

thoughtless actions; and the proposition is equivalent to this,

Thoughtless actions are dangerous. In the next example the predicate as

well as the subject are abstract names: "Whiteness is a colour;" or "The

colour of snow is a whiteness." These attributes being grounded on

sensations, the equivalent propositions in the concrete would be, The

sensation of white is one of the sensations called those of colour,--The

sensation of sight, caused by looking at snow, is one of the sensations

called sensations of white. In these propositions, as we have before

seen, the matter-of-fact asserted is a Resemblance. In the following

examples, the concrete terms are those which directly correspond to the

abstract names; connoting the attribute which these denote. "Prudence

is a virtue:" this may be rendered, "All prudent persons, _in so far as_

prudent, are virtuous:" "Courage is deserving of honour," thus, "All

courageous persons are deserving of honour _in so far_ as they are

courageous:" which is equivalent to this--"All courageous persons

deserve an addition to the honour, or a diminution of the disgrace,

which would attach to them on other grounds."

In order to throw still further light upon the import of propositions of

which the terms are abstract, we will subject one of the examples given

above to a minuter analysis. The proposition we shall select is the

following:--"Prudence is a virtue." Let us substitute for the word

virtue an 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 sequence, 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 analyse

the antecedent. Prudence is an attribute; and, in connexion with it, two

things besides itself are to be considered; prudent persons, who are the

_subjects_ of the attribute, and prudential conduct, which may be called

the _foundation_ of it. Now is either of these the antecedent? and,

first, is it meant, that the approval of God, or benefit to society, is

attendant upon all prudent _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 approbation and benefit

to mankind are supposed to be invariably consequent? Neither is this the

assertion meant, when it is said that prudence is a virtue; except with

the same reservation as before, and for the same reason, namely, that

prudential conduct, although in _so far as_ it is prudential it is

beneficial to society, may yet, by reason of some other of its

qualities, be productive of an injury outweighing the benefit, and

deserve a displeasure exceeding the approbation which would be due to

the prudence. Neither the substance, therefore, (viz. the person,) nor

the phenomenon, (the conduct,) is an antecedent on which the other term

of the sequence is universally consequent. But the proposition,

"Prudence is a virtue," is an universal proposition. What is it, then,

upon which the proposition affirms the effects in question to be

universally consequent? Upon that in the person, and in the conduct,

which causes them to be called prudent, and which is equally in them

when the action, though prudent, is wicked; namely, a correct foresight

of consequences, a just estimation of their importance to the object in

view, and repression of any unreflecting impulse at variance with the

deliberate purpose. These, which are states of the person's mind, are

the real antecedent in the sequence, the real cause in the causation,

asserted by the proposition. But these are also the real ground, or

foundation, of the attribute Prudence; since wherever these states of

mind exist we may predicate prudence, even before we know whether any

conduct has followed. And in this manner every assertion respecting an

attribute, may be transformed into an assertion exactly equivalent

respecting the fact or phenomenon which is the ground of the attribute.

And no case can be assigned, where that which is predicated of the fact

or phenomenon, does not belong to one or other of the five species

formerly enumerated: it is either simple Existence, or it is some

Sequence, Coexistence, Causation, or Resemblance.

And as these five are the only things which can be affirmed, so are they

the only things which can be denied. "No horses are web-footed" denies

that the attributes of a horse ever coexist with web-feet. It is

scarcely necessary to apply the same analysis to Particular affirmations

and negations. "Some birds are web-footed," affirms that, with the

attributes connoted by _bird_, the phenomenon web-feet is sometimes

co-existent: "Some birds are not web-footed," asserts that there are

other instances in which this coexistence 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

susceptible of, proof; or (which is the same thing) what they assert. In

the course of this preliminary investigation into the import of

Propositions, we examined the opinion of the Conceptualists, that a

proposition is the expression of a relation between two ideas; and the

doctrine of the Nominalists, that it is the expression of an agreement

or disagreement between the meanings of two names. We decided that, as

general theories, both of these are erroneous; and that, though

propositions may be made both respecting names and respecting ideas,

neither the one nor the other are the subject-matter of Propositions

considered generally. We then examined the different kinds of

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, Causation, and

Resemblance; that in every proposition one of these five is either

affirmed, or denied, of some fact or phenomenon, or of some object the

unknown source of a fact or phenomenon.

In distinguishing, however, the different kinds of matters of fact

asserted in propositions, we reserved one class of 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 arbitrary, such propositions are not, strictly speaking,

susceptible of truth or falsity, but only of conformity or disconformity

to usage or convention; and all the proof they are capable of, is proof

of usage; proof that the words have been employed by others in the

acceptation in which the speaker or writer desires to use them. These

propositions occupy, however, a conspicuous place in philosophy; and

their nature and characteristics are of as much importance in logic, as

those of any of the other classes of propositions previously adverted

to.

If all propositions respecting the signification of words were as simple

and unimportant as those which served us for examples when examining

Hobbes' theory of predication, viz. those of which the subject and

predicate are proper names, and which assert only that those names have,

or that they have not, been conventionally assigned to the same

individual, there would be little to attract to such propositions the

attention of philosophers. But the class of merely verbal propositions

embraces not only much more than these, but much more than any

propositions which at first sight present themselves as verbal;

comprehending a kind of assertions which have been regarded not only as

relating to things, but as having actually a more intimate relation with

them than any other propositions whatever. The student in philosophy

will 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

predicates which are said to be of the _essence_ of the subject. The

essence of a thing, they said, was that without which the thing could

neither be, nor be 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 respecting it, than any other proposition could

do. All properties, not of the essence of the thing, were called its

accidents; were supposed to have nothing at all, or nothing

comparatively, to do with its inmost nature; and the propositions in

which any of these were predicated of it were called Accidental

Propositions. A connexion may be traced between this distinction, which

originated with the schoolmen, and the well-known dogmas of _substantiæ

secundæ_ 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

modern times than might be conjectured from the disuse of the

phraseology. The false views of the nature of classification and

generalization which prevailed 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_ cannot be conceived without rationality. But

though _man_ cannot, a being may be conceived exactly like a man in all

points except that one quality, and those others which are the

conditions or consequences of it. All therefore which is really true in

the assertion that man cannot be conceived without rationality, is only,

that if he had not rationality, he would not be reputed a man. There is

no impossibility in conceiving the _thing_, nor, for aught we know, in

its existing: the impossibility is in the 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 meaning of the word man: is one of the attributes

connoted by the name. The essence of man, simply means the whole of the

attributes connoted 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 certain general substance, called gold in general, which substance,

together with all the properties that belonged to it, _inhered_ in every

individual piece of gold.[23] As they did not consider these universal

substances to be attached to all general names, but only to some, they

thought that an object borrowed only a part of its properties from an

universal substance, and that the rest belonged to it individually: the

former they called its essence, and the latter its accidents. The

scholastic doctrine of essences long survived the theory on which it

rested, that of the existence of real entities corresponding to general

terms; and it was reserved for Locke at the end of the seventeenth

century, to convince philosophers that the supposed essences of classes

were merely the signification of their names; nor, among the signal

services which his writings rendered to philosophy, was there one more

needful or more valuable.

Now, as the most familiar of the general names by which an object is

designated usually connotes not one only, but several attributes of the

object, each of which attributes 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 whatever possesses the whole of any set of attributes, must

possess any part of that same set. A proposition of this sort, however,

conveys no information to any one who previously understood the whole

meaning of the terms. The propositions, Every man is a corporeal being,

Every man is a living creature, Every man is rational, convey no

knowledge to any one who was already aware of the entire meaning of the

word _man_, for the meaning of the word 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 possessing 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 imperfection of language. It

arises from the ambiguity of the copula, which, in addition to its

proper office of a mark to show that an assertion is made, is also, as

formerly remarked, a concrete word connoting existence. The actual

existence of the subject of the 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 accidental, or non-essential, affirmation, does imply the

real existence of the subject, because in the case of a non-existent

subject there is nothing for the proposition to assert. Such a

proposition as, The ghost of a murdered person haunts the couch of the

murderer, can only have a meaning if understood as implying a belief in

ghosts; for since the signification of the word ghost implies nothing of

the kind, the speaker either means nothing, or means to assert a thing

which he wishes to be believed to have really taken place.

It will be hereafter seen that when any important consequences seem to

follow, as in mathematics, from an essential proposition, or, in other

words, from a proposition involved in the meaning of a name, what they

really flow from is the tacit assumption of the real existence of the

objects so named. Apart from this assumption of real existence, the

class of propositions 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 connotes, but nothing besides) answer no purpose but

that of unfolding the whole or some part of the meaning of the name, to

those who did not previously know it. Accordingly, the most useful, and

in strictness the only useful kind of essential propositions, are

Definitions: which, to be complete, should unfold the whole of what is

involved in the meaning of the word defined; that is, (when it is a

connotative word,) the whole of what it connotes. In defining a name,

however, it is not usual to specify its entire connotation, but so much

only as is sufficient to mark out the objects usually denoted by it from

all other known objects. And sometimes a merely accidental property, not

involved in the meaning of the name, answers this purpose equally well.

The various kinds of definition which these distinctions give rise to,

and the purposes to which they are respectively subservient, will be

minutely considered in the proper place.

§ 3. According to the above view of essential propositions, no

proposition can be reckoned such which relates to an 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 proposition, they affirmed the same

thing of the proposition, Julius Cæsar is a rational being. This

followed very naturally if genera and species were to be considered as

entities, distinct from, but _inhering_ in, the individuals composing

them. If _man_ was a substance inhering in each individual man, the

_essence_ of man (whatever that might mean) was naturally supposed to

accompany it; to inhere in John Thompson, and to form the _common

essence_ of Thompson and Julius Cæsar. 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

victory. It retreats slowly, defends every inch of ground, and often,

after it has been driven from the open country, retains a footing in

some remote fastness. The essences of individuals were an unmeaning

figment arising from a misapprehension of the essences of classes, yet

even Locke, when he extirpated the parent error, could not shake himself

free from that which was its fruit. He distinguished two sorts of

essences, Real and Nominal. His nominal essences were the essences of

classes, explained nearly as we have now explained them. Nor is anything

wanting to render the third book of Locke's Essay a nearly

unexceptionable treatise on the connotation of names, except to free its

language from the assumption of what are called Abstract Ideas, which

unfortunately is involved in the phraseology, though not necessarily

connected with the thoughts contained in that immortal Third Book.[24]

But, besides nominal essences, he admitted real essences, or essences of

individual objects, which he supposed to be the causes of the sensible

properties of those objects. We know not (said he) what these are; (and

this acknowledgment rendered the fiction comparatively innocuous;) but

if we did, we could, from them alone, demonstrate the sensible

properties of the object, as the properties of the triangle are

demonstrated from the definition of the triangle. I shall have occasion

to revert to this theory in treating of Demonstration, and of the

conditions under which one property of a thing admits of being

demonstrated from another property. It is enough here to remark that,

according to this definition, the real essence of an object has, in the

progress of physics, come to be conceived as nearly equivalent, in the

case of bodies, to their corpuscular structure: what it is now supposed

to mean in the case of any other entities, I would not take upon myself

to define.

§ 4. An essential proposition, then, is one which is purely verbal;

which asserts of a thing under a particular name, only what is asserted

of it in the fact of calling it by that name; and which therefore either

gives no information, or gives it respecting the name, not the thing.

Non-essential, or accidental propositions, on the contrary, may be

called Real Propositions, 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 propositions concerning things individually designated, and

all general or particular propositions in which the predicate connotes

any attribute not connoted by the subject. All these, if true, add to

our knowledge: they convey information, not already involved in the

names employed. When I am told that all, or even that some objects,

which have certain qualities, or which stand in certain relations, have

also certain other qualities, or stand in certain other relations, I

learn from this proposition a new fact; a fact not included in my

knowledge of the meaning of the words, nor even of the existence of

Things answering to the signification of those words. It is this class

of propositions only which are in themselves instructive, or from which

any instructive propositions can be inferred.[25]

Nothing has probably contributed more to the opinion so long prevalent

of the futility of the school logic, than the circumstance that almost

all the examples used in the common school books to illustrate the

doctrine of predication and that of the 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 _essence_ of the species: _Omne corpus est substantia_,

_Omne animal est corpus_, _Omnis homo est corpus_, _Omnis homo est

animal_, _Omnis homo est rationalis_, and so forth. It is far from

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 principle 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

presuppose what is about to be asserted; there are two different aspects

in which these, or rather such of them as are general propositions, may

be considered: 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

attributes, or at least never by all the attributes, signified by the

word god. But when the proposition is considered as a memorandum for

practical use, we shall find a different mode of expressing the same

meaning better adapted to 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 proposition. In reference to this purpose,

the proposition, All men are mortal, means that the attributes of man

are _evidence of_, are a _mark_ of, mortality; an indication by which

the presence of that 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 proposition 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 considers a Proposition as asserting that one

fact or phenomenon is a _mark_ or _evidence_ of another fact or

phenomenon, will be found almost indispensable. For the purposes of that

Theory, the best mode of defining the import of a proposition is not the

mode which shows most clearly what it is in itself, but that which most

distinctly suggests the manner in which it may be made available for

advancing from it to other propositions.

CHAPTER VII.

OF THE NATURE OF CLASSIFICATION, AND THE FIVE PREDICABLES.

§ 1. In examining into the nature of general propositions, we have

adverted much less than is usual with logicians to the ideas of a Class,

and Classification; ideas which, since the Realist doctrine of General

Substances went out of vogue, have formed the basis of almost every

attempt at a 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 potentially

a name of an indefinite number of objects; but it needs not be actually

the name of any; and if of any, it may be the name of only one. As soon

as we employ a name to connote attributes, the things, be they more or

fewer, which happen to possess those attributes, are constituted _ipso

facto_ a class. But in predicating the name we predicate only the

attributes; and the fact of belonging to a class does not, in many

cases, come into view at all.

Although, however, Predication does not presuppose Classification, and

though the theory of Names and of Propositions is not cleared up, but

only encumbered, by intruding the idea of classification into it, there

is nevertheless a close connexion 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 existence to classes. A general, which is as much as

to say a significant, name, is indeed mostly introduced because we have

a signification to express by it; because we need a word by means of

which to predicate the attributes which it connotes. But it is also true

that a name is sometimes introduced because we have found it convenient

to create a class; because we have thought it useful for the regulation

of our mental operations, that a certain group of objects should be

thought of together. A naturalist, for purposes connected with his

particular science, sees reason to distribute the animal or vegetable

creation into certain groups rather than into any others, and he

requires a name to bind, as it were, each of his groups together. It

must not 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 orders, _Plantigrades_, _Digitigrades_, &c., are as

much the expression of attributes as if those names had preceded,

instead of grown out of, his classification of animals. The only

peculiarity of the case is, that the convenience of classification was

here the primary motive for introducing the names; while in other cases

the name is introduced as a means of predication, and the formation of a

class denoted by it is only an indirect consequence.

The principles which ought to regulate Classification as a logical

process subservient to the investigation of truth, cannot be discussed

to any purpose until a much later stage of our inquiry. But, of

Classification as resulting from, and implied in, the fact of employing

general language, we cannot forbear to treat here, without leaving the

theory of general names and of their employment in predication,

mutilated and formless.

§ 2. This portion of the theory of general language is the subject of

what is termed the doctrine of the Predicables; a set of distinctions

handed down from Aristotle, and his follower Porphyry, many of which

have taken a firm root in scientific, and some of them even in popular,

phraseology. The predicables are a five-fold division of General Names,

not grounded as usual on a difference in their meaning, that is, in the

attribute which they connote, but on a difference in the kind of class

which they denote. We may predicate of a thing five different varieties

of class-name:--

A _genus_ of the thing ([Greek: genos]).

A _species_ ([Greek: eidos]).

A _differentia_ ([Greek: diaphora]).

A _proprium_ ([Greek: idion]).

An _accidens_ ([Greek: symbebêkos]).

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 exclusively species, or differentiæ; 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. _Rectangular_ is one of the Differentiæ of a geometrical

square; it is merely one of the Accidentia of the table at which I am

writing. The words genus, species, &c. are therefore relative terms;

they are names applied to certain predicates, to express the relation

between them and some given subject: a relation grounded, as we shall

see, not on what the predicate connotes, but on the class which it

denotes, and on the place which, in some given classification, that

class occupies relatively to the particular subject.

§ 3. Of these five names, two, Genus and Species, are not only used by

naturalists in a technical acceptation not precisely agreeing with their

philosophical meaning, but have also acquired a popular acceptation,

much more general than either. In this popular sense any two classes,

one of which includes the whole of the other and more, may be called a

Genus and a Species. Such, for instance, are Animal and Man; Man and

Mathematician. Animal is a Genus; Man and Brute are its two species; or

we may divide it into a greater number of species, as man, horse, dog,

&c. _Biped_, or _two-footed animal_, may also be considered a genus, of

which man and bird are two species. _Taste_ is a genus, of which sweet

taste, sour taste, salt taste, &c. are species. _Virtue_ is a genus;

justice, prudence, courage, fortitude, generosity, &c. are its species.

The same class which is a genus with reference to the 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 Mathematician. Animal is a genus, divided into two species, man

and brute; but animal is also a species, which, with another species,

vegetable, makes up the genus, organized being. Biped is a genus with

reference to man and bird, but a species with respect to the superior

genus, animal. Taste is a genus divided into species, but also a species

of the genus sensation. Virtue, a genus with reference to justice,

temperance, &c., is one of the species of the genus, mental quality.

In this popular sense the words Genus and Species have passed into

common discourse. And it should be observed that in ordinary parlance,

not the name of the class, but the class itself, is said to be the genus

or species; not, of course, the class in the sense of each individual of

the class, but the individuals collectively, considered as an aggregate

whole; the name by which the class is 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 predicating the genus. We predicate of man the _name_

mortal; and by predicating 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. We predicate 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

included in a larger class to be a species. Animal was by them

considered a genus; man and brute co-ordinate species under that genus:

_biped_, however, would not have been admitted to be a genus with

reference to man, but a _proprium_ or _accidens_ only. It was requisite,

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 classification they considered some one class as the

lowest or _infima_ 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 abstruse speculation, and to which so mysterious a

character was formerly, and by many writers is still, attached,--amounts

to nothing more than the difference between those attributes of the

class which are, and those which are not, involved in the signification

of the class-name. As applied to individuals, the word Essence, we

found, has no meaning, except in connexion with the 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.

Is there no difference, then, save this merely verbal one, between the

classes which the schoolmen admitted to be genera or species, and those

to which they refused the title? Is it an error to regard some of the

differences which exist among objects as differences _in kind_ (_genere_

or _specie_), and others only as differences in the accidents? Were the

schoolmen right or wrong in giving to some of the classes into which

things may be divided, the name of _kinds_, and considering others as

secondary divisions, grounded on differences of a comparatively

superficial nature? Examination will show that the Aristotelians did

mean something by this distinction, and something important; but which,

being but indistinctly conceived, was inadequately expressed by the

phraseology of essences, and the various other modes of speech to which

they had recourse.

§ 4. It is a fundamental principle in logic, that the power of framing

classes is unlimited, as long as there is any (even the smallest)

difference to found a distinction upon. Take any attribute whatever, and

if some things have it, and others have not, we may ground on the

attribute a division of all things into two classes; and we actually do

so, the moment we create a name which connotes the attribute. The number

of possible classes, therefore, is boundless; and there are as many

actual classes (either of real or of imaginary things) as there are

general names, positive and negative together.

