THE
PRINCIPLES OF LOGIC
Oxford University Press, Amen House, London E.G. 4
GLASGOW NEW YORK TORONTO MELBOURNE WELLINGTON
BOMBAY CALCUTTA MADRAS CAPE TOWN
Geoffrey Cumberlege, Publisher to the University
THE
PRINCIPLES OF LOGIC
BY
F. H. B R A D L E Y
O.M., LL.D., LATE FELLOW OF MERTON COLLEGE, OXFORD
SECOND EDITION
REVISED, WITH COMMENTARY AND
TERMINAL ESSAYS
VOL. I
OXFORD UNIVERSITY PRESS
LONDON: GEOFFREY CUMBERLEGE
FIRST EDITION, 1883
SECOND EDITION, IQ22
CORRECTED IMPRESSION OF IQ28
REPRINTED, 195
SET IN THE UNITED STATES OF AMERICA
REPRINTED FROM PLATES IN GREAT BRITAIN
AT THE UNIVERSITY PRESS, OXFORD
BY CHARLES BATEY, PRINTER TO THE UNIVERSITY
TO MY FRIEND
E- R-
THESE VOLUMES ARE
DEDICATED
PREFACE
IT is with mixed feelings that this reissue of an old work is
offered to the public. I am happy to find that a book of mine
is still alive, and that after some forty years it has seemed
worthy to reappear. On the other hand I regret that, while
Logic during this interval has lived and moved, I myself have
failed, except partially, to follow its advance. My available
energy has been expended mainly in fields which more or less
fall outside Logic proper. And it is too late for me now to
make good my shortcoming, and to endeavour to master those
more recent works which have succeeded in throwing, at the
lowest estimate, much light on their subject.
Hence I could not rewrite my book so as to offer it as an
adequate account of contemporary Logic. And on the other
hand simply to reprint it, or again, so far as I am concerned,
to let it die, seemed alike open to objection. I therefore de
cided, while reissuing the old volume, to add to it some notes
and an appendix with a view to correct and supplement some
part of its defects. At the same time I saw clearly that any
such addition would still leave the book largely incomplete.
The course which I have followed may even perhaps result
in some gain to the reader. He can, if he pleases, now verify
any advance which in 1883 may have been made by my work.
And its faults both of manner and matter faults which recall
to me those days when I was young may possibly with some
readers themselves be of service. They may be more than
excused if anywhere they help in any way to excite a more
living and personal interest in logical problems.
It is not that in this book or elsewhere I lay a claim to
original discovery. In these pages there is perhaps no result
which I do not owe, and where, if my memory served me
better, I could not acknowledge my debt. But when a man
has studied, however little, the great philosophers, and felt
vii
Vlll PREFACE
the distance between himself and them, I hardly understand
how, except on compulsion, he can be ready to enter on claims
and counterclaims between himself and his fellows. And all
I care to say for myself is that, if I had succeeded in owing
more, I might then perhaps have gained more of a claim to
be original.
The present volumes contain a reprint of the book published
in 1883. The text has not been altered except occasionally in
the punctuation, and by the removal of mere misprints and of
one or two obvious grammatical errors. The Commentary,
which is new, has been placed after each chapter in the form
of Additional Notes, and the Terminal Essays have none of
them been published before. The Index, which I hope will
be of service, is also new. But for this, however great its
merits, I cannot claim to be responsible.
I regret that Dr. Bosanquet s Implication and Linear In
ference came too late to be used. But I cannot end this
Preface without some expression of my gratitude to Dr.
Bosanquet for all that, since 1883, I have owed to him, and
without some acknowledgment of how deeply this reissue is
in debt to his invaluable works on Logic.
1922.
PREFACE TO FIRST EDITION
THE following work makes no claim to supply any sys
tematic treatment of Logic. I could not pretend to have
acquired the necessary knowledge ; and in addition I confess
that I am not sure where Logic begins or ends. I have
adopted the title Principles of Logic, because I thought that
my enquiries were mainly logical, and, for logic at least, must
be fundamental.
I feel that probability is against me. Experience has shown
that most books on Logic add little to their subject. There is
however one reflection which may weigh in my favour. Both
in England and in Germany that subject is in motion. Logic
is not where it was, and can not remain where it is. And
when one works with the stream a slight effort may bring
progress.
I have in general not referred to those works to which I
have been indebted. Amongst recent writers I owe most to
Lotze, and after him to Sigwart. Wundt s book would have
been more useful had it come to me earlier; and I may say
the same of Bergmann s. I am under obligations to both
Steinthal and Lazarus. And amongst English writers I have
learned most from the late Professor Jevons. I may mention
here that I should have owed certain observations to Mr.
Balfour s able work, had I not seen it first when my book was
completed. I should be glad to state my debts in detail, and
in this way to express the gratitude I feel, but I doubt if it is
now possible. I could not everywhere point out the original
owners of my borrowed material, and I could not clearly state
how much is not borrowed. I lay no claim to originality,
except that, using the result of others labour, I in some respects
have made a sensible advance.
I wished at first to avoid polemics altogether. But, though
I have not sought out occasions of difference, it is plain that
ix
X PREFACE TO FIRST EDITION
too much of my book is polemical. My impression is that it
will not suffice to teach what seems true. If the truth is not
needed the reader will not work for it, nor painfully learn it.
And he hardly will need it where he stands possessed of what
seems an easy solution. Philosophy now, as always, is con
fronted with a mass of inherited prejudice. And, if my
polemics bring uneasiness to one self-satisfied reader, I may
have done some service.
I fear that, to avoid worse misunderstandings, I must say
something as to what is called " Hegelianism." For Hegel
himself, assuredly I think him a great philosopher ; but I never
could have called myself an Hegelian, partly because I can
not say that I have mastered his system, and partly because
I could not accept what seems his main principle, or at least
part of that principle. I have no wish to conceal how much
I owe to his writings ; but I will leave it to those who can
judge better than myself, to fix the limits within which I have
followed him. As for the " Hegelian School " which exists in
our reviews, I know no one who has met with it anywhere
else.
What interests me is something very different. We want
no system-making or systems home-grown or imported. This
life-breath of persons who write about philosophy is not the
atmosphere where philosophy lives. What we want at present
is to clear the ground, so that English Philosophy, if it rises,
may not be choked by prejudice. The ground can not be
cleared without a critical, or, if you prefer it, a sceptical study
of first principles. And this study must come short, if we
neglect those views which, being foreign, seem most unlike our
own, and which are the views of men who, differing from one
another, are alike in having given an attention to the subject
which we have not given. This, I think, is a rational object
and principle, and I am persuaded that a movement which
keeps to this line will not be turned back.
In conclusion I may be allowed to anticipate two criticisms
which will be passed on my work. One reader will lament
that he is overdone with metaphysics, while another will stand
on his right to have far more. I would assure the first that
I have stopped where I could, and as soon as I was able. And
in answer to the second I can only plead that my metaphysics
PREFACE TO FIRST EDITION XI
are really very limited. This does not mean that, like more
gifted writers, I verify in my own shortcomings the necessary
defects of the human reason. It means that on all questions,
if you push me far enough, at present I end in doubts and
perplexities. And on this account at least no lover of meta
physics will judge of me hardly. Still in the end perhaps both
objectors are right. If I saw further I should be simpler.
But I doubt if either would then be less dissatisfied.
VOLUME I
Jn this Table the numbeis in parentheses refer to the sections of each chapter in
Bocks I-III, while in Essays I-XII the numbers refer to the pages.
BOOK I
JUDGMENT
CHAPTER I
THE GENERAL NATURE OF JUDGMENT
What judgment is. It implies ideas, and these are signs (1-3). A sign,
what (4-6). Two senses of "idea" (6-). In Judgment ideas are
meanings (9). Judgment defined (10), and errors refuted (11-12).
Mistaken views criticized. Judgment not "association" (13-14); nor
practical influence (15) ; nor a mere junction, nor an equation of
ideas (16). Truths contained in the above errors (17).
Development of Judgment. It is a late product (18), because at first
the mind has no ideas proper (19-20). Conditions required for
origin of Judgment (21-22). If the Association-theory were true
it could never have appeared (23) ; but from the first universals
operate in the mind (24-26) Pages 1-38
Additional Notes 38-40
CHAPTER II
THE CATEGORICAL AND HYPOTHETICAL FORMS OF JUDGMENT
Judgment is about fact (i). Preliminary objections answered (2).
But how if all judgment is hypothetical (3) ? And if judgment
keeps to ideas it all is hypothetical (4-6). This true of universal
and again of both classes of singular judgments (7-8).
But judgment is not confined to ideas. It refers to present reality (9).
On the other hand it does not refer to reality as present (10). This
explained and defended (11-14).
Search for Categorical Judgment. I. Analytic Judgments of sense, and
their varieties (15-16). Superstition as to names of Individuals
(17-18). II. Synthetic judgments of sense. How can these refer
to present reality (19) ? But they can not refer to mere ideas (20-
21 ). Their true subject is unique. Thisness and This. Idea of
"this" how used (21-27).
xiii
XIV CONTENTS
But how then can Synthetic Judgments be true of this given reality
(28)? Because the reality is not the mere appearance (29-30).
These judgments rest on continuity of content (31), and that upon
ideal identity (32-33). Past and future are not phenomena (34).
Recapitulation (35). Memory and prediction not mere imagination
(36-37)- Idea of Individual, what (38-39). Non-phenomenal Sin
gular Judgments (41). Existential Judgments (42). Transition to
Abstract Universal Judgments (43).
These are hypothetical (44). Collective Judgments really singular (45).
Hypothetical can not be reduced to Categoricals (46-47). A sup
position, what (48). Real assertion contained in Hypothetical Judg
ments (49-52). They are all universal (53-55). Result (56).
Pages 41-90
CHAPTER II (Continued)
With hypothetical we seem to have left the real world, but have
reached the world of Science (57). Presumption against the sin
gular judgment of sense (58). Its claim (59-60) is untenable be
cause it mutilates the facts (61-67). It is conditioned (68-70), and
conditional (71) ; and is even false (72-73). It is an impure and
imperfect hypothetical (74-78). Result (79-80). Remaining class
of Judgments (81) Pages 91-107
Additional Notes 107-113
CHAPTER III
THE NEGATIVE JUDGMENT
Negation depends on the real (i), but is more ideal than affirmation
is (2-3). It is not the denial of an affirmation (4), nor is it a kind
of affirmation (5), nor an affection of the copula (6). It has a
positive ground which is not explicit (6-7).
Opposition and Privation. These distinctions here not vital (8), but
call for explanation (9-11). Varieties of negative judgment. Nega
tive Existentials (12).
Logical negation is subjective, and is no real determination (13-14). It
does not assert the existence of the contradictory (15). Idea of the
contradictory, what (16). The asserted contrary not explicit (17).
Contrary opposition not dual (18). Ambiguity of denial. It rests
on covert assertion (19-20) Pages 114-125
Additional Notes 125-127
CHAPTER IV
THE DISJUNCTIVE JUDGMENT
It is not a mere combination of hypotheticals (1-2). Its basis is always
categorical (3-6). Alternatives are rigidly exclusive. Erroneous
views on this point (7-12). What disjunction presupposes (13).
Recapitulation (14) Pages 128-137
Additional Notes 137-140
CONTENTS XV
CHAPTER V
PRINCIPLES OF IDENTITY, CONTRADICTION, EXCLUDED MIDDLE,
AND DOUBLE NEGATION
Principle of Identity must- not be a tautology (1-3). What (if any
thing) it should mean (4-9). Principle of Contradiction does not
explain anything (10). What it means (11-14). Further criticism
and explanation (15-16). Principle of Excluded Middle is one
special case of disjunction (16-19). Goes beyond it, how (20-21).
Is wrongly objected to (22). Criticism of mistaken views (23-27).
Double Negation, wrong account of (28). True explanation (29-
31). Erroneous use of (Note) Pages 141-164
Additional Notes 164-167
CHAPTER VI
THE QUANTITY OF JUDGMENTS
Extension and intension (1-2). Mistakes about "connotation" (3-5).
Law of inverse proportion of intent to extent, shown to be
erroneous (6-10).
Every judgment has two aspects, and can be taken both extensionally
and in intension (11-12). The first defended against erroneous
views (13-21). The second explained, and mistakes removed
(22-29).
Universal, particular, and singular; what these mean, and how far they
can be real (30-36). The corresponding judgments, what (37-43).
Pages 168-193
Additional Notes 193-196
CHAPTER VII
THE MODALITY OF JUDGMENTS
Modality affects not the form but the content of Judgment (1-3).
Logical modality, what (4-5). The Assertorical (6). The Neces
sary is hypothetical (7-11). And so is the Possible (12). Varieties
of the latter (13-15).
Modality does not exist in fact (16). This shown of the necessary (17),
and the possible (18-19). But there must be a real basis for neces
sity (20), and for possibility (21-22).
Further explanations. The Potential not real (23). Conditions, as
such, not facts (24). Permanent Possibilities ambiguous (25).
The Problematic and Particular Judgments identical (26). The
Impossible, what (27). The possible not the same as the mere not-
impossible (28-31).
Probability. Its principles logical (32). Is neither objective nor sub
jective (33). Rests on an exhaustive disjunction (34~36), each
alternative of which is equally credible (37-38). Expression of the
XVI CONTENTS
chances by fractions (39-41). Inductive probability implies no fresh
principle (42-43).
Errors refuted. Probability objective as well as subjective (44-45). It
does not in its essence imply a series (46-50) ; nor a knowledge of
the future (51). Fiction of the "long run" (52-54), and the truth
which underlies this (55-57). Superstitious beliefs (58-59). Transi
tion to Inference (61-63) Pages 197-236
Additional Notes 236-242
BOOK IL PART I
THE GENERAL NATURE OF INFERENCE
CHAPTER I
SOME CHARACTERISTICS OF REASONING
We are really agreed on three features of inference. What these are
(1-3). Examples (4) Pages 245-246
CHAPTER II
SOME ERRONEOUS VIEWS
The major premise is a superstition (i). And the syllogism is not the
one type of reasoning (2). The ordinary syllogism in extension
criticized (3-5). Principle of nota notes (6). Possible reform of
the syllogism (7-8). Principle of "Related to same are related to
each other" criticized (9-10) Pages 247-254
Additional Notes 254-255
CHAPTER III
A GENERAL IDEA OF INFERENCE
Inference a perception ensuing on a synthesis (i). Demonstration is
seeing in a logical preparation, and that is an ideal construction
(2-4) Examples (5). Superstitions to be abandoned (6).
Pages 256-260
Additional Notes 260-261
CHAPTER IV
PRINCIPLES OF REASONING
These are special principles of interrelation (1-2). Examples of syn
theses (3). But in what sense are they principles (4)? Not as
canons and tests of individual inferences (5-6). No art of Reason-
CONTENTS XV11
ing (7). Illustration from Casuistry (8-9). Inadequacy of the
syllogism (10) Pages 262-271
Additional Notes 271-273
CHAPTER V
NEGATIVE REASONING
Its general nature (i) and special principles (2). Can you argue from
two negative premises? Yes, but not from two bare denials (3-7)
When one premise is negative can the conclusion be affirmative ? On
one special condition, yes (8-9) Pages 274-283
Additional Notes 283-284
CHAPTER VI
TWO CONDITIONS OF INFERENCE
Result reached (i). An identical point required in all reasoning (2).
Mere likeness not enough (3). Principle of Identity of Indiscerni-
bles stated and defended (4-9).
And one premise at least must be universal (10-13) . Pages 285-297
Additional Notes 297-298
BOOK II. PART II
INFERENCE CONTINUED
CHAPTER I
THE THEORY OF ASSOCIATION OF IDEAS
The fact of psychical association is certain, but the theory which ex
plains reproduction by the "Laws of Association" is false (1-7).
Main ground of objection (8). The true explanation of the fact
(9-12).
Errors refuted. No association by Contiguity (13-17), even if assisted
by Similarity (18). Similarity alone is left (19), and this too is a
fiction (20-22), which the facts do not require (23-25). The true
explanation (26-27). Misunderstandings removed (28-31). Wolff
and Maas adduced (32). An objection answered (33). Practical
conclusion (34-36).
Note. Indissoluble Association and the Chemistry of Ideas.
Pages 299-345
Additional Notes 346-347
2321. i h
XV111 CONTENTS
CHAPTER II
THE ARGUMENT FROM PARTICULARS TO PARTICULARS
This discussion has been anticipated (1-2). Supposed evidence for the
Argument (3) is an ignoratio elenchi (4-5). We never argue from
particulars as such (6-9), but from an universal (10-11). And we
can not do otherwise (12-13). Mr. Spencer s theory of inference
to be passed over (14) Pages 348-354
Additional Notes 054
CHAPTER III
THE INDUCTIVE METHODS OF PROOF
The question limited (1-2). Complete Induction (3). Mill s Canons
of Induction. Their claim to be demonstrative (4-5). But (I) they
can not start from fact (7-9). And (II) their conclusion need not
be more general than some of their premises (10). And (III) they
all have a logical flaw unless you confine them to the case in hand
(11-14). Result (15-16) Pages 355-368
Additional Notes 368-369
CHAPTER IV
JEVONS EQUATIONAL LOGIC
The Enquiry limited and subdivided (1-2). A. Propositions are not
equations, and can not assert mere identity (3-7). B. Reasoning
does not consist in Substitution of Similars. It rather connects dif
ferences (8-13). C. The Indirect Method (14) can not be reduced
to Substitution (15-18). The Logical Machine. Its merits and
defects (19-22). Result (23) Pages 370-387
Additional Notes t ..*,..... 387-388
VOLUME II
BOOK III. PART I
INFERENCE CONTINUED
CHAPTER I
THE ENQUIRY REOPENED
Our former account of inference was insufficient. There are infer
ences which will not come under our formula (1-9) Pages 389-392
Additional Notes 392-393
CHAPTER II
FRESH SPECIMENS OF INFERENCE
Tests of the existence of inference (1-3). Claim of fresh specimens.
A. Three-term Constructions (4-5). B. Arithmetic and Geometry
(6-15). C. Comparison and Distinction (16-17). D. Recognition
(18). E. Dialectic (19-22). F. Abstraction (23-24). G. Disjunc
tive Inference (25-29). H. Immediate Inferences (30-37).
Pages 394-423
Additional Notes 423-430
CHAPTER III
GENERAL CHARACTERISTICS OF INFERENCE
Further character of inference as an ideal experiment (1-4). This type
verified throughout our fresh instances (5-10).
Not every mental activity is reasoning (n). Judgment is not inference
(12-18) ; nor is all Reproduction (19-22) ; nor is Imagination (23-
24). Result obtained (25) Pages 431-446
Additional Notes 446-449
CHAPTER IV
THE MAIN TYPES OF INFERENCE
Analysis and Synthesis are two main types (i). This not apparent (2),
but shown throughout the whole of our instances (3-7). Tabular
statement (8) Pages 45O-455
Additional Notes 456
XX CONTENTS
CHAPTER V
ANOTHER FEATURE OF INFERENCE
A central identity required for each process of experiment (i). Dif
ficulties (2-3). The identity shown in Recognition and Dialectic
(4); and in Comparison and Distinction (5-6). This further ex
plained (7-9). The identity shown in spatial Construction and in
Arithmetic (10-12); and in Abstraction (13); and in Disjunctive
Inference (14). Result (15) Pages 457-467
Additional Notes 467-469
CHAPTER VI
THE FINAL ESSENCE OF REASONING
Principles of our processes (i). Analysis and Synthesis are two sides
of one process (2). Their sameness shown (3), and their differences
pointed out (4-7). Analytic and Synthetic Methods (8-10).
Judgment and Inference, how related (n). Every judgment involves
synthesis and analysis (12-14) ; but itself is not inference (15). If
however we go back far enough, judgment and inference seem two
sides of one process (16-22). Their connection shown in the work
ing of Reproduction (23-24).
Beside Analysis and Synthesis there is a third principle of reasoning
(25). Defects of Analysis and Synthesis (25-28). These defects
suggest a self -developing function (29-30), which appears in our
third principle (31-32). Recapitulation (33). Self-developement
shows itself through the whole process of reasoning (34-35).
Pages 470-494
Additional Notes 494-501
CHAPTER VII
THE BEGINNINGS OF INFERENCE
Gulf between explicit inference and the beginnings of soul-life (1-2).
Yet from the first an intellectual activity is present, which slowly
developes (3-8). Prevalent errors as to early intelligence (o-n).
Obstacles to the right study of it (12-15) . . Pages 502-514
Additional Notes SiS-Si8
CONTENTS XXI
BOOK III. PART II
INFERENCE CONTINUED
CHAPTER I
FORMAL AND MATERIAL REASONING
No reasoning with a bare form (2) ; nor need we even have a relative
form if that means a mere formula (3). No material reasoning if
that means an argument from the particular (4). There is a form
or principle in every inference, and there is an irrelevant detail
(5-6). We can extract this form (7) ; but it is not a major premise
(8-13). The form is the principle which neither proves, nor is
proved by, the instances (14-16) ; and this can be stated in a syl
logism (17). Other meanings of "formal" (18). Pages 519-532
Additional Notes 533-534
CHAPTER II
THE CAUSE AND THE BECAUSE
Is the middle the cause (i) ? Meaning of this term must be limited (2).
The cause is known by reasoning, since it implies ideal reconstruc
tion of the case (3-5). Futile to ask if cause comes from mere
habit (6). Explanation not perception of intermediate detail (7-10).
But the reason need not be the cause (n). Ambiguity of "because"
(12). The psychical cause and the logical ground distinguished
(13-14). The consequence not more complex than the cause or
ground (15). Result (16) Pages 535-548
Additional Notes 548-550
CHAPTER III
THE VALIDITY OF INFERENCE
The question has two main senses, but can here receive no final answer
(1-2). Is reasoning formally valid? Not if we have interfered to
make the conclusion (3). Do we interfere in Synthetical Construc
tion without elision (4-6), or with elision (7)? Is the process
capricious in Comparison, etc. (8-10), and again in Abstraction (n-
15) ? The Disjunctive Argument (16-20). Sceptical doubts (21-22).
Result (23).
Is a conclusive inference practicable? Question explained but not
answered (24-25) Pages 55^-572
Additional Notes . . 572-578
XX11 CONTENTS
CHAPTER IV
THE VALIDITY OF INFERENCE (Continued)
Is inference valid really as well as formally? Question stated (1-2).
Inference seems not always true of things. Instance of Comparison.
Three alternatives (3). Does reality change through our caprice,
or in harmony, or does it merely somehow correspond? Unless we
utterly revolutionize our beliefs, we must give up complete identity
of logic and fact (4-7).
Reasoning is never quite true of presented fact, since it must be dis
cursive (7-11). Even Dialectic, because discursive, seems unreal
(12). Nor, if logic answered to the known series of phenomena,
need it even thus be true; for that series is not given but inferred.
To be true of the presented logic must be true to sense, v/hich is
impossible (13-15).
Can we then, denying the truth of sense-presentation, take reality itself
as logical truth? Another alternative opposes us, and our logic still
may prove untrue (16). Yet why should truth and reality have
exactly the same nature (17)? Anyhow logic can not copy phe
nomena Pages S79-5QI
Additional Notes 591-595
TERMINAL ESSAYS
ESSAY I
ON INFERENCE (pp. 597~62l)
Logic, order in (597). Conclusion to be reached as to Inference
(597-8).
I. Inference defined (598-600). What Logic must assume (600). Can
the claim of Logic be in any case made good (601) ?
II. Specimens of Inference examined (601-11). Dialectical Method
(601-2). Disjunctive reasoning (602-3). Syllogism (603). Arith
metic (603-5). Construction, spatial and temporal (605-7). Anal
ysis and Abstraction (607-9). Comparison (609-11).
III. Defects of the above as inferences (611). A further failure in
all Logic is its abstraction from the psychical process. Different
scopes of Logic and Psychology. Each of these sciences alike is
independent but defective (611-13).
IV. Is Inference arbitrary and unreal? Objections as to triviality and
irrelevancy answered (614-16). But in what sense is Inference
"real" (616-17)?
CONTENTS XX111
V. Fallibility of all inference. Intrusion of what is merely psycho
logical (617). And the logical types themselves are imperfect (617-
18). Nor is any complete code possible, nor any " formal" criterion.
Individuality of inference (618-20).
VI. The Criterion what. Use and object of Logic (619-21).
ESSAY II
ON JUDGMENT (pp. 622-641)
Inference appears always as one kind of judgment, but not all judg
ment seems essentially to be inference (622-3). But this is never
theless to be maintained as true (623).
All judgment implies and is inference, and a mere judgment is merely
an abstraction (623-4). An objection answered (625-6).
The meaning of "judgment" and "idea," like that of "inference,"
varies according to the level at which it is used. Hence "judg
ment" has both a wider and a more restricted sense. But its
essence remains always the same and is confined to logical truth
(626).
An object, so far as aesthetic, is not in this sense true (627-8).
All judgment is selective, and yet the subject of every judgment is
the real Universe. An error here noted (628).
This duplicity of the subject in every judgment makes every judgment
an inference already in principle (629-30).
All judgment depends on abstraction from certain conditions of its
own being. Even as having an object it already abstracts, and, again,
its "real world" is a further abstraction (630-1). And judgment
abstracts always from its own psychical existence (631-2). It thus
depends throughout upon conditions upon a " because " which in
form it ignores. And hence, except in form, every judgment is
already an inference (632).
Further all judgment is not only condition^ but is also conditiona/
(633). On Ground and Conditions. On the difference between
"because" and "if." An objection answered (633-5).
The meaning of "if" further explained. Meaning of "uncondition
ally." How far does "conditionally" imply doubt (636-7)? On
"supposal" and on "hypothetical" (637-8).
Every judgment is conditional Ideal of knowledge, what No such
fact as a mere judgment, though in practice, here as everywhere,
the relative must more or less be taken as absolute (639-40).
And, as no "mere judgment," so also no "mere idea." The reality is
the concrete whole from which such things are abstractions. But
in Logic the order of treatment is to some extent artificial and so
optional (640-1).
XXIV CONTENTS
ESSAY III
ON THE EXTENSIONAL READING OF JUDGMENTS
(pp. 642-646)
Every judgment can be read in intension, but no judgment can be
read merely so. And the same thing holds (mutat. mutand.) as to
extensional reading (642-3).
Can, again, all judgment be taken as asserting or denying about some
"individual" or "individuals"? Certainly not so, if "individual"
is taken in its more ordinary sense (643). And the attempt to
read thus all judgments involves torture (643-4).
The possibility of taking any idea as one particular psychical event
makes applicable a mode of torture which still remains in principle
irrational (644-6).
ESSAY IV
UNIQUENESS (pp. 647-658)
Uniqueness two aspects of, one (a) positive and the other (b) nega
tive. But the second, even if perhaps always present, rests in any
case on the first. An objection answered (647-8).
Uniqueness is absolute or relative, and holds again either in principle
or merely de facto (648-9). Positive uniqueness as absolute.
Claims to its possession considered, (i) The Universe. (2) One
single quality (650). (3) Qualities as many. A distinction is to
be made here. The Many as mere particulars; but this is a false
abstraction and not a given fact (650-2). Attempts to defend its
claim (a) by external relations, and (b) by an appeal to Designation
(652-3). (4) The "This." Certainly it offers itself as unique, but
this claim holds only so long as we remain at the stage of Feel
ing (653-4). And even there the character of the "This" is incon
sistent and not self-contained, and hence the claim of the " This "
fails (654-5). (5) Finite Individuals. Their claim to uniqueness
must be allowed if you take them as members in and of a perfect
System (655-6). On the other hand this claim cannot be verified
completely in detail (656-7). Recapitulation (657-8).
ESSAY V
THE "THIS" (pp. 659-661)
" This " is not specially a mark of external perception. Like " mine "
and "now" it belongs to all Immediate Experience or Feeling
generally (659).
Can it as an idea be predicated beyond its actual self? Certainly it
CONTENTS XXV
can be so used, but it cannot be used beyond the Universe that is
indivisibly one with itself (659-61).
ESSAY VI
THE NEGATIVE JUDGMENT (pp. 662-667)
Every judgment is selective, and hence in consequence is in essence
both negative and disjunctive (662). But explicitly it need not be
so, since Judgment (like Inference) exists at diverse stages (662-3).
All Judgment involves the principle of Alternative ; and the negation
which it contains implies a positive ground on both sides, and a
whole which is disjunctive and systematic (663-5).
Negation is not "unreal" and "subjective." It is "real" always,
though we may be unable to see how in detail it is so. And it
never in truth can be merely "subjective" (665-6). The negative
is more real than what is taken as barely positive, since mere posi
tion and bare exclusion alike are unreal abstractions (666).
All negation must qualify, though we may be unable to see in detail
how precisely it does so. And no judgment anywhere, whether
negative or positive, can really be bare and purposeless (666-7).
ESSAY VII
ON THE IMPOSSIBLE, THE UNREAL, THE SELF-CONTRADICTORY,
AND THE UNMEANING (pp. 668-673)
The Possible what. Its dangerous ambiguities. Its negative aspect.
The Real in what sense "possible" (668-9).
The Impossible what. Its difference from the Unreal. " Nothing "
what (669-71). The Meaningless what (671). The Self -contra
dictory what. How it is thinkable, and in what sense it can
exist (671-2).
How far can the above ideas be used in practice indiscriminately?
Their ultimate reality what. They all consist in one-sided Ab
straction, which for finite experience is necessary, but which in the
ultimate concrete Reality is throughout made good (672-3).
ESSAY VIII
SOME REMARKS ON ABSOLUTE TRUTH AND ON PROBABILITY
(pp. 674-690)
No knowledge can rest on, or be affected by, the Unknown and by
ignorance taken as mere Privation (674). Absolute and Relative
Truth what. How a truth can be imperfect and yet absolute
(674 T 5).
Any objection to absolute truth on the ground of Probability is un-
XXvi CONTENTS
tenable (675-6). Proper and improper sense of Probability. The
former assumes a world of such a kind that the possibility of an
"otherwise" is in principle excluded (676-8).
General objections to absolute truth. In these there is nothing positive
which I on my side am unable to accept (678-9). This shown in
the case (i) of Irrationalism (679-80), and (2) of Pluralism and
Realism (680-4). So far as these differ from my view, is that
difference really anything positive (680-1) ? A compromise through
Relativism is not possible (681-2). But I can understand Realism
and Pluralism as urging nothing positive which is not accepted and
included in my view. And that view can explain the existence of
these other views (682-4). Recapitulation (684).
How can a lower and subordinate truth seem more probable than one
admittedly higher? This difficulty calls for examination (684-5).
An explanatory digression on higher and lower truths (685-6).
The above difficulty comes mainly from a false assumption as to
the superiority of the " real world " of events, and from the (per
haps unconscious) misplacing of a higher truth on this misleading
level (686-8). The above illustrated in two aspects (688-90).
ESSAY IX
A NOTE ON ANALYSIS (pp. 691-694)
A fundamental issue avoided by the Realist (691). A mistaken
dilemma. No relational view has ultimate truth (691). The "fact
of relatedness" must be, and yet is not, dealt with (692). The
empirical evidence against Analysis as yielding ultimate truth is
ignored. Terms and relations are abstractions, and they never are
given in immediate experience (693-4).
The category of Whole and Parts is not everywhere applicable, nor is
it ultimately valid (694).
ESSAY X
A NOTE ON IMPLICATION (pp. 695-698)
There is no sense in Implication unless it is indirect and through a
whole. And there is no Implication (proper) where or so far as
the whole is merely immediate (695).
The meaning of Implication rests on the fact of Immediate Experi
ence. And all predication, being relational, is irrational except so
far as conditional. Implication in the end is nonsense apart from
that which is both below and above the discursive stage of mind
and truth. No self-subsistent entity can imply another (695-7).
CONTENTS XXVli
Implication cannot be one-sided unless there is abstraction from or
alteration of conditions (697). "A before B" is really reciprocal.
Nor is there incompatibility between "before" and "after" except
under some condition (698).
ESSAY XI
ON THE POSSIBLE AND THE ACTUAL (pp. 699-712)
The enquiry limited. The Possible may be opposed in three senses to
the Actual, according as that is (i) not grounded, or (n) grounded
fully, or (in) both at once. The second sense is the main one (699).
The above illustrated. There is only one genuine Individual (699-
7oi).
The Actual is not the same as what " exists," nor is it always based
on Existence (701-2) ; nor is such a position saved by an appeal to
the distinction between relative and absolute possibility (702-3).
As against what is " imaginary," that which " exists " may be merely
possible (703).
And within the world of Truth the possible is still opposed to the
actual (703-5)- Why Logic can not be consistent ultimately (705).
Designation what (706). Recapitulation (706-7). Possible and
Actual within a grounded whole (707).
The above contrasted with an opposite view (707-10). The world as
a mere "And" or "Together" of independent entities (708). But
on any such view there is really no "world" at all, and possibility
can have in the end no meaning (708-10).
Reality and Truth their true relation stated (711-12).
ESSAY XII
ON THEORETICAL AND PRACTICAL ACTIVITY (pp. 713-728)
There is no such thing as a mere theoretical or mere practical activity
(713-14). All theoretical activity is also practical (714-15). And
all practical activity has a theoretical side and contains an idea and
a judgment (715)-
This position explained and defended against some errors (716-17).
(i) In Practice the judgment has different levels (717). (ii) But
its essence is not to anticipate a future fact even if any reference
at all to the future is essential (717-19). And any appeal here to a
lower stage of experience is useless (719-20). Further, Judgment
can not consist in a mere passage to the future (720-21). " Practice
for practice sake" as a gospel. Recapitulation (721-2).
How far and in what sense is the distinction of "theoretical" and
"practical" legitimate and useful? The answer to this question
explained and illustrated (722-4). Religion as the unity of one-
sidednesses (724-5).
XXV111 CONTENTS
A summary statement of some views which I advocate on Truth,
Activity, and Practice (725^8). Truth as Anticipation and Predic
tion, and as Experiment and Verification (726-7). Philosophy, its
limits and genuine task (727-8).
INDEX . . . 729-739
THE PRINCIPLES OF LOGIC
BOOK I JUDGMENT
CHAPTER I
THE GENERAL NATURE OF JUDGMENT
I. It is impossible, before we have studied Logic, to
know at what point our study should begin. And, after we
have studied it, our uncertainty may remain. In the absence of
any accepted order I shall offer no apology for beginning with
Judgment. If we incur the reproach of starting in the middle,
we may at least hope to touch the centre of the subject. 1
The present chapter will deal with the question of judgment
in general. It will (i) give some account of the sense in which
the term is to be used; it will (n) criticize, in the second place,
a considerable number of erroneous views; and will end
(in) with some remarks on the development of the function.
I. In a book of this kind our arrangement must be arbi
trary. The general doctrine we are at once to lay down, really
rests on the evidence of the following chapters. If it holds
throughout the main phenomena of the subject, while each
other view is in conflict with some of them, it seems likely
to be the true view. But it can not, for this reason, be put
forward at first, except provisionally.
Judgment presents problems of a serious nature to both
psychology and metaphysics. Its relation to other psychical
phenomena, their entangled development from the primary
basis of soul-life, and the implication of the volitional with
the intellectual side of our nature on the one hand, and on
the other hand the difference of subject and object, and the
question as to the existence of any mental activity, may be
indicated as we pass. But it will be our object, so far as is
possible, to avoid these problems. We do not mainly want
to ask, How does judgment stand to other psychical states,
and in ultimate reality what must be said of it. Our desire
i
2 THE PRINCIPLES OF LOGIC BOOK I
is to take it, so far as we can, as a given mental function;
to discover the general character which it bears, and further
to fix the more special sense in which we are to use it.
2. I shall pass to the latter task at once. Judgment, in
the strict sense, does not exist where there exists no knowl
edge of truth and falsehood; and, since truth and falsehood
depend on the relation of our ideas to reality, you can not
have judgment proper without ideas. And perhaps thus much
is obvious. But the point I am going on to, is not so obvious.
Not only are we unable to judge before we use ideas, but,
strictly speaking, we can not judge till we use them as ideas 2 .
We must have become aware that they are not realities, that
they are mere ideas, signs of an existence other than them
selves. Ideas are not ideas until they are symbols, and,
before we use symbols, we can not judge.
3. We are used to the saying, "This is nothing real,
it is a mere idea." And we reply that an idea, within my
head, and as a state of my mind, is as stubborn a fact as any
outward object. The answer is well-nigh as familiar as the
saying, and my complaint is that in the end it grows much too
familiar. In England at all events we have lived too long
in the psychological attitude 3 . We take it for granted and as
a matter of course that, like sensations and emotions, ideas
are phenomena. And, considering these phenomena as psy
chical facts, we have tried (with what success I will not ask)
to distinguish between ideas and sensations. But, intent on
this, we have as good as forgotten the way in which logic
uses ideas. We have not seen that in judgment no fact ever is
just that which it means, or can mean what it is ; and we have
not learnt that, wherever we have truth or falsehood, it is
the signification we use, and not the existence. We never
assert the fact in our heads, but something else which that fact
stands for And if an idea were treated as a psychical reality,
if it were taken by itself as an actual phenomenon, then it
would not represent either truth or falsehood. When we use it
in judgment, it must be referred away from itself. If it is not
the idea of some existence, then, despite its own emphatic actu
ality, its content remains but " a mere idea." It is a something
which, in relation to the reality we mean, is nothing at all.
4. For logical purposes ideas are symbols, and they are
CHAP. I THE GENERAL NATURE OF JUDGMENT 3
nothing but symbols. 4 And, at the risk of common-place,
before I go on, I must try to say what a symbol is.
In all that is we can distinguish two sides, (i) existence
and (ii) content. In other words we perceive both that it is
and what it is. But in anything that is a symbol we have
also a third side, its signification, or that which it means 5 . We
need not dwell on the two first aspects, for we are not con
cerned with the metaphysical problems which they involve.
For a fact to exist, we shall agree, it must be something. It
is not real unless it has a character which is different or
distinguishable from that of other facts. And this, which
makes it what it is, we call its content. We may take as an
instance any common perception. The complex of quali
ties and relations it contains, makes up its content, or
that which it is; and, while recognizing this, we recognize
also, and in addition, that it is. Every kind of fact must
possess these two sides of existence and content, and we
propose to say no more about them here.
But there is a class of facts which possess an other and
additional third side. They have a meaning; and by a sign
we understand any sort of fact which is used with a mean
ing. The meaning may be part of the original content, 6 or
it may have been discovered and even added by a further
extension. Still this makes no difference. Take anything
which can stand for anything else, and you have a sign.
Besides its own private existence and content, it has this
third aspect. Thus every flower exists and has its own
qualities, but not all have a meaning. Some signify nothing,
while others stand generally for the kind which they repre
sent, while others again go on to remind us of hope or love.
But the flower can never itself be what it means.
A symbol is a fact which stands for something else, and
by this, we may say, it both loses and gains, is degraded and
exalted. In its use as a symbol it forgoes individuality, and
self-existence. It is not the main point that this rose or
forget-me-not, and none other, has been chosen. We give it,
or we take it, for the sake of its meaning; and that may
prove true or false long after the flower has perished. The
word dies as it is spoken, but the particular sound of the
mere pulsation was nothing to our minds. Its existence was
4 THE PRINCIPLES OF LOGIC BOOK I
lost in the speech and the significance. The paper and the
ink are facts unique and with definite qualities. They are the
same in all points with none other in the world. But, in
reading, we apprehend not paper or ink, but what they
represent; and, so long as only they stand for this, their
private existence is a matter of indifference. A fact taken
as a symbol ceases so far to be fact. It no longer can be
said to exist for its own sake, its individuality is lost in its
universal meaning. It is no more a substantive, but be
comes the adjective that holds of another. But, on the
other hand, the change is not all loss. By merging its own
quality in a wider meaning, it can pass beyond itself and
stand for others. It gains admission and influence in a world
which it otherwise could not enter. The paper and ink cut the
throats of men, and the sound of a breath may shake the world.
We may state the sum briefly. A sign is any fact that
has a meaning, and meaning consists of a part of the content
(original or acquired), cut off, fixed by the mind, and con
sidered apart from the existence of the sign.*
5. I must be permitted at this point to make a digression,
which the reader may omit, if he does not need it. Through
out this volume I do not intend to use the word " symbol "
as distinct from "sign," though there is a difference which
elsewhere might become of importance. A symbol is certainly
always a sign, but the term may be appropriated to signs of a
very special character. In contrast with a symbol a sign may
be arbitrary. It can not, of course, be devoid of meaning, for,
in that case, it would be unable to stand for anything. But
it may stand for that with which internally it is not con
nected, and with which it has been joined by arbitrary chance.
But even when signs have a natural meaning, when their
content carries us direct to the object of which they are
used, yet, if we take symbol in a narrow sense, a natural
sign need not be a symbol. We may restrict the term to
*It would not be correct to add, "and referred away to another
real subject"; for where we think without judging, and where we
deny, that description would not be applicable. Nor is it the same
thing to have an idea, and to judge it possible. To think of a
chimsera is to think of it as real, but not to judge it even possible.
And it is not until we have found that all meaning must be adjectival,
that with every idea we have even the suggestion of a real subject
other than itself. 7
CHAP. I THE GENERAL NATURE OF JUDGMENT 5
secondary signs. For example a lion is the symbol of courage,
and a fox of cunning, but it would be impossible to say that
the idea of a fox stands for cunning directly. We mean by it
first the animal called a fox, and we then use this meaning to
stand as the sign for one quality of the fox. Just as the
image or presentation of a fox is taken by us in one part of its
content, and referred away to another subject, so this meaning
itself suffers further mutilation : one part of its content is fixed
by the mind and referred further on to a second subject, viz. the
quality in general, wherever found. It makes no difference
whether we begin with an image or a sensible perception, for
the perception itself, before it can be used, must be taken
ideally, recognized, that is, in one part of its content. And the
distinction again between the symbolism that is unconscious,
and that which is reflective, does not touch the main principle.
In order to obviate possible objections, I have thought it
best to make these remarks; but since I propose to use sign
and symbol quite indifferently, the discussion has hardly any
bearing on my argument.
6. We might say that, in the end, there are no signs
save ideas, but what I here wish to insist on, is that, for logic
at least, all ideas are signs. Each we know exists as a
psychical fact, and with particular qualities and relations.
It has its speciality as an event in my mind. It is a hard
individual, so unique that it not only differs from all others,
but even from itself at subsequent moments. And this char
acter it must bear when confined to the two aspects of ex
istence and content. But just so long as, and because, it
keeps to this character, it is for logic no idea at all. It be
comes one first when it begins to exist for the sake of its
meaning. And its meaning, we may repeat, is a part of the
content, used without regard to the rest, or the existence. I
have the " idea " of a horse, and that is a fact in my mind,
existing in relation with the congeries of sensations and
emotions and feelings, which make my momentary state. It
has again particular traits of its own, which may be difficult
to seize, but which, we are bound to suppose, are present. It
is doubtless unique, the same with no other, nor yet with
itself, but alone in the world of its fleeting moment. But, for
logic, and in a matter of truth and falsehood, the case is
2321. I B
6 THE PRINCIPLES OF LOGIC BOOK I
quite changed. The " idea " has here become an universal,
since everything else is subordinate to the meaning. That con
nection of attributes we recognize as horse, is one part of the
content of the unique horse-image, and this fragmentary part
of the psychical event is all that in logic we know of or care
for. Using this we treat the rest as husk and dross, which mat
ters nothing to us, and makes no difference to the rest. The
" idea," if that is the psychical state, is in logic a symbol. But
it is better to say, the idea is the meaning, for existence and un
essential content are wholly discarded. The idea, in the sense
of mental image, is a sign of the idea in the sense of meaning. 8
7. These two senses of idea, as the symbol and the
symbolized, the image and its meaning, are of course known
to all of us. But the reason why I dwell on this obvious
distinction, is that in much of our thinking it is systematically
disregarded. " How can any one," we are asked, " be so
foolish as to think that ideas are universal, when every single
idea can be seen to be particular, or talk of an idea which
remains the same, when the actual idea at each moment
varies, and we have in fact not one identical but many
similars ? " But how can any one, we feel tempted to reply,
suppose that these obvious objections are unknown to us?
When I talk of an idea which is the same amid change, I do
not speak of that psychical event which is in ceaseless flux,
but of one portion of the content which the mind has fixed, and
which is not in any sense an event in time. I am talking of
the meaning, not the series of symbols, the gold, so to speak,
not the fleeting series of transitory notes. The belief in uni
versal ideas does not involve the conviction that abstrac
tions exist, even as facts in my head. The mental event is
unique and particular, but the meaning in its use is cut off
from the existence, and from the rest of the fluctuating
content. It loses its relation to the particular symbol; it
stands as an adjective, to be referred to some subject, but
indifferent in itself to every special subject.
The ambiguity of " idea " may be exhibited thus. Thesis,
On the one hand no possible idea can be that which it means.
Antithesis, On the other hand no idea is anything but just
what it means. In the thesis the idea is the psychical image ;
in the antithesis the idea is the logical signification. In the
CHAP. I THE GENERAL NATURE OF JUDGMENT 7
first it is the whole sign, but in the second it is nothing but
the symbolized. In the sequel I intend to use idea mainly in
the sense of meaning*
8. For logical purposes the psychological distinction of
idea and sensation may be said to be irrelevant, while the
distinction of idea and fact is vital. The image, or psycho
logical idea, is for logic nothing but a sensible reality. It
is on a level with the mere sensations of the senses. For
both are facts and neither is a meaning. Neither is cut
from a mutilated presentation, and fixed as a connection.
Neither is indifferent to its place in the stream of psychi
cal events, its time and relations to the presented congeries.
Neither is an adjective to be referred from its existence, to
live on strange soils, under other skies and through chang
ing seasons. The lives of both are so entangled with their
environment, so one with their setting of sensuous particulars,
that their character is destroyed if but one thread is broken.
Fleeting and self -destructive as is their very endurance,
wholly delusive their supposed individuality, misleading and
deceptive their claim to reality, yet in some sense and some
how they are. They have existence; they are not thought
but given.f But an idea, if we use idea of the meaning, is
neither given nor presented but is taken. It can not as
such exist. It can not ever be an event, with a place in the
series of time or space. It can be a fact no more inside our
heads than it can outside them. And, if you take this mere
* There are psychological difficulties as to universal ideas, and we
feel them more, the more abstract the ideas become. The existence
and the amount, of the particular imagery or sensuous environment,
give rise to questions. But these questions need not be considered
here, for they have no logical importance whatever. I assume, after
Berkeley, that the mental fact contains always an irrelevant sensuous
setting, however hard it may be to bring this always to consciousness.
But I must repeat that this is not a vital question. It is a mistake in
principle to try to defend the reality of universals by an attempt to
show them as psychical events existing in one moment. For if the
universal we use in logic had actual existence as a fact in my mind,
at all events I could not use it as that fact. You must at any rate
abstract from the existence and external relations, and how much
further the abstraction is to go seems hardly an important or vital
issue.
fThis statement is subject to correction by Chapter II. 9
8 THE PRINCIPLES OF LOGIC BOOK I
idea by itself, it is an adjective divorced, a parasite cut loose, a
spirit without a body seeking rest in another, an abstraction
from the concrete, a mere possibility which by itself is nothing.
9. These paradoxical shadows and ghosts of fact are
the ideas we spoke of, when we said, Without ideas no judg
ment; and, before we proceed, we may try to show briefly
that in predication we do not use the mental fact, but only
the meaning. The full evidence for this truth must however
be sought in the whole of what follows.
(i) In the first place it is clear that the idea, which we use
as the predicate of a judgment, is not my mental state as
such. " The whale is a mammal " does not qualify real whales
by my mammal-image. For that belongs to me, and is an
event in my history; and, unless I am Jonah, it can not enter
into an actual whale. We need not dwell on this point, for
the absurdity is patent. If I am asked, Have you got the
idea of a sea-serpent? I answer, Yes. And again, if I am
asked, But do you believe in it, Is there a sea-serpent? I
understand the difference. The enquiry is not made about
my psychical fact. No one wishes to know if that exists
outside of my head; and still less to know if it really exists
inside. For the latter is assumed, and we can not doubt it.
In short the contention that in judgment the idea is my own
state as such, would be simply preposterous.
(ii) But is it possible, secondly, that the idea should be
the image, not indeed as my private psychical event, but still
as regards the whole content of that image? We have a
mental fact, the idea of mammal. Admit first that, as it
exists and inhabits my world, we do not predicate it. Is there
another possibility? The idea perhaps might be used apart
from its own existence, and in abstraction from its relations
to my psychical phenomena, and yet it might keep, without any
deduction, its own internal content. The " mammal " in my
head is, we know, not bare mammal, but is clothed with par
ticulars and qualified by characters other than mammality ; and
these may vary with the various appearances of the image.*
* I may point out that, even in this sense, the idea is a product of
abstraction. Its individuality (if it has such) is conferred on it by
an act of thought. It is given in a congeries of related phenomena,
and, as an individual image, results from a mutilation of this fact
(Vid. inf. Chap. II.).
CHAP. I THE GENERAL NATURE OF JUDGMENT 9
And we may ask, Is this whole, image used in judgment?
Is this the meaning? But the answer must be negative.
We have ideas of redness, of a foul smell, of a horse, and
of death; and, as we call them up more or less distinctly,
there is a kind of redness, a sort of ofTensiveness, some image
of a horse, and some appearance of mortality, which rises
before us. And should we be asked, Are roses red? Has
coal gas a foul smell ? Is that white beast a horse ? Is it true
that he is dead ? we should answer, Yes, our ideas are all true,
and are attributed to the reality. But the idea of redness may
have been that of a lobster, of a smell that of castor-oil, the
imaged horse may have been a black horse, and death perhaps
a withered flower. And these ideas are not true, nor did
we apply them. What we really applied was that part of their
content which our minds had fixed as the general meaning.
It may be desirable (as in various senses various writers
have told us) that the predicate should be determinate, but
in practice this need can not always be satisfied. I may
surely judge that a berry is poisonous, though in what way
I know not, and though " poisonous " implies some traits
which I do not attribute to this poison. I surely may believe
that AB is bad, though I do not know his vices, and have
images which are probably quite inapplicable. I may be sure
that a book is bound in leather or in cloth, thought the sort
of leather or cloth I must imagine I can not say exists.
The details I have never known, or at any rate, have forgot
ten them. But of the universal meaning I am absolutely
sure, and it is this which I predicate.
The extreme importance of these obvious distinctions
must excuse the inordinate space I allot to them. Our whole
theory of judgment will support and exemplify them; but I
will add yet a few more trivial illustrations. In denying that
iron is yellow, do I say that it is not yellow like gold, or
topaze, or do I say that it is not any kind of yellow? When
I assert, " It is a man or a woman or a child," am I reasonably
answered by, " There are other possibilities. It may be an
Indian or a girl " ? When I ask, Is he ill ? do I naturally look
for " Oh no, he has cholera "? Is the effect of, " If he has
left me then I am undone," removed by " Be happy, it was
by the coach that he deserted you " ?
IO THE PRINCIPLES OF LOGIC BOOK I
The idea in judgment is the universal meaning; it is not
ever the occasional imagery, and still less can it be the whole
psychical event.
10. We now know what to understand by a logical idea,
and may briefly, and in anticipation of the sequel, dog
matically state what judgment does with it. We must avoid,
so far as may be, the psychological and metaphysical dif
ficulties that rise on us.
Judgment proper is the act which refers an ideal content
(recognized as such) to a reality beyond the act. 10 This
sounds perhaps much harder than it is.
The ideal content is the logical idea, the meaning as just
defined. It is recognized as such, when we know that, by
itself, it is not a fact but a wandering adjective 11 . In the act
of assertion we transfer this adjective to, and unite it with, a
real substantive. And we perceive at the same time, that
the relation thus set up is neither made by the act, nor merely
holds within it or by right of it, but is real both independent
of and beyond it.*
If as an example we take once more the sea-serpent, we
have an idea of this but so far no judgment. And let us
begin by asking, Does it exist ? Let us enquire if " it exists "
is really true, or only an idea. From this let us go on, and
proceed to judge " The sea-serpent exists." In accomplish
ing this what further have we done? And the answer is,
we have qualified the real world by the adjective of the sea-
serpent, and have recognized in the act that, apart from our
act, it is so qualified. By the truth of a judgment we mean
that its suggestion is more than an idea, that it is fact or
in fact. We do not mean, of course, that as an adjective
of the real the idea remains an indefinite universal. The sea-
serpent, if it exists, is a determinate individual; and, if we
knew the whole truth, we should be able to state exactly how
it exists. Again when in the dusk I say, That is a quadruped,
I qualify the reality, now appearing in perception, by this uni
versal, while the actual quadruped is, of course, much besides
four legs and a head. But, while asserting the universal, I do
* I may remark that I am dealing at present only with affirmation ;
the negative judgment presents such difficulties that it can hardly be
treated by way of anticipation.
CHAP. I THE GENERAL NATURE OF JUDGMENT II
not mean to exclude its unknown speciality. Partial ignorance
need not make my knowledge fallacious, unless by a mistake
I assert that knowledge as unconditional and absolute 12 .