But if we contemplate any one of the classes so formed, such as the

class animal or plant, or the class sulphur or phosphorus, or the class

white or red, and consider in what particulars the individuals included

in the class differ from those which do not come within it, we find a

very remarkable diversity in this respect between some classes and

others. There are some classes, the things contained in which differ

from other things only in certain particulars which may be numbered,

while others differ in more than can be numbered, more even than we need

ever expect to know. Some classes have little or nothing in common to

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 experiments, in the

full confidence of discovering new properties which were by no means

implied in those we previously knew. While, if any one were to propose

for investigation the common properties of all things which are of the

same colour, the same shape, or the same specific gravity, the absurdity

would be palpable. We have no ground to believe that any such common

properties exist, except such as may be shown to be involved in the

supposition itself, or to be derivable from it by some law of causation.

It appears, therefore, that the properties, on which we ground our

classes, sometimes exhaust all that the class has in common, or contain

it all by some mode of implication; but in other instances we make a

selection of a few properties from among not only a greater number, but

a number inexhaustible by us, and to which as we know no bounds, they

may, so far as we are 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 classification is made by nature, the other by us for our

convenience, he will be right; provided he means no more than this:

Where a certain apparent difference between things (though perhaps in

itself of little moment) answers to we know not what number of other

differences, pervading not only their known properties, but properties

yet undiscovered, it is not optional but imperative to recognise this

difference as the foundation of a specific 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 for which the classification is made does not require attention

to those particular properties. The differences, however, are made by

nature, in both cases; while the recognition of those differences as

grounds of classification and of naming, is, equally in both cases, the

act of man: only in the one case, the ends of language and of

classification would be subverted if no notice were taken of the

difference, while in the other case, the necessity of taking notice of

it depends on the importance or unimportance of the particular qualities

in which the difference happens to consist.

Now, these classes, distinguished by unknown multitudes of properties,

and not solely by a few determinate ones--which are parted off from one

another by an unfathomable chasm, instead of a mere ordinary ditch with

a visible bottom--are the only classes which, by the Aristotelian

logicians, were considered as genera or species. Differences which

extended only to a certain property or properties, and there terminated,

they considered as differences only in the _accidents_ of things; but

where any class differed from other things by an infinite series of

differences, known and unknown, they considered the distinction as one

of _kind_, and spoke of it as being an _essential_ difference, which is

also one of the current meanings of that vague expression at the present

day.

Conceiving the schoolmen to have been justified in drawing a broad line

of separation between these two kinds of classes and of

class-distinctions, I shall not only retain the division itself, but

continue to express it in their language. According to that language,

the proximate (or lowest) Kind to which any individual is referrible, is

called its species. Conformably to this, Sir Isaac Newton would be said

to be of the species man. There are indeed numerous sub-classes included

in the class man, to which Newton also belongs; for example, Christian,

and Englishman, and Mathematician. But these, though distinct classes,

are not, in our sense of the term, distinct Kinds of men. A Christian,

for example, differs from other human beings; but he differs only in the

attribute which the word expresses, namely, belief in Christianity, and

whatever else that implies, either as involved in the fact itself, or

connected with it through some law of cause and effect. We should never

think of inquiring what properties, unconnected with Christianity either

as cause or effect, are common to all Christians and peculiar to them;

while in regard to all Men, physiologists are perpetually carrying on

such an inquiry; nor is the answer ever likely to be completed. Man,

therefore, we may call a species; Christian, or Mathematician, we

cannot.

Note here, that it is by no means intended to imply that there may not

be different Kinds, or logical species, of man. The various races and

temperaments, the two sexes, and even the various ages, may be

differences of kind, within our meaning of the term. I do not say that

they are so. For in the progress of physiology it may almost be said to

be made out, that the differences which really exist between different

races, sexes, &c., follow as consequences, under laws of nature, from a

small number of 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 afterwards proved not to be so. But if it turned out

that the differences were not capable of being thus accounted for, then

Caucasian, Mongolian, Negro, &c. would be really different Kinds of

human beings, and entitled to be ranked as species by the logician;

though not by the naturalist. For (as already noticed) the word species

is used in a different signification in logic and in natural history. By

the naturalist, organized beings are not usually said to be of different

species, if it is supposed that they could possibly have descended from

the same stock. That, however, is a sense artificially given to the

word, for the technical purposes of a particular science. To the

logician, if a negro and a white man differ in the same manner (however

less in degree) as a horse and a camel do, that is, if their differences

are inexhaustible, and not referrible to any common cause, they are

different species, whether they are descended from common ancestors or

not. But if their differences can all be traced to climate and habits,

or to some one or a few special differences in structure, they are not,

in the logician's view, specially distinct.

When the _infima 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 animals form a portion of the common properties of

the sub-class, man. And if there be any class which includes Socrates

without including man, that class is not a real Kind. Let the class for

example, be _flat-nosed_; that being a class which includes Socrates,

without including all men. To determine whether it is a real Kind, we

must ask ourselves this question: Have all flat-nosed animals, in

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

proximate Kind. Therefore, the properties of the proximate Kind do

comprehend those (whether known or unknown) of all other Kinds to which

the individual belongs; which was the point we undertook to prove. And

hence, every other Kind which is predicable of the individual, will be

to the proximate Kind in the relation of a genus, according to even the

popular acceptation of the terms genus and species; that is, it will be

a larger class, including it and more.

We are now able to fix the logical meaning of these terms. Every class

which is a real Kind, that is, which is distinguished from all other

classes by an indeterminate multitude of properties not derivable from

one another, is either a genus or a species. A Kind which is not

divisible into other Kinds, cannot be a genus, because it has no

species under it; but it is itself a species, both with reference to the

individuals below and to the genera above (Species Prædicabilis and

Species Subjicibilis.) But every Kind which admits of division into real

Kinds (as animal into mammal, bird, fish, &c., or bird into various

species of birds) is a genus to all below it, a species to all genera in

which it is itself included. And here we may close this part of the

discussion, and pass to the three remaining predicables, Differentia,

Proprium, and Accidens.

§ 5. To begin with Differentia. This word is correlative with the words

genus and species, and as all admit, it signifies the attribute which

distinguishes a given species from every other species of the same

genus. This is so far clear: but we may still ask, which of the

distinguishing attributes it 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 attributes 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 properties, nor even that there was anything

which caused it to have them. Logicians, however, not liking to admit

this, and being unable to detect what made the thing to be what it was,

satisfied themselves with what made it to be what it was called. Of the

innumerable properties, known and unknown, that are common to the class

man, a portion only, and of course a very small portion, are connoted by

its name; these few, however, will naturally have been thus

distinguished from the rest either for their greater obviousness, or for

greater supposed importance. These properties, then, which were connoted

by the name, logicians seized upon, and called them the essence of the

species; and not stopping there, they affirmed them, in the case of the

_infima species_, to be the essence of the individual too; for it was

their maxim, that the species contained the "whole essence" of the

thing. Metaphysics, that fertile field of delusion propagated by

language, does not afford a more signal instance of such delusion. On

this account it was that rationality, being connoted by the name man,

was allowed to be a differentia of the class; but the peculiarity of

cooking their food, not being connoted, was relegated to the class of

accidental properties.

The distinction, therefore, between Differentia, Proprium, and Accidens,

is not grounded in the nature of things, but in the connotation of

names; and we must seek it there, if we wish to find what it is.

From the fact that the genus includes the species, in other words

_de_notes 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, otherwise there might be men who are not animals; and

it must connote something more than animal connotes, otherwise all

animals would be men. This surplus of connotation--this which the

species connotes over and above the connotation of the genus--is the

Differentia, or specific difference; or, to state the same 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 human. The

Differentia, or specific difference, therefore, of man, as referred to

the genus animal, is that outward form and the possession of reason. The

Aristotelians said, the possession of reason, without the outward form.

But if they adhered to this, they would have been obliged to call the

Houyhnhnms men. The question never arose, and they were never called

upon to decide how such a case would have affected their notion of

essentiality. However this may be, they were satisfied with taking such

a portion of the differentia as sufficed to distinguish the species from

all other _existing_ things, though by so doing they might not exhaust

the connotation of the name.

§ 6. And here, to prevent the notion of differentia from being

restricted within too narrow limits, it is necessary to remark, that a

species, even as referred to the same genus, will not always have the

same differentia, but a different one, according to the principle and

purpose which preside over the particular classification. For example, a

naturalist surveys the various kinds of animals, and looks out for the

classification of them most in accordance with the order in which, for

zoological purposes, he considers it desirable that we should think of

them. With this view he finds it advisable that one of his fundamental

divisions should be into warm-blooded and cold-blooded animals; or into

animals which breathe with lungs and those which breathe with gills; or

into carnivorous, and frugivorous or graminivorous; or into those which

walk on the flat part and those which walk on the extremity of the foot,

a distinction on which two of Cuvier's families are founded. In doing

this, the naturalist creates as many new classes; which are by no means

those to which the individual animal is familiarly and spontaneously

referred; nor should we ever think of assigning to them so prominent a

position in our arrangement of the animal kingdom, unless for a

preconceived purpose of scientific convenience. And to the liberty of

doing this there is no limit. In the examples we have given, most of the

classes are real Kinds, since each of the peculiarities is an index to a

multitude of properties belonging to the class which it characterizes:

but even if the case were otherwise--if the other properties of those

classes could all be derived, by any process known to us, from the one

peculiarity on which the class is founded--even then, if these

derivative properties were of primary importance for the purposes of the

naturalist, he would be warranted in founding his primary divisions on

them.

If, however, practical convenience is a sufficient warrant for making

the main demarcations in our arrangement of objects run in lines not

coinciding with any distinction of Kind, and so creating genera and

species in the popular sense which are not genera or species in the

rigorous sense at all, _à 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 strongly recommend. If we

cut a species out of a given genus--the species man, for instance, out

of the genus animal--with an intention on our part that the peculiarity

by which we are to be guided in the application of the name man should

be rationality, then rationality is the differentia of the species man.

Suppose, however, that being naturalists, we, for the purposes of our

particular study, cut out of the genus animal the same species man, but

with an intention that the 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

rationality, but connotes the three other properties specified; for that

which we have expressly in view when we impose a name, assuredly forms

part of the meaning of that name. We may, therefore, lay it down as a

maxim, that wherever there is a Genus, and a Species marked out from

that genus by an assignable differentia, the name of the species must be

connotative, and must connote the 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 number or character of the teeth; in the Linnæan

system it connotes the number of incisor and canine teeth, but does not

connote rationality nor any particular form. The word _man_ has,

therefore, two different meanings; though not commonly considered as

ambiguous, because it happens in both cases to _de_note 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 Linnæus's three characteristics of

humanity, but not rational, or not of the human form. In ordinary

parlance, these animals would not be called men; but in natural history

they must still be called so by those, if any there be, who adhere to

the Linnæan 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

attribute corresponding to a certain sensation: but if we are making a

classification of colours, and desire to justify, or even merely to

point out, the particular place assigned to whiteness in our

arrangement, we may define it "the colour produced by the mixture of all

the simple rays;" and this fact, though by no means implied in the

meaning of the word whiteness as ordinarily used, but only known by

subsequent scientific investigation, is part of its meaning in the

particular essay or treatise, and becomes the differentia of the

species.[26]

The differentia, therefore, of a species may be defined to be, that part

of the connotation of the specific name, whether ordinary or special and

technical, which distinguishes the species in question from all other

species of the genus to which on the particular occasion we are

referring it.

§ 7. Having disposed of Genus, Species, and Differentia, we shall not

find much difficulty in attaining a clear conception of the distinction

between the other two predicables, as well as between them and the first

three.

In the Aristotelian phraseology, Genus and Differentia are of the

_essence_ of the subject; by which, as we have seen, is really meant

that the properties signified by the genus and those signified by the

differentia, form part of the connotation of the name denoting the

species. Proprium and Accidens, on the other hand, form no part of the

essence, but are predicated of the species only _accidentally_. Both are

Accidents, in the wider sense in which the accidents of a thing are

opposed to its essence; though, in the doctrine of the Predicables,

Accidens is used for one sort of accident only, Proprium being another

sort. Proprium, continue the schoolmen, is predicated _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 connexion whatever with the essence, but may come and go, and the

species still remain what it was before. If a species could exist

without its Propria, it must be capable of existing without that on

which its Propria are necessarily consequent, and therefore without its

essence, without that which constitutes it a species. But an Accidens,

whether separable or inseparable from the species in actual experience,

may be supposed separated, without the necessity of supposing any other

alteration; or at least, without supposing any of the essential

properties of the species to be altered, since with them an Accidens has

no connexion.

A Proprium, therefore, of the species, may be defined, any attribute

which belongs to all the individuals included in the species, and which,

though not connoted by the specific name, (either ordinarily if the

classification we are considering be for ordinary purposes, or specially

if it be for a special 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

consequently two kinds of Proprium. It may follow as a conclusion

follows premises, or it may follow as an effect follows a cause. Thus,

the attribute of having the opposite sides equal, which is not one of

those connoted by the word Parallelogram, nevertheless follows from

those connoted by it, namely, from having the opposite sides straight

lines and parallel, and the number of sides four. The attribute,

therefore, of having the opposite sides equal, is a Proprium of the

class parallelogram; and a Proprium of the first kind, which follows

from the connoted attributes by way of _demonstration_. 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 follows, or

can be inferred, from another; under what conditions this is possible,

and what is the exact meaning of the phrase; are among the questions

which will occupy us in the two succeeding Books. At present it needs

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

constitution either of our thinking faculty or of the universe.

§ 8. Under the remaining predicable, Accidens, are included all

attributes of a thing which are neither involved in the signification of

the name (whether ordinarily or as a term of art), nor have, so far as

we know, any necessary connexion with attributes which are so involved.

They are commonly divided into Separable and Inseparable Accidents.

Inseparable accidents are those which--although we know of no connexion

between them and the attributes constitutive of the species, and

although, therefore, so far as we are aware, they might be absent

without making the name inapplicable and the species a different

species--are yet never in fact known to be absent. A concise mode of

expressing the same meaning is, that inseparable 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, an

universal one. But if we were to discover a race of white birds, in

other respects resembling crows, we should not say, These are not crows;

we should say, These are white crows. Crow, therefore, does not connote

blackness; nor, from any of the attributes which it does connote,

whether as a word in popular use or as a term of art, could blackness be

inferred. Not only, therefore, can we conceive a white crow, but we know

of no reason why such an animal should not exist. Since, however, none

but black crows are known to exist, blackness, in the present state of

our 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 colour of an European is one of the separable accidents

of the species man, because it is not an attribute of all human

creatures. Being born, is also (speaking in the logical sense) a

separable accident of the species man, because, though an attribute of

all human beings, it is so only at one particular time. _À 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.

CHAPTER VIII.

OF DEFINITION.

§ 1. One necessary part of the theory of Names and of Propositions

remains to be treated of in this place: the theory of Definitions. As

being the most important of the class of propositions which we have

characterized as purely verbal, they have already received some notice

in the chapter preceding the last. But their fuller treatment was at

that time postponed, because definition is so closely connected with

classification, that, until the nature of the latter process is in some

measure understood, the former cannot be discussed to much purpose.

The simplest and most correct notion of a Definition is, a proposition

declaratory of the meaning of a word; namely, either the meaning which

it bears in common acceptation, or that which the speaker or writer, for

the particular purposes of his discourse, intends to annex to it.

The definition of a word being the proposition which enunciates its

meaning, words which have no meaning are unsusceptible of definition.

Proper names, therefore, cannot be defined. A proper name being a mere

mark put upon an individual, and of which it is the characteristic

property to be destitute of meaning, its meaning cannot of course be

declared; though we may indicate by language, as we might indicate still

more conveniently by pointing with the finger, upon what individual that

particular mark has been, or is intended to be, put. It is no definition

of "John Thomson" to say he is "the son of General Thomson;" for the

name John Thomson does not express this. Neither is it any definition of

"John Thomson" to say he is "the man now crossing the street." These

propositions may serve to make known who is the particular man to whom

the name belongs, but that may be done still more unambiguously by

pointing to him, which, however, has not been esteemed one of the modes

of definition.

In the case of connotative names, the meaning, as has been so often

observed, is the connotation; and the definition of a connotative name,

is the proposition which declares its connotation. This might be done

either directly or indirectly. The direct mode would be by a proposition

in this form: "Man" (or whatsoever the word may be) "is a name connoting

such and such attributes," or "is a name which, when predicated of

anything, signifies the possession of such and such attributes by that

thing." Or thus: Man is everything which possesses such and such

attributes: Man is everything which possesses corporeity, organization,

life, rationality, and certain 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 predicate of it another name or names of known signification,

which connote the same aggregation of attributes. This may be done

either by predicating of the name intended to be defined, another

connotative name exactly synonymous, as, "Man is a human being," which

is not commonly accounted a definition at all; or by predicating two or

more connotative names, which make up among them the whole connotation

of the name to be defined. In this last case, again, we may either

compose our definition of as many connotative names as there are

attributes, each attribute being connoted by one, as, Man is a

corporeal, organized, animated, rational being, shaped so and so; or we

may employ names which connote several of the attributes at once, as,

Man is a rational _animal_, shaped so and so.

The definition of a name, according to this view of it, is the sum total

of all the _essential_ propositions which can be framed with that name

for their subject. All propositions the truth of which is implied in the

name, all those which we are made aware of by merely hearing the name,

are included in the definition, if complete, and may be evolved from it

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

instance, "white," which connotes nothing but whiteness; "rational,"

which connotes nothing but the possession of reason. It might seem that

the meaning of such names could only be declared in two ways; by a

synonymous 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 definitions of attributes, or rather of

the names of attributes, that is, of abstract names.

In regard to such names of attributes as are connotative, and express

attributes of those attributes, there is no 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 an 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 correspond exactly to that of the corresponding

concrete name. For, as we define a concrete name by enumerating the

attributes which it connotes, and as the attributes connoted by a

concrete name form the entire signification of the corresponding

abstract name, the same enumeration will serve for the definition of

both. Thus, if the definition of _a human being_ be this, "a being,

corporeal, animated, rational, shaped so and so," the definition of

_humanity_ will be corporeity and animal life, combined with

rationality, and with such and such a shape.

When, on the other hand, the abstract name does not express a

complication of attributes, but a single attribute, we must remember

that every attribute is grounded on some fact or phenomenon, from which,

and which alone, it derives its meaning. To that fact or phenomenon,

called in a former chapter the foundation of the attribute, we must,

therefore, have recourse for its definition. Now, the foundation of the

attribute may be a phenomenon of any degree of complexity, consisting of

many different parts, either coexistent or in succession. To obtain a

definition of the attribute, we must analyse the phenomenon into these

parts. Eloquence, for example, is the name of one attribute only; but

this attribute is grounded on external effects of a complicated nature,

flowing from acts of the person to whom we ascribed the attribute; and

by resolving this phenomenon of causation into its two parts, the cause

and the effect, we obtain a definition of eloquence, viz. the power of

influencing the feelings by speech or writing.