" Are the angles of a triangle equal to two right angles? " 13
" I doubt if this is so," " I affirm that this is so." In these
examples we have got the same ideal content; the suggested
idea is the relation of equality between the angles of a
triangle and two right angles. And the affirmation, or judg
ment, consists in saying, This idea is no mere idea, but is a
quality of the real. The act attaches the floating adjective to
the nature of the world, and, at the same time, tells me it was
there already. The sequel, I hope, may elucidate the fore
going, but there are metaphysical problems, to which it gives
rise, that we must leave undiscussed.
ii. In this description of judgment there are two points
we may at once proceed to notice. The reader will have
observed that we speak of a judgment asserting one idea, or
ideal content, and that we make no mention of the subject
and copula. The doctrine most prevalent, on the other hand,
lays down that we have always two ideas, and that one is
the subject. But on both these heads I am forced to dis
sent. Our second chapter will deal further with the question,
but there are some remarks which may find a place here.
(i) It is not true that every judgment has two ideas. We
may say on the contrary that all have but one. 14 We take an
ideal content, a complex totality of qualities and relations,
and we then introduce divisions and distinctions, and w r e call
these products separate ideas with relations between them.
And this is quite unobjectionable. But what is objectionable,
is our then proceeding to deny that the whole before our
mind is a single idea; and it involves a serious error in
principle. The relations between the ideas are themselves ideal.
They are not the psychical relations of mental facts. They do
not exist between the symbols, but hold in the symbolized.
They are part of the meaning and not of the existence. And
the whole in which they subsist is ideal, and so one idea.
Take a simple instance. We have the idea of a wolf and
we call that one idea. We imagine the wolf eating a lamb,
and we say, There are two ideas, or three, or perhaps even
more. But is this because the scene is not given as a whole?
I2 THE PRINCIPLES OF LOGIC BOOK I
Most certainly not so. It is because in the whole there exist
distinctions, and those groupings of attributes we are ac
customed to make. But, if we once start on this line and
deny the singleness of every idea which embraces others, we
shall find the wolf himself is anything but one. He is the
synthesis of a number of attributes, and, in the end, we shall
find that no idea will be one which admits any sort of dis
tinction in itself. Choose then which you will say, There are
no single ideas, save the ideas of those qualities which are too
simple to have any distinguishable aspects, and that means
there are no ideas at all or, Any content whatever which
the mind takes as a whole, however large or however small,
however simple or however complex, is one idea, and its
manifold relations are embraced in an unity.*
We shall always go wrong unless we remember that the
relations within the content of any meaning, however complex,
are still not relations between mental existences. There is a
wolf and a lamb. Does the wolf eat the lamb? The wolf eats
the lamb. We have a relation here suggested or asserted
between wolf and lamb, but that relation is (if I may use the
word) not a factual connection between events in my head.
What is meant is no psychical conjunction of images. Just
as the idea of the wolf is not the whole wolf-image, nor the
idea of the lamb the imagined lamb, so the idea of their syn
thesis is not the relation as it exists in my imagination. In
the particular scene, which symbolizes my meaning, there are
details that disappear in the universal idea, and are neither
thought of nor enquired after, much less asserted.
To repeat the same thing the imagery is a sign, and the
meaning is but one part of the whole, which is divorced from
the rest and from its existence. In this ideal content there are
groups and joinings of qualities and relations, such as answer
to nouns and verbs and prepositions. But these various ele
ments, though you are right to distinguish them, have no valid
ity outside the whole content. That is one idea, which contains
* The psychological controversy as to the number of ideas we can
entertain at once, can hardly be settled till we know beforehand what
is one idea. If this is to exclude all internal complexity, what residuum
will be left? But, if it admits plurality, why is it one idea? If,
however, what otherwise we should call plurality, we now call single
just because we have attended to it as one, the question must clearly
alter its form. 15
CHAP. I THE GENERAL NATURE OF JUDGMENT 13
all ideas which you are led to make in it; for, whatever is
fixed by the mind as one, however simple or complex, is but
one idea. But, if this is so, the old superstition that judg
ment is the coupling a pair of ideas must be relinquished.
12. I pass now (ii) to the other side of this error, the
doctrine that in judgment one idea is the subject, and that
the judgment refers another to this. In the next chapter this
view will be finally disposed of, but, by way of anticipation,
we may notice here two points, (a) In " wolf eating lamb "
the relation is the same, whether I affirm, or deny, or doubt,
or ask 16 . It is therefore not likely that the differentia of
judgment will be found in what exists apart from all judg
ment. The differentia will be found in what differences the
content, as asserted, from the content as merely suggested. So
that, if in all judgment it were true that one idea is the subject
of the assertion, the doctrine would be wide of the essence
of the matter, and perhaps quite irrelevant. But (b) the doc
trine (as we shall see hereafter) is erroneous. " B follows
A," " A and B coexist," " A and B are equal," " A is south
of B " in these instances it is mere disregard of facts which
can hold to the doctrine. It is unnatural to take A or B as
the subject and the residue as predicate. And, where exist
ence is directly asserted or denied, as in, " The soul exists,"
or, " There is a sea-serpent," or, " There is nothing here,"
the difficulties of the theory will be found to culminate.
I will anticipate no further except to remark, that in every
judgment there is a subject of which the ideal content is
asserted. But this subject of course can not belong to the
content or fall within it, 17 for, in that case, it would be the
idea attributed to itself. We shall see that the subject is,
in the end, no idea but always reality; and, with this antici
pation, we must now go forward, since we have finished the
first division of this chapter. We must pass from the general
notion of judgment to the criticism of certain erroneous
views, a criticism, however, which is far from exhaustive,
and in some points must depend for its fuller evidence upon
the discussions of the following chapters.
II. 13. Wrong theories of judgment naturally fall into
two classes, those vitiated by the superstition of subject,
!4 THE PRINCIPLES OF LOGIC BOOK I
predicate and copula, and those which labour under other
defects. We will take the last first.
(i) Judgment is neither the association of an idea with a
sensation, nor the liveliness or strength of an idea or ideas.
At the stage we have reached, we need subject these views to
no detailed examination. The ideas which they speak of are
psychical events, whereas judgment, we have seen, has to do
with meaning, an ideal content which is universal, and which
assuredly is not the mental fact. While all that we have is a
relation of phenomena, a mental image, as such, in juxta
position with or soldered to a sensation, we can not as yet
have assertion or denial, a truth or a falsehood. We have
mere reality, which is, but does not stand for anything, and
which exists, but by no possibility could be true.
We will not anticipate the general discussion of " Asso
ciation " (vid. Book II. Part II. Chap. I.), and will pass by
those extraordinary views the school holds as to universals.
We will come at once to the result. There is an idea, in the
sense of a particular image, in some way conjoined with or
fastened to a sensation. I have, for instance, sensations of
coloured points; and images of movement and hardness and
weight are " called up " by these sensations, are attracted to,
and cohere with them. And this sounds very well till we
raise certain difficulties. An orange presents us with visual sen
sations, and we are to add to these the images just mentioned.
But each of these images is a hard particular, and qualified
by relations which exclude it from all others. If you simply
associate this bundle of facts, who would take them as one
fact ? But if you blend their content, if, neglecting the exist
ence, you take a part of the quality of each, and transfer that
to the object, then you may call your process by what name you
please, but it certainly is not association (Vid. infr. Book II.) .
But let us suppose that the ideas are united somehow
with the sensation, yet where is the judgment, where is truth
or falsehood? The orange is now before my sense or imagi
nation. For my mind it exists, and there is an end of it.
Or say, " Caesar will be angry." Caesar here is the percep
tion, which, when further qualified, becomes " Caesar angry."
But this image again is simply what it is, it does not stand for
anything, and it can mean nothing.
CHAP. I THE GENERAL NATURE OF JUDGMENT 15
Let us suppose in the first place that the " idea " main
tains itself, then no doubt, as one fact, it stands in mental
relation with the fact of the sensation. The two phenomena
coexist as a headache may coexist with a syllogism; but such
psychical coherence is far from assertion. There is no affirma
tion; and what is there to affirm? Are we to assert the
relation between the two facts? But that is given, and either
to assert it or deny it would be senseless.* Is one fact to
be made the predicate of another fact? That seems quite
unintelligible. If in short both sensation and idea are facts,
then not only do we fail to find any assertion, but we fail to
see what there is left to assert.
But in the second place (giving up association proper)
let us suppose that the " idea," as such, disappears, and that its
mutilated content is merged in the sensation. In this case the
whole, produced by blending, comes to my mind as a single
presentation. But where is the assertion, the truth or false
hood ? We can hardly say that it lies in the bare presentation
itself. We must find it, if anywhere, in the relation of this
presentation to something else. And that relation would be
the reference of judgment. But on the present view both the
something else and the reference are absent. We have first
an unmodified and then a modified sensation.
The only way to advance would be to suppose, in the first
place, that, while the " idea " maintains itself, it is dis
tinguished from its content; and to suppose, in the second
place, that both of these are distinguished from the sensation.
We have then two facts, a sensation and an image, and beside
these a content held apart from the image. We have now
reached a condition which would make judgment possible,
but the advance to this condition is not explicable by Associa
tion. Nor could the further steps be accounted for. You have
the transference of the content from the image to the sensa
tion, and the qualification of the latter as a subject; but both
would be inexplicable. We may add that it is impossible for
a sensation or sensations to serve as the subject in every
judgment (vid. Chap. II.). And finally the consciousness
that, what my act joins, is joined apart from it, is a fact not
*We might say that, on this view, the denial of a falsehood must
ipso facto be false.
j5 THE PRINCIPLES OF LOGIC BOOK I
compatible with the psychology we are considering 1 . To sum
up the whole to merge the content of an image in a modi
fied presentation, is but one step towards judgment, and
it is a very long step beyond association: while conjunction
or coherence of psychical phenomena is not only not judg
ment, but would not serve as its earliest basis and beginning.*
14. But the definition, I shall be told, is a "lively idea
associated with a present impression," and I shall be asked if
lively makes no difference. And I answer, Not one particle ;
it makes no difference even if you suppose it true, and in
addition it is false. The liveliness removes none of the
objections we have been developing. Let it be as lively as
you please, it is a mere presentation, and there is no judg
ment. The liveliness of the idea not only is not judgment, but
it is not always even a condition. The doctrine that an idea
judged true must be stronger than one not so judged, will not
bear confrontation with the actual phenomena. You may go
on to increase an idea in strength till it passes into a sensa
tion, and there yet may be no judgment. I will not dwell
on this point, since the unadulterated facts speak loudly for
themselves, but will give one illustration. We most of us
have at times the images of the dead, co-inhabitants of the
rooms we once shared with the living. These images, mostly
faint, at times become distressing, from their strength and
particularity and actual localization in those parts of the
room which we do not see. In an abnormal state such images,
it is well known, may become hallucinations, and take their
place in the room before our eyes as actual perceptions. But
with an educated man they would be recognized as illusions,
and would not be judged to be outwardly real, any more than
the fainter and normal images are judged to be anywhere
but in our own minds. Yet lively ideas associated with present
* It has been often remarked that, on Hume s theory of belief, there
can be no difference between imagination and reality, truth and false
hood, and that why we make this difference is incomprehensible. J. S.
Mill with great openness professed on this head the total bankruptcy
of the traditional doctrine. He seems somehow to have thought that
a complete break-down on a cardinal point was nothing against the
main doctrine of his school, nor anything more than a somewhat
strange fact. It was impossible that he should see the real cause of
failure. We shall deal with Professor Bain s views lower down.
CHAP. I THE GENERAL NATURE OF JUDGMENT 17
impressions if we have not got them here, where are they?
15. We turn with relief from the refutation of a doctrine,
long dead and yet stubbornly cumbering the ground, to con
sider a fresh error, the confusion of judgment with practical
belief. I cannot enquire how far any psychical activity is
consistent with the theory of Professor Bain, nor can I dis
cuss the nature of a psychical activity which seems physiolog
ically to consist in muscular innervation; though I am bound
to add that (doubtless owing to my ignorance) Professor
Bain s physiology strikes me here as being astonishingly misty.
And I must pass by the doubt whether, if we accept his view,
we shall find the confusion between image and meaning in
any way lessened 19 .
We must remember that the question, Is judgment always
practical, does not mean, Is the will in any way concerned in
it. In that case it might be argued that all generation of
psychical phenomena comes under the head Will. The ques
tion means, Does the essence of judgment lie, not in the
production of truth and falsehood states which alter nothing
in the things they represent but rather in the actual produc
tion of a change in real existence. Or, more simply, when an
idea is judged to be true, does this mean that it moves some
other phenomenon, and that its assertion or denial is nothing
but this motion? The doctrine admits that an idea or ideas,
when held true, differ vitally from the same when suggested;
and it proceeds to assert that the differentia is the effect of the
idea on our conduct, and that there is no other differentia at all.
There is a logical mistake we may point out before pro
ceeding, for it is the error which has led Professor Bain astray.
Assume that an asserted idea causes action, and that an idea,
not believed in, does not influence conduct. From these
premises can we conclude, Therefore judgment is influence?
If, in other words, when A changes to B, we have an unfailing
difference q, and q is not found except after A, does this war
rant the assertion, that the alteration consists in q ? Is it not
quite possible that q follows from p, and that p is what really
turns A into B ? We shall do well to keep our eye on this logi
cal fallacy. The assertion we are to examine is not that prac
tical influence induces us to judge, or results from a judgment :
What is asserted is that judgment is nothing else whatever.
l8 THE PRINCIPLES OF LOGIC BOOK I
Against this false differentia I shall briefly maintain, (o)
that the differentia may be absent from the fact, (b) that it
may be present with other facts, (c) that the fact contains
other characteristics, which are the true differentia, and are
absent from the false one, (d) that the latter has a positive
quality which. excludes the fact.
(a) If we test the theory by abstract instances such as,
The angles of a triangle are equal to two right angles, it
collapses at once. It is impossible to find always a practical
influence exerted by the ideas. We may be answered " But
they might exert it, you surely would act on them." And
such an answer may pass in the school of " Experience " ; but
a poor " transcendentalist " will perhaps be blamed if he
usurps such a privilege. He at least is not allowed to take
tendency and possibility and mere idea for fact. And he can
hardly be prevented from pressing the question, Is the influence
there or not? If it is not there, then either Professor Bain s
theory disappears, or he should alter his definition, and say that
an idea passes into a judgment when enriched by potentialities
and eventual tendencies 20 . If these are not ideas we should be
told what they are ; but if they are only ideas that go with the
first ideas, then our answer is plain. In the first place it is not
true that they are always there; in the second place it is not
true that, when added, they must exert a practical influence.
(b) In the second place ideas may influence me, though I
never do hold them for true. The feelings and emotions
associated with an idea can often prevent or produce volitions,
although the idea is not affirmed as true, and even while it is
recognized as false. . Though I do not believe that a slow-
worm can bite, or a drone can sting, I may shrink from
touching them. I may avoid a churchyard though I believe
in no ghosts. An illusion no doubt, if recognized as such,
does not influence volition either so much, or always in the
same way; but still it may operate in spite of disbelief.*
And it can hardly be a true view which forces us to say, If
you judged it an illusion you would wholly disregard it, for
such disregard is judgment.
* It may be said that when it operates the denial is suspended. But
I confess I can find no ground for such a statement. At any rate it
is certain that the idea can operate though a positive judgment is not
there.
CHAP. I THE GENERAL NATURE OF JUDGMENT 1 9
I will not dwell on a point it would be easy to illustrate.
In passing, however, I may remind the reader of that class of
ideas which influences our actions without seeming to be true.
I refer to practical ideas, the representation of a satisfied
desire which is now felt to be unsatisfied. It is certain that
these move us to active pursuit, and it is equally certain they
are not judged to be real 21 ; for, if they were, then for that
reason they would fail to move us.*
(c) But suppose that all judgment did really move to
action. Would this show that judgment was nothing but
such motion? Most certainly not so. We can observe what
takes place in us, when a suggested idea is judged to be
true; and clearly an activity (however hard to describe) does
show itself there, and yet is not directed (except per accidens)
towards making a change in the world and in ourselves.
And if this true differentia can be verified, that should settle the
question 22 . And again, apart from direct observation, we can
argue indirectly. Assertion and denial, together with the dif
ference of truth and falsehood, are real phenomena, and there
is something in them which falls outside the influence of ideas
on the will. It is comic if the judgment, It will rain to-morrow,
is the same as buying an umbrella to-day ; or, Put on your thick
boots, is a truer form of, It rained hard yesterday. And when
a child sees a berry and, as we say, judges, It made me sick
before, it seems strange that the act of affirmation should con
sist in practical abstention to-day and should be nothing else.
(d) And not only are the genuine characteristics absent
from a mere practical attitude, but we find present there a qual
ity which is absent from real judgment. The truth of a sug
gestion is not a matter of degree, and the act which attributes
an idea to reality either refers it, or does not refer it. It can
hardly do either a little more or less and to a certain degree
(cf. Chap. VII.). In strictness of speech all half-truths are no
truths, and, " It is more or less true," really means, " It is true
with a qualification," or " More or less of it is true, though as a
whole it is not true." But the practical influence of ideas must
have degree, and so possess a quality which judgment has not.
For these reasons, each of which can stand almost alone,
it seems clear that the doctrine before us has failed. And
* I may refer on this point to my Ethical Studies, Essay VII.
20 THE PRINCIPLES OF LOGIC BOOK I
one cause of the error seems to lie in the neglect of some
important distinctions we may proceed to notice. Judgment
is primarily logical, and as such has no degrees; the relation
of the ideal content to reality must be there or not there.
Belief, on the other hand, is primarily psychological, and,
whether theoretic or practical, exists in a degree, (a) Intel
lectual belief or conviction is the general state which corre
sponds to the particular acts of judgment. To believe that A
is B may mean that, whenever the idea A B is suggested, I
go on to affirm it ; or, further, that the idea fills much space in
my mind, is a persistent habit and ruling principle, which
dominates my thoughts and fills my imagination, so that the
assertion A B is frequently made and has wide intellectual
ramifications and connections. I should believe A B less, if
it more seldom arose, by itself or by implication, and had in
ferior influence. I should believe less still if, when A B was
suggested, I sometimes doubted it; and even less, if I affirmed
it more seldom, and then with hesitation, against doubts, and
with inability to maintain the attitude. On the other hand I
should not believe at all, if I only were more or less convinced,
perceiving more or less reason on both sides, inclined in one
direction, but unable to cross the line and to affirm, (b) But
in practical belief, beside these degrees of intellectual convic
tion, there is another element of more and less. Not only is
the truth of the intellectual content more or less present, but
in addition it can influence my will more or less. A desire
stronger or more persistent, or more dominant generally, may
answer to it on the one side, or on the other a weaker and
more fleeting impulse. Beside existing more or less, it can
move more or less. It is, I think, not easy to keep clear of con
fusion unless these ambiguities are noticed and avoided. But
the main logical mistake which Professor Bain has committed
is to argue from the (false) premise, " Belief must induce ac
tion," to the inconsequent result " Belief is that inducement." *
* In the third edition of his Emotions (1875) Prof. Bain apparently
reconsiders the question, but I can neither tell if he abandons his
theory, nor what it is that, if so, he puts in its place. As I am entirely
unable to understand this last theory, my remarks must be taken to
apply to the earlier one. Since this volume was written I have made
acquaintance with Mr. Sully s criticism on Prof. Bain s doctrine (Sensa-
CHAP. I THE GENERAL NATURE OF JUDGMENT 21
1 6. (ii) Leaving now the first group of erroneous views
we may proceed to consider another collection. These may
be classed as labouring under a common defect, the false
notion that in judgment we have a pair of ideas. We were
engaged with this fallacy in n, and it will meet us again in
the following chapter, so that here some brief remarks may
suffice. In their ordinary acceptation the traditional subject,
predicate, and copula are mere superstitions 24 . The ideal
matter which is affirmed in the judgment, no doubt possesses
internal relations, and in most cases (not all) the matter may
be arranged as subject and attribute 25 . But this content, we
have seen, is the same both in the assertion and out of it 26 . If
you ask instead of judging, what is asked is precisely the
same as what is judged. So that it is impossible that this
internal relation can itself be the judgment ; it can at best be
no more than a condition of judging. We may say then, if
the copula is a connection which couples a pair of ideas, it
falls outside judgment; and, if on the other hand it is the sign
of judgment, it does not couple. Or, if it both joined and
judged, then judgment at any rate would not be mere joining.
I will dwell here no more on the general error. We shall see
its effects in some mistaken views we may proceed to notice.
(a) Judgment is not inclusion in, or exclusion from, a
class. The doctrine that in saying, " A is equal to B," or " B
is to the right of C," or " To-day precedes Monday," I have in
my mind a class, either a collection or a description, of " things
equal to B," or " to the right of C," or " preceding Monday,"
is quite opposed to fact. It is as absurd as the assertion that,
in " It is our son John," or " It is my best coat," or " 9 = 7 +
2," I think of a class of " our sons John," or " my best coats,"
or " that which is equal to 7 + 2." If the view stood apart
from implied preconceptions, and by itself as an interpreta
tion of fact, it would scarcely, I think, be so much as discussed.
And, as we shall be forced to recur to it hereafter (Chap. VI.),
we may so leave it here.
lion and Intuition, 2nd ed. 1880). But he, I find, treats Prof.
Bain s third edition (1875), in which an earlier edition of his own
criticism is treated with the greatest respect, as if it either had no
existence, or at all events was somehow irrelevant to the issue. For
myself I must say that for the reason given above I confine myself
to the earlier theory. 23
2321. i c
22 THE PRINCIPLES OF LOGIC BOOK I
(b) Judgment is not inclusion in, or exclusion from, the
subject. By the subject I mean here not the ultimate subject,
to which the whole ideal content is referred, but the subject
which lies within that content, in other words the grammatical
subject. In " A is simultaneous with B," " C is to east of
D," "E is equal to F," it is unnatural to consider A, C,
and E as sole subjects, and the rest as attributive. It is
equally natural to reverse the position, and perhaps more
natural still to do neither, but to say instead, " A and B are
synchronous," " C and D lie east and west," " E and F are
equal." The ideal complex, asserted or denied, no doubt in
most cases will fall into the arrangement of a subject with
adjectival qualities, but in certain instances, and those not a
few, the content takes the form of two or more subjects
with adjectival relations existing between them. I admit you
may torture the matter from the second form into the first, but,
if torture is admitted, the enquiry will become a mere struggle
between torturers. It requires no great skill to exhibit every
subject together with its attributes as the relation between
independent qualities (subjects), or again even to make that
relation the subject, and to predicate all the remainder as an
attribute. Thus, in " A is simultaneous with B," it is as easy
to call " exists in the case of AB " an attribute of simultaneity,
as it is to call " simultaneous with B " an attribute of A. We
may finally observe that existential judgments do not lend
themselves easily to the mistake we are considering. And
such negative judgments as " Nothing is here," will be found
hard to persuade. But on both these points I must refer to
the sequel (Chaps. II. and III.J.
(c) Judgment is not the assertion that subject and predi
cate are identical or equal. This erroneous doctrine is the
natural result of former errors. You first assume that in
judgment we have a relation between two ideas, and then go
on to assume that these ideas must be taken in extension.
But both assumptions are vicious; and, if we consider the
result, asking not if it is useful but whether it is true, we can
hardly, I think, remain long m hesitation. That in " You are
standing before me," or " A is north of C," or " B follows D,"
what we really mean is a relation either of equality or
identity is simply incredible; and torture of the witness goes
CHAP. I THE GENERAL NATURE OF JUDGMENT 23
to such lengths that the general public is not trusted to
behold it.*
However useful within limits the equation of the terms
may be found, if you treat it as a working hypothesis (vid.
Book II. Part II. Chap. IV.), yet as a truth it will not bear
any serious examination. Let us look at it more closely.
(i) If what is asserted be equality, then that of course is
identity in quantity, and is nothing else whatever 27 . And I
must venture to complain of the reckless employment of this
term. To use the sign for qualitative sameness, or for
individual identity (I do not ask here if these are different), is
surely barbarous. No harm perhaps may come, but there
should be some limit to the abuse and confusion we allow
ourselves in practice. Let us then first take equality in its
proper sense, to stand for an identity in respect of quantity.
But, if so, if the subject and predicate are equated, if " Negroes
are men," when written " All negroes = some men," is on a
level with 2= 12 10 if what is said and signified is that
between the terms, if you compare them numerically, there is
no difference whatever, we can at once pass on. It is certain
that some judgments, at least, can not express this relation of
quantity, and it is certain again that, of those which can, it is
only a very small class which do. Illustration is hardly
wanted. " Hope is dead " would mean that, " In hope and a
fraction of dead things there is exactly the same sum of
units." And, in asserting that " Judgment is not an equation,"
I should express my belief that to divide both by 2 would not
give the same quantity.
But the sign = does not seem to mean equality. It does
not mean that the units of the subject and predicate are iden
tical in quantity. It would appear to mean that they are the
same altogether. The identity it asserts is not quantitative, but
seems absolute. In " All Negroes = some men," the " = " rep
resents exclusion of difference both quantitative and qualitative.
(ii) The identity is (a) not likeness ; it is not a relation con
sisting in a partial qualitative identity, definite or indefinite.
" Iron some metal " can hardly mean " Some metal is similar
to iron." Not only do the facts exclude this interpretation, but
the theory would not work with it. If " similars " and " like-
* Vid. Jevons, Principles of Science, Chap. i. 12.
24 THE PRINCIPLES OF LOGIC BOOK I
ness " are phrases that occur, this is a proof that here, as in
the case of =, the theory does not mean what it says, or quite
know what it is doing. That when A is like B you may write
one for the other, is of course quite untrue (cf. Book II.).
(b) The identity again is not definitely partial, consisting
in sameness in some particular point or points of quality.
For, on this interpretation, you could make no advance, until
the point of sameness had been specified. And even then
the equational theory would not work.
(c) Unless we suppose that both sides differ only in
name, and that this difference of names is the import of the
judgment a view we shall glance at in a future chapter
(Chap. VI.) we must take the sign = to mean total sameness
to the exclusion of all difference. But, if so, the theory
must reform itself at once, if it desires to be consistent. It
will not be true that " Negroes = some men," for certainly
" some men " are not " = negroes." Nor again will it be true
that negroes are equal to a certain stated fraction of mankind.
That stated fraction is an universal adjective which might
be applicable to other men as well as to negroes. If "is " or
" = " stands for " is the same as," then it is as false to say
" A is H B," as it was before to say " A is some B." " Some
B" covers not only the B which is A; it may hold just as
much of the other B, which we take as not-A. And it is so
with " ^ B " ; that applies just as much to the % which are
not-A, as it does to the third which is identical with A. The
quantification of the predicate is a half-hearted doctrine,
which runs against facts, if " = " does mean equal, is ridicu
lous if " = " comes to no more than plain " is" and is down
right false if " = " stands for " is the same as."