A name, therefore, whether concrete or abstract, admits of definition,

provided we are able to analyse, that is, to distinguish into parts, the

attribute or set of attributes which constitute the meaning both of the

concrete name and of the corresponding abstract: if a set of attributes,

by enumerating them; if a single attribute, by dissecting the fact or

phenomenon (whether of perception or of internal consciousness) which is

the foundation of the attribute. But, further, even when the fact is one

of our simple feelings or states of consciousness, and therefore

unsusceptible of analysis, the names both of the object and of the

attribute still admit of definition: or rather, would do so if all our

simple feelings had names. Whiteness may be defined, the property or

power of exciting the sensation of white. A white object may be defined,

an object which excites the sensation of white. The only names which are

unsusceptible of definition, because their meaning is unsusceptible of

analysis, are the names of the simple feelings themselves. These are in

the same condition as proper names. They are not indeed, like proper

names, unmeaning; for the words _sensation of white_ signify, that the

sensation which I so denominate resembles other sensations which I

remember to have had before, and to have called by that name. But as we

have no words by which to recal those former sensations, except the very

word which we seek to define, or some other which, being exactly

synonymous with it, requires definition as much, words cannot unfold the

signification of this class of names; and we are obliged to make a

direct appeal to the personal experience of the individual whom we

address.

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

proceed to examine some opinions of philosophers, and some popular

conceptions on the subject, which conflict more or less with that idea.

The only adequate definition of a name is, as already remarked, one

which declares the facts, and the whole of the facts, which the name

involves in its signification. But with most persons the object of a

definition does not embrace so much; they look for nothing more, in a

definition, than a guide to the correct use of the term--a protection

against applying it in a manner inconsistent with custom and convention.

Anything, therefore, is to them a sufficient definition of a term, which

will serve as a correct index to what the term denotes; though not

embracing the whole, and sometimes, perhaps, not even any part, of what

it connotes. This gives rise to two sorts of imperfect, or unscientific

definition; Essential but incomplete Definitions, and Accidental

Definitions, or Descriptions. In the former, a connotative name is

defined by a part only of its connotation; in the latter, by something

which forms no part of the connotation at all.

An example of the first kind of imperfect definitions is the

following:--Man is a rational animal. It is impossible to consider this

as a 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 _differentiam_. It would include, with the

name of the superior genus, not merely _some_ attribute which

distinguishes the species intended to be defined from all other species

of the same genus, but _all_ the attributes implied in the name of the

species, which the name of the superior genus has not already implied.

The assertion, however, that a definition must of necessity consist of a

genus and differentiæ, is not tenable. It was early remarked by

logicians, that the _summum genus_ in any classification, having no

genus superior to itself, could not be defined in this manner. Yet we

have seen that all names, except those of our elementary feelings, are

susceptible of definition in the strictest sense; by setting forth in

words the constituent parts of the fact or phenomenon, of which the

connotation of every word is ultimately composed.

§ 4. Although the first kind of imperfect definition, (which defines a

connotative term by a part only of what it connotes, but a part

sufficient to mark out correctly the boundaries of its denotation,) has

been considered by the ancients, and by logicians in general, as a

complete definition; it has always been deemed necessary that the

attributes employed should really form part of the connotation; for the

rule was that the definition must be drawn from the _essence_ of the

class; and this would not have 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

anything which, whether it expounds the meaning of the name or not,

enables us to discriminate the things denoted by the name from all other

things, and consequently to employ the term in predication without

deviating from established usage. This purpose is duly answered by

stating any (no matter what) of the attributes which are common to the

whole of the class, and peculiar to it; or any combination of attributes

which happens to be peculiar to it, though separately each of those

attributes may be common to it with some other things. It is only

necessary that the definition (or description) thus formed, should be

_convertible_ with the name which it professes to define; that is,

should be exactly co-extensive with it, being predicable of everything

of which it is predicable, and of nothing of which it is not predicable;

though the attributes specified may have no connexion with those which

mankind had in view when they formed or recognised the class, and gave

it a name. The following are correct definitions of Man, according to

this test: Man is a mammiferous animal, having (by nature) two hands

(for the human species answers to this description, and no other animal

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

What would otherwise be a mere description, may be raised to the rank of

a real definition by the peculiar purpose which the speaker or writer

has in view. As was seen in the preceding chapter, it may, for the ends

of a particular art or science, or for the more convenient statement of

an author's particular doctrines, be advisable to give to some general

name, without altering its denotation, a special connotation, different

from its ordinary one. When this is done, a definition of the name by

means of the attributes which make up the special connotation, though in

general a mere accidental definition or description, becomes on the

particular occasion and for the particular purpose a complete and

genuine definition. This actually occurs with respect to one of the

preceding examples, "Man is a mammiferous animal having two hands,"

which is the scientific definition of man, considered as one of the

species in Cuvier's distribution of the animal kingdom.

In cases of this sort, though the definition is still a declaration of

the meaning which in the particular instance the name is appointed to

convey, it cannot be said that to state the meaning of the word is the

purpose of the definition. The purpose is not to expound a name, but a

classification. The special meaning which Cuvier assigned to the word

Man, (quite foreign to its ordinary meaning, though involving no change

in the denotation of the word,) was incidental to a plan of arranging

animals into classes on a certain principle, that is, according to a

certain set of distinctions. And since the definition of Man according

to the ordinary connotation of the word, though it would have answered

every other purpose of a definition, would not have pointed out the

place which the species ought to occupy in that particular

classification; he gave the word a special connotation, that he might be

able to define it by the kind of attributes on which, for reasons of

scientific convenience, he had resolved to found his division of

animated nature.

Scientific definitions, whether they are definitions of scientific

terms, or of common terms used in a scientific sense, are almost always

of the kind last spoken of: their main purpose is to serve as the

landmarks of scientific classification. And since the classifications in

any science are continually modified as scientific knowledge advances,

the definitions in the sciences are also constantly varying. A striking

instance is afforded by the words Acid and Alkali, especially the

former. As experimental discovery advanced, the substances classed with

acids have been constantly multiplying, and by a natural consequence the

attributes connoted by the word have receded and become fewer. At first

it connoted the attributes, of combining with an alkali to form a

neutral substance (called a salt); being compounded of a base and

oxygen; causticity to the taste and touch; fluidity, &c. The true

analysis of muriatic acid, into chlorine and hydrogen, caused the second

property, composition from a base and oxygen, to be excluded from the

connotation. The same discovery fixed the attention of chemists upon

hydrogen as an important element in acids; and more recent discoveries

having led to the recognition of its presence in sulphuric, nitric, and

many other acids, where its existence was not previously suspected,

there is now a tendency to include the presence of this element in the

connotation of the word. But carbonic acid, silica, sulphurous acid,

have no hydrogen in their composition; that property cannot therefore be

connoted by the term, unless those substances are no longer to be

considered acids. Causticity and fluidity have long since been excluded

from the characteristics of the class, by the inclusion of silica and

many other 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

_differentiæ_ 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 Introductory Chapter of this work,) the definition of a science must

necessarily be progressive and provisional. Any extension of knowledge

or alteration in the current opinions respecting the subject matter, may

lead to a 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 differentiæ for defining its name.

In the same manner in which a special or technical definition has for

its object to expound the artificial classification out of which it

grows; the Aristotelian logicians seem to have imagined that it was also

the business of ordinary definition to expound the ordinary, and what

they deemed the natural, classification of things, namely, the division

of them into Kinds; and to show the place which each Kind occupies, as

superior, collateral, or subordinate, among other Kinds. This notion

would account for the rule that all definition must necessarily be _per

genus et differentiam_, and would also explain why a single differentia

was deemed sufficient. But to expound, or express in words, a

distinction of Kind, has already been shown to be an impossibility: the

very meaning of a Kind is, that the properties which distinguish it do

not grow out of one another, and cannot therefore be set forth in words,

even by implication, otherwise than by enumerating them all: and all are

not known, nor are ever likely to be so. It is idle, therefore, to look

to this as one of the purposes of a definition: while, if it be only

required that the definition of a Kind should indicate what Kinds

include it or are included by it, any definitions which expound the

connotation of the names will do this: for the name of each class must

necessarily connote enough of its properties to fix the boundaries of

the class. If the definition, therefore, be a full statement of the

connotation, it is all that a definition can be required to be.

§ 5. Of the two incomplete and popular modes of definition, and in what

they differ from the complete or philosophical mode, enough has now been

said. We shall next 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 definitions may be divided, viz. definitions of names,

and definitions of things. The former are intended to explain the

meaning of a term; the latter, the nature of a thing; the last being

incomparably the most important.

This opinion was held by the ancient philosophers, and by their

followers, with the exception of the Nominalists; but as the spirit of

modern metaphysics, until a recent period, has been on the whole a

Nominalist spirit, the notion of definitions of things has been to a

certain extent in abeyance, still continuing, however, to breed

confusion in logic, by its consequences indeed rather than by itself.

Yet the doctrine in its own proper form now and then breaks out, and has

appeared (among other places) where it was scarcely to be expected, in a

justly admired work, Archbishop Whately's _Logic_.[27] In a review of

that work published by me in the _Westminster Review_ for January 1828,

and containing some opinions which I no longer entertain, I find the

following observations on the question now before us; observations with

which my present view of that question is still sufficiently in

accordance.

"The distinction between nominal and real definitions, between

definitions of words and what are called definitions of things, though

conformable to the ideas of most of the Aristotelian logicians, cannot,

as it appears to us, be maintained. We apprehend that no definition is

ever intended to 'explain and unfold the nature of a thing.' It is some

confirmation of our opinion, that none of those writers who have thought

that there were definitions of things, have ever 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 proposition in which any quality

whatever is predicated of the thing, unfolds some part of its nature.

The true state of the case we take to be this. All definitions are of

names, and of names only; but, in some definitions, it is clearly

apparent, that nothing is intended except to explain the meaning of the

word; while in others, besides explaining the meaning of the word, it is

intended to be implied that there exists a thing, corresponding to the

word. Whether this be or be not implied in any given case, cannot be

collected from the mere form of the expression. 'A centaur is an animal

with the upper parts of a man and the lower parts of a horse,' and 'A

triangle is a rectilineal figure with three sides,' are, in form,

expressions precisely similar; although in the former it is not implied

that any _thing_, conformable to the term, really exists, while in the

latter it is; as may be seen by substituting, in both definitions, the

word _means_ for _is_. In the first expression, 'A centaur means an

animal,' &c., the sense would remain unchanged: in the second, 'A

triangle means,' &c., the meaning would be altered, since it would be

obviously impossible to deduce any of the truths of geometry from a

proposition expressive only of the manner in which we intend to employ a

particular sign.

"There are, therefore, expressions, commonly passing for definitions,

which include in themselves more than the mere explanation of the

meaning of a term. But it is not correct to call an expression of this

sort a peculiar kind of definition. Its difference from the other kind

consists in this, that it is not a definition, but a definition and

something more. The definition above given of a triangle, obviously

comprises not one, but two propositions, perfectly distinguishable. The

one is, 'There may exist a figure, bounded by three straight lines;' the

other, 'And this figure may be termed a triangle.' The former of these

propositions is not a definition at all: the latter is a mere nominal

definition, or explanation of the use and application of a term. The

first is susceptible of truth or falsehood, and may therefore be made

the foundation of a train of reasoning. The latter can neither be true

nor false; the only character it is susceptible of is that of conformity

or disconformity to the ordinary usage of language."

There is a real distinction, then, between definitions of names, and

what are erroneously called definitions of things; but it is, that the

latter, along with the meaning of a name, covertly asserts a matter of

fact. This covert assertion is not a definition, but a postulate. The

definition is a mere identical 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.

We have already made, and shall often have to repeat, the remark, that

the philosophers who overthrew Realism by no means got rid of the

consequences of Realism, but retained long afterwards, in their own

philosophy, numerous propositions which could only have a rational

meaning as part of a Realistic system. It had been handed down from

Aristotle, and probably from earlier times, as an obvious truth, that

the science of Geometry is deduced from definitions. This, so long as a

definition was 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 declares the nature of the thing, or does

anything but state the meaning of a name; yet he continued to affirm as

broadly as any of his predecessors, that the [Greek: archai],

_principia_, or original premises of mathematics, and even of all

science, are definitions; producing the singular paradox, that systems

of scientific truth, nay, all truths whatever at which we arrive by

reasoning, are deduced from the arbitrary conventions of mankind

concerning the signification of words.

To save the credit of the doctrine that definitions are the premises of

scientific knowledge, the proviso is sometimes added, that they are so

only under a certain condition, namely, that they be framed conformably

to the phenomena of nature; that is, that they ascribe such meanings to

terms as shall suit objects actually existing. But this is only an

instance of the attempt so often made, to escape from the necessity of

abandoning old language after the ideas which it expresses have been

exchanged for contrary ones. From the meaning of a name (we are told) it

is possible to infer physical facts, provided the name has corresponding

to it an existing thing. But if this proviso be necessary, from which of

the two is the inference really drawn? From the existence of a thing

having the properties, or from the existence of a name meaning them?

Take, for instance, any of the definitions laid down as premises in

Euclid's Elements; the definition, let us say, of a circle. This, being

analysed, consists of two propositions; the one an assumption with

respect to a matter of fact, the other a genuine definition. "A figure

may exist, having all the points in the line which bounds it equally

distant from a single point within it:" "Any figure possessing this

property is called a circle." Let us look at one of the demonstrations

which are said to depend on this definition, and observe to which of the

two propositions contained in it the demonstration really appeals.

"About the centre A, describe the circle B C D." Here is an assumption

that a figure, such as the definition expresses, _may_ be described;

which is no other than the postulate, or covert assumption, involved in

the so-called definition. But whether that figure be called a circle or

not is quite immaterial. The purpose would be as well answered, in all

respects except brevity, were we to say, "Through the point B, draw a

line returning into itself, of which every point shall be at an equal

distance from the point A." By this the definition of a circle would be

got rid of, and rendered 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 B C D is a circle, but because B C D is a figure with the radii

equal. Our warrant for assuming that such a figure about the centre A,

with the radius B A, may be made to exist, is the postulate. Whether the

admissibility of these postulates rests on intuition, or on proof, may

be a matter of dispute; but in either case they are the premises on

which the theorems depend; and while these are retained it would make no

difference in the certainty of geometrical truths, though every

definition in Euclid, and every technical term therein defined, were

laid aside.

It is, perhaps, superfluous to dwell at so much length on what is so

nearly self-evident; but when a distinction, obvious as it may appear,

has been confounded, and by powerful 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 consequences flowing from the supposition that

definitions, as such, are the premises in any of our reasonings, except

such as relate to words only. If this supposition were true, we might

argue correctly from true premises, and arrive at a false conclusion. We

should only have to assume as a premise the definition of a nonentity;

or rather of a name which has no entity corresponding to it. Let this,

for instance, be our definition:

A dragon is a serpent breathing flame.

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 existence of an object with properties corresponding

to the definition, would, in the present instance, be false. Out of this

definition we may carve the premises of the following syllogism:

A dragon is a thing which breathes flame:

A dragon is a serpent:

From which the conclusion is,

Therefore some serpent or serpents breathe flame:--

an unexceptionable syllogism in the first mode of the third figure, in

which both premises are true and yet the conclusion false; which every

logician knows to be an absurdity. The conclusion being false and the

syllogism correct, the premises cannot be true. But the premises,

considered as parts of a definition, are true. Therefore, the premises

considered as parts of a definition cannot be the real ones. The real

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, according to the recommendation in a previous page, substitute

_means_ for _is_. We then have--

Dragon is _a word meaning_ a thing which breathes flame:

Dragon is _a word meaning_ a serpent:

From which the conclusion is,

Some _word or words which mean_ a serpent, also mean a thing which

breathes flame:

where the conclusion (as well as the premises) is true, and is the only

kind of conclusion which can ever follow from a definition, namely, a

proposition relating to the meaning of words.

There is still another shape into which we may transform this syllogism.

We may suppose the middle term to be the 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 follows from the existence of the psychological phenomenon

called the idea of a dragon; and therefore still from the tacit

assumption of a matter of fact.[28]

When, as in this last syllogism, the conclusion is a proposition

respecting an idea, the assumption on which it depends may be merely

that of the existence of an idea. But when the conclusion is a

proposition concerning a Thing, the postulate involved in the definition

which stands as the 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 will 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 being included in the

definition of a circle.

§ 6. One of the circumstances which have contributed to keep up the

notion, that demonstrative truths follow from definitions rather than

from the postulates implied in those definitions, is, that the

postulates, even in those sciences which are considered to surpass all

others in demonstrative certainty, are not always exactly true. It is

not true that a circle exists, or can be described, which has all its

radii _exactly_ equal. Such accuracy is ideal only; it is not found in

nature, still less can it be realized by art. People had a difficulty,

therefore, in conceiving that the most certain of all 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 support

as much as is true of the conclusion. Philosophers, however, to whom

this view had not occurred, or whom it did not satisfy, have thought it

indispensable that there should be found in definitions something _more_

certain, or at least more 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 distance from a given point within it,"

was considered by them, not as an assertion that any real circle has

that property, (which would not be exactly true,) but that we _conceive_

a circle as having it; that our abstract idea of a circle is an idea of

a figure with its radii exactly equal.

Conformably to this it is said, that the subject-matter of mathematics,

and of every other demonstrative science, is not things as they really

exist, but abstractions of the mind. A geometrical line is a line

without breadth; but no such line exists in nature; it is a notion

merely suggested to the mind by its experience of nature. The definition

(it is said) is a definition of this mental line, not of any actual

line: and it is only of the mental line, not of any line existing in

nature, that the theorems of geometry are accurately true.

Allowing this doctrine respecting the nature of demonstrative truth to

be correct (which, in a subsequent place, I shall endeavour to prove

that it is not;) even on that supposition, the conclusions which seem to

follow from a definition, do not follow from the definition as such, but

from an implied postulate. Even if it be true that there is no object in

nature answering to the definition of a line, and that the geometrical

properties of lines are not true of any lines in nature, but only of the

idea of a line; the definition, at all events, postulates the real

existence of such an idea: it assumes that the mind can frame, or rather

has framed, the notion of length without breadth, and without any other

sensible property whatever. To me, indeed, it appears that the mind

cannot form any such notion; it cannot 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. But even what I hold to be the false doctrine on the subject,

leaves the conclusion that our reasonings are grounded on the matters of

fact postulated in definitions, and not on the definitions themselves,

entirely unaffected; and accordingly this conclusion is one which I have

in common with Dr. Whewell, 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 respecting the ultimate

analysis are such as (though with unfeigned respect) I cannot but regard

as fundamentally erroneous.

§ 7. Although, according to the opinion here presented, Definitions are

properly of names only, and not of things, it does not follow from this

that definitions are arbitrary. How to define a name, may not only be an

inquiry of considerable difficulty and intricacy, but may involve

considerations going deep into the nature of the things which are

denoted by the name. Such, for instance, are the inquiries which form

the subjects of the most important of Plato's Dialogues; as, "What is

rhetoric?" the topic of the Gorgias, or "What is justice?" that of the

Republic. Such, also, is the question scornfully asked by Pilate, "What

is truth?" and the fundamental 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

attributes 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 distinctly intended by them to be conveyed

by it. The first person who used the word white, as applied to snow or

to any other object, knew, no doubt, very well what quality he intended

to predicate, and had a perfectly distinct conception in his mind of the

attribute signified by the name.