To be consistent we must not merely quantify the predi
cate, we must actually specify it. The men that are negroes
are not any and every set of men, who have a certain number.
They are those men who are negroes, and this is the predicate.
Negroes = negro-men, and iron = iron-metal. The predicate
now really and indeed seems the subject, and can be substi
tuted for it. The idea is a bold one, and its results have
been considerable; but if we look not at working power but
at truth, the idea is not bold enough, and wants courage
to remove the last contradiction.
CHAP. I THE GENERAL NATURE OF JUDGMENT 25
That A should be truly the same as AB, and AB entirely
identical with A, is surely a somewhat startling result. If
A = A, can it also be true that to add B on one side leaves the
equation where it was? If B does not mean o, one would be
inclined to think it must make some difference. But, if it
does make a difference, we can no longer believe that A = AB,
and AB = A. If "iron-metal" is the same as "iron," how
misleading it is to set down the two sides as different terms.
If there really is a difference between the two, then your
statement is false when by your " = " you deny it. But if
there is no difference, you are wrong in affirming it, and in
opposing " iron " to " iron-metal."
There is only one issue. If A is AB, then the A that is
AB is not A but AB. Both sides of the assertion are just
the same, and must be so stated. Negro-men are negro-men,
and iron-metal is iron-metal.* For consider the dilemma.
B either is or is not an addition to A. If it is not an addition,
its insertion is gratuitous; it means nothing on either side,
may fall upon whichever side we choose, is absurd on both
alike, and should be got rid of then A = A. But if B is an
addition, then A = AB cannot be true. We must add B on
both sides, and AB = AB. In short B must disappear or
have a place on each side.
We have now reached consistency, and the reader may
ask, Is the result still false? I do not like to seem obstinate,
and I prefer to reply, Do you think it is true? 1 will accept
your answer. If you say that identical propositions are all
false, I shall not contradict you (cf. Chap. V. i), for I also
believe that a judgment which asserts no difference is nothing.
But if you pronounce on the side of truth, I should like to
ask a question. For an assertion to be true must it not
assert something, and what is it that you take to be asserted
above? That where there is no difference, there is no differ
ence, that AB will be AB as long as it is AB? You can
hardly mean that. Is the existence of AB what is secretly
asserted ? But, if so, we should say openly " AB exists," and
our reduplication of AB is surely senseless. We know that
it exists, not because we double it, but, I suppose, because we
know of its existence.
* Cf. Lotze, Logik, 80-2.
2,6 THE PRINCIPLES OF LOGIC BOOK I
But what then do we assert by AB = AB ? It seems
we must own that we do not assert anything. The judg
ment has been gutted and finally vanishes. We have followed
our premises steadily to the end, and in the end they have
left us with simply nothing. In removing the difference of
subject and predicate we have removed the whole judgment.*
17. We have seen the main mistakes of the foregoing
doctrines. It is a more pleasing task to consider the main
truth which each one of them has seized, (i) The views we
began to criticize in 13, have avoided the error of subject
predicate and copula. They have seen that in judgment the
number of ideas is not the main question, and that the
essence of the matter does not lie in the ideas, but in some
thing beyond them. Nor, to be more particular, is the impli
cation of will in all judgment a complete mistake. It is
true that, in an early stage of development, the intelligence is
so practical that it hardly can be said to operate independ
ently. It is true again that, in the evolution of self-con
sciousness, the opposition of idea and reality depends, to a
degree I will not here discuss, upon volitional experience.
And in these points there is truth in the theory, which, how
ever much he may abandon it, we shall place to the credit
of Professor Bain. And the view that in judgment we have
an association of idea with sensation, and a coalescence of
both elements, is far from being wholly destitute of truth.
For (as we shall see in the following Chapter) the subject
in all judgment is ultimately the real which appears in per
ception; and again it holds good that the lowest stage, in
the development of judgment and inference alike, is the red
integration of ideal elements with sensuous presentation, in
* It is not worth while to criticize in detail a doctrine we can show
is fallacious in principle. Cf. Chap. V. But among minor objections
to the quantification of the predicate is its claim to silence you, and
prevent you from saying what indubitably you know. It tells you
you must not say "A is B," unless you also certify how much of B is
A. But, even supposing that " so much of B " is the truth that you
would affirm if you could, in numerous cases you can not affirm it.
You know that A possesses a quality B, and, as to how the B, that is A,
stands in extent to the B which is not A, you have no information.
You must either then decline to quantify, or must abstain from speak
ing the truth you know. But it is not worth while to criticize in detail.
CHAP. I THE GENERAL NATURE OF JUDGMENT 27
such a manner that the two are not distinguished, but run
into one whole.
(ii) And from the second class of errors we may also
collect important results. In the first place it is true that the
content asserted is always complex. It can never be quite
simple, but must always involve relations of elements or
distinguishable aspects. And hence, after all, in judgment
there must be a plurality of ideas. And, in particular, (a)
though it is false that the predicate is a class in which the
subject is inserted, and a fundamental error to take the
universal in the form of a collection, yet it is entirely true
that the predicate must be always an universal. For every
idea, without exception, is universal. And again (&) though
assertion is not attribution to a subject in the judgment,
though it is false that the grammatical subject is the reality of
which the predicate is held true, yet in every judgment there
must be a subject. The ideal content, the adjective divorced,
is made real once again by union with a substantive. And
(c) the doctrine of equation, or identity of the terms, has itself
grasped a truth, a truth turned upside down and not brought
to the light, but for all that a deep fundamental principle.
Turned upside down, and made false, it runs thus. The
object of judgment is, despite their difference in meaning, to
assert the identity of subject and predicate when taken in
extension. But turned the right way up it runs thus. The
object of judgment is, under and within the identity of a
subject, to assert the synthesis of different attributes. When
ever we write " = " there must be a difference, or we should
be unable to distinguish the terms we deal with (cf. Chap. V.).
And when a judgment is turned into an equation, it is just
this difference that we mean to state. In " S = P " we do
not mean to say that S and P are identical. We mean to say
that they are different, that the diverse attributes S and P are
united in one subject; that S P is a fact, or that the
subject S is not bare S, but also S P. And the reason why
the theory of equation works, and is not mere nonsense, is
that in fact it is an indirect way of stating difference. " The
subject is the same " implies, and may be meant to convey,
the truth that the attributes differ. We must refer to the
sequel for further explanation, but at present our concern is
28 THE PRINCIPLES OF LOGIC BOOK I
briefly to point out that an identity must underlie every judg
ment.
But how is this possible ? A is " prior to B," or " to the
left of C," or "equal to D." The judgment asserts the
equality, or sequence, or position of two subjects, and it surely
does not say that both are the same. We must try to
explain. We saw that all judgment is the attribution of an
ideal content to reality, and so this reality is the subject of
which the content is predicated. Thus in " A precedes B,"
this whole relation A B is the predicate, and, in saying this
is true, we treat it as an adjective of the real world. It is
a quality of something beyond mere A B. But, if this is so,
the reality to which the adjective A B is referred is the
subject of A B, and is the identity which underlies this
synthesis of differences.
It is identical, not because it is simply the same, but because
it is the same amid diversity. In the judgment, beside the
mere distinction of the terms, we have an opposition in time
of A to B. And the subject of which A B is asserted,
being subject to these differences, is thus different in itself,
while remaining the same. In this sense every judgment
affirms either the identity which persists under difference, or
the diversity which is true of one single subject. It would
be the business of metaphysics to pursue this discussion into
further subtleties. We should there have to ask if, in the
end, every possible relation does not involve a something in
which it exists, as well as somethings between which it exists,
and it might be difficult to reconcile the claims of these prepo
sitions. But we have already reached the limit of our
enquiries. The real subject which is implied in judgment, 28
will meet us again in the following Chapter ; and that, we hope,
may make clearer some points which at present remain obscure.
III. 1 8. We have given some preliminary account of
judgment, and have tried to dispose of some erroneous views.
We pass now to our third task, and must make some remarks
on the development of the function. As we have defined it
above, judgment does not show itself at all the stages of
psychical evolution. It is a comparatively late acquisition of
the mind, and marks a period in its upward growth. We
CHAP. I THE GENERAL NATURE OF JUDGMENT 2Q
should probably be wrong if we took it as a boundary which
divides the human from the animal intelligence; and in any
case we should be ill-advised to descend here into the arena
of theological and anti-theological prejudice (vid. Book III.
Part I. Chap. VII.). It is better to treat the mind as a single
phenomenon, progressing through stages, and to avoid all
discussion as to whether the lines, by which we mark out this
progress, fall across or between the divisions of actual classes
of animals. Thus with judgment we are sure that, at a cer
tain stage, it does not exist, and that at a later stage it is
found in operation; and, without asking where the transition
takes place, we may content ourselves with pointing out the
contrast of these stages. The digression, if it be such, will
throw out into relief the account we have already given of
judgment. For judgment is impossible where truth and false
hood, with their difference, are not known ; and this difference
cannot be known where ideas are not recognized and where
nothing exists for the mind but fact. 29
19. I do not mean that the lower forms, or that any
form, of soul-life is confined to the apprehension of simple
sensations. If the soul is ever the passive recipient of a given
product, to which it does not contribute and which it does not
idealize, yet in all actual mind a further step is made, and
we always possess more than what is given through sense. 30
The impression, so to speak, is supplemented and modified
by an ideal construction, which represents the results of past
experience. And thus, in a sense, the lowest animals both
judge and reason, and, unless they did so, they must cease
to adjust their actions to the environment. But, in the strict
sense, they can neither reason nor judge; for they do not
distinguish between ideas and perceived reality.
That the thing as it is, and as it appears in perception, are
not the same thing, is, we all are aware, a very late after
thought. But it is equally an afterthought, though not equally
late, that there is any kind of difference between ideas and
impressions. For a more primitive mind a thing is or it
is not, is a fact or is nothing. That a fact should be, and
should yet be an appearance, should be true of, and belong
to, something not itself; or again should be illusion, should
exist and yet be false, because its content is an adjective
3O THE PRINCIPLES OF LOGIC BOOK I
neither of itself nor of any other substantive these distinc
tions are impossible for an early intelligence. A nonentity is
not anything it can apprehend, and to it an error is never an
illusion. And hence for this mind ideas never could be sym
bols. They are facts because they are.
20. The presentations of the moment, the given sensa
tions, are received into a world of past experience, and this
past experience now appears in the form of ideal suggestion.
In the lowest stages of mind there is as clear a difference
between the datum that is given and the construction that is
made, as there can be in the highest. But it is one thing to
have a difference in the mind and another to perceive it; and
for an early intelligence this contrast between sensation and
idea, is quite non-existent. A presentation AB, by a feeling d,
produces an action de, or, by an ideal transition b-d, is trans
formed into ABD ; or may become AC, by the action of a-g,
if g banishes B, and c is supplied. But, in all these cases, and
in any other possible case, the process remains entirely latent.
The product is received as a mere given fact, on a level with
any other fact of sense.
If the object, as first perceived, could be compared with
the object as finally constructed, there might be room for a
doubt if the fact has become, or has been made by the mind.
And still more if the ideas which perception excludes were
ever attended to; if rejected suggestion, conflicting supple
ment, wrong interpretation, and disappointed action, were held
before the mind, then a reflection might take place, which
would antedate the slow result of development ; and the sense
of illusion would awaken the contrast of idea and reality, truth
and falsehood. But all this is impossible. For the leading
feature of the early mind is its entire and absolute practicality. 31
The fact occupies the soul no longer and no further
than it tends to produce immediate action. The past and the
future are not known except as modifications of the present.
There is no practical interest in anything but the given, and
what does not interest is not anything at all. Hence nothing is
retained in its original character. The object, in its relation to
present desire, changes ceaselessly in conformity with past
adventures of failure or success. It contracts or extends itself,
as the case may be, but it still remains the mere given object.
CHAP. I THE GENERAL NATURE OF JUDGMENT 31
And while the ideas it assimilates become part of presentation,
the ideas it excludes are simply nothing at all.
At a late stage of mind, among intelligent savages, the
doctrine of a dream-world brings home to us the fact, that a
mere idea, which exists and is unreal, is a thought not easy to
lay hold of thoroughly. And, if we descend in the scale no
further than to dogs, we are struck by the absence of theo
retical curiosity. Let them see an appearance to be not what
is seemed, and it instantly becomes a mere nonentity. An
idea, we may say, is the shadow of an object; and that to a
savage is another kind of object, but to a dog it is the thing
or just nothing at all. The dog has not entered on that
process of reflection which perhaps has not led to any very
sure result. When his heart, like ours, is baffled and
oppressed, and gives matter to his brain it has no strength to
cope with, he can neither send his hopes into another world
than this, nor repeat like a charm, and dream that he believes,
that appearances may be nothing to a soul which feels them.
I do not know the formula which would prove to his mind a
satisfactory solution of his practical troubles; but his system
of logic, if he had one, would be simple; for it would begin,
I am sure, and would end with this axiom, " What is smells,
and what does not smell is nothing."
21. It would be difficult to detail the steps of the process
by which ideas, as such, become objects of knowledge, and
with truth and falsehood judgment comes in. And, apart from
this difficulty, there is a question of fact which would con
stantly arise. Given a certain stage of development, does
judgment already exist there or not? It might perhaps be
right to connect the distinctions of truth and falsehood in
general with the acquisition of language, but it is hard to say
where language begins. And, in the stage before language,
there are mental phenomena which certainly suggest the
effective distinction of sensation and idea.
The provision made beforehand for changes to come can
not always be taken as valid evidence. It seems clear that,
in many cases, we should be wrong in supposing any know
ledge of the future, as opposed to the present. It is certain
at least that a presentation, accompanied by or transformed
by feelings, is as effective practically as the clearest idea. But
32 THE PRINCIPLES OF LOGIC BOOK I
in certain animals there are much stronger indications. When
artful contrivances, suitable to unseen events, are used in the
pursuit of prey, 32 we are led to conclude that the difference of
the situation, as it actually is and as it is anticipated, must
come before the mind. And, where desire is unsatisfied, it is
not always mere feeling, as against the object, which pervades
the soul. The image of the desired, as against present per
ception, floats or is held before the attention, and the feeling
of pain, we may suppose, must sharpen the contrast until at
length the difference is seen. And we can mention here what
perhaps may be an outward symptom of the change. No
one can have been much with domestic animals, and failed
to observe their constant and increasing use of the imperative.
They seem at least to know what they desire, to expect assist
ance, and to be surprised at non-compliance. And though
mere urgency of feeling, in the absence of ideas, might account
for their tone, this interpretation would at times somewhat
strain the phenomena.
But, if this is so, then judgment must come before lan
guage, and certainly cannot be distinctively human. And, just
as after language has been developed, we do often dispense
with it; just as the lowest, and perhaps the highest of our
thinking, goes on without any words in the mind, so, we may
suppose, before speech was developed, the differentia of judg
ment already existed.
We are not concerned in the controversy to which this
might give rise. If we only know what we mean by judg
ment, it is little to our purpose where first it appears, and
what animal first reaches it. The question is not at all easy
to settle, and in passing I will merely suggest a reflection. It
is not enough to show that in the mind of an animal an image
exists together with a presentation of sense, and that this
image, partly the same as the presented, is in collision with it,
and again leads to action in relation to the presented. All
this may exist, and yet the differentia still be absent; the
image may not be seen to be mere appearance, to be either
not real at all, or less real than the sensation. For, if the
image is taken in relation to the perception, they may both be
apprehended as one continuous changing fact ; the prey may
be seen as pursued and captured, and the actual object may
CHAP. I THE GENERAL NATURE OF JUDGMENT 33
appear to pass into the desired. And, where failure makes
this impossible, what may after all be wanting is the intel
lectual identification of the image with the object. Apart
from this logical process, we have a mere collision in the mind
of two realities, whose struggle is felt. We have contest, and
perhaps a following ejection; but we have no subjection, no
degradation of one fact to the level of an appearance, that
exists but in our heads. And in this case judgment would
not have taken place.
22. It might be interesting elsewhere to discuss at length
these puzzles in psychology, but it will repay us better to pass
to what is more certain. It is, in the first place, the retention
of the false idea which tends to provoke comparison with
reality, and which leads the way to the knowledge of appear
ance and truth and falsehood. And, in the second place, it is
language which, if it does not originate, at least ensures and
sharpens the contrast. When gregarious animals utter their
ideas, the word is in a manner more permanent than the
thought, and maintains itself against the fact it tries to ex
press. And the spoken thoughts of the different individuals
are sometimes in collision. They are not the same with one
another, and therefore not the same with the single fact. And
speech in its perversion to lies and deceit makes the dullest
comprehend that words and ideas can be and be real, and can
yet be illusion and wholly unreal in relation to facts. At this
point it is seen that the word and the thought are not like
other things. They not only exist but also mean something,
and it is their meaning alone which is false or true. They are
seen to be symbols, and this insight it is which in the strict
sense constitutes judgment.
For in the early stage, to repeat it once more, the image
is not a symbol or idea. It is itself a fact, or else the facts
eject it. The real, as it appears to us in perception, connects
the ideal suggestion with itself, or simply expels it from the
world of reality. But judgment is the act which, while it
recognizes the idea as appearance, nevertheless goes on to
predicate it. It either attributes the idea to reality, and so
affirms that it is true, or pronounces it to be merely a bare
idea, and that the facts exclude the meaning it suggests. The
ideal content which is also fact, and the ideal content which is
34 THE PRINCIPLES OF LOGIC BOOK I
nothing beyond itself, are truth and falsehood as they appear
in judgment.
23. Our object in the foregoing has been, not to
chronicle a psychological transition, but to mark out distinc
tive stages and functions. We must endeavour, in conclusion,
to obviate a very fatal mistake. The gulf between the stage
of mind that judges and the mind that has not become aware
of truth, may seem hard to bridge, and the account we have
given may seem to rend facts apart. We may be thought in
our extremity, when with natural conditions no progress is
possible, to have forced upon the stage a heaven-sent faculty.
On one side of your line, we may be told, you possess explicit
symbols all of which are universal, and on the other side you
have a mind which consists of mere individual impressions
and images, grouped by the laws of a mechanical attraction.
The distinction you have made amounts to a divorce. The
higher stage can not exist as you describe it, or can not at
least be developed from the lower.
In the sequel I shall criticize the whole doctrine of the
" Association of ideas," but at present I will say thus much by
anticipation. 33 I agree that, if the lower stages of the mind
were really what they are in most English psychologies, it
never would in any way be possible to pass to the stage where
ideas are used in judgment. And this consequence I desire
to accentuate and to emphasize. But the fashionable doctrine
of "association," in which particular images are recalled by
and unite with particular images, is, I think, not true of any
stage of mind (vid. Book II. Part II. Chap. I). It does not
exist outside our psychology. From the very first beginnings
of soul-life universals are used. It is because the results of
experience are fixed in an ideal and universal form, that
animals are able, I do not say to progress, but to maintain
themselves in bare existence.
24. In England, I am afraid, the faithful tradition of
accumulated prejudice, in which are set the truths of the
" Philosophy of Experience," well-nigh makes idle an appeal
to the fact. But I will try to state the fact, however idly. It
is not true that particular images are ever associated. It is
not true that among lower animals universal ideas are never
used. What is never used is a particular idea, and, as for
CHAP. I THE GENERAL NATURE OF JUDGMENT 35
association, nothing ever is associated without in the process
being shorn of particularity. I shall hereafter have to enlarge
on the latter statement, and at present will deal with the false
assertion, that merely individual ideas are the early furniture
of the primitive mind.
In the first place it seems patent that the lower animals
have not any idea about the individual. To know a thing as
the one thing in the world, and as different from all others, is
not a simple achievement. If we reflect on the distinctions
it implies, we must see that it comes late to the mind. And,
on turning to facts, we find that animals of superior intelli
gence are clearly without it, or give us at least no reason
at all to think that they possess it. The indefinite universal,
the vague felt type, which results from past perceptions and
modifies present ones, is palpably the process of their intel
lectual experience. And when young children call all men
father, it is the merest distortion of fact to suppose that they
perceive their father as individual, and then, perceiving other
individuals, confuse a distinction they previously have made.
But this is hardly the real point at issue. To know the
individual as such will be admitted to be a late achievement.
It can hardly be maintained that a rude intelligence, when it
holds a type and rejects what disagrees with it, can be aware
of that type as an unique individual. The question is really as
to the use made of images in early knowledge. Are they used
as universals, or used as particulars?
25. It is agreed on both sides that, as psychical exist
ences, ideas are particular like all other phenomena. The
controversy is confined to the use we make of them. I should
maintain that, so far as they remain particular, they are simple
facts, and not ideas at all ; and that, where they are employed
to extend or to modify experience, they are never used in
their particular form. When A-B is presented in perception,
we are told that the result of a past perception B-C appears
as particular images b-c, and that these images, called up,
unite with the presentation. But nothing could be more false.
It is not true that all the marks, and relations, and differences,
which constitute the particularity of b and c, appear in the
resultant A-B-C, or were in any way used in order to produce
it. The image c, besides its content as c, had the indefinite
36 THE PRINCIPLES OF LOGIC BOOK I
detail of all psychical phenomena; but it was not this but
the universal c which was used in A-B-C, and it is the per
ception A-B that re-particularizes c in accordance with itself.
And, if this is so, we must say that what really operates is a
connection between universal ideas. We have already, in an
unconscious form, what, when made explicit, is the meaning
of symbols.
I must trust to the sequel for elucidation (vid. Book II. II.
Chap. I.), but the subject is so important that I will venture to
insert some illustrations. When to-day I reach the place where
yesterday my dog has either chased a cat or fought with an
antagonist, the perception as we say " calls up " the ideas, and
he runs eagerly forward. His experience, we will suppose,
was of a white cat or a black retriever with a large brass
collar. To-day images are " called up," not so definite perhaps,
but still certainly with some detail, and we will suppose that
the detail reproduces the experience. To-day it is a black
cat that is found in the place, but with an ordinary dog that
will make no difference. The whiteness of the image is quite
irrelevant. 3 * Or again, if to-day another dog be perceived, if
only that dog be not glaringly different, an ordinary dog will
certainly attack him, and the less intelligent he is the more
catholic is his action. For it is not the whole image but a
portion of the content which operates in his mind. He may
turn from a small dog or a white dog or a smooth-coated dog,
but size, blackness, and roughness, are the typical ideas which
will certainly operate. It may be said, no doubt, that the
ideas are particular, that they differ from the perception, and
that it is the fault of the animal which fails to distinguish
them. But why, I reply, does it fail to distinguish? Is a
creature, intelligent as is a terrier, unable to see the difference
between a white and black cat, or a Newfoundland and a
sheep dog? "Yes," I shall be told, "he can if he attends to
them, but here, although they both are present,* he does not
* This is a false assumption as will be shown hereafter. In the first
place it is not true that, when the mind goes from A B to C, it has to
pass through a particular image b. In the next place, if the particu
lar b be present, we have no reason to suppose that it will have the
qualities of the original perception B. If a white cat has been seen
to-day, we saw that next day, if its image is white, the whiteness
of that image need not be used; and again if its whiteness was not an
CHAP. I THE GENERAL NATURE OF JUDGMENT 37
attend to them." But if so, I must rejoin, if the differences
are not used, but remain inoperative, is not this a clear proof
that what operates, and what is used, is a portion of the con
tent, which is permanent amid differences, and which later
becomes the universal meaning?
Again, if an animal has been burnt one day at the kitchen
fire, the next day it may shrink from a lighted match. But
how different are the two. How much more unlike than like.
Will you say then that the match can not operate unless it
first summons up, and then is confused with the image of a
kitchen fire; or will you not rather say that a connection
between elements, which are none of them particular, is pro
duced in the mind by the first experience? But, if so, from
the outset universals are used, and the difference between the
fact and the idea, the existence and the meaning, is uncon
sciously active in the undeveloped intelligence.
26. We must anticipate no further. In another place
we shall show the fictitious nature of the " Laws of Asso
ciation," as they have been handed down by our prevalent
tradition. Our object here has been, in passing, to show that
the symbolic use of ideas in judgment, although no early
process of the mind, is a natural result of mental develop
ment. From the very first beginnings of intelligence it is
the type that operates and not the image. The instance as
such is never, and can never be, retained in the soul. The
connection of certain elements in its content is all it leaves
behind. You may call it, if you please, mere impotence of our
imagination, or you may call it that idealizing function of the
mind which is the essence of intelligence, still the fact remains
that never at any stage can any fact be retained without some
mutilation, some removal of that detail which makes it par
ticular. The lower we descend in the growth of our own
functions, or in the scale of animate nature, the more typical,
the less individual, the less distinct, the more vaguely uni
versal and widely symbolic is the deposit of experience. It
is not symbolic in the sense that the meaning is at first per
ceived to be other than the fact. It is not universal in the
object of interest, there is no reason whatever why the image should
be white, and not of some other hue. The generalized result left by
past experience is always mutilated.
2321.1 D
38 THE PRINCIPLES OF LOGIC BOOK I
sense that analysis has distinguished the relevant from the
irrelevant detail, and found elements more simple, and syn
theses wider than are suggested by mere sense. But in the
sense of not using the particular as particular, and of taking
the meaning while leaving the existence, in the sense of in
variably transcending the given, and of holding true always
and valid everywhere what has ever and anywhere once been
experienced, the earliest and the latest intelligence are the
same from one end to the other of the scale of life.
ADDITIONAL NOTES
1 On the question of Order in Logic cf . T. E. I.
2 "We can not judge till we use them as ideas." This requires
correction. See Appearance, Index, and Essays, pp. 32-3 and Index.
And cf. the Index of this book s. v. Idea.
3 " In England." This was published in 1883.
**" Symbols." This is wrong or at least inaccurate. A " sign " or
"symbol" implies the recognition of its individual existence, and this
recognition is not implied in an "idea." See Essays, p. 29, and the
Index, s. v. Idea.
s "That," "what," "means" and "stands for" (cf. Chap. VI. 2).
All of these distinctions imply judgment, though that may not be
explicit. And wherever you have any such distinction you have
transcendence and an idea though not always an explicit idea (see
Note 2). Each of these distinctions, again, if you could perfect it,
would imply and pass into all the rest.
6 " Original content." This distinction (cf . the words " content
(original or acquired)" at the end of 4) refers to the difference
pointed out in 5. The point is, however, irrelevant, and 5 should
have been omitted.
7 This footnote is wrong throughout, for there are no ideas not so
" referred." See Essays, Chap. Ill and Index. The words in the text,
"cut off, etc." are also incorrect. There are no ideas before or apart
from their use, and that at first is unconscious. See Note 2.