But where the resemblances and differences on which our classifications

are founded are not of this palpable and easily determinable kind;

especially where they consist not in any one quality but in a number of

qualities, the effects of which being blended together are not very

easily discriminated, and referred each to its true source; it often

happens that names are applied to nameable objects, with no distinct

connotation present to the minds of those who apply them. They are only

influenced by a general resemblance between the new object and all or

some of the old familiar objects which they have been accustomed to call

by that name. This, as we have seen, is the law which even the mind of

the philosopher must follow, in giving names to the simple elementary

feelings of our nature: but, where the things to be named are complex

wholes, a philosopher is not content with noticing a general

resemblance; he examines what the resemblance consists in: and he only

gives the same name to things which resemble one another in the same

definite particulars. The philosopher, therefore, habitually employs his

general names with a definite connotation. But language was not made,

and can only in some small degree be mended, by philosophers. In the

minds of the real arbiters of language, general names, especially where

the classes they denote cannot be brought before the 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 demeanour,

_statesman_ or _charlatan_ of any personage figuring in politics, do

they mean to affirm of those various subjects any determinate

attributes, of whatever kind? No: they merely recognise, as they think,

some likeness, more or less vague and loose, between these and some

other things which they have been accustomed to denominate or to hear

denominated by those appellations.

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 purpose

upon a _class_ of objects, but is first applied to one thing, and then

extended by a series of transitions to another and another. By this

process (as has been remarked by several writers, and illustrated with

great force and clearness by Dugald Stewart in his Philosophical Essays)

a name not unfrequently passes by successive links of resemblance from

one object to another, until it becomes 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 continual mending in

order to be passable.

From this it is already evident, why the question respecting the

definition of an abstract name is often one of so much difficulty. The

question, What is justice? is, in other words, What is the attribute

which mankind mean to predicate when they call an action just? To which

the first answer is, that having come to no precise agreement on the

point, they do not mean to predicate distinctly any attribute at all.

Nevertheless, all believe 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 mankind agree sufficiently with one another

as to the particular actions which they do or do not call just, to

render the inquiry, what quality those actions have in common, a

possible one: if so, whether the actions really have any quality in

common; and if they have, what it is. Of these three, the first alone is

an inquiry into usage and convention; the other two are inquiries into

matters of fact. And if the second question (whether the actions form a

class at all) has been answered negatively, there remains a fourth,

often more arduous than all the rest, namely, how best to form a class

artificially, which the name may denote.

And here it is fitting to remark, that the study of the spontaneous

growth of languages is of the utmost importance to those who would

logically remodel them. The classifications rudely made by established

language, when retouched, as they almost all require to be, by the hands

of the logician, are often in themselves excellently suited to his

purposes. As compared with the classifications of a philosopher, they

are like the customary law of a country, which has grown up as it were

spontaneously, compared with laws methodized and digested into a code:

the former are a far less perfect instrument than the latter; but being

the result of a long, though unscientific, 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 which has struck great

numbers of persons during a series of years and ages. Even when a name,

by successive extensions, has come to be applied to things among which

there does not exist this gross resemblance 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

connexions between the things denoted by them, which might otherwise

escape the notice of thinkers; of those at least who, from using a

different language, or from any difference in their habitual

associations, have fixed their attention in preference on some other

aspect of the things. The history of philosophy abounds in examples of

such oversights, committed for want of perceiving the hidden link that

connected together the seemingly disparate meanings of some ambiguous

word.[29]

Whenever the inquiry into the definition of the name of any real object

consists of anything else than a mere comparison of authorities, we

tacitly assume that a meaning must be found for the name, compatible

with its continuing to denote, if possible all, but at any rate the

greater or the more important part, of the things of which it is

commonly predicated. The inquiry, therefore, into the definition, is an

inquiry into the resemblances and differences among those things:

whether there be any resemblance running through them all; if not,

through what portion of them such a general resemblance can be traced:

and finally, what are the common attributes, the possession of which

gives to them all, or to that portion of them, the character of

resemblance which has led to their being classed together. When these

common attributes have been ascertained and specified, the name which

belongs in common to the resembling objects acquires a distinct instead

of a vague connotation; and by possessing this distinct connotation,

becomes susceptible of definition.

In giving a distinct connotation to the general name, the philosopher

will endeavour to fix upon such attributes as, while they are common to

all the things usually denoted by the name, are also of greatest

importance in themselves; either directly, or from the number, the

conspicuousness, or the interesting character, of the consequences to

which they lead. He will select, as far as possible, such _differentiæ_

as lead to the greatest number of interesting _propria_. For these,

rather than the more obscure and recondite qualities on which they often

depend, give that general character and aspect to a set of objects,

which determine the groups into which they naturally fall. But to

penetrate to the more hidden agreement on which these obvious and

superficial agreements depend, is often one of the most difficult of

scientific problems. As it is among the most difficult, so it seldom

fails to be among the most important. And since upon the result of this

inquiry respecting the causes of the properties of a class of things,

there incidentally depends the question what shall be the meaning of a

word; some of the most profound and most valuable 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.

FOOTNOTES:

[1] _Computation or Logic_, chap. ii.

[2] In the original "had, _or had not_." These last words, as involving

a subtlety foreign to our present purpose, I have forborne to quote.

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

[4] _Notare_, to mark; _con_notare, to mark _along with_; to mark one

thing _with_ or _in addition to_ another.

[5] Archbishop Whately, who, in the later editions of his _Elements of

Logic_, aided in reviving the important distinction treated of in the

text, proposes the term "Attributive" as a substitute for "Connotative"

(p. 22, 9th ed.) The expression is, in itself, appropriate; but as it

has not the advantage of being connected with any verb, of so markedly

distinctive a character as "to connote," it is not, I think, fitted to

supply the place of the word Connotative in scientific use.

[6] A writer who entitles his book _Philosophy; or, the Science of

Truth_, charges me in his very first page (referring at the foot of it

to this passage) with asserting that _general_ names have properly no

signification. And he repeats this statement many times in the course of

his volume, with comments, not at all flattering, thereon. It is well to

be now and then reminded to how great a length perverse misquotation

(for, strange as it appears, I do not believe that the writer is

dishonest) can sometimes go. It is a warning to readers, when they see

an author accused, with volume and page referred to, and the apparent

guarantee of inverted commas, of maintaining something more than

commonly absurd, not to give implicit credence to the assertion without

verifying the reference.

[7] 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 different

from that in which it is here used. He uses the word in a sense

coextensive with its etymology, applying it to every case in which a

name, while pointing directly to one thing, (which is 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 _de_notation 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 signification. This necessity can scarcely be

felt in its full force by any one who has not found by experience how

vain is the attempt to communicate clear ideas on the 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 diverted from that purpose by being taken to fulfil

another, for which it does not seem to me to be at all required; I am

unable to find any expression to replace it, but such as are commonly

employed in a sense so much more general, that it would be useless

attempting to associate them peculiarly with this precise idea. Such are

the words, to involve, to imply, &c. By employing these, I should fail

of 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.

[8] Or rather, all objects except itself and the percipient mind; for,

as we shall see hereafter, to ascribe any attribute to an object,

necessarily implies a mind to perceive it.

The simple and clear explanation given in the text, of relation and

relative names, a subject so long the opprobrium of metaphysics, was

given (as far as I know) for the first time, by Mr. James Mill, in his

Analysis of the Phenomena of the Human Mind.

[9] _Philosophy of the Inductive Sciences_, vol. i. p. 40.

[10] _Discussions on Philosophy_, &c. Appendix I. pp. 643-4.

[11] 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

irreconcileable. See the third and other chapters of _An Examination of

Sir William Hamilton's Philosophy_.

[12] "Nous savons qu'il existe quelque chose hors de nous, parceque nous

ne pouvons expliquer nos perceptions sans les rattacher à des causes

distinctes de nous-mêmes; nous savons de plus que ces causes, dont nous

ne connaissons pas d'ailleurs l'essence, produisent les effets les plus

variables, les plus divers, et même les plus contraires, selon qu'elles

rencontrent telle nature ou telle disposition du sujet. Mais savons-nous

quelque chose de plus? et même, vu le caractère indéterminé des causes

que nous concevons dans les corps, y a-t-il quelque chose de plus à

savoir? Y a-t-il lieu de nous enquérir si nous percevons les choses

telles qu'elles sont? Non évidemment.... Je ne dis pas que le problème

est insoluble, _je dis qu'il est absurde et enferme une contradiction_.

Nous _ne savons pas ce que ces causes sont en elles-mêmes_, et la raison

nous défend de chercher à le connaître: mais il est bien évident _à

priori_, qu'_elles ne sont pas en elles-mêmes ce qu'elles sont par

rapport à nous_, puisque la présence du sujet modifie nécessairement

leur action. Supprimez tout sujet sentant, il est certain que ces causes

agiraient encore puisqu'elles continueraient d'exister; mais elles

agiraient autrement; elles seraient encore des qualités et des

propriétés, mais qui ne ressembleraient à rien de ce que nous

connaissons. Le feu ne manifesterait plus aucune des propriétés que nous

lui connaissons: que serait-il? C'est ce que nous ne saurons jamais.

_C'est d'ailleurs peut-être un problème qui ne répugne pas seulement à

la nature de notre esprit, mais à l'essence même des choses._ Quand même

en effet on supprimerait par la pensée tous les sujets sentants, il

faudrait encore admettre que nul corps ne manifesterait ses propriétés

autrement qu'en relation avec un sujet quelconque, et dans ce cas _ses

propriétés ne seraient encore que relatives_: en sorte qu'il me paraît

fort raisonnable d'admettre que les propriétés déterminées des corps

n'existent pas indépendamment d'un sujet quelconque, et que quand on

demande si les propriétés de la matière sont telles que nous les

percevons, il faudrait voir auparavant si elles sont en tant que

déterminées, et dans quel sens il est vrai de dire qu'elles

sont."--_Cours d'Histoire de la Philosophie Morale au 18me siècle_, 8me

leçon.

[13] An attempt, indeed, has been made by Reid and others, to establish

that although some of the properties we ascribe to objects exist only in

our sensations, others exist in the things themselves, being such as

cannot possibly be copies of any impression upon the senses; and they

ask, from what sensations our notions of extension and figure have been

derived? The gauntlet thrown down by Reid was taken up by Brown, who,

applying greater powers of analysis than had previously been applied to

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 favour of the better

doctrine. M. Cousin recognises, in opposition to Reid, the essential

subjectivity of our conceptions of what are called the primary qualities

of matter, as extension, solidity, &c., equally with those of colour,

heat, and the remainder of the so-called secondary qualities.--_Cours_,

ut supra, 9me leçon.

[14] This doctrine, which is the most complete form of the philosophical

theory known as the Relativity of Human Knowledge, has, since the recent

revival in this country of an active interest in metaphysical

speculation, been the subject of a greatly increased amount of

discussion and controversy; and dissentients have manifested themselves

in considerably greater number than I had any knowledge of when the

passage in the text was written. The doctrine has been attacked from two

sides. Some thinkers, among whom are the late Professor Ferrier, in his

_Institutes of Metaphysic_, and Professor John Grote in his _Exploratio

Philosophica_, appear to deny altogether the reality of Noumena, or

Things in themselves--of an unknowable substratum or support for the

sensations which we experience, and which, according to the theory,

constitute all our knowledge of an external world. It seems to me,

however, that in Professor Grote's case at least, the denial of Noumena

is only apparent, and that he does not essentially differ from the other

class of objectors, including Mr. Bailey in his valuable _Letters on the

Philosophy of the Human Mind_, and (in 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 Things

themselves.

With the first of these opinions, that which denies Noumena, I have, as

a metaphysician, no quarrel; but, whether it be true or false, it is

irrelevant to Logic. And since all the forms of language are in

contradiction to it, nothing but confusion could result from its

unnecessary introduction into a treatise, every essential doctrine of

which could stand equally well with the opposite and accredited opinion.

The other and rival doctrine, that of a direct perception or intuitive

knowledge of the outward object as it is in itself, considered as

distinct from the sensations we receive from it, is of far greater

practical moment. But even this question, depending on the nature and

laws of Intuitive Knowledge, is not within the province of Logic. For

the grounds of my own opinion concerning it, I must content myself with

referring to a work already mentioned--_An Examination of Sir William

Hamilton's Philosophy_; several chapters of which are devoted to a full

discussion of the questions and theories relating to the supposed direct

perception of external objects.

[15] _Analysis of the Human Mind_, i. 126 et seq.

[16] It may, however, be considered as equivalent to an universal

proposition with a different predicate, viz. "All wine is good _quâ_

wine," or "is good in respect of the qualities which constitute it

wine."

[17] Dr. Whewell (_Philosophy of Discovery_, p. 242) questions this

statement, and asks, "Are we to say that a mole cannot dig the ground,

except he has an idea of the ground, and of the snout and paws with

which he digs it?" I do not know what passes in a mole's mind, nor what

amount of mental apprehension may or may not accompany his instinctive

actions. But a human being does not use a spade by instinct; and he

certainly could not use it unless he had knowledge of a spade, and of

the earth which he uses it upon.

[18] "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 others. For it is true (for

example) that _man is a living creature_, but it is for this reason,

that it pleased men to impose both these names on the same

thing."--_Computation or Logic_, ch. iii. sect. 8.

[19] "Men are subject to err not only in affirming and denying, but also

in perception, and in silent cogitation.... Tacit errors, or the errors

of sense and cogitation, are made by passing from one imagination to the

imagination of another different thing; or by feigning that to be past,

or future, which never was, nor ever shall be; as when by seeing the

image of the sun in water, we imagine the sun itself to be there; or by

seeing swords, that there has been, or shall be, fighting, because it

uses to be so for the most part; or when from promises we feign the mind

of the promiser to be such and such; or, lastly, when from any sign we

vainly imagine something to be signified which is not. And errors of

this sort are common to all things that have sense."--_Computation or

Logic_, ch. v. sect. 1.

[20] Ch. iii. sect. 3.

[21] To the preceding statement it has been objected, that "we naturally

construe the subject of a proposition in its extension, and the

predicate (which therefore may be an adjective) in its intension,

(connotation): and that consequently coexistence of attributes does not,

any more than the opposite theory of equation of groups, correspond with

the living processes of thought and language." I acknowledge the

distinction here drawn, which, indeed, I had myself laid down and

exemplified a few pages back (p. 104). But though it is true that we

naturally "construe the subject of a proposition in its extension," this

extension, or in other words, the extent of the class denoted by the

name, is not apprehended or indicated directly. It is both apprehended

and 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 Philosophy_, ch. xxii.

[22] Book iv. ch. vii.

[23] The doctrines which prevented the real meaning of Essences from

being understood, had not assumed so settled a shape in the time of

Aristotle and his immediate followers, as was afterwards given to them

by the Realists of the middle ages. Aristotle himself (in his Treatise

on the Categories) expressly denies that the [Greek: deuterai ousiai],

or Substantiæ Secundæ, inhere in a subject. They are only, he says,

predicated of it.

[24] The always acute and often profound author of _An Outline of

Sematology_ (Mr. B. H. Smart) justly says, "Locke will be much more

intelligible if, in the majority of places, we substitute 'the knowledge

of' for what he calls 'the Idea of'" (p. 10). Among the many criticisms

on Locke's use of the word Idea, this is the one which, as it appears to

me, most nearly hits the mark; and I quote it for the additional reason

that it precisely expresses the point of difference respecting the

import of Propositions, between my view and what I have spoken of as the

Conceptualist view of them. Where a Conceptualist says that a name or a

proposition expresses our Idea of a thing, I should generally say

(instead of our Idea) our Knowledge, or Belief, concerning the thing

itself.

[25] 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.

[26] 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 any way

applicable to attributes, it of course follows that although attributes

may be put into classes, those classes can be admitted to be genera or

species only by courtesy.

[27] In the fuller discussion which Archbishop Whately has given to this

subject in his later editions, he almost ceases to regard the

definitions of names and those of things as, in any important sense,

distinct. He seems (9th ed. p. 145) to limit the notion of a Real

Definition to one which "explains anything _more_ of the nature of the

thing than is implied in the name;" (including under the word "implied,"

not only what the name connotes, but everything which can be deduced by

reasoning from the attributes connoted). Even this, as he adds, is

usually called, not a Definition, but a Description; and (as it seems to

me) rightly so called. A Description, I conceive, can only be ranked

among Definitions, when taken (as in the case of the zoological

definition of man) to fulfil the true office of a Definition, by

declaring the connotation given to a word in some special use, as a term

of science or art: which special connotation of course would not be

expressed by the proper definition of the word in its ordinary

employment.

Mr. De Morgan, exactly reversing the doctrine of Archbishop Whately,

understands by a Real Definition one which contains _less_ than the

Nominal Definition, provided only that what it contains is sufficient

for distinction. "By _real_ definition I mean such an explanation of the

word, be it the whole of the meaning or only part, as will be sufficient

to separate the things contained under that word from all others. Thus

the following, I believe, is a complete definition of an elephant: An

animal which naturally drinks by drawing the water into its nose, and

then spurting it into its mouth."--_Formal Logic_, p. 36. Mr. De

Morgan's general proposition and his example are at variance; for the

peculiar mode of drinking of the elephant certainly forms no part of the

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.

[28] In the only attempt which, so far as I know, has been made to

refute the preceding argumentation, it is maintained that in the first

form of the syllogism,

A dragon is a thing which breathes flame,

A dragon is a serpent,

Therefore some serpent or serpents breathe flame,

"there is just as much truth in the conclusion as there is in the

premises, or rather, no more in the latter than in the former. If the

general name serpent includes both real and imaginary serpents, there is

no falsity in the conclusion; if not, there is falsity in the minor

premise."

Let us, then, try to set out the syllogism on the hypothesis that the

name serpent includes imaginary serpents. We shall find that it is now

necessary to alter the predicates; for it cannot be asserted that an

imaginary creature breathes flame: in predicating of it such a fact, we

assert by the most positive implication that it is real and not

imaginary. The conclusion must run thus, "Some serpent or serpents

either do or are _imagined_ to breathe flame." And to prove this

conclusion by the instance of dragons, the premises must be, A dragon is

_imagined_ as breathing flame, A dragon is a (real or imaginary)

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 myself said of the premise,

considered as a statement of fact: but it is not false as part of the

definition of a dragon; and since the premises, or one of them, must be

false, (the conclusion being so,) the real premise cannot be the

definition, which is true, but the statement of fact, which is false.

[29] "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 connexion, upon which, though perhaps unable to give a logical

account of it, he will found a perfectly valid argument, which his

critic, not having so keen an insight into the Things, will mistake for

a fallacy turning on the double meaning of a term. And the greater the

genius of him who thus safely leaps over the chasm, the greater will

probably be the crowing and vain-glory of the mere logician, who,

hobbling after him, evinces his own superior wisdom by pausing on its

brink, and giving up as desperate his proper business of bridging it

over."

BOOK II.

OF REASONING.

[Greek: Diôrismenôn de toutôn legômen êdê, dia tinôn, kai pote, kai pôs

ginetai pas syllogismos hysteron de lekteon peri apodeixeôs. Proteron

gar peri syllogismou lekteon, ê peri apodeixeôs, dia to katholou mallon

einai ton syllogismon. Hê men gar apodeixis, syllogismos tis; ho

syllogismos de ou pas, apodeixis.]

ARIST. _Analyt. Prior._ l. i. cap. 4.

CHAPTER I.

OF INFERENCE, OR REASONING, IN GENERAL.

§ 1. In the preceding Book, we have been occupied not with the nature of

Proof, but with the nature of Assertion: the import conveyed by a

Proposition, 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 necessary to understand what that is to which proof is applicable;

what that is which can be a subject of belief or disbelief, of

affirmation or denial; what, in short, the different kinds of

Propositions assert.

This preliminary inquiry we have prosecuted to a definite result.

Assertion, in the first place, relates either to the meaning of words,

or to some property of the things which words signify. Assertions

respecting the meaning of words, among which definitions are the most

important, hold a place, and an indispensable one, in philosophy; but as

the meaning of words is essentially arbitrary, this class of assertions

are not susceptible of truth or falsity, nor therefore of proof or

disproof. Assertions respecting Things, or what may be called Real

Propositions, in contradistinction to verbal ones, are of various sorts.

We have analysed the import of each sort, and have ascertained the

nature of the things they relate to, and the nature of what they

severally assert respecting those things. We found that whatever be the

form of the 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,

Causation, or Resemblance. This, then, is the theory of the Import of

Propositions, reduced to its ultimate elements: but there is another and

a less abstruse expression for it, which, though stopping short in an

earlier stage of the analysis, is sufficiently scientific for many of

the purposes for which such a general expression is required. This

expression recognises the commonly received distinction between Subject

and Attribute, and gives the following as the analysis of the meaning of

propositions:--Every Proposition asserts, that some given subject does

or does not possess some attribute; or that some attribute is or is not

(either in all or in some portion of the subjects in which it is met

with) conjoined with some other attribute.

We shall now for the present take our leave of this portion of our

inquiry, and proceed to the peculiar problem of the Science of Logic,

namely, how the assertions, of which we have analysed the import, are

proved or disproved; such of them, at least, as, not being amenable to

direct consciousness or intuition, are appropriate subjects of proof.

We say of a fact or statement, that it is proved, when we believe its

truth by reason of some other fact or statement from which it is said to

_follow_. Most of the propositions, whether affirmative or negative,

universal, particular, or singular, which we believe, are not believed

on their own evidence, but on the ground of something previously

assented to, from which they are said to be _inferred_. To infer a

proposition from a previous proposition or propositions; to give

credence to it, or claim credence for it, as a conclusion from something

else; is to _reason_, in the most extensive sense of the term. There is

a narrower sense, in which the name reasoning is confined to the form of

inference which is termed ratiocination, and of which the syllogism is

the general type. The reasons for not conforming to this restricted use

of the term were stated in an earlier stage of our inquiry, and

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

inferences can legitimately be drawn, we shall first mention some cases

in which the inference is apparent, not real; and which require notice

chiefly that they may not be confounded with cases of inference properly

so called. This occurs when the proposition ostensibly inferred from

another, appears on analysis to be merely a repetition of the same, or

part of the same, assertion, which was contained in the first. All the

cases mentioned in books of Logic as examples of æquipollency or

equivalence of propositions, are of this nature. Thus, if we were to

argue, No man is incapable of reason, for every man is rational; or, All

men are mortal, for no man is exempt from death; it would be plain that

we were not proving the proposition, but only appealing to another mode

of wording it, which may or may not be more readily comprehensible by

the hearer, or better adapted to suggest the real proof, but which

contains in itself no shadow of proof.

Another case is where, from an universal proposition, we affect to infer

another which differs from it only in being particular: as All A is B,

therefore Some A is B: No A is B, therefore Some A is not B. This, too,

is not to conclude one proposition from another, but to repeat a second

time something which had been 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 affirmed of Socrates when he was asserted to be a

man. If the propositions are negative, we must invert their order, thus:

Socrates is not a living creature, therefore he is not a man; for if we

deny the less, the greater, which includes it, is already denied by

implication. These, therefore, are not really cases of inference; and

yet the trivial examples by which, in manuals of Logic, the rules of the

syllogism are illustrated, are often of this ill-chosen kind; formal

demonstrations of conclusions to which whoever understands the terms

used in the statement of the data, has already, and consciously,

assented.

The most complex case of this sort of apparent inference is what is

called the Conversion of propositions; which consists in turning the

predicate into a subject, and the subject into a predicate, and framing

out of the same terms thus reversed, another proposition, which must be

true if the former is true. Thus, from the particular affirmative

proposition, Some A is B, we may infer that Some B is A. From the

universal negative, No A is B, we may conclude that No B is A. From the

universal affirmative proposition, All A is B, it cannot be inferred

that all B is A; though all water is liquid, it is not implied that all

liquid is water; but it is implied that some liquid is so; and hence the

proposition, All A is B, is legitimately convertible into Some B is A.

This process, which converts an universal proposition into a particular,

is termed conversion _per accidens_. From the proposition, Some A is not

B, we cannot even infer that some B is not A; though some men are not

Englishmen, it does not follow that some Englishmen are not men. The

only mode usually recognised of converting a particular 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 contraposition. In this

case, however, the predicate and subject are not merely reversed, but

one of them is changed. Instead of [A] and [B], the terms of the new

proposition are [a thing which is not B], and [A]. The original

proposition, Some A _is not_ B, is first changed into a proposition

æquipollent with it, Some A _is_ "a thing which is not B;" and the

proposition, being now no longer a particular negative, but a particular

affirmative, _admits_ of conversion in the first mode, or as it is

called, _simple_ conversion.[1]

In all these cases there is not really any inference; there is in the

conclusion no new truth, nothing but what was already asserted in the

premises, 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 Import of Propositions. When we say, for example, that

some lawful sovereigns are tyrants, what is the meaning of the

assertion? That the attributes connoted by the term "lawful sovereign,"

and the attributes connoted by the term "tyrant," sometimes coexist in

the same individual. Now this is also precisely what we mean, when we

say that some tyrants are lawful sovereigns; which, therefore, is not a

second proposition inferred from the first, any more than the English

translation of Euclid's Elements is a collection of theorems different

from, and 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 coexist in the same subject; which is also the exact meaning which

would be expressed by saying, that no rash man is a great general. When

we say that all quadrupeds are warm-blooded, we assert, not only that

the attributes connoted by "quadruped" and those connoted by

"warm-blooded" sometimes coexist, but that the former never exist

without the latter: now the proposition, Some warm-blooded creatures are

quadrupeds, expresses the first half of this meaning, dropping the

latter half; and therefore has been already affirmed in the antecedent

proposition, All quadrupeds are warm-blooded. But 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 cannot be inferred. In order

to reassert, in an inverted form, the whole of what was affirmed in the

proposition, All quadrupeds are warm-blooded, we must convert it by

contraposition, thus, Nothing which is not warm-blooded is a quadruped.

This proposition, and the one from which it is derived, are exactly

equivalent, and either of them may be substituted for the other; for,

to say that when the attributes of a quadruped 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 æquipollency of propositions. For, though

that cannot be called reasoning or inference which is a mere reassertion

in different words of what had been asserted before, there is no more

important intellectual habit, nor any the cultivation of which falls

more strictly within the province of the art of logic, than that of

discerning rapidly and surely the identity of an assertion when

disguised under diversity of language. That important chapter in logical

treatises which relates to the Opposition of Propositions, and the

excellent technical language which logic provides for distinguishing the

different kinds or modes of opposition, are of use chiefly for this

purpose. Such considerations as these, that contrary propositions may

both be false, but cannot both be true; that subcontrary propositions

may both be true, but cannot both be false; that of two contradictory

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 universal, but not _vice versâ_;[2] are apt to appear, at first

sight, very technical and mysterious, but when explained, seem almost

too obvious to require so formal a statement, since the same amount of

explanation which is necessary to make the principles intelligible,

would enable the truths which they convey 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 mathematics. That things which are

equal to the same thing are equal to one another, is as obvious in any

particular case as it is in the general statement: and if no such

general maxim had ever been laid down, the demonstrations in Euclid

would never have halted for any difficulty in stepping across the gap

which this axiom at present serves to bridge over. Yet no one has ever

censured writers on geometry, for placing a list of these elementary

generalizations at the head of their treatises, as a first exercise to

the learner of the faculty which will be required in him at every step,

that of apprehending a _general_ truth. And the student of logic, in the

discussion even of such truths as we have cited above, acquires habits

of circumspect interpretation of words, and of exactly measuring the

length and breadth of his assertions, which are among the most

indispensable conditions of 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 repetition of the logical antecedent; we now pass to those which

are cases of inference in the proper acceptation of the term, those in

which we set out from known truths, to arrive at others really distinct

from them.

Reasoning, in the extended sense in which I use the term, and in which

it is synonymous with Inference, is popularly said to be of two kinds:

reasoning from particulars to generals, and reasoning from generals to

particulars; the former being called Induction, the latter Ratiocination

or Syllogism. It will presently be shown that there is a third species

of 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

particulars to generals, and reasoning from generals to particulars, are

recommended 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 proposition, not alone (for

from a single proposition nothing can be concluded which is not involved

in the terms), but by combining it with other propositions, we infer a

proposition of the same degree of generality with itself, or a less

general proposition, or a proposition merely individual, the process is

Ratiocination. When, in short, the conclusion is more general than the

largest of the premises, the argument is commonly called Induction; when

less general, or equally general, it is 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 for their evidence, before attempting to point out the

original spring from which both ultimately take their rise. The

advantages of this order of proceeding in the present instance will

manifest themselves as we advance, in a manner superseding the necessity

of any further justification or explanation.

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 examined; 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 which we have not observed, and even

to facts not capable of being now observed; future facts, for example;

but which we do not hesitate to believe on the sole evidence of the

induction itself.

Induction, then, is a real process of Reasoning or Inference. Whether,

and in what sense, as much can be said of the Syllogism, remains to be

determined by the examination into which we are about to enter.

CHAPTER II.

OF RATIOCINATION, OR SYLLOGISM.

§ 1. The analysis of the Syllogism has been so accurately and fully

performed in the common manuals of Logic, that in the present work,

which is not designed as a manual, it is sufficient to recapitulate,

_memoriæ causâ_, the leading results of that analysis, as a foundation

for the remarks to be afterwards made on the functions of the syllogism,

and the place which it holds in science.

To a legitimate syllogism it is essential that there should be three,

and no more than three, propositions, namely, the conclusion, or

proposition to be proved, and two other propositions which together

prove it, and which are called the premises. It is essential that there

should be three, and no more than three, terms, namely, the subject and

predicate of the conclusion, and another called the middleterm, which

must be found in both premises, since it is by means of it that the

other two terms are to be connected together. The predicate of the

conclusion is called the major term of the syllogism; the subject of the

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 middleterm which is in them both. The

premise which contains the middleterm and the major term is called the

major premise; that which contains the middleterm and the minor term is

called the minor premise.

Syllogisms are divided by some logicians into three _figures_, by others

into four, according to the position of the middleterm, which may either

be the subject in both premises, the predicate in both, or the subject

in one and the predicate in the other. The most common case is that in

which the middleterm is the subject of the major premise and the

predicate of the minor. This is reckoned as the first figure. When the

middleterm is the predicate in both premises, the syllogism belongs to

the second figure; when it is the subject in both, to the third. In the

fourth figure the middleterm is the subject of the minor premise and the

predicate of the major. Those writers who reckon no more than three

figures, include this case in the first.

Each figure is divided into _moods_, according to what are called the

_quantity_ and _quality_ of the propositions, that is, 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 middleterm.

FIRST FIGURE.

All B is C No B is C All B is C No B is C

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

therefore therefore therefore therefore

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

SECOND FIGURE.

No C is B All C is B No C is B All C is B

All A is B No A is B Some A is B Some A is not B

therefore therefore therefore therefore

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

THIRD FIGURE.

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

is not C

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

therefore therefore therefore therefore therefore therefore

Some A is C Some A Some A is C Some A is C Some A Some A

is not C is not C is not C

FOURTH FIGURE.

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

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

therefore therefore therefore therefore therefore

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

In these exemplars, or blank forms for making syllogisms, no place is

assigned to _singular_ propositions; not, of course, because such

propositions are not used in ratiocination, but because, their predicate

being affirmed or denied of the whole of the subject, they are ranked,

for the purposes of the syllogism, with universal propositions. Thus,

these two syllogisms--

All men are mortal, All men are mortal,

All kings are men, Socrates is a man,

therefore therefore

All kings are mortal, Socrates is mortal,

are arguments precisely similar, and are both ranked in the first mood

of the first figure.

The reasons why syllogisms in any of the above forms are legitimate,

that is, why, if the premises are true, the conclusion must inevitably

be so, and why this is not the case in any other possible mood, (that

is, in any other combination of universal and particular, affirmative

and negative propositions,) any person taking interest in these

inquiries may be presumed to have either learned from the common school

books of the syllogistic logic, or to be capable of discovering for

himself. The reader may, however, be referred, for every needful

explanation, to Archbishop Whately's _Elements of Logic_, where he will

find stated with philosophical precision, and explained with remarkable

perspicuity, the whole of the common doctrine of the syllogism.

All valid ratiocination; all reasoning by which, from general

propositions previously admitted, other propositions equally or less

general are inferred; may be exhibited in some of the above forms. The

whole of Euclid, for example, might be thrown without difficulty into a

series of syllogisms, regular in mood and figure.

Though a syllogism framed according to any of these formulæ is a valid

argument, all correct ratiocination admits of being stated in syllogisms

of the first figure alone. The rules for throwing an argument in any of

the other figures into the first figure, are called rules for the

_reduction_ of syllogisms. It is done by the _conversion_ of one or

other, or both, of the premises. Thus an argument in the first mood of

the second figure, as--

No C is B

All A is B

therefore

No A is C,

may be reduced as follows. The proposition, No C is B, being an

universal negative, admits of simple conversion, and may be changed into

No B is C, which, as we showed, is the very same assertion in other

words--the same fact differently expressed. This transformation having

been effected, the argument assumes the following form:--

No B is C

All A is B

therefore

No A is C,

which is a good syllogism in the second mood of the first figure. Again,

an argument in the first mood of the third figure must resemble the

following:--

All B is C

All B is A

therefore

Some A is C,

where the minor premise, All B is A, conformably to what was laid down

in the last chapter respecting universal affirmatives, does not admit of

simple conversion, but may be converted _per accidens_, thus, Some A is

B; which, though it does not express the whole of what is asserted in

the proposition All B is A, expresses, as was formerly shown, part of

it, and must therefore be true if the whole is true. We have, then, as

the result of the reduction, the following syllogism in the third mood

of the first figure:--

All B is C

Some A is B,

from which it obviously follows, that

Some A is C.

In the same manner, or in a manner on which after these examples it is

not necessary to enlarge, every mood of the second, third, and fourth

figures may be reduced to some one of the four moods of the first. In

other words, every conclusion which can be proved in any of the last

three figures, may be proved in the first figure from the same premises,

with a slight alteration in the mere manner of expressing them. Every

valid ratiocination, therefore, may be stated in the first figure, that

is, in one of the following forms:--

Every B is C No B is C

All A } is B, All A } is B,

Some A } Some A }

therefore therefore

All A } is C. No A is } C.

Some A } Some A is not }

Or if more significant symbols are preferred:--

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

form:--

All animals are mortal;

All men }

Some men } are animals;

Socrates }

therefore

All men }

Some men } are mortal.

Socrates }

To prove a negative, the argument must be capable of being expressed in

this form:--

No one who is capable of self-control is necessarily vicious;

All negroes }

Some negroes } 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 suitably into each of the four figures; and his

investigation is characterized by great ingenuity and clearness of

thought.[3] 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 everything 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,

cannot possibly happen with the only class of arguments which are of

first-rate scientific importance, those in which the conclusion is an

universal affirmative, such conclusions being susceptible of proof in

the first figure alone.[4]

§ 2. On examining, then, these two general formulæ, we find that in

both of them, one premise, the major, is an universal proposition; and

according as this is affirmative or negative, the conclusion is so too.

All ratiocination, therefore, starts from a _general_ proposition,

principle, or assumption: a proposition in which a predicate is

affirmed or denied of an entire class; that is, in which some attribute,

or the negation of some attribute, is 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 included in, the class respecting which something was

affirmed or denied in the major premise. It follows that the attribute

affirmed or denied of the entire class may (if that affirmation or

denial was correct) be affirmed or denied of the object or objects

alleged to be 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 thing. The maxim is, That whatever can be

affirmed (or denied) of a class, may be affirmed (or denied) of

everything included in the class. This axiom, supposed to be the basis

of the syllogistic theory, is termed by logicians the _dictum de omni et

nullo_.

This maxim, however, when considered as a principle of reasoning,

appears suited to a system of metaphysics once indeed generally

received, but which for the last two centuries has been considered as

finally abandoned, though there have not been wanting in our own day

attempts at its revival. So long as what are termed Universals were

regarded as a peculiar kind of substances, having an objective existence

distinct from the individual objects classed under them, the _dictum de

omni_ conveyed an important meaning; because it expressed the

intercommunity of nature, which it was necessary on that theory that we

should suppose to exist between those general substances and the

particular substances which were subordinated to them. That everything

predicable of the universal was predicable of the various individuals

contained under it, was then no identical proposition, but a statement

of what was conceived as a fundamental law of the universe. The

assertion that the entire nature and properties of the _substantia

secunda_ formed part of the nature and properties of each of the

individual 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 vastly superior to them in dignity. Now, however, when it is

known that a class, an universal, a genus or species, is not an entity

_per se_, but neither more nor less than the 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 the name; what, I should be glad to know,

do we learn by being told, that whatever can be affirmed of a class, may

be affirmed of every object contained in the class? The class is nothing

but the objects contained in it: and the _dictum de omni_ merely amounts

to the identical proposition, that whatever is true of certain objects,

is true of each of those objects. If all ratiocination were no more than

the application of this maxim to particular cases, the syllogism would

indeed be, what it has so often been declared to be, solemn trifling.

The _dictum de omni_ is on a par with another truth, which in its time

was also reckoned of great importance, "Whatever is, is." To give any

real meaning to the _dictum de omni_, we must consider it not as an

axiom, but as a 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

scholastic 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 under them. Yet, though nominally

rejected, this very doctrine, whether disguised under the Abstract Ideas

of Locke (whose speculations, however, it has less vitiated than those

of perhaps any other writer who has been infected with it), under the

ultra-nominalism of Hobbes and Condillac, or the ontology of the later

Kantians, has never ceased to poison philosophy. Once accustomed to

consider scientific investigation as essentially consisting in the study

of universals, men did not drop this habit of thought when they ceased

to regard universals as possessing an independent existence: and even

those who went the length of considering them as mere names, could not

free themselves from the notion that the investigation of truth

consisted entirely or partly in some kind of conjuration or juggle with

those names. When a philosopher adopted fully the Nominalist view of the

signification of general language, retaining along with it the _dictum

de omni_ as the foundation of all reasoning, two such premises fairly

put together were likely, if he was a consistent thinker, to land him in

rather startling conclusions. Accordingly it has been seriously held, by

writers of deserved celebrity, that the process of arriving at new

truths by reasoning consists in the mere substitution of one set of

arbitrary signs for another; a doctrine which they suppose to derive

irresistible 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 Condillac, that a science is nothing, or scarcely anything,

but _une langue bien faite_; in other words, that the one sufficient

rule for discovering the nature and properties of objects is to name

them properly: as if the reverse were not the truth, that it is

impossible to name them properly except in proportion as we are already

acquainted with their nature and properties. Can it be necessary to say,

that none, not even the most trivial knowledge with respect to Things,

ever was or could be originally got at by any 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? Philosophical analysis

confirms the indication of common sense, that the function of names is

but that of enabling us to _remember_ and to _communicate_ our thoughts.