8 Here again we must remember that we are not to say (i) that an
idea is there apart from its being used, or (ii) that, in using it, we
must be aware of it as a mental thing. Further (iii) I was wrong to
speak, here and elsewhere, as if with every idea you have what may
be called an " image." How far and in what sense the psychical exist
ence is always capable of being verified in observation is a difficult
point to which I have perhaps not sufficiently attended. Still every
idea, I must assume, has an aspect of psychical event, and so is
qualified as a particular existence. In the footnote to p. 7 " sensuous "
should have been "psychical." The amount of imagery required is
CHAP. I THE GENERAL NATURE OF JUDGMENT 39
much exaggerated in p. 9. Cf. on the other side Chap. II, 36,
37.
9 What I meant here was probably to remind the reader that the
" categorical " may turn out to be really " conditional."
10 " Judgment (proper) is etc." (i) In this definition the word
" act " raises a question, important in psychology and in metaphysics
(see Appearance and Essays, the Indexes), but (so far as I see) not
necessary in logic, (ii) "Recognized as such" is wrong (see Note 2).
What I should recognize on reflection I may in fact ignore. Cf. 10
and 13. (iii) "Beyond the act," and (below) "independent of it," are
right for logic. For metaphysics, on the other hand, the problem raised
here can not be ignored (see Essays, Index, s. v. Act}. But as to
recognition of the act (to return to that) the text is wrong. A per
ceived object changed by an idea, and the change ignored except as
the development of the object though not of the mere perceived
object here is the beginning of judgment in the proper sense. But,
again, to take judgment as present wherever we have an object at all
before the mind is a view which is tenable.
11 " Wandering adjective" should be "loosened adjective." And
(three lines lower down) "relation" should be "union."
12 " Partial ignorance absolute." The meaning and the great im
portance of these words have, I hope, been to some extent brought
out in this book and in my later writings.
13 (i) "Are the angles &c.?". The false doctrine of "floating
ideas " is involved here. See Essays, Index, (ii) " The same ideal
content." Not so. See ibid. And cf. Bosanquet, K 6- R, pp. 114-15,
119, and Logic, I. 33.
14 This statement (cf. pp. 49, 56) requires correction. It is true
that the ideal meaning is one; but it is also true that the subject
is a special subject, and that it, in its special sense, must be there
within the meaning (cf. Bosanquet, loc. cit.). The twofold nature
of Reality as the subject of judgment was not sufficiently recognized
by me. See below on p. 13. And cf. pp. 114, 477, and Index.
15 Cf. Mind, N. S. No. 41, pp. 20 foil.
16 " The relation is the same." But see Note 13.
17 "The subject can not belong to the content." This statement
again requires correction. We have not a case here of mere Yes or
mere No. See T. E. II. and Index. And cf. Essays, and again Appear
ance, the Indexes.
18 " And finally, &c." See Note 10.
19 On Bain s theory of Will cf. Mind O. S. No. 49, PP- 27 foil.
The unjust neglect of Bain by Pragmatists, or their inability to learn
from his adventurous errors, has, I think, cost them dear. See Essays,
pp. 70-1. The reader will notice that, already in 1883, I was dealing with
the question, What is practical? See for this the Note on p. 506, and
T. E. No. XII.
20 Cf. here Essays (ibid.).
21 "Not judged to be real." We should here add "in our existing
4Q THE PRINCIPLES OF LOGIC BOOK I
world," as otherwise the statement is not true. See Essays, Chap. Ill,
and specially p. 35, and cf. T. E. XII of this work.
22 On the nature of the feeling of Consent see Essays, p. 377, note,
and Mind, N. S. No. 46, PP- 13 foil.
23 Whether (see Prof. Sully, p. 79, note) Bain really modified his
view, it is needless here to enquire. My own difficulty with Bain
was to get any rational idea as to what he meant by " intellect " and
" knowledge " which apparently can remain itself in the absence of
belief. He (like J. S. Mill) is faced here by a problem, which, on
their inherited premises, is quite insoluble, because radically perverted.
See Essays f pp. 376-7. Bain s view of intellect is again noticed in
pp. 324, 491 of the present work.
24 "Copula." Dr. Bosanquet (K & R, pp. 167 foil.) rightly remarks
here that the copula is essential, so far as it points to the analysis and
synthesis, and the conditioned assertion of reality, which are present
in all judgment.
25 "(Not all)" should be "(though not in all cases except in the
end)" Cf. below, 16, 17. And see Note 28.
26 " The same both in the assertion and out of it." But see Note 13.
2 ? " Equality." The reader may consult here Dr. Bosanquet s re
marks (K & R, pp. 104 foil.) though I do not wholly assent to them.
28 All judgment falls fn the end under the head of subject and
attribute, in the sense that every judgment in the end asserts of a
subject both diversity in unity and identity in difference this subject
being at once the ultimate and also a special reality. For this funda
mental and all-important doctrine see the Index of this work.
29 The reader must not forget here that our definition of judgment
was more or less arbitrary. See Note 10.
30 The reader will notice that, in 19 and 20, much too little is
made of movement and action following direct on sensation. But for
the purpose here in hand this point is perhaps not material.
si " Absolute practicality." But see Bk. III. Pt. I. Chap. VII. For
the character of "the early mind" cf. Essays, pp. 356-7, 376. The
further statement about "the dog" is of course exaggerated.
32 " In the pursuit of prey," and of course also otherwise. With
regard to the Imperative, though I still think that this remark was
certainly worth making, I would emphasize the need of caution here
as to correct interpretation of the facts.
33 On "Association &c." See later, Bk. II. Pt. II. Chap. I. The
remark on " most English psychologies " belongs, of course, to the date
1883.
34 There is some exaggeration here as to the amount of particular
detail, but what is said holds good, I think, in principle.
CHAPTER II
THE CATEGORICAL AND HYPOTHETICAL FORMS OF
JUDGMENT
I. In the foregoing chapter we have attempted roughly to
settle the main characteristics of judgment. The present chap
ter will both support and deepen our conclusion. It will deal
with problems, in part familiar to those who have encountered
the well-known discussion aroused by Herbart. The length
and the difficulty of this second chapter may perhaps be little
warranted by success, but I must be allowed to state before
hand that both are well warranted by the importance of the
subject in modern logic.
A judgment, we assume naturally, says something about
some fact or reality. If we asserted or denied about anything
else, our judgment would seem to be a frivolous pretence.
We not only must say something, but it must also be about
something actual that we say it. For consider; a judgment
must be true or false, and its truth or falsehood can not lie in
itself. They involve a reference to a something beyond. And
this, about which or of which we judge, if it is not fact, what
else can it be?
The consciousness of objectivity or necessary connection,
in which the essence of judgment is sometimes taken to lie,
will be found in the end to derive its meaning from a reference
to the real. A truth is not necessary unless in some way it
is compelled to be true (vid. Chap. VII.). And compulsion is
not possible without something that compels. It will hence
be the real, which exerts this force, of which the judgment is
asserted. We may indeed not affirm that the suggestion S P
itself is categorically true of the fact, and that is not our
judgment. 1 The actual judgment asserts that S P is forced
on our minds by a reality x. And this reality, whatever it
may be, is the subject of the judgment. It is the same with
objectivity. 2 If the connection S P holds outside my judg
ment, it can hardly hold nowhere or in nothingness. It must
42 THE PRINCIPLES OF LOGIC BOOK I
surely be valid in relation to something, and that something
must be real. No doubt, as before, S P may not be true
directly of this fact; but then that again was not what we
asserted. The actual judgment affirms that S P is in connec
tion with x. And this once again is an assertion about fact.
There is a natural presumption that truth, to be true, must
be true of reality. And this result, that comes as soon as we
reflect, will be the goal we shall attain in this chapter. But
we shall reach it with a struggle, distressed by subtleties, and
perhaps in some points disillusioned and shaken.
2. Less serious difficulties we may deal with at once. " A
four-cornered circle is an impossibility," we are told, does not
assert the actual existence of a four-cornered circle (Herbart,
I. 93). But the objection is irrelevant, unless it is maintained
that in every case we affirm the reality of the grammatical
subject.* And this clearly is not always what we mean to
assert. And such further examples as " There are no ghosts,"
or " This thought is an illusion," may be likewise disposed of.
It is not the first form and haphazard conjunction of every
proposition which represents reality. But, in every proposi
tion, an analysis of the meaning will find a reality of which
something else is affirmed or denied. " The nature of space
excludes the connection of square and round," " The world
is no place where ghosts exist," " I have an idea, but the
reality it refers to is other than its meaning," we may offer
these translations as preliminary answers to a first form of
attack. And when Herbart assails us with " The wrath of
the Homeric gods is fearful " (I. 99), we need give no ground
before such a weapon. In Homer it is so ; and surely a poem,
surely any imagination, surely dreams and delusions, and
surely much more our words and our names are all of them
facts of a certain kind. Such plain distinctions as those be
tween existences of different orders 3 should never have been
confused, and the paradox lies on the side of those who urge
such an objection, f
*Ueberweg seems to make this mistake, Loglk, 68.
fl admit that there are difficulties which for the moment we
ignore. When no one reads Homer, of what subject can we predicate
the wrath of his deities? Though the meaning of a term is a fact,
most certain and quite undeniable, yet where is that fixed connection
CHAP. II FORMS OF JUDGMENT 43
And if, further, the discussion take the misleading form of
an enquiry into the copula, we find merely the same misunder
standings unknowingly reproduced. Wherever we predicate,
we predicate about something which exists beyond the judg
ment, and which (of whatever kind it may be) is real, either
inside our heads or outside them. And in this way we must
say that " is " never can stand for anything but " exists." *
3. But Herbart, we shall find, is not so easily disposed of.
He was not the man first uncritically to swallow the common-
sense doctrine that judgment is of things, and then to stagger
at the discovery that things are not words, or fall prostrate
before a supposed linguistic revelation of the nature of the
copula. In denying that judgment asserts a fact, he knew
well what he stood on. It was no puzzle about the gram
matical subject, but a difficulty as to the whole nature of truth
and of ideas. We reflect about judgment, and, at first of
course, we think we understand it. Our conviction is that it
is concerned with fact; but we also see that it is concerned
with ideas. And the matter seems at this stage quite simple.
We have a junction or synthesis of ideas in the mind, and this
junction expresses a similar junction of facts outside. Truth
and fact are thus given to us together, the same thing, so to
speak, in different hemispheres or diverse elements.
But a further reflection tends to dissipate our confidence.
Judgments, we find, are the union of ideas, and truth is not
found except in judgments. How then are ideas related to
realities? They seemed the same, but they clearly are not
so, and their difference threatens to become a discrepancy.
A fact is individual, an idea is universal ; a fact is substantial,
to be found? Does it lie in the dictionaries when no one opens them,
or in the usage when no one is employing the word? But these
questions bear as hardly on fact as on legend, and on things as on
names. Mathematical truths at the least hold good inside mathematics.
But where are mathematics? And we all believe that arsenic
poisons, but if at the moment no dose is operating, nor any one in
the world is thinking of arsenic, it poisons nothing. We shall here
after return to the discussion of this problem.
* The reader may consult Jordan. Die Zwcideutigkeit des Copula
bei Stuart Mill, Gymn. Prog. Stuttgart, 1870; Brentano, Psychologic,
Buch ii. Cap. 7. On the other side see Drobisch. Logik, 55-6,
Sigwart, Logik, I. 94.
44 THE PRINCIPLES OF LOGIC BOOK I
an idea is adjectival; a fact is self -existent, an idea is sym
bolical. Is it not then manifest that ideas are not joined in
the way in which facts are? Nay the essence of an idea, the
more it is considered, is seen more and more to diverge from
reality. And we are confronted by the conclusion that, so far
as anything is true, it is not fact, and, so far as it is fact, it can
never be true. Or the same result may have a different form.
A categorical judgment makes a real assertion in which some
fact is afBrmed or denied. But, since no judgment can do
this, they all in the end are hypothetical. They are true only
of and upon a supposition. In asserting S P I do not mean
that S, or P, or their synthesis, is real. I say nothing about
any union in fact. The truth of S P means that, if I sup
pose S, I am bound in that case to assert S P. In this way
all judgments are hypothetical.*
The conclusion, thus urged upon us by Herbart, follows, I
think, irresistibly from the premises. But the premises are
not valid. Judgment, we saw in the foregoing chapter, can
not consist in the synthesis of ideas. And yet it will repay
us to pause awhile, and to enlarge on the consequences of this
erroneous doctrine. To see clearly that, if judgment is the
union of ideas, there then can be no categorical judgment, is
a very great step in the understanding of Logic. And, through
the next few sections, we shall endeavour to make this con
clusion plain.
4. The contrast and comparison of reality and truth no
doubt involve very ultimate principles. To enquire what is
fact, is to enter at once on a journey into metaphysics, the
end of which might not soon be attained. For our present
purpose we must answer the question from a level not much
above that of common sense. 4 And the account which repre
sents the ordinary view, and in which perhaps we may most
of us agree, is something of this sort.
The real is that which is known in presentation or intuitive
knowledge. It is what we encounter in feeling or perception.
Again it is that which appears in the series of events that
occur in space and time. It is that once more which resists
our wills; a thing is real if it exercises any kind of force or
* Herbart, Werke, I. 92. He refers here to Wolff, by whom, in this
point, he had been partially anticipated. Cf. Fichte, Werke, I. 69, 93.
CHAP. II FORMS OF JUDGMENT 45
compulsion, or exhibits necessity. It is briefly what acts and
maintains itself in existence. And this last feature seems
connected with former ones. We know of no action, unless it
shows itself by altering the series of either space or time, or
both together ; 5 and again perhaps there is nothing which
appears unless it acts. But the simplest account, in which the
others possibly are all summed up, is given in the words, The
real is self-existent. And we may put this otherwise by saying,
The real is what is individual.
It is the business of metaphysics to subject these ideas to
a systematic examination. We must content ourselves here
with taking them on trust, and will pause merely to point out
a common misunderstanding. It is a mistake to suppose
that " The real is individual " means either that the real is
abstractly simple, or is merely particular. Internal diversity
does not exclude individuality, and still less is a thing made
self-existent by standing in a relation of exclusion to others.
Metaphysics can prove that, in this sense, the particular is
furthest removed from self -existence. The individual is so far
from being merely particular that, in contrast with its own
internal diversity, it is a true universal (cf. Chap. VI.). Nor
is this a paradox. We are accustomed to speak of, and believe
in, realities which exist in more than one moment of time or
portion of space. Any such reality would be an identity
which appears and remains the same under differences; and
it therefore would be a real universal.*
5. Such, we may say, are some of the points which con
stitute reality. And truth has not one of them. It exists,
as such, in the world of ideas. And ideas, we have seen, are
merely symbols. They are general and adjectival, not sub
stantive and individual. Their essence lies within their mean
ing and beyond their existence. The idea is the fact with its
existence disregarded, and its content mutilated. It is but a
portion of the actual content cut off from its reality, and
*The following reflection may interest the reader. If space and
time are continuous, and if all appearance must occupy some time or
space and it is not hard to support both these theses we can at once
proceed to the conclusion, no mere particular exists. Every phenom
enon will exist in more times or spaces than one ; and against that
diversity will be itself an universal.
46 THE PRINCIPLES OF LOGIC BOOK I
used with a reference to something else. No idea can be
real.
If judgment is the synthesis of two ideas, then truth con
sists in the junction of unreals. When I say, Gold is yellow,
then certainly some fact is present to my mind. But universal
gold and universal yellowness are not realities, and, on the
other hand, what images 6 of yellow and gold I actually pos
sess, though as psychical facts they have real existence, are
unfortunately not the facts about which I desired to say any
thing. We have seen (Chap. I.) that I do not mean, This
image of gold is in my mind joined psychically with this other
image of yellow. I mean that, quite apart from my mental
facts, gold in general has a certain kind of colour. I strip
away certain parts from the mental facts, and, combining these
adjectival remnants, I call the synthesis truth.
But reality is not a connection of adjectives, nor can it so
be represented. Its essence is to be substantial and individual.
But can we reach self -existence and individual character by
manipulating adjectives and putting universals together? If
not, the fact is not given directly in any truth whatsoever.
It can never be stated categorically. And yet, because adjec
tives depend upon substantives, the substantive is implied.
Truth will then refer to fact indirectly. The adjectives of
truth presuppose a reality, and in this sense all judgment will
rest on a supposal. It is all hypothetical; itself will confess
that what directly it deals with, is unreal.
6. More ordinary considerations might perhaps have led
us to anticipate this result. The common-sense view of facts
outside us passing over into the form of truth within us, or
copying themselves in a faithful mirror, is shaken and per
plexed by the simplest enquiries. What fact is asserted in
negative judgments? Has every negation I choose to invent
a real counterpart in the world of things? Does any logical
negation, as such, correspond to fact? Consider again hypo
thetical judgments. // something is, then something else fol
lows, but should neither exist, would the statement be false?
It seems just as true without facts as with them, and, if so,
what fact can it possibly assert? The disjunctive judgment
will again perplex us. " A is b or c " must be true or false,
but how in the world can a fact exist as that strange ambiguity
CHAP. II FORMS OF JUDGMENT 47
" b or c?" We shall hardly find the flesh and blood alterna
tive which answers to our " or."
If we think these puzzles too technical or sought out, let
us take more obvious ones. Have the past and the future we
talk of so freely any real existence? Or let us try a mere
ordinary categorical affirmative judgment, " Animals are
mortal." This seems at first to keep close to reality; the
junction of facts seems quite the same as the junction of ideas.
But the experience we have gained may warn us that, if ideas
are adjectives, this can not be the case. If we are uncon
vinced, let us go on to examine. " Animals " seems perhaps
to answer to a fact, since all the animals who exist are real.
But, in " Animals are mortal," is it only the animals now
existing that we speak of? Do we not mean to say that the
animal born hereafter will certainly die? The complete col
lection of real things is of course the same fact as the real
things themselves, but a difficulty arises as to future individ
uals. And, apart from that, we scarcely in general have in
our minds a complete collection. We mean, " Whatever is an
animal will die," but that is the same as // anything is an
animal then it is mortal. The assertion really is about mere
hypothesis; it is not about fact.
In universal judgments we may sometimes understand that
the synthesis of adjectives, which the judgment expresses,
is really found in actual existence. But the judgment does
not say this. It is merely a private supposition of our own.
It arises partly from the nature of the case, and partly again
from our bad logical tradition. The fact that most adjectives
we conjoin in judgment can be taken as the adjectives of
existing things, leads us naturally to expect that this will
always be the case. And, in the second place, a constant
ambiguity arises from the use of " all " in the subject. We
write the universal in the form " All animals," and then take
it to mean each actual animal, or the real sum of existing
animals. But this would be no more an universal judgment
than " A B and C are severally mortal." And we mean noth
ing like this. In saying " All animals," if we think of a collec
tion, we never for a moment imagine it complete; we mean
also " Whatever besides may be animal must be mortal too."
In universal judgments we never mean " all." What we mean
48 THE PRINCIPLES OF LOGIC BOOK I
is "any," and "whatever," and "whenever." But these
involve " if."
We may see this most easily by a simple observation. If
actual existence were really asserted, the judgment would be
false if the existence failed. And this is not the case. It
would be a hazardous assertion that, supposing all animal life
had ceased, mortality would at once be predicated falsely,
and, with the re-appearance of animal existence, would again
become true. But cases exist where no doubt is possible.
" All persons found trespassing on this ground will be prose
cuted," is too often a prophecy, as well as a promise. But it
is not meant to foretell, and, though no one trespasses, the
statement may be true. " All triangles have their angles equal
to two right angles " would hardly be false if there were no
triangles. And, if this seems strange, take the case of a
chiliagon. Would statements about chiliagons cease to be
true, if no one at the moment were thinking of a chiliagon?
We can hardly say that, and yet where would any chiliagons
exist? There surely must be scientific propositions, which
unite ideas not demonstrable at the moment in actual existence.
But can we maintain that, if the sciences which produce these
became non-existent, these judgments would have ipso facto
become false, as well as unreal?
The universal judgment is thus always hypothetical. It
says " Given one thing you will then have another," and it
says no more. No truth can state fact.
7. This result is however not easy to put up with. For,
if the truth is such, then all truths, it would seem, are no
better than false. We can not so give up the categorical
judgment, for, if that is lost, then everything fails. Let us
make a search and keep to this question, Is there nowhere to
be found a categorical judgment? And it seems we can find
one. Universal judgments were merely hypothetical, because
they stated, not individual substantives, but connections of
adjectives. But in singular judgments the case is otherwise.
Where the subject, of which you affirm categorically, is one
individual, or a set of individuals, your truth expresses fact.
There is here no mere adjective and no hypothesis.
These judgments are divisible into three great classes. 7
And the distinction will hereafter be of great importance, (i)
CHAP. II FORMS OF JUDGMENT 49
We have first those judgments which make an assertion about
that which I now perceive, or feel, or about some portion of
it. " I have a toothache," " There is a wolf," " That bough is
broken." In these we simply analyze the given, and may there
fore call them by the name of Analytic judgments of sense *
Then (ii) we have Synthetic judgments of sense, which state
either some fact of time or space, or again some quality of the
matter given, which I do not here and now directly perceive.
" This road leads to London," " Yesterday it rained," " To
morrow there will be full moon." They are synthetic because
they extend the given through an ideal construction, and they
all, as we shall see, involve an inference. The third class (Hi),
on the other hand, have to do with a reality which is never a
sensible event in time. " God is a spirit," " The soul is a sub
stance." We may think what we like of the validity of these
judgments, and may or may not decline to recognize them in
metaphysics. But in logic they certainly must have a place.
8. But, if judgment is the union of two ideas, we have
not so escaped. And this is a point we should clearly recog
nize. Ideas are universal, and, no matter what it is that
we try to say and dimly mean, what we really express and
succeed in asserting, is nothing individual. For take the
analytic judgment of sense. The fact given us is singular, it
is quite unique; but our terms are all general, and state a
truth which may apply as well to many other cases. In " I
have a toothache" both the I and the toothache are mere
generalities. The actual toothache is not any other toothache,
and the actual I is myself as having this very toothache. But
the truth I assert has been and will be true of all other tooth
aches of my altering self. Nay " I have a toothache," is as
true of another s toothache as of my own, and may be met by
the assertion, " Not so, but / have one." It is in vain that we
add to the original assertion " this," " here," and " now," for
they are all universals. They are symbols whose meaning
extends to and covers innumerable instances.
Thus the judgment will be true of any case whatsoever
* These analytic and synthetic judgments must not for one moment
be confounded with Kant s. Every possible judgment, we shall see
hereafter, is both analytic and synthetic. Most, if not all, judgments
of sense are synthetic in the sense of transcending the given.
5O THE PRINCIPLES OF LOGIC BOOK I
of a certain sort; but, if so, it can not be true of the reality;
for that is unique, and is a fact, not a sort. " That bough is
broken," but so are many others, and we do not say which.
" This road leads to London " may be said just as well of a
hundred other roads. " To-morrow it will be full moon," does
not tell us what to-morrow. Hereafter it will constantly be
true that, on the day after this day, there will be a full moon.
And so, failing in all cases to state the actual fact, we state
something else instead. What is true of all does not express
this one. The assertion sticks for ever in the adjectives; it
does not reach the substantive. And adjectives unsupported
float in the air ; their junction with reality is supposed and
not asserted. So long as judgments are confined to ideas,
their reference to fact is a mere implication. It is presupposed
outside the assertion, which is not strictly true until we qualify
it by a suppressed condition. As it stands, it both fails as a
singular proposition, and is false if you take it as a strict
universal (cf. 62 foil.). 8
9. But judgment, as we saw in the foregoing Chapter, is
not confined to ideas, and can not by any means consist in
their synthesis. The necessity for two ideas is a mere delusion,
and, if before we judged we had had to wait for them, we
certainly should never have judged at all. And the necessity
for the copula is a sheer superstition. Judgments can exist
without any copula and with but one idea.
In the simplest judgment an idea is referred to what is
given in perception, and it is identified therewith as one of its
adjectives. There is no need for an idea to appear as the
subject, and, even when it so appears, we must distinguish the
fact from grammatical show. 9 It is present reality which is
the actual subject, and the genuine substantive of the ideal
content. We shall see hereafter that, when " this " " here "
and " now " seem to stand as subjects, the actual fact which
appears in perception is the real subject, to which these
phrases serve to direct our attention. But of this in the
sequel; we have seen already, and have further to see, that
all judgments predicate their ideal content as an attribute of
the real which appears in presentation.
It is from this point of view that we must resume the
discussion. Standing on this basis, we must examine afresh
CHAP. II FORMS OF JUDGMENT 5!
the various judgments which have passed before us, and must
ask for their meaning and further validity. Some difficulties
in our search for categorical judgments may have already
disappeared; but others as formidable must perhaps be
awaited. And, if we come to the result that all truth in the
end is true of reality, we must not expect to maintain that
doctrine in its crude acceptation.
10. Our first movement however must be towards a
definition. A phrase we have used was designedly am
biguous. Are we to hold that the real, which is the ultimate
subject, and which, as we said, appears in perception, is
identical with the merely momentary appearance? We shall
see that this can not be, and that such a view could not
possibly account for the facts. At present we may offer
a preliminary argument against this mistake.
The subject which appears in the series of time, and to
which we attribute our ideas as predicates, must itself be real.
And, if real, it must not be purely adjectival. On the
contrary it must be self-existent and individual. But the
particular phenomenon, the momentary appearance, is not
individual, and is so not the subject which we use in judgment.
11. We naturally think that the real, at least as we
know it, must be present. Unless I come into contact with it
directly, I can never be sure of it. Nothing in the end but
what I feel can be real, and I can not feel anything unless it
touches me. But nothing again can immediately encounter
me save that which is present. 10 If I have it not here and now,
I do not have it at all.
" The present is real " ; this seems indubitable. And are
we to say that the momentary appearance is therefore real?
This indeed would be mistaken. If we take the real as that
which is confined to a single " here " or a single " now " (in
this sense making it particular), we shall have questions on
our hands we shall fail to dispose of. For, beside the diffi
culties as to the truth of all universal judgments, we are
threatened with the loss of every proposition which extends
beyond the single instant. Synthetic judgments must at once
be banished if the real is only the phenomenon of a moment.
Nothing either past or future in time, nor any space I do not
52 THE PRINCIPLES OF LOGIC BOOK I
directly perceive, can be predicated as adjectives of our one
" now " and " here." All such judgments would be false,
for they would attribute to the existent qualities which con
fessedly are non-existent, or would place the real as one
member in a series of utter unrealities.
But perhaps we feel we may escape this consequence ; or at
all events feel so sure of our premise that we can not give it
up. " The real is confined to one here or one now." But
supposing this true, are we sure we know what it is we under
stand by our " now " and " here " ? For time and extension
seem continuous elements; the here is one space with the
other heres round it; and the now flows ceaselessly and
passes for ever from the present to the past.
We may avoid this difficulty, we may isolate the time we
call the present, and fix our now as the moment which is, and
has neither past, nor future, nor transition in itself. But here
we fall into a hopeless dilemma. This moment which we
take either has no duration, and in that case it turns out no
time at all; or, if it has duration, it is a part of time, and is
found to have transition in itself.
If the now in which the real appears is purely discrete,
then first we may say that, as characterized by exclusion, the
phenomenon, if apparent, is not self-subsistent, and so not real.
But apart from that objection, and to return to our dilemma,
the now and the here must have some extension. For no
part of space or time is a final element. We find that every
here is made up of heres, and every now is resolvable into
nows. And thus the appearance of an atomic now could not
show itself as any one part of time. But, if so, it could never
show itself at all. Or, on the other hand, if we say the
appearance has duration, then, like all real time, it has suc
cession in itself, and it would not be the appearance of our
single now.* From all which it is clear that a momentary ap
pearance will not give us the subject of which we are in search.
* It is the business of metaphysics to prove these points at length.
If time consists of discrete parts, it is hard to see how the fact of
succession can possibly be explained, unless time be taken between
these parts of time. And that would lead to untenable conclusions.
But it is the fact of change which shows that time is continuous.
The rate of change, the number of events in every part of time, may,
CHAP. II FORMS OF JUDGMENT 53
12. It is a mistake to suppose that the present is a part
of time, indivisible and stationary, and that here and now can
be solid and atomic. In one sense of the word the present is
no time. Itself no part of the process, it is a point we take
within the flow of change. It is the line that we draw across
the stream, to fix in our minds the relations of one successive
event to another event. " Now," in this sense, stands for
" simultaneous with " ; it signifies not existence but bare po
sition in the series of time. The reality is not present in the
sense of given in one atomic moment.
What we mean, when we identify presence with reality, is
something different. The real is that with which I come into
immediate contact, and the content of any part of time, any
section of the continuous flow of change, is present to me if I
directly encounter it. What is given in a perception, though
it change in my hands, is now and here if only I perceive it.
And within that perception any aspect or part, which I spe
cially attend to, is specially present, is now and here in
another sense than the rest of that content. The present is
the filling of that duration in which the reality appears to me
directly ; and there can be no part of the succession of events
so small or so great, that conceivably it might not appear as
present.
In passing we may repeat and may trace the connection
of those shades of meaning we have found in " presence." (i)
Two events in time are now to one another, if both are given
simultaneously in my series, (ii) Since the real appears in the
series of time, the effort to find it both present and existmg
within that series, creates the fiction of the atomic now. (iii)
If the real can never exist in time, but only appear there, then
that part of the series in which it touches me is my present,
(iv) And this suggests the reflection that presence is really
the negation of time, and never can properly be given in the
so far as we know, be increased indefinitely; and this means that in
every part. of time more than one event may take place. If the parts
be discrete, then not only will motion imply that a thing is in several
places in one time (and this is a fact), but also (which is absurd)
that throughout all these places no time elapses, that they are strictly
contemporaneous. I should be glad to enter into the discussion at
length, but the subject cannot properly be treated by logic.
2321. I E
54 THE PRINCIPLES OF LOGIC BOOK I
series. It is not the time that can ever be present, but only
the content.
13. But we must leave these intricacies. We must be
satisfied with knowing that the real, which (we say) appears
in perception, does not appear in one single moment. And
if we will pause and reflect for a little, we shall see how
hardened we are in superstitions. When we ask for reality,
we at once encounter it in space and time. We find opposed
to us a continuous element of perpetual change. We begin to
observe and to make distinctions, and this element becomes
a series of events. And here we are tempted to deceive our
selves grossly. We allow ourselves to talk as if there existed
an actual chain of real events, and as if this chain were some
how moved past us, or we moved along it, and as if, whenever
we came to a link, the machinery stopped and we welcomed
each new link with our " here " and our " now." Still we do
not believe that the rest of the links, which are not here and
now, do all equally exist, and, if so, we can hardly be quite
sure of our chain. And the link, if we must call it so, which
is now and here, is no solid substance. If we would but
observe it, we should see it itself to be a fluid sequence whose
parts offer no resistance to division, and which is both now,
and itself without end made up of nows.
Or we seem to think that we sit in a boat, and are carried
down the stream of time, and that on the banks there is a
row of houses with numbers on the doors. And we get out
of the boat, and knock at the door of number 19, and, re-
entering the boat, then suddenly find ourselves opposite 20,
and, having there done the same, we go on to 21. And, all
this while, the firm fixed row of the past and future stretches
in a block behind us and before us.
If it really is necessary to have some image, perhaps the
following may save us from worse. Let us fancy ourselves in
total darkness hung over a stream and looking down on it.
The stream has no banks, and its current is covered and filled
continuously with floating things. Right under our faces is a
bright illuminated spot on the water, which ceaselessly widens
and narrows its area, and shows us what passes away on the
current. And this spot that is light is our now, our present.
We may go still further and anticipate a little. We have
CHAP. II FORMS OF JUDGMENT 55
not only an illuminated place, and the rest of the stream in
total darkness. There is a paler light which, both up and
down stream, is shed on what comes before and after our
now. And this paler light is the offspring of the present.
Behind our heads there is something perhaps which reflects the
rays from the lit-up now, and throws them more dimly upon
past and future. Outside this reflection is utter darkness;
within it is gradual increase of brightness, until we reach
the illumination immediately below us.
In this image we shall mark two things, if we are wise. It
is possible, in the first place, that the light of the present may
come from behind us, and what reflects the light may also
bestow it. We can not tell that, but what we know is, that
our now is the source of the light that falls on the past and
future. Through it alone do we know there exists a stream
of floating things, and without its reflection past and future
would vanish. And there is another point we must not lose
sight of. There is a difference between the brightness of
the now, and the paler revelation of past and future. But,
despite this difference, we see the stream and what floats in it
as one. We overcome the difference. And we do so by see
ing the continuity of the element in past, present and future.
It is because, through the different illuminations, there are
points of connection offered by what floats, in other words, a
sameness of content, that the stream and its freightage be
come all one thing to us, and we even forget that most of
what we see is not self-subsistent but borrowed and adjecti
val. We shall perceive hereafter that time and space beyond
here and now are not strictly existent in the sense in which
the present is. They are not given directly but are inferred
from the present. And they are so inferred because the
now and here, on which the light falls, are the appearance
of a reality which for ever transcends them, and upon which
resting we go beyond them.
14. But this is to anticipate. The result, which at pres
ent we have wished to make clear, is that the now and here,
in which the real appears, are not confined within simply
discrete and resting moments. They are any portion of that
continuous content with which we come into direct relation.
Examination shows that not only at their edges they dissolve
56 THE PRINCIPLES OF LOGIC BOOK I
themselves over into there and then, but that, even within
their limits as first given, they know no repose. Within the
here is both here and there; and in the ceaseless process of
change in time you may narrow your scrutiny to the smallest
focus, but you will find no rest. The appearance is always a
process of disappearing, and the duration of the process which
we call our present has no fixed length.
It will be seen hereafter that in the above reflections we have
not been wandering. Nor will it be long before we return to
them, but we must now rediscuss from a better point of view
those forms of judgment we before laid down (7).
15. Judgment is not the synthesis of ideas, but the refer
ence of ideal content to reality. From this basis we must
now endeavour to interpret the various kinds of judgment we
have met with. And, beginning with the singular judgments
of 7, let us take the first division of these, which were called
Analytic judgments of sense.
I. The essence of these is to hold only of the now, and not
to transcend the given presentation. They may have neither
grammatical subject nor copula, or again, on the other hand,
may possess one or both.
A. In the judgments that have neither copula nor subject,
an idea is referred (a) to the whole sensible reality, or (/?) to
some part of it. 11
(a) When we hear the cry of "Wolf," or "Fire," or
" Rain," it is impossible to say that we hear no assertion. He
who raises the cry is always taken to affirm, to have uttered a
sign and to have used it of the real. The practical man would
laugh at your distinction that, in exclaiming " Wolf," I can
not be a liar, because I use no subject or copula, but that, if
I go so far as " This is a wolf," I am thereby committed.
Such a plea, we must allow, would be instantly dismissed. In
the " Wolf " or " Rain " the subject is the unspecified present
environment, and that is qualified by the attribution of the
ideal content " Wolf " or " Rain." It is the external present
that is here the subject. But in some moment of both outward
squalor and inward wretchedness, where we turn to one an
other with the one word " miserable," the subject is here the
whole given reality.
CHAP. II FORMS OF JUDGMENT 57
Such single words, it may perhaps be said, are really
interjections and never predicates. If they were really inter
jections, we must stubbornly maintain, they could not be the
vehicle of truth and falsehood. And a real interjection that
is nothing besides, is not so common as some persons suppose.
An habitual interjection soon gets a meaning, and becomes
the sign of a received idea, which, in reference to the content,
may be an assertion of truth or falsehood.
But the fact is really beyond all question. You may utter
a word which conveys to you, and which you know conveys
to others also, a statement about fact. Unless then you are
deceiving, you must be judging. And you certainly are judg
ing without any other subject than the whole sensible present.
(/?) But this is an extreme case; in nearly all instances
but one piece of the present is the real subject. We qualify
by our idea some one given aspect. But no subject or copula
appears even here. A common understanding, or the pointing
of a finger, is all that serves to limit the reference. Of a
visible wolf I may predicate the words " asleep " or " running,"
or in watching a sunset, it is enough for me to say the word
" down " or " gone," and every one knows I am judging and
affirming. It might be said, no doubt, that the subject is
elided, but this would be a mere linguistic prejudice. The
genuine subject is not an idea, elided or expressed, but it is
the immediate sensible presentation.*
And again it might be said that what we call the predicate
is really the subject of an unexpressed existential judgment.
But this cardinal mistake will be soon disposed of, when here
after we deal with that class of judgments (42).
15. B. We pass next to those analytic judgments where
a subject is expressed. The ideal content of the predicate is
here referred to another idea, which stands as a subject. But
in this case, as above, the ultimate subject is no idea, but is
the real in presentation. It is this to which the content of
both ideas, with their relation, is attributed. The synthesis of
the ideal elements is predicated either (a) of the whole, or (yj)
of a part, of that which appears.
(a) In such judgments as " Now is the time," " It s all so
dreary," or " The present is dark," an idea takes the place of
*For a further explanation, vid. Chap. III. 2.
58 THE PRINCIPLES OF LOGIC BOOK I
the unspoken reference of the preceding section. But the
subject remains in both cases the same. An idea, it is true,
intervenes between the reality and the predicate, and holds the
place of immediate subject. But a moment s consideration
will assure us that the subject of our assertion is still the
presented. The immediate subject is the sign of a reference,
either simple or embodying implications, to the whole given
reality.
(/?) We have a further advance when the presented fact
is not the whole sensible environment, but only a part of it.
In " There is a wolf," " This is a bird," or " Here is a fire,"
" there " " this " and " here " are certainly ideas, and stand no
doubt for the subject of the judgment : * but, the moment we
examine them, we find once more a reference to the reality,
not now indefinite and embracing the whole, but still no more
than a sign of distinction and indication. If these ideas are
the true subject of a judgment, then so is a silent pointing
with the finger.
1 6. There is really no change when we go a step further,
and take such judgments as " This bird is yellow," " That stone
is falling," " This leaf is dead." The idea, which stands as the
grammatical subject, is certainly more than an indefinite refer
ence, more even than a sign of indication. It not only distin
guishes a part from the environment, but it also characterizes
and qualifies it. But if, before, the subject we meant was not
an idea, but was presented fact, so also now does this remain
the truth. It is not the bare idea, symbolized by " this bird,"
of which we go on to affirm the predicate. It is the fact dis
tinguished and qualified by " this bird," to which the adjective
" yellow " is really attributed. The genuine subject is the
thing as perceived, the content of which our analysis has
divided into " this bird " and " yellow," and of which we predi
cate indirectly those ideal elements in their union.
The same account holds throughout all the variety of these
analytic judgments. Let us complicate our assertion. " The
cow, which is now being milked by the milk-maid, is standing
*It sounds, perhaps, rather shocking to call "there" or "here"
subjects, but, if the text is understood, I need make no defence. On
the nature of the ideas of "this," "now," and "here," we shall find
later on a good deal to say.
CHAP. II FORMS OF JUDGMENT 59
to the right of the hawthorn tree yonder." In this judgment
we have not one thing but several, and more than one state
ment about their relations. But it is still a part of the pre
sented environment which is actually the subject and the real
substantive of which this whole complex is indirectly asserted.
If you deny this, then show me where you draw your line,
and what point it is in the scale of judgments at which the
idea takes the place of the sensible fact, and becomes the true
subject. And confine the assertion to mere ideas. Take the
ideal elements of a cow and a hawthorn tree and a milk-maid,
and combine them ideally in any way you please. Then after
they are combined, stand in presence of the fact, and ask
yourself if that does not enter into your judgment. If, with
the fact before you, you begin to reflect, you will find that,
if you keep to mere ideas, you remove from the assertion just
the thing you mean. In 20 we shall return to this point,
but at present we may deal with a popular error.
17. There is a curious illusion, now widely spread, on
the subject of proper names. 12 We find it laid down that a
proper name has not got connotation, or, to use the more
common technical term, it has no intension. In ordinary lan
guage, it stands for something but does not mean anything.
If this were true, it would be hard to understand what is
signified by such judgments as "John is asleep." There are
thinkers indeed, who fear no consequence, and who will tell us
that here the name John is the subject of the proposition. And
against these adversaries I confess I have no heart to enter
the lists. They may say what they please without hindrance
from me. But, if we are inclined to accept a less heroic
solution, and to suppose the man John to be the subject of the
judgment, then I do not quite see the purpose of the name, if
we are not to mean by it anything at all. Why not simply
omit it, and, pointing to the man, say the word " asleep " ?
" But it stands for the man," I shall hear the reply, " and,
even when he is present, it is a mark which serves to dis
tinguish him much more clearly than pointing." But that is
just what puzzles me. If there is an idea conveyed by the
name, whenever it is used, then it surely means something, or,
in the language which pleases you, it must be " connotative."
But if, on the other hand, it conveys no idea, it would appear
60 THE PRINCIPLES OF LOGIC BOOK I
to be some kind of interjection. If you say that, like " this "
and " here," it is merely the ideal equivalent of pointing, then
at once it assuredly has a meaning, but unfortunately that
meaning is a vague universal. For anything and everything is
" this " and " here." But if you asseverate that it is the ideal
counterpart of pointing in particular to John, then you must
allow me to doubt if you comprehend what you are saying.
The word " mark " has two senses which perhaps we may
confuse. It is something which may be made a means of
distinction, or something which has been made such a means.
I suppose, for I can do no more than suppose, that mark is
not taken in the former sense, and that our man was not seen
to be distinct from other men, because he was found to have
the marking John. But, if it is the latter of these senses we
adopt, then a name is a mark because it is a sign, and mark
and sign are here identical.
Now a sign can not possibly be destitute of meaning.
Originally imposed as an arbitrary mark, that very process,
which makes it a sign and associates it firmly with the thing
it signifies, must associate with it also some qualities and
characters of that which it stands for. If it did not to some
extent get to mean the thing, it never could get to stand for it
at all. And can any one say that a proper name, if you are
aware of its designation, brings no ideas with it, or that these
ideas are mere chance conjunction? What connection, I would
ask, would be left between the bare name and the thing it
stands for, if every one of these ideas were removed? All
would vanish together.
The matter is so plain I do not know how to explain it.
The meaning of a sign need of course not be fixed. But is
the thing it stands for quite invariable? If the " connotation "
is unsteady, does the " denotation " never change? But where
the latter is fixed there the former on its side (within limits)
is stationary. You may have no idea what " William " con
notes, but if so you can hardly know what it stands for. The
whole question arises from a simple mistake and misunder
standing.
18. " But after all the name is the sign of an individual,
and meanings are generic and universal. Therefore the name
can not have any content of which it is the sign." I have
CHAP. II FORMS OF JUDGMENT 6l
purposely put an objection in that form which suggests the
conclusion I wish to arrive at. The name of a man is the
name of an individual, which remains amid changing par
ticulars, and therefore no judgment about such an individual
is wholly analytic. It transcends the given, it becomes syn
thetic, and with it we pass into the second great division of
singular judgments.
Proper names have a meaning which always goes beyond
the presentation of the moment. It is not indeed true that
such names must stand for objects, which endure through a
train of altering perceptions. The unique thing they designate
may appear but once, as an event shut up within one presen
tation. But that object would not be unique, nor proper to its
own especial self, if it did not involve a reference to a series
from which it was excluded. And mere analysis of sense
could never suggest that limiting relation which gives it
uniqueness.
And, when we take the proper names of objects which last
and which reappear, then the given is transcended in a still
higher sense. The meaning of such a name is universal, and
its use implies a real universality, an identity which transcends
particular moments. For, unless the person were recognized
as distinct, he would hardly get a name of his own, and his
recognition depends on his remaining the same throughout
change of context. We could not recognize anything unless
it possessed an attribute, or attributes, which from time to
time we are able to identify. The individual remains the same
amid that change of appearance which we predicate as its
quality. And this implies that it has real identity. Its proper
name is the sign of a universal, of an ideal content which
actually is in the real world.
This assumption, and the practice of giving proper names,
may no doubt be indefensible. What concerns us here is
that the practice transcends presented reality. In "John is
asleep," the ultimate subject can not be the real as it is now
given ; for " John " implies a continuous existence, not got by
mere analysis. We have reached the class of synthetic judg
ments.
19. II. In this second class of singular judgments (7)
we make generally some assertion about that which appears
62 THE PRINCIPLES OF LOGIC BOOK I
in a space or time that we do not perceive, and we predicate
of a presentation something not got by analysis of its content.
If I say " There is a garden on the other side of that wall,"
the judgment is synthetic, for it goes beyond perception. And
in "Yesterday was Sunday," "William conquered England,"
" Next month is June," I certainly do not analyze what is
merely given. In synthetic judgments there is always an
inference, 13 for an ideal content is connected with the sensible
qualities that are given us. In other words we have always
a construction, which depends on ideas, and which only indi
rectly is based on perception (vid. Book II.).
And, this being so, it seems as if now we were unable to
proceed. If the subject is the real that appears in perception,
how can events in the past and future, or a world in space out
side the presentation, and how even can qualities not given to
sense be referred to the object and considered as its adjectives?
We have already glanced at the solution of this problem, and
what we now wish to show is the following. In synthetic
judgments the ultimate subject is still the reality. That is not
the same as the momentary appearance, and yet synthetic
judgments are possible only by being connected with what is
given at this very instant. The ideas of past and future events
are projected from the base of present perception. It is only
in that point that they encounter the reality of which they
wish to be true.
" But past and future," the reader may object, " are surely
realities." Perhaps they are, but our question is, Given a
synthesis of ideas within my mind, how and where am I able
to get at a reality to which to attribute them ? 14 How am I to
judge unless I go to presentation? Let the past and future
be as real as you please, but by what device shall I come in
contact with them, and refer to them my ideas, unless I
advance directly to the given, and to them indirectly? It is
possible, I am aware, to assert that past realities are directly
presented, and possible also (for all I know) to say the same
of the future, and of all the space I am not in contact with,
and of all the qualities that I do not perceive. In this way,
no doubt, we dispose of the difficulty, and indeed may make
a very simple matter of any kind of problem, if indeed any
problems any longer will exist.
CHAP. II FORMS OF JUDGMENT 63
20. But the persons I write for, and who are not so
blessed with easy intuitions, will feel this difficulty, and there
may come a temptation to fall back once more on the aban
doned heresy and to say, In these synthetic judgments the
subject can not possibly be the reality. It must be an idea,
and in the junction of ideas must lie the truth. And I think,
perhaps, at the cost of repetition, we had better see where
this temptation leads us.
When we say " It rained last Tuesday," we mean this last
Tuesday, and not any other; but, if we keep to ideas, we do
not utter our meaning. Nothing in the world that you can
do to ideas, no possible torture will get out of them an asser
tion that is not universal. We can not escape by employing
ideas of events in time, particulars as we call them. The
event you describe is a single occurrence, but what you say
of it will do just as well for any number of events, imaginary
or real. If you keep to ideas it is useless to make a reference
to the present, and say, " The Tuesday that came before this
day." For we have seen before (8), that in analytic judg
ments we are equally helpless. The real is inaccessible by
way of ideas. In attempting to become concrete and special,
you only succeed in becoming more abstract and wholly in
definite. " This " " now " and " mine " are all universals.
And your helpless iteration, " not this but this," will not get
your expression any nearer to your meaning. If judgment is
only the union of ideas, no judgment is ever about the indi
vidual.
21. We must get rid of the erroneous notion (if we have
it) that space and time are " principles of individuation," in
the sense that a temporal or spatial exclusion will confer
uniqueness upon any content. It is an illusion to suppose that,
by speaking of " events," we get down to real and solid par
ticulars, and leave the airy region of universal adjectives. For
the question arises, What space and time do we really mean,
and how can we express it so as not to express what is as
much something else ? It is true that, in the idea of a series of
time or complex of space, uniqueness is in one sense involved ;
for the parts exclude one another reciprocally. But they do
not exclude, unless the series is taken as one continuous whole,
and the relations between its members are thus fixed by the
64 THE PRINCIPLES OF LOGIC BOOK I
unity of the series. Apart from this unity, a point on its recur
rence could not be distinguished from the point as first given.
And elsewhere we might ask, how far such an unity is itself
the negation of mere exclusivity.
But, to pass by this question, it is clear that exclusion
within a given series does not carry with it an absolute unique
ness. There is nothing whatever in the idea of a series to
hint that there may not be any number of series, internally all
indistinguishable from the first. How can you, so long as you
are not willing to transcend ideas, determine or in any way
characterize your series, so as to get its difference from every
possible series within your description? It is idle to say
" this," for " this " does not exclude except in this sphere, and
it is idle to say " my," for it is only in my element that yours
and mine collide. Outside it they are indifferent, and the ex
pression " my " will not distinguish one world from the other.
If we simply attend to the series itself, 15 and, declining to look
outside, confine ourselves to the consideration of its character,
then all that it contains might be the common property of innu
merable subjects, existing and enjoyed in the world of each, a
general possession appropriated by none. The mere quality
of appearance in space or time can not give singularity.
22. The seeking for judgment in the synthesis of ideas
once more has led us where there is no exit. With however
little hope we must return to the doctrine, that judgment is
the reference of an ideal content to the real which appears in
time and space, which is to be encountered directly in presen
tation, but which can not be limited to a momentary instance.
It is not by its quality as a temporal event or phenomenon of
space, that the given is unique. It is unique, not because it
has a certain character, but because it is given. It is by the
reference of our series to the real, as it appears directly within
this point of contact, or indirectly in the element continuous
with this point, that these series become exclusive. We per
haps may be allowed to express this otherwise by saying, it
is only the " this " which is real, and ideas will suffice so far
as " thisness," but can never give " this." It is perhaps a hard
saying, and announces difficulties we shall need both courage
and patience to contend with.
23. Everything that is given us, all psychical events, be
CHAP. II FORMS OF JUDGMENT 65
they sensations, or images, or reflections, or feelings, or ideas,
or emotions every possible phenomenon that can be present
both is " this " and has " thisness." But its stamp of unique
ness and singularity comes to it from the former and not from
the latter. If we distinguish the aspects of existence and
content 16 (Chap. I. 4), and put on the one side that anything
is, and on the other side what it is, then the thisness falls
within the content, but the this does not fall there. It is the
mere sign of my immediate relation, my direct encounter in
sensible presentation with the real world. I will not here ask
how " this " is related to existence, how far it holds of the
actual fact, and how far only of the mere appearance ; whether
it is or is only for me. Apart from that, at least so much is
certain, that we find uniqueness in our contact with the real,
and that we do not find it anywhere else. The singularity
which comes with presentation and is what we call " this," is
not a quality of that which is given.
But thisness on the other hand does belong to the content,
and is the general character of every appearance in space or
time. Thisness, if we like, we may call particularity. Every
thing that is given us is given, in the first place, surrounded
and immersed in a complex detail of innumerable relations to
other phenomena in space or time. In its internal quality
we find again a distinction of aspects, which we always can
carry to a certain length, and can never be sure we have quite
exhausted. And the internal relations of its component ele
ments in space or time are again indefinite. We are never
at the end of them. This detail appears to come to us on
compulsion; we seem throughout to perceive it as it is, and
in no sense to make or even to alter it. And this detail it is
which constitutes thisness.*
*The apprehension of this character, it may be objected, takes time,
and, if any time for observation is given, the product, for all we know,
has been altered. But this difficulty occurs in all observation. We
everywhere assume, first, that things are not different unless we can
discriminate them. And we assume, in the second place, our ability to
distinguish a change in ourselves from a change in the object. We
assume that more of the same object is observed, unless we have
reason either to suppose that our fancy has wandered away from
that object, or that the object itself has undergone a change. I do not
here ask if these assumptions are valid. But I may remark in passing,
66 THE PRINCIPLES OF LOGIC BOOK I
But such particularity in space or time, such an exclusive
nature, after all, is only a general character. It falls in the
content and does not give the existence. It marks the sort
but it misses the thing. In abstraction from the this it is
merely ideal, and, apart from the this, ideas as we know can
not reach to uniqueness. No amount of thisness which an
event possesses will exclude the existence of self -same events
in other like series. Such exclusiveness falls all within the
description, and that which is only of this description is simply
such and can not be this.
In every judgment, where we analyze the given, and where
as the subject we place the term " this," it is not an idea which
is really the subject. In using " this " we do use an idea, and
that idea is and must be universal; but what we mean, and
fail to express, is our reference to the object which is given
as unique.
24. And here we encounter an awkward question. The
reader possibly may be willing to accept our account of this
ness. He may agree that, so far as in our use of the term we
mean mere relativity in space or time, in other words particu
larity, we do not at all go beyond the content. And he may
allow the consequence that we have so an idea which is
only universal. But in using "this," he may go on
to object that we have in addition another idea. We have
the idea of immediate contact with the presented reality;
and it is that idea which is signified by "this," and which
qualifies the idea which stands as the subject of our analytic
judgment.
We answer, Assuredly, if such were the case, the reference
to fact would inevitably and always fall outside the judgment.