That they also strengthen, even to an incalculable extent, the power of

thought itself, is most true: but they do this by no intrinsic and

peculiar virtue; they do it by the power inherent in an artificial

memory, an instrument of which few have adequately considered the

immense potency. As an artificial memory, language truly is, what it has

so often been called, an instrument of thought; but it is one thing to

be the instrument, and another to be the exclusive subject upon which

the instrument is exercised. We think, indeed, to a considerable extent,

by means of names, but what we think of, are the things called by those

names; and there cannot be a greater error than to imagine that thought

can be carried on with nothing in our mind but names, or that we can

make the names think for us.

§ 3. Those who considered the _dictum de omni_ as the foundation of the

syllogism, looked upon arguments in a manner corresponding to the

erroneous view which Hobbes took of propositions. Because there are some

propositions which are merely verbal, Hobbes, in order apparently that

his definition might be rigorously universal, defined a proposition as

if no propositions declared anything except the meaning of words. If

Hobbes was right; if no further account than this could be given of the

import of propositions; no theory could be given but the commonly

received one, of the combination of propositions in a syllogism. If the

minor premise asserted nothing more than that something belongs to a

class, and if the major premise asserted nothing of that class except

that it is included in another class, the conclusion would only be that

what was included in the lower class is included in the higher, and the

result, therefore, nothing except that the classification is consistent

with itself. But we have seen that it is no sufficient account of the

meaning of a proposition, to say that it refers something to, or

excludes something from, a class. Every proposition which conveys real

information asserts a matter of fact, dependent on the laws of nature,

and not on classification. It asserts that a given object does or does

not possess a given attribute; or it asserts that two attributes, or

sets of attributes, do or do not (constantly or occasionally) coexist.

Since such is the purport of all propositions which convey any real

knowledge, and since ratiocination is a mode of acquiring real

knowledge, any theory of ratiocination which does not recognise this

import of propositions, cannot, we may be sure, be the true one.

Applying this view of propositions to the two premises of a syllogism,

we obtain the following results. The major 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 attribute (or attributes). The minor premise asserts that

the thing or set of things which are the subject of that premise, have

the first-mentioned attribute; and the conclusion is, that they have (or

that they have not) the second. Thus in our former example,

All men are mortal,

Socrates is a man,

therefore

Socrates is mortal,

the subject and predicate of the major premise are connotative terms,

denoting objects and connoting attributes. The assertion in the major

premise is, that along with one of the two sets of attributes, we always

find the other: that the attributes connoted by "man" never exist unless

conjoined with the attribute called mortality. The assertion in the

minor premise 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

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

incompatibility exists between the attribute omnipotence and those

constituting a king. In a similar manner we might analyse any other

example of the syllogism.

If we generalize this process, and look out for the principle or law

involved in every such inference, and presupposed in every syllogism,

the propositions of which are anything more than merely verbal; we find,

not the unmeaning _dictum de omni et nullo_, but a fundamental

principle, or rather two principles, strikingly resembling the axioms of

mathematics. The first, which is the principle of affirmative

syllogisms, is, that things which coexist with the same thing, coexist

with one another. The second is the principle of negative syllogisms,

and is to this effect: that a thing which coexists with another thing,

with which other a third thing does not coexist, is not coexistent with

that third thing. These axioms manifestly relate to facts, and not to

conventions; and one or other of them is the ground of the legitimacy of

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

of.[5]

§ 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[6] that all propositions, and of course therefore all

combinations of propositions, might be expressed. We observed that a

proposition might be considered in two different lights; 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 possesses

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.

And again,

The attributes of man are a mark of the attribute mortality,

The attributes of a king are a mark of the attributes of man,

therefore

The attributes of a king are a mark of the attribute mortality.

And, lastly,

The attributes of man are a mark of the absence of

the attribute omnipotence,

The attributes of a king are a mark of the attributes of man,

therefore

The attributes of a king are a mark of the absence of

the attribute signified by the word omnipotent

(or, are evidence of the absence of that attribute).

To correspond with this alteration in the form of the syllogisms, the

axioms on which the syllogistic process is founded must undergo a

corresponding transformation. In this altered phraseology, both those

axioms may be brought under one general expression; namely, that

whatever has any mark, has that which it is a mark of. Or, when the

minor premise as well as the major is universal, we may state it thus:

Whatever is a mark of any mark, is a mark of that which this last is a

mark of. To trace the identity of these axioms with those previously

laid down, may be left to the intelligent reader. We shall find, as we

proceed, the great convenience of the phraseology into which we have

last thrown them, and which is better adapted than any I am acquainted

with, to express with precision and force what is aimed at, and actually

accomplished, in every case of the ascertainment of a truth by

ratiocination.

CHAPTER III.

OF THE FUNCTIONS AND LOGICAL VALUE OF THE SYLLOGISM.

§ 1. We have shown what is the real nature of the truths with which the

Syllogism is conversant, in contradistinction to the more superficial

manner in which their import is conceived in the common theory; and what

are the fundamental axioms on which its probative force or

conclusiveness depends. We have now to inquire, whether the syllogistic

process, that of reasoning from generals to particulars, is, or is not,

a process of inference; a progress from the known to the unknown: a

means of coming to a knowledge of something which we did not know

before.

Logicians have been remarkably unanimous in their mode of answering this

question. It is universally allowed that a syllogism is vicious if there

be anything more in the conclusion than was assumed in the premises. But

this is, in fact, to say, that nothing ever was, or can be, proved by

syllogism, which was not known, or assumed to be known, before. Is

ratiocination, then, not a process of inference? And is the syllogism,

to which the word reasoning has so often been represented to be

exclusively appropriate, not really entitled to be called reasoning at

all? This seems an inevitable consequence of the doctrine, admitted by

all writers on the subject, that a syllogism can prove no more than is

involved in the premises. Yet the acknowledgment so explicitly made, has

not prevented one set of writers from continuing to 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 general theorem respecting the

logical value of the syllogism to its legitimate corollary, have been

led to impute uselessness and frivolity to the syllogistic theory

itself, on the ground of the _petitio principii_ which they allege to be

inherent in every syllogism. As I believe both these opinions to be

fundamentally erroneous, I must request the attention of the reader to

certain considerations, without which any just appreciation of the true

character of the syllogism, and the functions it performs in philosophy,

appears to me impossible; but which seem to have been either overlooked,

or insufficiently adverted to, both by the defenders of the syllogistic

theory and by its assailants.

§ 2. It must be granted that in every syllogism, considered as an

argument to prove the conclusion, there is a _petitio principii_. When

we say,

All men are mortal,

Socrates is a man,

therefore

Socrates is mortal;

it is unanswerably urged by the adversaries of the syllogistic theory,

that the proposition, Socrates is mortal, is presupposed in the more

general assumption, All men are mortal: that we cannot be assured of the

mortality of all men, unless we are already certain of the mortality of

every individual man: that if it be still doubtful whether Socrates, or

any other individual we choose to name, be mortal or not, the same

degree of uncertainty must hang over the assertion, All men are mortal:

that the general principle, instead of being given as evidence of the

particular case, cannot itself be taken for true without exception,

until every shadow of doubt which could affect any case comprised with

it, is dispelled by evidence _aliundè_; and then what remains for the

syllogism to prove? That, in short, no reasoning from generals to

particulars can, as such, prove anything: since from a general principle

we cannot infer any particulars, but those which the principle itself

assumes as known.

This doctrine appears to me irrefragable; and if logicians, though

unable to dispute it, have usually exhibited a strong disposition to

explain it away, this was not because they could discover any flaw in

the argument itself, but because the contrary opinion seemed to rest on

arguments equally indisputable. In the syllogism last referred to, for

example, or in any of those which we previously constructed, is it not

evident that the conclusion may, to the person to whom the syllogism is

presented, be actually and _bonâ fide_ a new truth? Is it not matter of

daily experience that truths previously unthought of, facts which have

not been, and cannot be, directly observed, are arrived at by way of

general reasoning? We believe that the Duke of Wellington is mortal. We

do not know this by direct observation, so long as he is not yet dead.

If we were asked how, this being the case, we know the duke to be

mortal, we should probably answer, Because all men are so. Here,

therefore, we arrive at the knowledge of a truth not (as yet)

susceptible of observation, by a reasoning which admits of being

exhibited in the following syllogism:--

All men are mortal,

The Duke of Wellington is a man,

therefore

The Duke of Wellington is mortal.

And since a large portion of our knowledge is thus acquired, logicians

have persisted in representing the syllogism as a process of inference

or proof; though none of them has cleared up the difficulty which arises

from the inconsistency between that assertion, and the principle, that

if there be anything in the conclusion which was not already asserted in

the premises, the argument is vicious. For it is impossible to attach

any serious scientific value to such a mere salvo, as the distinction

drawn between being involved _by implication_ in the premises, and being

directly asserted in them. When Archbishop Whately says[7] that the

object of reasoning is "merely to expand and unfold the assertions wrapt

up, as it were, and implied in those with which we set out, and to bring

a person to perceive and 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 "wrapt up" in a few definitions and axioms. Nor does this

defence of the syllogism differ much from what its assailants urge

against it as an accusation, when they charge it with being of no use

except to those who seek to press the consequences of an admission into

which a person has been entrapped without having considered and

understood its full force. When you admitted the major premise, you

asserted the conclusion; but, says Archbishop Whately, you asserted it

by implication merely: this, however, can here only mean that you

asserted it unconsciously; that you did not know you were asserting it;

but, if so, the difficulty revives in this shape--Ought you not to have

known? Were you warranted in asserting the general proposition without

having satisfied yourself of the truth of everything which it fairly

includes? And if not, is not the syllogistic art _primâ facie_ what its

assailants affirm it to be, a contrivance for catching you in a trap,

and holding you fast in it?[8]

§ 3. From this difficulty there appears to be but one issue. The

proposition that the Duke of Wellington is mortal, is evidently an

inference; it is got at as a conclusion from something else; but do we,

in reality, conclude it from the proposition, All men are mortal? I

answer, no.

The error committed is, I conceive, that of overlooking the distinction

between two parts of the process of 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 unable to answer it, he may refresh his memory by turning

to a memorandum which he carries about with him. But if he were asked,

how the fact came to his knowledge, he would scarcely answer, because it

was set down in his note-book: unless the book was written, like the

Koran, with a quill from the wing of the angel Gabriel.

Assuming that the proposition, The Duke of Wellington is mortal, is

immediately an inference from the proposition, All men are mortal;

whence do we derive our knowledge of that general truth? Of course from

observation. Now, all which man can observe are individual cases. From

these all general truths must be drawn, and into these they may be again

resolved; for a general truth is but an aggregate of particular truths;

a comprehensive expression, by which an indefinite number of individual

facts are affirmed or denied at once. But a general proposition is not

merely a compendious form for recording and preserving in the memory a

number of particular facts, all of which have been observed.

Generalization is not a process of mere naming, it is also a process of

inference. From instances which we have 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 communicate. 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 intermediate stage; but it is not in the latter half of the process,

the descent from all men to the Duke of Wellington, that the _inference_

resides. The inference is finished when we have asserted that all men

are mortal. What remains to be performed afterwards is merely

decyphering our own notes.

Archbishop Whately has contended that syllogizing, or reasoning from

generals to particulars, is not, agreeably to the vulgar idea, a

peculiar _mode_ of reasoning, but the 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 cannot help thinking that

the vulgar notion is, in this case, the more correct. If, from our

experience of John, Thomas, &c., who once were living, but are now dead,

we are entitled to conclude that all human beings are mortal, we might

surely without any logical inconsequence have concluded at once from

those instances, that the Duke of Wellington is mortal. The mortality of

John, Thomas, and company is, after all, the whole evidence we have for

the mortality of the Duke of Wellington. Not one iota is added to the

proof by interpolating a general 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 insufficient for the one

purpose, cannot be sufficient for the other; I am unable to see why we

should be forbidden to take the shortest cut from these sufficient

premises to the conclusion, and constrained to travel the "high priori

road," by the arbitrary fiat of logicians. I cannot perceive why it

should be impossible to journey from one place to another unless we

"march up a hill, and then march down again." It may be the safest road,

and there may be a resting-place at the top of the hill, affording a

commanding view of the surrounding country; but for the mere purpose of

arriving at our journey's end, our taking that road is perfectly

optional; it is a question of time, trouble, and danger.

Not only _may_ we reason from particulars to particulars without passing

through generals, but we perpetually do so reason. All our earliest

inferences are of this nature. From the first dawn of intelligence we

draw inferences, but years elapse before we learn the use of general

language. The child, who, having burnt his fingers, avoids to thrust

them again into the fire, has reasoned or inferred, though he has never

thought of the general maxim, Fire burns. He knows from memory that he

has been burnt, and on this evidence believes, when he sees a candle,

that if he puts his finger into the flame of it, he will be burnt again.

He believes this in every case which happens to arise; but without

looking, in each instance, beyond the present case. He is not

generalizing; he is inferring a particular from particulars. In the same

way, also, brutes reason. There is no ground for attributing to any of

the lower animals the use of signs, of such a nature as to render

general propositions possible. But those animals profit by experience,

and avoid what they have found to cause them pain, in the same manner,

though not always with the same skill, as a human creature. Not only the

burnt child, but the burnt dog, dreads the fire.

I believe that, in point of fact, when drawing inferences from our

personal experience, and not from maxims handed down to us by books or

tradition, we much oftener conclude from particulars to particulars

directly, than through the intermediate agency of any general

proposition. We are constantly reasoning from ourselves to other people,

or from one person to another, without giving ourselves the trouble to

erect our observations into general maxims of human or external nature.

When we conclude that some person will, on some given occasion, feel or

act so and so, we sometimes 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 conduct of the same person in some

previous instance, or from considering how we should feel or act

ourselves. It is not only the village matron, who, when called to a

consultation upon the case of a neighbour's child, pronounces on the

evil and its remedy simply on the recollection and authority of what she

accounts the similar case of her Lucy. We all, where we have no definite

maxims to steer by, guide ourselves in the same way: and if we have an

extensive experience, and retain its impressions strongly, we may

acquire in this manner a very considerable power of accurate judgment,

which we may be utterly incapable of justifying or of communicating to

others. Among the higher order of practical intellects there have been

many of whom it was remarked how admirably they suited their means to

their ends, without being able to give any sufficient reasons for what

they did; and applied, or seemed to apply, recondite principles which

they were wholly unable to state. This is a natural consequence of

having a mind stored with appropriate particulars, and having been long

accustomed to reason at once from these to fresh particulars, without

practising the habit of stating to oneself or to others the

corresponding general propositions. An old warrior, on a rapid glance at

the outlines of the ground, is able at once to give the necessary orders

for a skilful arrangement of his troops; though if he has received

little theoretical instruction, and has seldom been called upon to

answer to other people for his conduct, he may never have had in his

mind a single general theorem respecting the relation between ground and

array. But his experience of encampments, in circumstances more or less

similar, has left a number of vivid, unexpressed, 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

exact throw which brings down his game, or his enemy, in the manner most

suited to his purpose, under the operation of all the conditions

necessarily involved, the weight and form of the weapon, the direction

and distance of the object, the action of the wind, &c., owes this power

to a long series of previous experiments, the results of which he

certainly never framed into any verbal theorems or rules. The same thing

may generally be said of any other extraordinary manual dexterity. Not

long ago a Scotch manufacturer procured from England, at a high rate of

wages, a working dyer, famous for producing very fine colours, with the

view of teaching to his other workmen the same skill. The workman came;

but his mode of proportioning the ingredients, in which lay the secret

of the effects he produced, was by taking them up in handfuls, while the

common method was to weigh them. The manufacturer sought to make him

turn his handling system into an equivalent weighing system, that the

general principle of his peculiar mode of proceeding might be

ascertained. This, however, the man found himself quite unable to do,

and therefore could impart his skill to nobody. He had, from the

individual cases of his own experience, established a connexion in his

mind between fine effects of colour, and tactual perceptions in handling

his dyeing materials; and from these perceptions he could, in any

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 court of justice, without previous judicial practice or legal

education. The advice was to give his decision boldly, for it would

probably be right; but never to venture on assigning reasons, for they

would almost infallibly be wrong. In cases like this, which are of no

uncommon occurrence, it would be absurd to 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 framing general principles from them, and that if

he attempted to frame any such he would assuredly fail. Lord Mansfield,

however, would not have doubted that a man of equal experience who had

also a mind stored with general propositions derived by legitimate

induction from that experience, would have been greatly 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 generalization, though a help, the most

important indeed of all helps, is not an essential.

Even the scientifically instructed, who possess, in the form of general

propositions, a systematic record of the results of the experience of

mankind, need not always revert to those general propositions in order

to apply that experience to a new case. It is justly remarked by Dugald

Stewart, that though the reasonings in mathematics depend entirely on

the axioms, it is by no means necessary to our seeing the conclusiveness

of the proof, that the axioms should be expressly adverted to. When it

is inferred that AB is equal to CD because each of them is equal to EF,

the most uncultivated understanding, as soon as the propositions were

understood, would assent to the inference, without having ever heard of

the general truth that "things which are equal to the same thing are

equal to one another." This remark of Stewart, consistently followed

out, goes to the root, as I conceive, of the philosophy of

ratiocination; and it is to be regretted that he himself stopt short at

a much more limited application of it. He saw that the general

propositions on which a reasoning is said to depend, may, in certain

cases, be altogether omitted, without impairing its 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 example, of the circle is

to the properties of the circle, what the laws of equilibrium and of the

pressure of the atmosphere are to the rise of the mercury in the

Torricellian tube. Yet all that he had asserted respecting the function

to which the axioms are confined in the demonstrations of geometry,

holds equally true of the definitions. Every demonstration in Euclid

might be carried on without them. This is apparent from the ordinary

process of proving a proposition of geometry by means of a diagram. What

assumption, in fact, do we set out from, to demonstrate by a diagram any

of the properties of the circle? Not that in all circles the radii are

equal, but only that they are so in the circle ABC. As our warrant for

assuming this, we appeal, it is true, to the definition of a circle in

general; but it is only necessary that the assumption be granted in the

case of the particular circle supposed. From this, which is not a

general but a singular proposition, combined with other propositions of

a similar kind, some of which _when generalized_ are called definitions,

and others axioms, we prove that a certain conclusion is true, not of

all circles, but of the particular circle ABC; or at least would be so,

if the facts precisely accorded with our assumptions. The enunciation,

as it is called, that is, the general theorem which stands at the head

of the demonstration, is not the proposition actually demonstrated. One

instance only is demonstrated: but the process by which this is done, is

a process which, when we consider its nature, we perceive might be

exactly copied in an indefinite number of other instances; in every

instance which conforms to certain conditions. The contrivance of

general language furnishing us with terms which connote these

conditions, we are able to assert this indefinite multitude of truths in

a single expression, and this expression is the general theorem. By

dropping the use of diagrams, and substituting, in the demonstrations,

general phrases for the letters of the alphabet, we might prove the

general theorem directly, that is, we might demonstrate all the cases at

once; and to do this we must, of course, employ as our premises, the

axioms and definitions in their general form. But this only means, that

if we can prove an individual conclusion by assuming an individual fact,

then in whatever case we are warranted in making an exactly similar

assumption, we may draw an exactly similar conclusion. The definition is

a sort of notice to ourselves and others, what assumptions we think

ourselves entitled to make. And so in all cases, the general

propositions, whether called definitions, axioms, or laws of nature,

which we lay down at the beginning of our reasonings, are merely

abridged statements, in a kind of short-hand, of the 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 selected, what by the statement of the

definition or principle we announce that we intend to assume in all

cases which may arise. The definition of the circle, therefore, is to

one of Euclid's demonstrations, exactly what, according to Stewart, the

axioms are; that is, the demonstration does not depend on it, but yet if

we deny it the demonstration fails. The proof does not rest on the

general assumption, but on a similar assumption confined to the

particular case: that case, however, being chosen as a specimen 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

explained presently, so far as explanation is requisite. But, that

unpractised learners, even in making use of one theorem to demonstrate

another, reason rather from particular to particular than from the

general proposition, is manifest from the difficulty they find in

applying a theorem to a case in which the configuration of the diagram

is extremely unlike that of the diagram by which the original theorem

was demonstrated. A difficulty which, except in cases of unusual mental

power, long practice can alone remove, and removes chiefly by rendering

us familiar with all the configurations consistent with the general

conditions of the theorem.