Once again we should be floating in the air, and never be more
than hypothetical. But the question raised need not so be
dismissed, for it leads to an interesting if subtle reflection.
that the doubt if in introspection we examine a present, or only a past
state of mind, should change its form. It should not take the two as
exclusive here, unless it faces the same problem elsewhere. For the
observation of external phenomena labours under the identical diffi
culty. If an internal fact can not possibly be both present and past,
then an external fact must be likewise restricted. The two kinds of
observation are not essentially different. External facts are not abso
lutely fixed, nor are internal facts in absolute flux. 17
CHAP. II FORMS OF JUDGMENT 67
The idea of " this," unlike most ideas, can not be used as a
symbol in judgment.
It is certain, in the first place, that we have the idea. 18
Indeed we could scarcely deny that we had it, unless in so
doing we actually used it. Beside the idea of exclusion in a
series, which is mere thisness, we have also the idea of my
immediate sensible relation to reality, and, if so, we have
" this." We are able to abstract an idea of presence from that
direct presentation which is never absent; and presence,
though it does not fall within the content, though we can
hardly call it a quality of the appearance, yet is recognized as
the same amid a change of content, is separable from it, and
makes a difference to it. Thus ideally fixed " this " becomes
an universal among other universals.
25. But, despite the likeness, it is very different from an
ordinary idea. Ideas, we shall remember, are used as symbols
(Chap. I.). In my idea of a "horse " we have (i) the exist
ence of an image in my head, (ii) its whole content, and (iii)
its meaning. In other words we may always distinguish (i)
that it is, and (ii) what it is, and (iii) what it signifies. The
two first of these aspects belong to it as a fact. The third is
the universal which does not belong to it, but is thought of
without a relation to its existence, and in actual judgment is
referred away to some other subject.
The idea of " this " has a striking difference. Distin
guished as an aspect of presented reality, when we call it up
we take any perception or feeling that is given, and, attending
to the aspect of presence within it, recognize that as
the meaning of our term. We contemplate it ideally, with
out any reference to the content of that which is actually
before us.
But how shall we fare when, attempting a judgment, we
attribute the adjective we have so cut loose to another sub
stantive? It is here we are stopped. For any judgment so
made we discover must be false. The other fact can not be
presented without ipso facto altering the given. It degrades
our given to one element within a larger presentation, or else
it wholly removes it from existence. The given disappears
and with itself carries our idea away. We are now unable to
predicate the idea, since we no longer possess it, or if we still
68 THE PRINCIPLES OF LOGIC BOOK I
have it, then what supports it excludes that other fact to which
we wish to refer it.
26. To repeat the above, the presented instance of reality
is unique. By discrimination we are able to fix that uniqueness
in the shape of an idea. We thereupon try to make it the
idea of something else. But, for the idea to be true of some
thing else, that something else must be present and unique.
We have then either two unique presentations, or one must
disappear. If the first one goes, the idea goes with it. If
the last one goes, there is now no fact for the idea to be re
ferred to. In either case there can be no judgment. The idea,
we see, is not the true idea of anything other than its own
reality. It is a sign which, if we judge, can signify nothing
except itself. To be least alone then when most alone, and to
enjoy the delights of solitude together, are phrases which have
a very good sense ; but, taken in their bare and literal meaning,
they would exemplify the contradiction we have here before us.
Between the fact and the idea of the " this " in judgment,
there can be no practical difference. The idea of this would
be falsely used, unless what it marks were actually presented.
But in that case we should be trying to use a sign, when we
have before us the fact which is signified. We can use the
idea so far as to recognize the fact before us as a fact which
is " this ; " but such a use does not go beyond the given. It
affirms of the subject a predicate without which the subject
disappears. It implies discrimination within the fact in which,
since the aspect discriminated is not separable from the given,
that given with its aspect still remains as the subject. So that
the addition of the idea adds nothing to the subject. And
if again it were possible to import the idea from the content
of another fact, the operation would be uncalled for and quite
inoperative.
And it is not possible. It would be, as we have seen, the
attempt to have before us two unique facts at once. What
we mean by " this " is the exclusive focus of presentation
which lights up its content, and it is of that singular content
that we use the idea. And to treat that idea as a meaning
which could be true elsewhere, would be to bring into our focus
another content. But since both must be unique, as well as
the same, a dilemma arises which we need not draw out.
CHAP. II FORMS OF JUDGMENT 69
27. And if " this " be used in a different sense, if it does
not mark the presence of the whole sensible detail that falls
within the focus ; if it is used for that which I specially attend
to, the result will be the same. If I make A my object to the
exclusion of all others, then this special relation to myself
must be false, if used of any other. If applied to A it can not
possibly also be applied to B.
" But," it may be said, " I exclusively attend to both. A
and B are both elements within the given this, and hence I
can predicate this of either. I can transfer the idea, which
I find is true of one, and use it as a predicate which is true of
the other. And so, after all, the idea of this will be used
symbolically." I am afraid of losing the main question in
subtleties, but I must reply by pointing out a confusion. Since
A and B are both taken together, you can not exclusively
deal with each separately. So much is now clear. But, on
the other hand, if you take each by itself as a mere element in
the " this," then you can not predicate " this " of either. Both
will belong to the " this," but neither will be that to which
they belong. They will be presented, but neither by itself will
be the unique presentation. They will not have the " this " in
common, but the " this " will have them. It will be their
common substantive which will share its own exclusive nature
with nothing.
I hardly think that by further intricacies we shall make
more clear what can not be made obvious. If anything in the
above has been grasped by the reader, I trust to have shown
that the use of " this," as a symbol in judgment, is not only
impossible, but that, if it existed, it would be wholly nugatory.*
28. We escape from ideas, and from mere universals, by
a reference to the real which appears in perception. It is thus
* " This " is not the only idea which can never be true as a symbol.
I will not ask to what extent " this " means " for me," but what has
been said of " this " will hold in the main of " I ", " me " and " mine."
But there are difficulties here which we can not discuss. We may
remark in passing that, for the purposes of metaphysics, it would be
necessary to find all those ideas whose content appears not able to be
used as the adjective of something else. This would bear on the
so-called " ontological proof." For the ideas of uniqueness &c., vid.
infr. 38, 39- 19
2321. I F
70 THE PRINCIPLES OF LOGIC BOOK I
our assertion attains the uniqueness without which it would
not correspond to the fact. And analytic judgments, it may
seem, are thus secured to us. But now, when we return to
the question we asked in 19, and when we pass to judgments
that are synthetic, and extend to spaces and times not falling
within the radius of direct presentation, we seem at first
sight to be no better off. What we have gained, it may
now appear, has been at the expense of everything beyond.
The series of all our spaces and times will now have to be
referred to the one unique point of contact with reality.
It is only so that their content can, be stamped with
the mark of fact. But it seems impossible to establish this
relation.
The content of these synthetic assertions we know is uni
versal. It may be true of innumerable other series. This
unsubstantial chain, if left to itself, does not touch the ground
in any one point. On the other hand, the given source of
reality refuses, it seems, to have anything to do with these
floating threads. Their symbolic content can not be directly
attributed to the presentation, because it is irreconcileable
with the content of that. And, if we can not have another
presentation, where is the fact in connection with which our
universals can attain reality?
29. We must turn in our difficulty to a result we got
from a former discussion. 20 We saw that the real, which
appears in perception, is not identical with the real just as it
appears there. If the real must be " this," must encounter us
directly, we cannot conclude that the " this " we take is all
the real, or that nothing is real beyond the "this." It is
impossible, perhaps, to get directly at reality, except in the
content of one presentation : we may never see it, so to speak,
but through a hole. But what we see of it may make us
certain that, beyond this hole, it exists indefinitely. If by
" this " we understand unique appearance, then, as " this " was
not any part of the content, so neither is it any quality of the
real, in such a sense as to shut up the real within that quality.
It would belong to metaphysics to discuss this further, and we
must here be content with a crude result. The real is what
appears to me. The appearance is not generic but unique.
CHAP. II FORMS OF JUDGMENT 71
But the real itself is not unique, in the sense in which its
appearance is so. 21
The reality we divined to be self -existent, substantial, and
individual ; but, as it appears within a presentation, it is none
of these. The content throughout is infected with relativity,
and, adjectival itself, the whole of its elements are also
adjectival. Though given as fact every part is given as
existing by reference to something else. The mere perpetual
disappearance in time of the given appearance is itself the
negation of its claim to self -existence. And again, if we take
it while it appears, its limits, so to speak, are never secured
from the inroads of unreality. In space or in time its outside
is made fact solely by relation to what is beyond. Living by
relation to what it excludes, it transcends its limits to join
another element, and invites that element within its own
boundaries. But with edges ragged and wavering, that flow
outward and inward unstably, it already is lost. It is ad
jectival on what is beyond itself. Nor within itself has it any
stability. There is no solid point of either time or space.
Each atom is merely a collection of atoms, and those atoms
again are not things but relations of elements that vanish.
And when asked what is ultimate, and can stand as an indi
vidual, you can answer nothing.
The real can not be identical with the content that appears
in presentation. It for ever transcends it, and gives us a title
to make search elsewhere.
30. The endeavour to find the completeness of the real,
which we feel can not exist except as an individual, will lead
us first to Synthetic judgments of time and space. But, before
we proceed, we may pause for a moment, to reflect on the
general nature of the attempt. If the reality is self-existent,
self-contained, and complete, it needs, one would think, no
great effort of reason to perceive that this character is not to
be found in a mere series of phenomena. It is one thing to
seek the reality in that series ; it is quite another thing to try
to find it as the series. A completed series in time or space
can not possibly exist. 22 It is the well-known phantasm of the
spurious infinite, a useful fiction, it may be, for certain purposes
and at certain levels of thought, but none the less a phantasm
72 THE PRINCIPLES OF LOGIC BOOK I
which, until it is recognized, stops the way of all true philo
sophic thought. It emerges often in the school of " experience,"
in its Logic and again in its Hedonistic Ethics, where it begets
and will continue to beget chimeras. We shall meet it again
in the present chapter, but must return to our search for reality
within a series of phenomena, a search not yet degraded to a
pursuit of phantasms, but carrying in itself the root of illusion.
31. The real then itself transcends the presentation, and
invites us to follow it beyond that which is given. On the
other hand, we seem to find contact with reality and to touch
ground nowhere, so to speak, outside the presented. How
then is a content to be referred to the real, if it can not be
referred to the real as perceived? We must answer that the
content is referred indirectly. It is not attributed to the given
as such; but, by establishing its connection with what is
presented, it is attributed to the real which appears in that
given. Though it is not and can not be found in presentation,
it is true because it is predicated of the reality, and unique
because it is fixed in relation with immediate perception.
The ideal world of spaces beyond the sensible space, and of
times not present but past and future, fastens itself on to the
actual world by fastening itself to the quality of .the immediate
this. In a single word continuity of content is taken to
show identity of element.
32. But such continuity, and the consequent extension
of the " this " as given, depend, like every other ideal con
struction, on identity. 23 An inference always, we shall see
hereafter, stands on the identity of indiscernibles. Sameness
of quality proves real sameness (vid. Book II. Part I. Chap.
VI.). And the identity here has a double form, (i) In the
first place the symbolical content must have " thisness."
(ii) In the second place it must share some point with the
" this."
To explain, (i) the idea we are to connect with perception
must be the idea of something in space or some event in time.
It must have the character of particularity, the general idea of
indefinite detail and endless relation. We know by this that
it is of the same sort as the content of the given. The de
scription of both is one and the same. They both have
" thisness," and therefore their element may be identical.
CHAP. II FORMS OF JUDGMENT 73
(ii) But, so far as we have gone, we still are left in the
world of universals, which may or might touch the ground in
some place and meet the fact which appears in perception,
but which do not certainly do thus. We wish, on the one side,
to pass beyond presented content, and, on the other side, to
connect with this content an ideal series; and we seek for a
link by which to fasten them together.
That link is found by establishing a point which is the
same in both, and is the same because its quality is the same.
The " this " contains a complex of detail, either times or
spaces (or both) in series, which we may call c. d. e. f. The
idea, on its side, contains a series of particulars a. b. c. d.
The identity of c. d. in each extends the perception c. d. e. f.
by the ideal spaces or times a. b., and the whole is given
by synthetical construction as a single fact a. b. c. d. e. f.
The whole series now is referred to the real, and by the con
nection with unique presentation, has become a series of events
or spaces, itself unique and the same as no other series in the
world. It is thus by inference that we transcend the given
through synthetic judgments, and our following Books must
explain more clearly the nature of inference, and the enormous
assumption on which it reposes.
33. Mental pathology will afford an illustration. There
are cases where the subject or, if we please, the Ego seems
divided in two. When one self is present the other is absent,
and the memories of either self are distinct. Their pasts and
futures do not ever touch. The explanation that is offered,
and which seems sufficient, will illustrate our theme. It is
because the present selves are different, that the past and
future selves are foreign. It is because one system of ideas
has not got a point of connection with the other system, or
has rather some point which excludes the connection, 24 that
the one can never be used to extend ideally a present which
belongs to the other. Some mode of morbid feeling or dis
eased perception, given now in presentation, links on to itself
the ideas that are grouped by the same characteristic. The
whole ideal region where that colouring fails, may perhaps be
suggested, but can never be fixed in continuous relation with
the present perception.*
*Cf. Lotze, Mikrokosmus, I. 371.
74 THE PRINCIPLES OF LOGIC BOOK I
34. If we mean by phenomena the things we perceive,
or the facts or appearances that are given to us, then the
whole of England below our horizon (to say nothing at all of
America and Asia), and every event that is past or future are
not phenomena. They are not perceived facts. They exist in
our minds as mere ideas, as the meaning of symbols. A phe
nomenon, I repeat, that is past or future is a sheer self-contra
diction. It is time we thought of giving up our habit of talking
about the " series of phenomena," or " thread of perceptions,"
or Heaven knows what else, as though we held these facts in
our hands. One thing or the other. Either a phenomenon
may be ideal, the content of a symbol and not even predicated
directly of the present perception, or there is no phenomenon
but what I here and now perceive. It is idle perhaps to ap
peal to facts in protest against the philosophy of " analysis "
and the school of " experience." It is impossible, I know, to
persuade the man who is wedded to these names, that he has
failed to earn a legitimate title to neglect the first and to be
false to the second. Profuse protestations, and jealousy of
the untitled, are services found not too exacting, and which
satisfy those who have long ago and cheaply become
cool. But, for the sake of others, I will repeat once
more. If a fact or event is what is felt or perceived, then
a fact that is past is simple nonsense (cf. Book II. Part II.
Chap. I.).
Of course, I know, it is easy to say that past events are all
really there, and, being there, are remembered; as I presume
the future, being all there, is anticipated. But suppose that
there is a series of facts, both past and future, outside our
minds, the question remains, How can they get in? You may
say, if you like, They are fond of a change, and walk in and
out bodily and meet and converse there. Or an omnipotent
Creator has endowed the mind with an extraordinary organ,
which perpetually can do what no one understands, and, defy
ing the insidious arts of the analyst, proves by the way the
immortality of the soul. Or perhaps you may find it a " final
inexplicability." Ultimate facts always are inexplicable, and
we must not be put out if they contradict those doctrines they
must know to be true. For it is natural for the inexplicable
to behave inexplicably.
CHAP. II FORMS OF JUDGMENT 75
But perhaps there are readers content to remain on a level
with ourselves. If so they will continue to believe the conclu
sion that facts have brought to us. And that conclusion is that
events past and future, and all things not perceived, exist
for us only as ideal constructions connected, by an inference
through identity of quality, with the real that appears in
present perception. In what character (if any) these things
may really exist for themselves, is a question for meta
physics. 25
35. Synthetic judgments thus cease to be merely adjec
tival, and they express a series of unique events by indirect
reference to the real which appears in unique presentation.
They are connected by an inference with the content of this
appearance, and so far are directly related to perception. But
their ideas are never referred as adjectives to the presentation
itself. They are attributed to the reality, which both shows
itself there, and extends itself beyond. The content of our
perceptions, and the content of our ideal constructions, are
both the adjectives of one reality. They are both appear
ances, which come to us in different ways, but which both
(unless our assumptions are false) are valid and true of the
real world.
36. Memory of the past, and prediction of the future,
are separated clearly from mere imagination. 26 In the former
we have the reference to that reality which appears in per
ception. We have a judgment which is either true or false,
because it implies a relation to fact. But imagination is with
out this reference. The merely imagined, we have seen before
(Chap. I. 14), may be stronger than that which we judge to
be true. What we only fancy may have more thisness; it
may have more compulsory and particular detail than that
which we remember. But what it wants is a point of identity
by which to fasten it on to the " this." And without such a
link it must fall outside the series.
We generally, it is true, take forcible detail and strong
particularity as a sign of fact, and look for its place in the
series of events. But, if the place is not found, the imagined
fact is never secured to us. The visions of dreams may
be very definite, but the content of those visions refuses to
link itself to the series of events connected with perception,
76 THE PRINCIPLES OF LOGIC BOOK I
and so, if we cannot get rid of the ideas, at least we stamp
them as mere illusions.
If this were the place for an excursion into psychology, we
should find some difficulties and many interesting questions.
When once we have referred a content to the real, we generally
tend to refer it again. We say that we know it happened at
some time, though when we can not say. And we might be
tempted perhaps to think that such ideas have greater strength
or fuller detail than mere imaginations. This would be er
roneous. It is not strength or detail which marks these ideas,
but something so dim that we can not grasp it. It may be the
general idea of reference to the " this," which, repelled by the
content of the given " this," transcends it vaguely. It may be,
on the other hand, some unconscious element of idea or feel
ing, which serves to identify in an indefinite way the imagined
with fact. For it is a mistake to suppose that these links
with reality need be anything explicit. A feeling so obscure
that we are not aware of it, and which perhaps no effort of
attention would be able to distinguish from its vague totality
of consciousness, may serve as the basis by which we sepa
rate a truth from a fiction (33). We must remember again
that the point of connection may be, so to speak, in our in
ward selves, and not at all in the outward series. If a false
hood imagined is in the end believed, it is not always because
it gains some kind of direct connection with outward fact.
In the end it may actually identify itself with the habitual
feeling which we have of ourselves. And this common
meeting-ground of illusion and truth serves often to confuse
them together in our minds. But we can not here further
pursue these discussions.
37. To resume, It is not the mere symbolic use of ideas
which distinguishes truth from bare imagination. For imagi
nation is not confined to particular images. Just as in percep
tion it is hard to say where inference first appears, and where
the analytic judgment becomes synthetic, so in much imagina
tion we shall find the presence of a discursive element. The
idea of a circle, we might say and say falsely, was nothing
but an image; but the idea of a chiliagon would show us at
once that there is a point where our imagery fails. And it is
obvious that ideas of abstract relations may be held before the
CHAP. II FORMS OF JUDGMENT 77
mind without any judgment. This, however, is a content
which is wholly symbolic, and yet (where no hypothetical
judgment comes in) it is purely imaginary. It is detached
from the existence of the image in our minds, but it is not
attached to another reality. 27
38. We now perhaps are able to say what it is we mean
by the idea of an individual (or, we had better say, of a par
ticular) fact. We saw the futility of seeking to find this in
the proper names of persons, for what they stand for is never
confined to a single event. The idea of particularity implies
two elements. We must first have a content qualified by
" thisness," and we must add to that content the general idea
of reference to the reality. In other words a particular must
first be represented in a series ; this gives us the first element.
But so far we do not get beyond mere " thisness ; " the
members are exclusive, within the series, but the whole col
lection is not unique. To get the complete idea of a par
ticular fact we must make our series, so to speak, externally
exclusive as well and thus particular. And we do not do this
till we qualify it by the idea of reference to our unique
reality.
If we actually attributed the series to reality, we not only
should have got the idea that we wanted, but also more. 28 We
should have judged that our idea was true in fact. And in
this case we do not wish to go so far. We desire to have the
idea of uniqueness, but not to assert the reality of the idea.
We possess, as we have seen ( 24) in the idea of "this,"
the idea of immediate contact with the real, and it is this idea
we must add to our series. When we think of the series both
as a whole, and as touching the real in a point of presentation,
we have thought of it then as truly particular. But there we
must stop. For if we went on to judge our idea to be true,
we should have to find it a special place in the unique series
which extends perception. And we saw that to use the idea
of " this " as the symbol of another content in judgment, was
quite impossible. So long, however, as we abstain from judg
ment, we can attach the aspect of " this " to a content other
than that which is really presented.
This is what we mean by the idea of a particular. There
is a difference when we come to an individual person. Our
78 THE PRINCIPLES OF LOGIC BOOK I
idea is there particular, since it has limits within a particular
series. But it also involves a real identity persisting through
out a change of events. And so it falls outside the class of
mere synthetic judgments.
39. Uniqueness is merely the negative side of the idea of
" this." A content is unique when, although of a sort (and
that means regarded from the aspect of content) it neverthe
less is the same as no other, is the only one there is of its
sort. Uniqueness implies the idea of a series, 29 and is then
relative or absolute. It is relative when the series, which con
tains the element which excludes the others, is itself not
unique. In any universe our fancy constructs, a thing may be
unique but only unique within that universe. We have, on
the other hand, absolute uniqueness when the series is con
nected with direct presentation. In that case the relations
within the series fix against each other the elements it holds,
and nothing can be fact without its appearing in that one
series. But the real subject, which, in predicating uniqueness,
excludes any other event of the kind, we must remember, is
not the particular event as such and taken by itself. It is
rather the real which appears in that particular and so ex
cludes others. We have here a negative existential judg
ment, for the nature of which we must consult our Third
Chapter.
40. After meeting many difficulties, some of which, I
trust, may have been overcome, we have finished our account
of the second division of singular judgments. We must pass
to the third, the assertions not confined to an event or a num
ber of events in time (7). But, before we proceed, let us
pause for a moment, and, however dangerous the experiment
may be, let us try to put before our very eyes a synthetic
judgment. Let us call before our mind some series of pictures,
like Hogarth s Progress of the harlot or rake ; but let us also
imagine something beside. One picture in the series must be
the reality, the actual person in a real room, and on the walls
of this real room must be hung the series of earlier and later
pictures. By virtue of the sameness in the quality of the man,
as he is in the room and is in the pictures, we, neglecting the
appearance in particular frames, arrange the whole series as
his past and future. We transcend in this way the visible room
CHAP. II FORMS OF JUDGMENT 79
and the presented scene, and view the real life of the person
extending itself as a series in time.
But the man in the real room that we see, is body and
bones and breath and blood, while his past and future, if we
mean by reality a sensible fact, are nothing in the world but
glass and wood and paint and canvas. It is the same with
all our future and past. The events of memory and of
anticipation are facts now in our minds, but they no more
are the reality they represent than paint and canvas are a
throbbing heart. No doubt they stand for reality, and we
flatter ourselves that, if they can not be fact, at least they are
true. True indeed they may be if truth means a natural and
inevitable way of representing the real. But if by their truth
we understand more than this; if we say that the reality is
as it appears in our ideal construction, and that actually there
exists a series of facts past present and future I am afraid
that truth, if we came to examine it, would change into false
hood. It would be false if measured by the test of perception,
and it may be, if tried by another standard, it would be falser
still.
41. The life of a man can not be presented in any one
scene, and our very illustration has gone farther than we
thought. That life is not even a mere succession of serial
events, but contains (so we think of it) a something the
same, a real identity which appears in all, but which is not any,
nor even every, event. We find ourselves brought to the third
main class of singular judgments, 30 and are speaking of a sub
ject which is not an event. These judgments are separated
into two divisions, according as the individual with which they
deal is related to some given period of time, or not to any
time in particular.
III. (i) In the history of a man or nation we have a
content referred to the real, but to the real as it appears
throughout one certain part of that series which is deter
mined by relation to given perception, (ii) In the second
division we must place any judgments we make about the
Universe or God or the soul, if we take the soul to be eternal. 31
Our ideas are here identified with the real that we find in per
ception, but they do not not attach themselves to any one part
of the phenomenal series. It may be said, of course, that such
80 THE PRINCIPLES OF LOGIC BOOK I
judgments are illusory. But, as we saw, that conclusion, if
true, could only be established by a metaphysical enquiry we
have no place for. The judgments exist, and logic can do
nothing else but recognize them.
This third and last class of singular judgments is distinct
from the others. Its essence is that its ultimate subject is
not the real, as it appears in the " this " or in any one event
in the series. But the distinction is to a certain extent un
stable. Just as analytic judgments are always tending to be
come synthetic, so here it is impossible to separate sharply the
first division of this class from synthetic judgments. On the
one hand the continuity of the element of time strictly ex
cludes a mere serial character. 32 In every judgment about
events we unknowingly are asserting the existence of an iden
tity. On the other hand an individual living in a series seems
naturally to belong to that class of judgment which constructs
a series. Since, however, when an individual is concerned,
we explicitly recognize something real, enduring throughout
the changes of events, it is better perhaps to keep up a dis
tinction which in principle must be admitted to fluctuate. The
example of an individual person took us from analytic to
synthetic judgments. And it has served again to carry us on
further.
42. 3 3 We have now considered all the three classes of
singular judgments, and have seen in what way they attribute
an idea to the real which appears. We have already antici
pated the account to be given of Existential judgments, and
may deal with them rapidly. Confining ourselves here to those
which are affirmative, we can say at once that the subject in
all of them is the ultimate reality, either (a) as it appears in
some part of the series determined by the "this," or (b) as it
underlies the whole series of phenomena. When I say " A
exists," or " A is real," the content A is in truth the predicate.
We use it to qualify existence or reality, in one of the two
senses we have now mentioned.
The enquiry into existential propositions reduces to ab
surdity the notion that judgment consists in ideas. If we
add to the adjectival idea of A another adjectival idea of
reality, then, failing wholly in reference to fact, we fall
CHAP. II FORMS OF JUDGMENT 8l
entirely short of judgment. But this is not all. The idea of
reality, like the idea of " this," is not an ordinary symbolic
content, to be used without any regard to its existence. 34 The
idea of what is real, or of that which exists, is found as an
element in that actual reality and actual existence which we
encounter directly. It can not in judgment be removed from
this, and be transplanted away to another reality. We have
here the same obstacle which met us before ( 25-27). The
idea cannot be predicated of anything except its own reality.
For, to get the idea, you must take it by a distinction from
what is given. If you then make it a predicate of anything
not given, you have a collision, and your judgment disappears.
But if, on the other hand, you predicate it of that which
actually is given, your procedure is idle. Why employ an idea
to assert reality when you have the fact, and when your ideal
synthesis is a mere analysis of this given reality, and at
tributed in the end to that as subject? " Real " is clearly the
adjective of " reality," and we know no reality but what ap
pears in presentation. The idea then, to be true, must be
true of that reality. But, if so, we must have the subject
before us in the shape of fact, and, if we did not, the idea
would at once become false. For a more detailed discussion
we may refer to 25-27.