§ 4. From the considerations now adduced, the following conclusions seem

to be established. All inference is from particulars to particulars:

General propositions are merely registers of such inferences already

made, and short formulæ for making more: The major premise of a

syllogism, consequently, is a formula of this description: and the

conclusion is not an inference drawn _from_ the formula, but an

inference drawn _according_ to the formula: the real logical antecedent,

or premise, being the particular facts from which the general

proposition was collected by induction. Those facts, and the individual

instances which supplied them, may have been 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 inference. 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 ensure our doing so.

This view of the functions of the syllogism is confirmed by the

consideration of precisely those cases which might be expected to be

least favourable to it, namely, those in which ratiocination is

independent of any previous induction. We have already observed that the

syllogism, in the ordinary course of our reasoning, is only the latter

half of the process of travelling from premises to a conclusion. There

are, however, some peculiar cases in which it is the whole process.

Particulars alone are capable of being subjected to observation; and all

knowledge which is derived from observation, begins, therefore, of

necessity, in particulars; but our knowledge may, in cases of certain

descriptions, be conceived as coming to us from other sources than

observation. It may present itself as coming from testimony, which, on

the occasion and for the purpose in hand, is accepted as of an

authoritative character: and the information thus communicated, may be

conceived to comprise not only particular facts but general

propositions, as when a scientific doctrine is accepted without

examination on the authority of writers, or a theological doctrine on

that of Scripture. Or the generalization may not be, in the ordinary

sense, an assertion at all, but a command; a law, not in the

philosophical, but in the moral and political sense of the term: an

expression of the desire of a superior, that we, or any number of other

persons, shall conform our conduct to certain general instructions. So

far as this asserts a fact, namely, a volition of the legislator, that

fact is an individual fact, and the proposition, therefore, is not a

general proposition. But the description therein contained of the

conduct which it is the will of the legislator that his subjects should

observe, is general. The proposition asserts, not that all men _are_

anything, but that all men _shall_ do something.

In both these cases the generalities are the original data, and the

particulars are elicited from them by a process which correctly resolves

itself into a series of syllogisms. The real nature, however, of the

supposed deductive process, is evident 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 authorities have signified, the

cases which they meant to certify or to influence may be known. The

object of the inquiry is to make out the witness's or the legislator's

intention, through the indication given by their words. This is a

question, as the Germans express it, of hermeneutics. The operation is

not a process of inference, but a process of interpretation.

In this last phrase we have obtained an expression which appears to me

to 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 assertion and the other his command. In like manner, when

the premises are derived from observation, the function of Reasoning is

to ascertain what we (or our predecessors) formerly thought might be

inferred from the observed facts, and to do this by interpreting a

memorandum of ours, or of theirs. The memorandum reminds us, that from

evidence, more or less carefully weighed, it formerly appeared that a

certain attribute might be inferred wherever we perceive a certain mark.

The proposition, All men are mortal (for instance) shows that we have

had experience from which we thought it followed that the attributes

connoted by the term man, are a mark of mortality. But when we conclude

that the Duke of Wellington is mortal, we do not infer this from the

memorandum, but from the former experience. All that we infer from the

memorandum is our own previous belief, (or that of those who transmitted

to us the proposition), concerning the inferences which that former

experience would warrant.

This view of the nature of the syllogism renders consistent and

intelligible 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 anything, the truth of which would

contradict something to which we had previously on good grounds given

our assent. And they tell us, that the sole ground which a syllogism

affords for assenting to the conclusion, is that the supposition of its

being false, combined with the supposition that the premises are true,

would lead to a contradiction in terms. Now this would be but a lame

account of the real grounds which we have for believing the facts which

we learn from reasoning, in contradistinction to observation. The true

reason why we believe that the Duke of Wellington will die, is that his

fathers, and our fathers, and all other persons who were cotemporary

with them, have died. Those facts are the real premises of the

reasoning. But we are not led to infer the conclusion from those

premises, by the necessity of avoiding any verbal inconsistency. There

is no contradiction in supposing that all those persons have died, and

that the Duke of Wellington may, notwithstanding, live for ever. But

there would be a contradiction if we first, on the ground of those same

premises, made a general assertion including and covering the case of

the Duke of Wellington, and then refused to stand to it in the

individual case. There is an inconsistency to be avoided between the

memorandum we make of the inferences which may be justly drawn in future

cases, and the inferences we actually draw in those cases when they

arise. With this view we interpret our own formula, precisely as a judge

interprets a law: in order that we may avoid drawing any inferences not

conformable to our former intention, as a judge avoids giving any

decision not conformable to the legislator's intention. The rules for

this interpretation are the rules of the syllogism: and its sole purpose

is to maintain consistency between the 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 testimony) an inference from particulars to particulars;

authorized by a previous inference from particulars to generals, and

substantially the same with it; of the nature, therefore, of Induction.

But while these conclusions appear to me undeniable, I must yet enter a

protest, as strong as that of Archbishop Whately himself, against the

doctrine that the syllogistic art is useless for the purposes of

reasoning. The reasoning lies in the act of generalization, not in

interpreting the record of that act; but the syllogistic form is an

indispensable collateral security for the correctness of the

generalization itself.

It has already been seen, that if we have a collection of particulars

sufficient for grounding an induction, we need not frame a general

proposition; we may reason at once from those particulars to other

particulars. But it is to be remarked withal, that whenever, from a set

of particular cases, we can legitimately draw any inference, we may

legitimately make our inference a general one. If, from observation and

experiment, we can conclude to one new case, so may we to an indefinite

number. If that which has held true in our past experience will

therefore hold in time to come, it will hold not merely in some

individual case, but in all cases of some given description. Every

induction, therefore, which suffices to prove one fact, proves an

indefinite multitude of facts: the experience which justifies a single

prediction must be such as will suffice to bear out a general theorem.

This theorem it is extremely important to ascertain and declare, in its

broadest form of generality; and thus to place before our minds, in its

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

anything.

This throwing of the whole body of possible inferences from a given set

of particulars, into one general expression, operates as a security for

their being just inferences, in more ways than one. First, the general

principle presents a larger object to the imagination than any of the

singular propositions which it contains. A process of thought which

leads to a comprehensive generality, is felt as of greater importance

than one which terminates in an insulated fact; and the mind is, even

unconsciously, led to bestow greater attention upon the process, and to

weigh more carefully the sufficiency of the experience appealed to, for

supporting the inference grounded upon it. There is another, and a more

important, advantage. In reasoning from a course of individual

observations to some new and unobserved case, which we are but

imperfectly acquainted with (or we should not be inquiring into it), and

in which, since we are inquiring into it, we probably feel a peculiar

interest; there is very little to prevent us from giving way to

negligence, or to any bias which may affect our wishes or our

imagination, and, under that influence, accepting 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

inferrible from our premises, if that one particular conclusion is so;

there is then a considerable likelihood that if the premises are

insufficient, and the general inference, therefore, groundless, it will

comprise within it some fact or facts the reverse of which we already

know to be true; and we shall thus discover the error in our

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

legitimate, of referring to a parallel case, is universally

acknowledged. But by ascending to the general proposition, we bring

under our view not one parallel case only, but all possible parallel

cases at once; all cases to which the same set of evidentiary

considerations are applicable.

When, therefore, we argue from a number of known cases to another case

supposed to be analogous, it is always possible, and generally

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 interpretation, 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 argument is

maintainable. If, therefore, any fact fairly coming within the range of

one of these general propositions, and consequently asserted by it, is

known or suspected to be other than the proposition asserts it to be,

this mode of stating the argument causes us to know or to suspect that

the original observations, which are the real grounds of our conclusion,

are not sufficient to support it. And in proportion to the greater

chance of our detecting the inconclusiveness of our evidence, will be

the increased reliance we are entitled to place in it if no such

evidence of defect shall appear.

The value, therefore, of the syllogistic form, and of the rules for

using it correctly, does not consist in their being the form and the

rules according to which our reasonings are necessarily, or even

usually, made; but in their furnishing us with a mode in which those

reasonings may always be represented, and which is admirably calculated,

if they are inconclusive, to bring their inconclusiveness to light. An

induction from particulars to generals, followed by a 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_ reason, 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.[9]

These are the uses of syllogism, as a mode of verifying any given

argument. Its ulterior uses, as respects the general course of our

intellectual operations, hardly require illustration, being in fact the

acknowledged uses of general language. They amount substantially to

this, that the inductions may be made once for all: a single careful

interrogation of experience may suffice, and the result may be

registered in the form of a general proposition, which is committed to

memory or to writing, and from which afterwards we have only to

syllogize. The particulars of our experiments may then be dismissed from

the memory, in which it would be impossible to retain so great a

multitude of details; while the knowledge which those details afforded

for future use, and which would otherwise be lost as soon as the

observations were forgotten, or as their record became too bulky for

reference, is retained in a commodious and immediately available shape

by means of general language.

Against this advantage is to be set the countervailing inconvenience,

that inferences originally made on insufficient evidence, become

consecrated, and, as it were, hardened into general maxims; and the mind

cleaves to them from habit, after it has outgrown any liability to be

misled by similar fallacious appearances if they were now for the first

time presented; but having forgotten the particulars, it does not think

of revising its own former decision. An inevitable 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 personal 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 persons would get much beyond those simple inferences

which are drawn by the more intelligent of the brutes. Though not

necessary to reasoning, general propositions are necessary to any

considerable progress in reasoning. It is, therefore, natural and

indispensable to separate the process of investigation into two parts;

and obtain general formulæ 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 formulæ; and the rules of

syllogism are a system of securities for the correctness of the

application.

§ 6. To complete the series of considerations connected with the

philosophical character of the syllogism, it is requisite to consider,

since the syllogism is not the universal type of the reasoning process,

what is the real type. This resolves itself into the question, what is

the nature of the minor premise, and in what manner it contributes to

establish the conclusion: for as to the major, we now fully understand,

that the place which it nominally occupies in our reasonings, properly

belongs to the individual facts or observations of which it expresses

the general result; the major itself being no real part of the argument,

but an intermediate halting-place for the mind, interposed by an

artifice of language between the real premises and the conclusion, by

way of a security, which it is in a most material degree, for the

correctness of the process. The minor, however, being an indispensable

part of the syllogistic expression of an argument, without doubt either

is, or corresponds to, an equally indispensable part of the argument

itself, and we have only to inquire what part.

It is perhaps worth while to notice here a speculation of a philosopher

to whom mental science is much indebted, but who, though a very

penetrating, was a very hasty thinker, and whose want of due

circumspection rendered him fully as remarkable for what he did not see,

as for what he saw. I allude to Dr. Thomas Brown, whose theory of

ratiocination is peculiar. He saw the _petitio principii_ which is

inherent in every syllogism, if we consider the major to be itself the

evidence by which the conclusion is proved, instead of being, what in

fact it is, an assertion of the existence of evidence sufficient to

prove any conclusion of a given description. Seeing this, Dr. Brown not

only failed to see the immense advantage, in point of security for

correctness, which is gained by interposing this step between the real

evidence and the conclusion; but he thought it incumbent on him to

strike out the major altogether from the reasoning process, without

substituting anything else, and maintained that our reasonings consist

only of the minor premise and the 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 analysing our own general notions, or abstract

ideas; and that the proposition, Socrates is mortal, is evolved from the

proposition, Socrates is a man, simply by recognising the notion of

mortality as already contained in the notion we form of a man.

After the explanations so fully entered into on the subject of

propositions, much further discussion cannot be necessary to make the

radical error of this view of ratiocination apparent. If the word man

connoted mortality; if the meaning of "mortal" were involved in the

meaning of "man;" we might, undoubtedly, evolve the conclusion from the

minor alone, because the minor would have already asserted it. But if,

as is in fact the case, the word man does not connote mortality, how

does it appear that in the mind of every person who admits Socrates to

be a man, the idea of man must include the idea of mortality? Dr. Brown

could not help seeing this difficulty, and in order to avoid it, was

led, contrary to his intention, to re-establish, under another name,

that step in the argument which corresponds to the major, by affirming

the necessity of _previously perceiving_ the relation between the idea

of man and the idea of mortal. If the reasoner has not previously

perceived this relation, he will not, says Dr. Brown, infer because

Socrates is a man, that Socrates is mortal. But even this admission,

though amounting to a surrender of the doctrine that an argument

consists of the minor and the conclusion alone, will not save the

remainder of Dr. Brown's theory. The failure of assent to the argument

does not take place merely because the reasoner, for want of due

analysis, does not perceive that his idea of man includes the idea of

mortality; it takes place, much more commonly, because in his mind that

relation between the two ideas has never existed. And in truth it never

does exist, except as the result of experience. Consenting, for the sake

of the argument, to discuss the question on a supposition of which we

have recognised the radical incorrectness, namely, that the meaning of a

proposition relates to the ideas of the things spoken of, and not to

the things themselves; I must yet observe, that the idea of man, as an

universal idea, the common property of all rational creatures, cannot

involve anything but what is strictly implied in the name. If any one

includes in his own private idea of man, as no doubt is always the case,

some other attributes, such for instance as mortality, he does so only

as the consequence of experience, after having satisfied himself that

all men possess that attribute: so that whatever the idea contains, in

any person's mind, beyond what is included in the conventional

signification of the word, has been added to it as the result of assent

to a proposition; while Dr. Brown's theory requires us to suppose, on

the 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

conclusion, except with the assistance of the major, or of that which

the major represents, namely, the various singular propositions

expressive of the series of observations, of which the generalization

called the major premise is the result.

In the argument, then, which proves that Socrates is mortal, one

indispensable part of the premises will be as follows: "My father, and

my father's father, A, B, C, and an indefinite number of other persons,

were mortal;" which is only an expression in different words of the

observed fact that they have died. This is the major premise divested of

the _petitio principii_, and cut down to as much as is really known by

direct evidence.

In order to connect this proposition with the conclusion Socrates is

mortal, the additional link necessary is such a proposition as the

following: "Socrates resembles my father, and my father's father, and

the other individuals specified." This proposition we assert when we say

that Socrates is a man. By saying so we likewise assert in what respect

he resembles them, namely, in the attributes connoted by the word man.

And we conclude that he further resembles them in the attribute

mortality.

§ 7. We have thus obtained what we were seeking, an universal type of

the reasoning process. We find it resolvable in all cases into the

following 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 language; but when the two

propositions assert facts which are _bonâ 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 heretofore 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 recognise as tests of the correct performance

of that great mental operation.

Meanwhile, however, it is certain, as before remarked, that if this

inference can be drawn as to Socrates, it can be drawn as to all others

who resemble the observed individuals in the same attributes in which he

resembles them; that is (to express the thing concisely) of all mankind.

If, therefore, the argument be admissible in the case of Socrates, we

are at liberty, once for all, to treat the possession of the attributes

of man as a mark, or satisfactory evidence, of the attribute of

mortality. This we do by laying down the 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 operation into two steps;

first, that of ascertaining what attributes are marks of mortality; and,

secondly, whether any given individuals possess those marks. And it will

generally be advisable, in our speculations on the reasoning process, to

consider this double operation as in fact taking place, and all

reasoning as carried on in the form into which it must necessarily be

thrown to enable us to apply to it any test of its correct performance.

Although, therefore, all processes of thought in which the ultimate

premises are particulars, whether we conclude from particulars to a

general formula, or from particulars to other particulars according to

that formula, are equally Induction: we shall yet, conformably to usage,

consider the name 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, Deduction. And we shall consider every

process by which anything is inferred respecting an unobserved case, as

consisting of an Induction followed by a Deduction; because, although

the process needs not necessarily be carried on in this form, it is

always susceptible of the form, and must be thrown into it when

assurance of scientific accuracy is needed and desired.

§ 8. The theory of the syllogism, laid down in the preceding pages, has

obtained, among other important adhesions, three of peculiar value;

those of Sir John Herschel,[10] Dr. Whewell[11] and Mr. Bailey;[12] Sir

John Herschel considering the doctrine, though not strictly "a

discovery,"[13] 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 cannot be better or more succinctly stated than by

borrowing a sentence from Archbishop Whately.[14] "In every case where

an inference is drawn from Induction (unless that name is to be given to

a mere random guess without any grounds at all) we must form a judgment

that the instance or instances adduced are _sufficient_ to authorize the

conclusion; that it is _allowable_ to take these instances as a sample

warranting an inference respecting the whole class;" and the expression

of this judgment in words (it has been said by several of my critics)

_is_ the major premise.

I quite admit that the major is an affirmation of the sufficiency of the

evidence on which the conclusion rests. That it is so, is the very

essence of my own theory. And whoever admits that the major premise is

_only_ this, adopts the theory in its essentials.

But I cannot concede that this recognition of the sufficiency of the

evidence--that is, of the correctness of the induction--is a part of the

induction itself; unless we ought to say that it is a part of everything

we do, to satisfy ourselves that it has been done rightly. We conclude

from known instances to unknown by the impulse of the generalizing

propensity; and (until after a considerable amount of practice and

mental discipline) the question of the sufficiency of the evidence is

only raised by a retrospective act, turning back upon our own footsteps,

and examining whether we were warranted in doing what we have already

done. To speak of this reflex operation as part of the original one,

requiring to be expressed in words in order that the verbal formula may

correctly represent the psychological process, appears to me false

psychology.[15] We review our syllogistic as well as our inductive

processes, and recognise that 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 recognises

that the transcript has been correctly made. But we do not call the

examination of the copy a part of the act of copying.

The conclusion in an induction is inferred from the evidence itself, and

not from a recognition of the sufficiency of the evidence; as I infer

that my friend is walking towards me because I see him, and not because

I recognise that my eyes are open, and that eyesight is a means of

knowledge. In all operations which require care, it is good to assure

ourselves that the process has been performed accurately; but the

testing of the process is not the process itself; and, besides, may have

been omitted altogether, and yet the process be correct. It is precisely

because that operation is omitted in ordinary unscientific reasoning,

that there is anything gained in certainty by throwing reasoning into

the syllogistic form. To make sure, as far as possible, that it shall

not be omitted, we make the testing operation a part of the reasoning

process itself. We insist that the inference from particulars to

particulars shall pass through a general proposition. But this is a

security for good reasoning, not a condition of all reasoning; and in

some cases not even a security. Our most familiar inferences are all

made before we learn the use of general propositions; and a person of

untutored sagacity will skilfully apply his acquired experience to

adjacent cases, though he would bungle grievously in fixing the limits

of the appropriate general theorem. But though he may conclude rightly,

he never, properly speaking, knows whether he has done so or not; he has

not tested his reasoning. Now, this is precisely 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 test has been applied, and the sufficiency of the evidence

recognised,--if it is sufficient to support the general proposition, it

is sufficient also to support an inference from particulars to

particulars without passing through the general proposition. The

inquirer who has logically satisfied himself that the conditions of

legitimate induction were 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 is never legitimate,

unless the particular one would be so too; and in no sense, intelligible

to me, can the particular conclusion be said to be drawn from the

general one. Whenever there is ground for drawing any conclusion at all

from particular instances, there is ground for a general conclusion; but

that this general conclusion should be actually drawn, however useful,

cannot be an indispensable condition of the validity of the inference in

the particular case. A man gives away sixpence by the same power by

which he disposes of his whole fortune; but it is not necessary to the

legality 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.[16]

§ 9. The preceding considerations enable us to understand the true

nature of what is termed, by recent writers, Formal Logic, and the

relation between it and Logic in the widest sense. Logic, as I conceive

it, is the entire theory of 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 directly concerned with the process of Reasoning or

Inference in the sense in which that process is a part of the

Investigation of Truth. What, then, is Formal Logic? The name seems to

be properly applied to all that portion of doctrine which relates to the

equivalence of different modes of expression; the rules for determining

when assertions in a given form imply or suppose the truth or falsity of

other assertions. This includes the theory of the Import of

Propositions, and of their Conversion, Æquipollence, and Opposition; of

those falsely called Inductions (to be hereafter spoken of[17]), 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 inferences or conclusions in complete consistency with our

general formulæ or directions for drawing them. The Logic of Consistency

is a necessary auxiliary to the logic of truth, not only because what is

inconsistent with itself or with other truths cannot be true, but also

because truth can only be successfully pursued by drawing inferences

from experience, which, if warrantable at all, admit of being

generalized, and, to test their warrantableness, require to be exhibited

in a generalized form; after which the correctness of their application

to particular cases is a question which specially concerns the Logic of

Consistency. This Logic, not requiring any preliminary knowledge of the

processes or conclusions of the various sciences, may be studied with

benefit in a much earlier stage of education than the Logic of Truth:

and the practice which has empirically obtained of teaching it apart,

through elementary treatises which do not attempt to include anything

else, though the reasons assigned for the practice are in general very

far from philosophical, admits of a philosophical justification.

CHAPTER IV.

OF 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 case and some cases

previously known; while the major premise asserts something which,

having been found true of those known cases, we consider ourselves

warranted in holding true of any other case resembling the former in

certain given particulars.

If all ratiocinations resembled, as to the minor premise, the examples

which were exclusively employed in the preceding chapter; if the

resemblance, which that premise asserts, were obvious to the senses, as

in the proposition "Socrates is a man," or were at once ascertainable by

direct observation; there would be no necessity for trains of reasoning,

and Deductive or Ratiocinative Sciences would not exist. Trains of

reasoning exist only for the sake of extending an induction founded, as

all inductions must be, on observed cases, to other cases in which we

not only cannot directly observe what is to be proved, but cannot

directly observe even the mark which is to prove it.

§ 2. Suppose the syllogism to be, All cows ruminate, the animal which is

before me is a cow, therefore it ruminates. The minor, if true at all,

is obviously so: the only premise the establishment of which requires

any anterior process of inquiry, is the major; and provided the

induction of which that premise is the expression was correctly

performed, the conclusion respecting the animal now present will be

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 poisonous. The truth of

the minor may not here be obvious at first sight; it may not be

intuitively evident, but may itself be known only by inference. It may

be the conclusion of another argument, which, thrown into the

syllogistic form, would stand thus:--Whatever when lighted produces a

dark spot on a piece of white porcelain held in the flame, which spot is

soluble in hypochlorite of calcium, is arsenic; the substance before me

conforms to this condition; therefore it is arsenic. To establish,

therefore, the ultimate conclusion, The substance before me is

poisonous, requires a process, which, in order to be syllogistically

expressed, stands in need of two syllogisms; and we have a Train of

Reasoning.

When, however, we thus add syllogism to syllogism, we are really adding

induction to induction. Two separate inductions must have taken place to

render this chain of inference possible; inductions founded, probably,

on different sets of individual instances, but which converge in their

results, so that the instance which is the subject of inquiry comes

within the range of them both. The record of these inductions is

contained in the majors of the two syllogisms. First, we, or others for

us, have examined various objects which yielded under the given

circumstances a dark spot with the given property, and found that they

possessed the properties connoted by the word arsenic; they were

metallic, volatile, their vapour had a smell of garlic, and so forth.

Next, we, or others for us, have examined various specimens which

possessed this metallic and volatile character, whose vapour had this

smell, &c., and have invariably found that they were poisonous. The

first observation we judge that we may extend to all substances 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 the material

points, but _inferred_ to do so, because resembling them in something

else, which we have been led by quite a different set of instances to

consider as a mark of the former resemblance.

This first example of a train of reasoning is still extremely simple,

the series consisting of only two syllogisms. The following is somewhat

more complicated:--No government, which earnestly seeks the good of its

subjects, is likely to be overthrown; some particular government

earnestly seeks the good of its subjects, therefore it is not likely to

be overthrown. The major premise in this argument we shall suppose not

to be derived from considerations _à priori_, but to be a generalization

from history, which, whether correct or erroneous, must have been

founded on observation of governments concerning whose desire of the

good of their subjects there was no doubt. It has been found, or thought

to be found, that these were not easily overthrown, and it has been

deemed that those instances warranted an extension of the same predicate

to any and every government which resembles them in the attribute of

desiring earnestly the good of its subjects. But _does_ the government

in question thus resemble them? This may be debated _pro_ and _con_ by

many arguments, and must, in any case, be proved by another induction;

for we cannot directly observe the sentiments and desires of the persons

who carry on the government. To prove the minor, therefore, we require

an argument in this form: Every government which acts in a certain

manner, desires the good of its subjects; the supposed government acts

in that particular manner, therefore it desires the good of its

subjects. But is it true that the government acts in the manner

supposed? This minor also may require proof; still another induction, as

thus:--What is asserted by intelligent and disinterested witnesses, may

be believed to be true; that the government acts in this manner, is

asserted by such witnesses, therefore it may be believed to be true. The

argument hence consists of three steps. Having the evidence of our

senses that the case of the government under consideration resembles a

number of former cases, in the circumstance of having something asserted

respecting it by intelligent and disinterested 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 resemblance with those other governments

or persons; and since they were known to desire the good of the people,

it is thereupon, by a second induction, inferred that the particular

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 government is also likely to

escape. This is still reasoning from particulars to particulars, but we

now reason to the new instance from three distinct sets of former

instances: to one only of those sets of instances do we directly

perceive the new one to be similar; but from that similarity we

inductively infer that it has the attribute by which it is assimilated

to the next set, and brought within the corresponding induction; after

which by a repetition of the same operation we infer it to be similar to

the third set, and hence a third induction conducts us to the ultimate

conclusion.

§ 3. Notwithstanding the superior complication of these examples,

compared with those by which in the preceding chapter we illustrated the

general theory of reasoning, every doctrine which we then laid down

holds equally true in these more intricate cases. The successive general

propositions are not steps in the reasoning, are not intermediate links

in the chain of inference, between the particulars observed and those to

which we apply the observation. If we had sufficiently capacious

memories, and a sufficient power of maintaining order among a huge mass

of details, the reasoning could go on without any general propositions;

they are mere formulæ for inferring particulars from particulars. The

principle of general 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 cannot, we determine once

for all what are the distinguishing marks by which such cases may be

recognised. The subsequent process is merely that of identifying an

object, and ascertaining it to have those marks; whether we identify it

by the very marks themselves, or by others which we have ascertained

(through another and a similar process) to be marks of those marks. The

real inference is always from particulars to particulars, from the

observed instances to an unobserved one: but in drawing this 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 inference could, and

when it could not, be drawn. The real premises are the individual

observations, even though they may have been forgotten, or, being the

observations of others and not of ourselves, may, to us, never have been

known: but we have before us proof that we or others once thought them

sufficient for an induction, and we have marks to show whether any new

case is one of those to which, if then known, the induction would have

been deemed to extend. These marks we either recognise at once, or by

the aid of other marks, which by another previous induction we collected

to be marks of the first. Even these marks of marks may only be

recognised through a third set of marks; and we may have a train of

reasoning, of any length, to bring a new case within the scope of an

induction grounded on particulars its similarity to which is only

ascertained in this indirect manner.

Thus, in the preceding example, the ultimate inductive inference was,

that a certain government was not likely to be overthrown; this

inference was drawn according to a formula in which desire of the public

good was set down as a mark of not being likely to be overthrown; a mark

of this mark was, acting in a particular manner; and a mark of acting in

that manner was, being asserted to do so by intelligent and

disinterested witnesses: this mark, the government under discussion was

recognised by the senses as possessing. Hence that government fell

within the last induction, and by it was brought within all the others.

The perceived resemblance of the case to one set of observed particular

cases, brought it into known resemblance with another set, and that with

a third.

In the more complex branches of knowledge, the deductions seldom

consist, as in the examples hitherto exhibited, of a single chain, _a_ a

mark of _b_, _b_ of _c_, _c_ of _d_, therefore _a_ a mark of _d_. They

consist (to carry on the same metaphor) of several chains united at the

extremity, as thus: _a_ a mark of _d_, _b_ of _e_, _c_ of _f_, _d e f_

of _n_, therefore _a b c_ a mark of _n_. Suppose, for example, the

following combination of circumstances; 1st, rays of light impinging on

a reflecting surface; 2nd, that surface parabolic; 3rd, 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 parabolic 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 reflection

must coincide with the other of the two equal angles, that formed by a

line drawn to the focus; and this again, by the fundamental axiom

concerning straight lines, is a mark that the reflected rays pass

through the focus. Most chains of physical deduction are of this more

complicated type; and even in mathematics such are abundant, as in all

propositions where the hypothesis includes numerous conditions: "_If_ a

circle be taken, and _if_ within that circle a point be taken, not the

centre, and _if_ straight lines be drawn from that point to the

circumference, then," &c.

§ 4. The considerations now stated remove a serious difficulty from the

view we have taken of reasoning; which view might otherwise have seemed

not easily reconcileable with the fact that there are Deductive or

Ratiocinative Sciences. It might seem to follow, if all reasoning be

induction, that the difficulties of philosophical investigation must lie

in the inductions 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 Mathematics, requiring the highest scientific

genius in those who contributed to its creation, and calling for a most

continued and vigorous exertion of intellect in order to appropriate it

when created, may seem hard to be accounted for on the foregoing theory.

But the 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 one within

which the case evidently falls, to bring it within others in which it

cannot be directly seen to be included.

When the more obvious of the inductions which can be made in any science

from direct observations, have been made, and general formulas have been

framed, determining the limits within which these inductions are

applicable; as often as a new case can be at once seen to come within

one of the formulas, the induction is applied to the new case, and the

business is ended. But new cases are continually arising, which do not

obviously come within any formula whereby the question we want solved in

respect of them could be answered. Let us take an instance from

geometry: and as it is taken only for illustration, let the reader

concede to us for the present, what we shall endeavour to prove in the

next chapter, that the first principles of geometry are results of

induction. Our example shall be the fifth proposition of the first book

of Euclid. The inquiry is, Are the angles at the base of an isosceles

triangle equal or unequal? The first thing to be considered is, what

inductions we have, from which we can infer equality or inequality. For

inferring equality we have the following formulæ:--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 formulæ 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 formulæ. The angles at the base of an isosceles triangle do not

obviously come within any of these. The formulæ specify certain marks of

equality and of inequality, but the angles cannot be perceived

intuitively to have any of those marks. On examination it appears that

they have; and we ultimately succeed in bringing them within the

formula, "The differences of equal things are equal." Whence comes the

difficulty of recognising these angles as the differences of equal

things? Because each of them is the difference not of one pair only, but

of innumerable pairs of angles; and out of these we had to imagine and

select two, which could either be intuitively perceived to be equals, or

possessed some of the marks of equality set down in the various formulæ.

By an exercise of ingenuity, which, on the part of the first inventor,

deserves to be regarded as considerable, two pairs of angles were hit

upon, which united these requisites. First, it could be perceived

intuitively that their differences were the angles at the base; and,

secondly, they possessed one of the marks of equality, namely,

coincidence when applied to one another. This coincidence, however, was

not perceived intuitively, but inferred, in conformity to another

formula.

For greater clearness, I subjoin an analysis of the demonstration.

Euclid, it will be remembered, demonstrates his fifth proposition by

means of the fourth. This it is not allowable for us to do, because we

are undertaking to trace deductive truths not to prior deductions, but

to their original inductive foundation. We must therefore use the

premises of the fourth proposition instead of its conclusion, and prove

the fifth directly from first principles. To do so requires six

formulas. (We must begin, as in Euclid, by prolonging the equal sides

AB, AC, to equal distances, and joining the extremities BE, DC.)

[Illustration]

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 being applied to one another

coincide._

AC, AB, are within this formula by supposition; AD, AE, have been

brought within it by the preceding step. Both these pairs of straight

lines have the property of equality; which, according to the second

formula, is a mark that, if applied to each other, they will coincide.

Coinciding altogether means coinciding in every part, 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

induction; 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 induction

immediately preceding. This train of reasoning being also applicable,

_mutatis mutandis_, to the angles EBC, DCB, these also are brought

within the fifth formula. And, finally,

SIXTH FORMULA. _The differences of equals are equal._

The angle ABC being the difference of ABE, CBE, and the angle ACB being

the difference of ACD, DCB; which have been proved to be equals; ABC and

ACB are brought within the last formula by the whole of the previous

process.

The difficulty here encountered is chiefly that of figuring to ourselves

the two angles at the base of the triangle ABC as remainders made by

cutting one pair of angles out of another, while each pair shall be

corresponding angles of triangles which have two sides and the

intervening angle equal. It is by this happy contrivance that so many

different inductions are brought to bear upon the same particular case.

And this not being at all an obvious thought, it may be seen from an

example so near the threshold of mathematics, how much scope there may

well be for scientific dexterity in the higher branches of that and

other sciences, in order so to combine a few simple inductions, as to

bring within each of them innumerable cases which are not obviously

included in it; and how long, and numerous, and complicated may be the

processes 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 formulæ

of which are the Axioms, and a few of the so-called Definitions. The

remainder of the science is made up of the processes employed for

bringing unforeseen cases within these inductions; or (in syllogistic

language) for proving the minors necessary to complete the syllogisms;

the majors being the definitions and axioms. In those definitions and

axioms are laid down the whole of the marks, by an artful combination of

which it has been found possible to discover and prove all that is

proved in geometry. The marks being so few, and the inductions which

furnish them being so obvious and familiar; the connecting of several of

them together, which constitutes 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[18] that there are weighty scientific

reasons for giving to every science as much of the character of a

Deductive Science as possible; for endeavouring to construct the science

from the fewest and the simplest possible inductions, and to make these,

by any combinations however complicated, suffice for proving even such

truths, relating to complex cases, as could be proved, if we chose, by

inductions from specific experience. Every branch of natural philosophy

was originally experimental; each generalization rested on a special

induction, and was derived from its own distinct set of observations and

experiments. From being sciences of pure experiment, as the phrase is,

or, to speak more correctly, sciences in which the reasonings mostly

consist of no more than one step, and are expressed by single

syllogisms, all these sciences have become to some extent, and some of

them in nearly the whole of their extent, sciences of pure reasoning;

whereby multitudes of truths, already known by induction from as many

different sets of experiments, have come to be exhibited as deductions

or corollaries from inductive propositions of a simpler and more

universal character. Thus mechanics, hydrostatics, optics, acoustics,

thermology, have successively been rendered mathematical; and astronomy

was brought by Newton within the laws of general mechanics. Why it is

that the substitution of this circuitous mode of proceeding for a

process apparently much easier and more natural, is held, and justly, to

be the greatest triumph of the investigation of nature, we are not, in

this stage of our inquiry, prepared to examine. But it is necessary to

remark, that although, by this progressive transformation, all sciences

tend to become more and more Deductive, they are not, 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 Experimental. 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 cannot be observed to have the

requisite marks, have, however, marks of those marks.

We can now, therefore, perceive what is the generic distinction between

sciences which can be made Deductive, and those which must as yet remain

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 anything to connect

_a_ or _b_ with _c_ or _d_; we have a science of detached and mutually

independent generalizations, such as these, that acids redden vegetable

blues, and that alkalies colour them green; from neither of which

propositions could we, directly or indirectly, infer the other: and a

science, so far as it is composed of such propositions, is purely

experimental. Chemistry, in the present state of our knowledge, has not

yet thrown off this character. There are other sciences, however, of

which the propositions are of this kind: _a_ a mark of _b_, _b_ a mark

of _c_, _c_ of _d_, _d_ of _e_, &c. In these sciences we can mount the

ladder from _a_ to _e_ by a process of ratiocination; we can conclude

that _a_ is a mark of _e_, and that every object which has the mark _a_

has the property _e_, although, perhaps, we never were able to observe

_a_ and _e_ together, and although even _d_, our only direct mark of

_e_, may not be perceptible in those objects, but only inferrible. Or,

varying the first metaphor, we may be said to get from _a_ to _e_

underground: the marks _b_, _c_, _d_, which indicate the route, must all

be possessed somewhere by the objects concerning which we are inquiring;

but they are below the surface: _a_ is the only mark that is visible,

and by it we are able to trace in succession all the rest.

§ 6. We can now understand how an experimental may transform itself into

a deductive science by the mere progress of experiment. In an

experimental science, the inductions, as we have said, lie detached, as,

_a_ a mark of _b_, _c_ a mark of _d_, _e_ a mark of _f_, and so on: now,

a new set of instances, and a consequent new induction, may at any time

bridge over the interval between two of these unconnected arches; _b_,

for example, may be ascertained to be a mark of _c_, which enables us

thenceforth to prove deductively that _a_ is a mark of _c_. Or, as

sometimes happens, some comprehensive induction may raise an arch high

in the air, which bridges over hosts of them at once: _b_, _d_, _f_, and

all the rest, turning out to be marks of some one thing, or of things

between which a connexion has already been traced. As when Newton

discovered that the motions, whether regular or apparently anomalous, of

all the bodies of the solar system, (each of which motions had been

inferred by a separate logical operation, from separate marks,) were all

marks of moving round a common centre, with a centripetal force varying

directly as the mass, and inversely as the square of the distance from

that centre. This is the greatest example which has yet occurred of the

transformation, at one stroke, of a science which was still to a great

degree merely experimental, into a deductive science.

Transformations of the same nature, but on a smaller scale, continually

take place in the less advanced branches of physical knowledge, without

enabling them to throw off the character of experimental sciences. Thus