Nor would it repay us here to examine the somewhat
surprising view which Herbart has advocated (vid. 75).
Our enquiries in this chapter should have prepared us for the
result that the ultimate subject is never an idea, and that the
idea of existence is never a true predicate. The subject, in
the end, is always reality, which is qualified by adjectives of
ideal content.
43. We cannot say there is a class of existential judg
ments, for all singular judgments have by this time been shown
to be existential. And, with this conclusion, we may pass be
yond them to another branch of affirmative judgments. In
these we no longer have to do with any particular facts or
in any sense with separate individuals. They are universal in
the sense of transcending what is singular. They are not
" concrete " but " abstract," since, leaving things, they assert
about qualities, alone or in synthesis. In this respect, we may
remark in passing, there is no real difference between the
82 THE PRINCIPLES OF LOGIC BOOK I
" general " and the " abstract ; " for, taken in comparison with
the particular thing, 35 the general idea is a mere abstraction.
44. We have reached the common type of universal
judgment; and the point in this which we notice at once, is
that every such judgment is concerned with adjectivals. 36
They assert a connection between elements of content, and
say nothing about the place of those elements in the series of
events. In " Equilaterial triangles are equiangular " all I affirm
is that with one set of qualities you will have the other set,
but I make no assertion about where and when. And " Mam
mals are warm-blooded " does not tell me anything about this
or that mammal. It merely assures me that, finding one at
tribute, I shall find the other.
The fact that is asserted in an abstract judgment is not
the existence of the subject or predicate (6), but simply the
connection between the two. And this connection rests on a
supposal. The abstract universal, " A is B," means no more
than " given A, in that case B," or " if A, then B." In short,
such judgments are always hypothetical and can never be
categorical. And the proper terms by which to introduce them
are " given," or " if," or " whenever," or " where," or " any,"
or "whatever." We should beware of "all."
45. For the use of "all," we have seen above (6), is
most misleading and dangerous. It encourages that tendency
to understand the universal in the sense of a collection, 27 which
has led to so many mistaken consequences. We shall glance
elsewhere at that extraordinary teaching on the subject of
quantity, in which the traditional logic delights. And we shall
see hereafter, when we come to inference, the absurd incom
petence of the dictum de omni. For our present purpose we
need criticize no further the attempt to understand the " all "
collectively. Even if that use were justifiable in itself, it
would be irrelevant; for a judgment where "all" means a
real collection of actual cases, 38 belongs to a class we have al
ready disposed of. If " all " signifies a number of individual
facts, the judgment is concerned with actual particulars. And
so it obviously is but one form of the singular judgment.
" All A is B," will be an abbreviated method of setting forth
that this A is B, and that A is B, and the other A is B, and
CHAP. II FORMS OF JUDGMENT 83
so on until the lot is exhausted. Such judgments fall clearly
under the head of singular.
But, when this class is banished to the preceding category,
have we any universal judgments left us? We can not doubt
that; for there are judgments which do not assert the exist
ence of particular cases. We come at once upon the judg
ments that connect adjectival elements, and that say nothing
about the series of phenomena. These abstract universals are
always hypothetical and never categorical.*
46. At this point we must pause to encounter an objec
tion. " The distinction," we may be told, " between categorical
and hypothetical is really illusory. Hypothetical judgments
can all be reduced to, and in the end are nothing but, a kind
of categorical." If this were well founded, it would certainly
occasion us serious difficulty. But I do not think we need much
disturb ourselves.
" If A is B it is C," we may be told, " is equivalent to The
instances or cases of A that are B are also C, and this is
surely a categorical judgment." I answer, if " the cases of A
that are B " means the existing cases of A B, and no others,
then the judgment no doubt is categorical, but it is not an ab
stract universal. It is merely collective, and it most certainly
does not mean what we meant by our hypothetical judgment.
" If butter is held to the fire it melts " is no assertion about
mere existing pats of butter. And when it is reduced to the
form, " All cases of the holding of butter, &c.," it does not
become any more categorical. " All cases " means here
"Suppose any case."
Indeed, if we steadily keep in view the difference between
a simple assertion about fact and an assertion on the strength
of and about a supposition, we may perhaps be puzzled, but
we are not likely to be led far astray by these elementary mis
takes.
47. And with this remark I could leave the matter. But
* The extensional theory of judgment and reasoning is dealt with
elsewhere (Chap. VI. and Book II. Part II. Chap. IV.). We may here
remark that, taking " A is B " to mean " the things that are A are the
things that are B," the judgment must be singular, if an existing set
of things be denoted, and will be universal and abstract if possible
things are included as well. 39
84 THE PRINCIPLES OF LOGIC BOOK I
it is perhaps worth while, by another instance, 10 illustrate
the futility of this attempt to turn hypothetical into categorical
judgments. J. S. Mill in his Logic (I. 4, 3) approaches the
subject with an air of easy superiority. " A conditional
proposition is a proposition concerning a proposition."
" What is asserted is not the truth of either of the proposi
tions but the inferribility of the one from the other." " 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. J:
How this doctrine is connected with Mill s other views as to
the import of propositions, an expert in Mill-philology no
doubt could inform us. But, left to ourselves, we can only
conjecture the doctrine he here intended to teach, (i) If he
really meant "inferribility" then cadit qucestio. For at once
the statement is not about what is, but what may be or might
be. It is not simply about existing propositions, but clearly
involves a supposal of some kind, and is therefore not reduced
to categorical form. It is still Suppose you have got AB, then
you may go legitimately to CD. (ii) But no doubt there is
more than this verbal quibble. He tells us that one is an
inference from the other. Does this mean (a) that both are
actually asserted, and that I further assert that I really have
argued to the second from the first ? Surely not that ; but then
what else? (&) Can it mean that, without asserting either
proposition, I hold them in my mind, and affirm their con
nection? It may mean this. But then this process of taking
up a statement without believing it, and of developing its con
sequences, is in fact nothing else than a supposition. The
connection asserted is not between realities, and the proposi
tion is still hypothetical, (iii) But the extraordinary illus
trations towards the end of the section point to another
interpretation ; " The subject and predicate are names of propo
sitions." Without, however, attempting the hopeless task of
understanding, we may perhaps state the issue in the form
of a dilemma. Either (a) one proposition, in the sense of
a little heap of words, does, as a particular event in my head,
now follow another such heap; or (&) it would follow, if
the other were there. The second alternative is of course still
hypothetical. In the former at last we have got to something
CHAP. II FORMS OF JUDGMENT 85
categorical, but nothing to which a hypothetical judgment
(or indeed any judgment) could possibly be reduced. It would
be an error too gross to merit refutation.
Whatever else may be the meaning of the writer, we after
all may remain sure of this. Either the categorical judgment,
to which he professes to reduce the hypothetical, is not its
equivalent; or else it contains, under some flimsy veil of
verbal ambiguity, a supposition which is the condition of the
judgment.
48. Such universal judgments are all hypothetical, and
with this conclusion we are landed once more in our former
difficulties (6). Judgment, we saw, always meant to be true,
and truth must mean to be true of fact. But here we en
counter judgments which seem not to be about fact. For a
hypothetical judgment must deal with a supposal. It appears
to assert a necessary connection, which holds between ideas
within my head but not outside it. But, if so, it can not be a
judgment at all; while on the other hand it plainly does
assert and can be true or false.
We are not able to rest in this conclusion, and yet we can
not take back our premises. Let us then try to look more
closely at the problem, and ask more narrowly what is involved
in these judgments. And, in the first place, we can not expect
to succeed until we know what a supposal is.
A supposition, in the first place, is known to be ideal, and
known perhaps to diverge from fact. At a low stage of mind,
where everything is fact (cf. Chap. I.), it could not exist. For
the supposed must be known as an ideal content, and, in
addition, it has to be retained before the mind without a
judgment. It is not referred as an adjective, either posi
tively or negatively, to the real. In other words reality is not
qualified either by the attribution or the exclusion of it. But
though it does not judge, a supposition is intellectual, for (as
such) it excludes desire and emotion. And again it is more
than mere imagination, for it is fixed by attention and pre
serves, or should preserve, its identity of content (vid. Book
III. Chap, III. 23, 24). It certainly is all this, and yet this
is not all. For to think of a chimsera is not quite the same
thing as to suppose a chimaera.
A supposition means thinking for a particular end, and in
86 THE PRINCIPLES OF LOGIC BOOK I
a special way. It is not a mere attending to a certain meaning,
or an analysis of its elements. It has a reference to the real
world, and it involves a desire to see what happens. We may
illustrate perhaps from other usages. " Say it is so for argu
ment s sake," "Treat it as this and then you will see," are
much the same as, " Suppose it to be so." A supposal is, in
short, an ideal experiment. 40 It is the application of a con
tent to the real, with a view to see what the consequence is,
and with a tacit reservation that no actual judgment has taken
place. The supposed is treated as if it were real, in order to see
how the real behaves when qualified thus in a certain
manner.
You might say it is the adding the idea of existence to a
given thought, while you abstain from judgment. But that I
do not think would be satisfactory. For it is not the mere
idea of existence that is used. What we use is the real that is
always in immediate contact with our minds, and which in a
variety of judgments we already have qualified by a certain
content. And it is to this that we bring up another idea, in
order to see what result will come of it.
. 49. So far there is neither truth nor falsehood, for we
have not judged. The operation, we may say, is so far
"subjective." It is all our own doing, and all of it holds
inside our heads, and not at all outside. The real is not
qualified by the attribute we apply to it. But, so soon as we
judge, we have truth or falsehood, and the real is at once
concerned in the matter. The connection of the consequence,
of the " then " with the " if," of the result of our experiment
with its conditions, is the fact that is asserted, and that is true
or false of the reality itself.
But the question is how. You do not assert the existence
of the ideal content you suppose, and you do not assert the
existence of the consequence. And you can not assert the
existence of the connection, for how can a connection remain
as a fact when no facts are connected? "If you only had
been silent you would have passed for a philosopher." But
you were not silent, you were not thought a philosopher, and
one was not, and could not possibly be, a result of the other.
If the real must be qualified by the connection of the two, it
seems that it will not be qualified at all. Neither condition,
CHAP. II FORMS OF JUDGMENT 87
nor result, nor relation can be ascribed to it ; and yet we must
ascribe something, for we judge. But what can it be?
50. When I go to a man with a fictitious case, and lay
before him a question of conduct, and when he replies to me,
* I should act in this way, and not in the other way," I may
come from him with some knowledge of fact. But the fact is
not the invented position, nor yet the hypothetical course of
action, nor the imaginary relation between the two. The fact
is the quality in the man s disposition. 41 It has answered to a
trial in a certain way. But the test was a fiction, and the
answer is no fact, and the man is not qualified by one or the
other. It is his latent character that is disclosed by the
experiment.
It is so with all hypothetical judgment. The fact that is
affirmed as an adjective of the real, and on which depends the
truth or falsehood, does not explicitly appear in the judgment.
Neither conditions nor result of the ideal experiment are taken
to be true. What is affirmed is the mere ground of the con
nection; not the actual existing behaviour of the real, but a
latent quality of its disposition, a quality which has appeared
in the experiment, 42 but the existence of which does not de
pend on that experiment. "If you had not destroyed our
barometer, it would now forewarn us." In this judgment we
assert the existence in reality of such circumstances, and such
a general law of nature, as would, if zve suppose some condi
tions present, produce a certain result. But assuredly those
conditions and their result are not predicated, nor do we even
hint that they are real. They themselves and their connection
are both impossible. It is the diminution of pressure and
the law of its effect, which we affirm of the actual world
before us. And of course that law is resolvable further
(52).
51. In all judgment the truth seems none of our mak
ing. 43 We perhaps need not judge, but, if we judge, we lose
all our liberty. In our relation to the real we feel under
compulsion (4). In a categoric judgment the elements them
selves are not dependent on our choice. Whatever we may
think or say, they exist. But, in a hypothetic judgment, there
is no compulsion as regards the elements. The second, in
deed, depends on the first, but the first is arbitrary. It depends
88 THE PRINCIPLES OF LOGIC BOOK I
on my choice. I may apply it to the real, or not, as I please ;
and I am free to withdraw the application I have made. And,
when the condition goes, the result goes too. The compulsion
extends no further than the connection, and yet it does not
extend to the connection as such. The relation of the ele
ments in a hypothetical judgment is not an actual attribute of
the real, for that relation itself is arbitrary. It need not be
true outside the experiment. The fact which existed before
the experiment, and remains true after it, and in no way
depends on it, is neither the elements, nor the relation be
tween them, but it is a quality. It is the ground of the
sequence that is true of the real, and it is this ground which
exerts compulsion.
52. This quality of the real is not explicit in the judg
ment, and, in respect of that judgment, is occult or latent. We
know it is there because of its effects, but we are not able to
say what it is. We can not even tell, without further enquiry,
that it is not the same as what we have asserted in another
judgment, the elements of which, and also their relation, were
very 44 different (cf. Chap. III. 19). And, when we push
the investigation further, and ask, Are these qualities, that
thus seem to lie at the base of our judgments, altogether
latent, or only latent each in respect of its peculiar judgment,
then we get at once into difficult questions. It is certain on
the one hand that we can find the grounds of many such
judgments, which thus have relatively become explicit. But
this only serves to bring us nearer to the doubt, whether in the
end they have ceased to be latent. Do we ever get to a ground
of judgment which we can truly ascribe to the real as its
quality? Or are we left with ultimate judgments, which are
certainly true, but neither the elements nor relations of which
are true of reality? Must we say, in the end, that the quality,
which we know is the base of our synthesis, remains in other
ways altogether unknown and is finally occult? We seem here
to be asking, in another form, for the limits of explanation,
and it would be the task of metaphysics to pursue an enquiry
which must here be broken off. 45
53- We have seen that, what hypothetical judgments
assert, is simply the quality which is the ground of the con
sequence. And all abstract universal, we have seen are
CHAP. II FORMS OF JUDGMENT 89
hypothetical. It may here be asked, Are the two things
one? Are all hypothetical judgments thus universal?
This might for a moment appear to be doubtful, since the
real, to which application is made, is at times an individual.
And for the purposes of this, and the following section, I will
give some examples; "If God is just the wicked will be
punished," " Had I a toothache I should be wretched," " If
there were a candle in this room it would be light," "If it is
now six o clock we shall have dinner in an hour," " If this
man has taken that dose, he will be dead in twenty minutes/*
It may surprise some readers to hear that these judgments are
as universal as " All men are mortal : " but I think we shall
find that such is the case. 46
In the first place it is certain that in none of these judg
ments is the subject taken to be actually real. We do not
say above that a just God exists, or that I have a toothache;
we only suppose it. The subject is supposed, and, if we
consider further, we shall find that subject is nothing more
than an ideal content, and that what is asserted is not any
thing beside a connection of adjectives. The " that," the
"this," the "I," the "now," do not really pass into the
supposition. They are the point of reality to which we apply
our ideal experiment, but they themselves are in no case sup
posed. More or less of their content is used in the hypothesis,
and passes into the subject. But, apart from themselves, their
content can not possibly be called individual.
54. This would hardly be doubtful, were it not for the
ambiguity of all these assertions, a point to which we should
carefully attend. " If he had murdered he would have been
hanged," may perhaps assert nothing but the general connec
tion of hanging with murder, and the " he " is irrelevant. But
" if God is just the wicked will be punished," may perhaps
not say that punishment would follow from any justice, but
only from justice that is qualified by omnipotence. On the
other hand, when you say " If this man has taken that dose,
&c.," you do not tell me if his speedy death would happen
because the dose would poison any one, or would only poison
such a man as he is, or would not even poison such a kind of
man, unless under present special conditions. And the other
examples would all entangle us in similar ambiguities. The
go THE PRINCIPLES OF LOGIC BOOK I
supposition is not made evident, and reflection convinces us
that, supposing we know the subject of the judgment, at all
events we do not display our knowledge.
55. And since this is so, since the adjectival content is
not made explicit, since all we have is an indefinite reference
to this or that case, we fall into the mistake of thinking it is
the particular we have to deal with. But our real assertion,
when we come to analyze it, never takes in the " that," or the
" now," or the " this." It is always the content about which
we assert. But, because we are not clear what that content is,
and because we know it is to be found in the individual as
supposed, we fire, so to speak, a charge of shot instead of a
bullet, and take the individual as the point of reality to which
our supposition is to be confined. In this way we give rise
to the erroneous idea that the reality itself passes into the
supposal. The fact, as we have seen, is that some of the
content either is or makes part of the adjectival condition
about which we assert. But, because that content has not
been analyzed, we go to the individual to get it in the lump.
The real judgment is concerned with nothing but the indi
vidual s qualities, and asserts no more than a connection of
adjectives. In every case it is strictly universal as well as
hypothetical.
56. We have found, thus far, that all abstract judgments
are hypothetical, and in this connection we have endeavoured
to show what a supposition is, and to lay bare that occult
affirmation as to the real, which is made in every hypothetical
judgment. Singular judgments we have already discussed,
and we found that, be they analytic or synthetic, they all at
first sight seem categorical. They do not merely attribute
to the real a latent quality, which manifests itself in an unreal
relation, but they qualify the real by the actual content which
appears in the judgment. It is not the mere connection, but
the very elements which they declare to exist.
We have still remaining another kind of judgment (7),
but, before we proceed, it is better to consider the result we
have arrived at. That result perhaps may call for revision,
and it is possible that the claim of the singular judgment to
a categoric position may not maintain itself.
CHAP. II FORMS OF JUDGMENT QI
CHAPTER II (Continued)
57- What is the position in which we now find our
selves? We began with the presumption that a judgment,
if true, must be true of reality. On the other hand we found
that every abstract universal judgment was but hypothetical.
We have endeavoured to reconcile these conflicting views by
showing in what way, and to what extent, a conditional judg
ment asserts of the fact. But singular judgments stand apart,
and have claimed to be wholly categorical, and true of the
reality; and hence they demand a position above that given
to universal judgments. We must now scrutinize this pre
tension. We must still defer all notice of those individual
judgments which transcend the series of events in time. Con
fining ourselves to judgments about the phenomenal series, let
us proceed to ask, Are they categorical? Do they truly and
indeed rank higher, and closer to the real world, than those
universal judgments which we found were hypothetical? We
shall perhaps do well to prepare our minds for an unwelcome
conclusion.
In passing from the singular to the universal judgment, we
seem to have been passing away from reality. Instead of a
series of actual phenomena connected with the point of present
perception, we have but a junction of mere adjectivals, the
existence of which we do not venture to affirm. In the one
case we have what seem solid facts ; in the other we have noth
ing but a latent quality, the mere name of which makes us
feel uneasy. We have not quite lost our hold of the real, but
we seem to have left it a long way off. We keep our con
nection by an impalpable thread with a veiled and somewhat
ambiguous object.
But our thoughts may perhaps take a different colour, if
we look around us in the region we have come to. However
strange it may seem to us at first, yet our journey towards
shadows and away from the facts has brought us at last to
g 2 THE PRINCIPLES OF LOGIC BOOK I
the wo-ld of science. The end of science, we all have been
taught, is the discovery of laws; and a law is nothing but a
hypothetical judgment. It is a proposition which asserts a
synthesis of adjectivals. It is universal and abstract. And it
does not assert the existence of either of the elements it
connects. 47 It may imply this (6), but such an implication is
not essential. In mathematics,* for instance, the truth of our
statement is absolutely independent of the existence of either
subject or predicate. In physics or chemistry the truth does
not depend on the actual existence at the present moment of
the elements and their relation. If it did so, the law might be
true at one instant and false at the next. When the physio
logist, again, tells us that strychnine has a certain effect on
nerve-centres, he does not wait to enunciate his law until he is
sure that some dose of strychnine is operating in the world ; nor
does he hasten to recall it as soon as he has lost that assurance.
It would be no advantage to dwell upon this point. It may be
regarded now as a certain result, that the strict expression for
all universal laws must begin with an " if," and go on with a
" then."
58. And from this we may draw a certain presumption.
If the singular judgment is nearer the fact, and if, in leaving
it, we have actually receded from reality, yet at least in sci
ence that is not felt to be the case. And there is another pre
sumption which may help to strengthen us. In common life
we all experience the tendency to pass from one single case to
some other instance. We take what is true at one time and
place to be always true at all times and places. We generalize
from a single example. We may deplore this tendency as an
ineradicable vice of the unphilosophic mind, or we may recog
nize it as the inevitable condition of all experience, and the
sine qua non of every possible inference (vid. Book II.).
But in either case, let us recognize it or deplore it, we still do
not feel the passage we have made as an attempt to go from
the stronger to the weaker, from that which is more true to
that which is less. And yet, without doubt, it is a transition
away from the individual to the universal and hypothetical.
59. But a matter of this sort is not settled by presump
tions. There are prejudices, it may be, that operate both
ways. And we may be told, on behalf of the singular judg-
CHAP. II FORMS OF JUDGMENT 93
ment, that it is the fact that these judgments are categorical.
For they do assert the actual existence of their adjectival con
tent, and, attributing to the real an explicit quality, they are
truer than any hypothetical judgment, if indeed they are not
the only true judgments. Such, we take it, is the claim of the
singular judgment, and it can not be denied that its claim in
one respect is very well founded. It does assert the existence
of its content, and does affirm directly of the real. But the
answer we must make is that, although it does so assert and
affirm, yet, when we leave the popular view and look more
closely at the truth of things, the assertion and affirmation
which it makes are false, and the claim it puts forward rests
on a mistake. We must subject the pretensions of the singu
lar judgment to an examination which we think may prove
fatal. 48
60. We need spend no time on the synthetic judgment.
In transcending what is given by actual perception, we without
any doubt make use of an inference. A synthesis of ad
jectives is connected with the present by virtue of the identity
of a point of content. By itself this synthesis is merely uni
versal, and is therefore hypothetical. It becomes categoric
solely by relation to that which is given, and hence the whole
weight of the assertion rests on the analytic judgment. If that
is saved, it will then be time to discuss its extension; but if,
on the other hand, the analytic be lost, it carries with it the
synthetic judgment.
61. Let us turn at once to the judgments which assert
within what is given in present perception. These seem
categorical because they content themselves with the analysis of
the given, and predicate of the real nothing but a content
that is directly presented. And hence it appears that the ele
ments of these judgments must actually exist. An ideal con
tent is attributed to the real, which that very real does now
present to me. I am sure that nothing else is attributed. I
am sure that I do not make any inference, and that I do not
generalize. And how then can my assertion fail to be true?
How, if true, can it fail to be categorical?
We maintain, on the other hand, that analytic judgments
of sense are all false. There are more ways than one of
saying the thing that is not true. It is not always necessary to
Q4 THE PRINCIPLES OF LOGIC BOOK I
go beyond the facts. It is often more than enough to come
short of them. And it is precisely this coming short of the
fact, and stating a part as if it were the whole, which makes
the falseness of the analytic judgment.
62. The fact, which is given us, is the total complex of
qualities and relations which appear to sense. But what we
assert of this given fact is, and can be, nothing but an ideal
content. And it is evident at once that the idea we use can
not possibly exhaust the full particulars of what we have
before us. A description, we all know, can not ever reach to
a complete account of the manifold shades, and the sensuous
wealth of one entire moment of direct presentation. As soon
as we judge, we are forced to analyze, and forced to dis
tinguish. We must separate some elements of the given from
others. We sunder and divide what appears to us as a sen
sible whole. It is never more than an arbitrary selection
which goes into the judgment. We say " There is a wolf," or
" This tree is green ; " but such poor abstractions, such mere
bare meanings, are much less than the wolf and the tree which
we see; and they fall even more short of the full particulars,
the mass of inward and outward setting, from which we
separate the wolf and the tree. If the real as it appears is
= abcdefgh, then our judgment is nothing but X = a,
or X = dr-b. But a-b by itself has never been given, and is not
what appears. It was in the fact and we have taken it out.
It was of the fact and we have given it independence. We
have separated, divided, abridged, dissected, we have muti
lated the given.* And we have done this arbitrarily : we have
selected what we chose. But, if this is so, and if every
analytic judgment must inevitably so alter the fact, how can
it any longer lay claim to truth ?
63. No doubt we shall be told, " This is idle subtlety.
The judgment does not copy the whole perception, but why
should it do so? What it does say, and does reproduce, at all
events is there. Fact is fact, and given is given. They do not
cease to be such because something beside themselves exists.
To maintain that There is a wolf is false, because an ab
stract wolf is not given entirely by itself, is preposterous and
ridiculous."
* Cf. here Lotze s admirable chapter, Logik, II. VIII.
CHAP. II FORMS OF JUDGMENT 95
And I am afraid that with some readers this will end the
discussion. But to those who are willing to venture further,
I would suggest as encouragement that a thing may seem
ludicrous, not because it is at all absurd in itself, but because
it conflicts with hardened prejudice. And it is a prejudice of
this kind that we have now encountered.
64. It is a very common and most ruinous superstition
to suppose that analysis is no alteration, and that, whenever
we distinguish, we have at once to do with divisible existence.
It is an immense assumption to conclude, when a fact comes
to us as a whole, that some parts of it may exist without any
sort of regard for the rest. Such naive assurance of the
outward reality of all mental distinctions, such touching con
fidence in the crudest identity of thought and existence, is
worthy of the school which so loudly appeals to the name of
Experience. Boldly stated by Hume (cf. Book II. II. Chap. I.
5)5 this cardinal principle of error and delusion has passed
into the traditional practice of the school, and is believed too
deeply to be discussed or now recognized. The protesta
tions of fidelity to fact have been somewhat obtrusive, but
self-righteous innocence and blatant virtue have served once
more here to cover the commission of the decried offence in
its deadliest form. If it is true in any sense (and I will not
deny it) that thought in the end is the measure of things, yet
at least this is false, that the divisions we make within a
whole all answer to elements whose existence does not depend
on the rest. It is wholly unjustifiable to take up a complex,
to do any work we please upon it by analysis, and then simply
predicate as an adjective of the given these results of our ab
straction. These products were never there as such, and in
saying, as we do, that as such they are there, we falsify the
fact. You can not always apply in actual experience that
coarse notion of the whole as the sum of its parts into which
the school of " experience " so delights to torture phenomena.
If it is wrong in physiology to predicate the results, that are
reached by dissection, simply and as such of the living
body, it is here infinitely more wrong. The whole that is
given us is a continuous mass of perception and feeling; and
to say of this whole, that any one element would be what it is
there, when apart from the rest, is a very grave assertion. We
96 THE PRINCIPLES OF LOGIC BOOK I
might have supposed it not quite self-evident, and that it was
possible to deny it without open absurdity.*
65. I should like to digress so far as to adduce two
examples of error, which follow from the mistake we are
now considering. When we ask " What is the composition of
Mind," we break up that state, which comes to us as a whole,
into units of feeling. But since it is clear that these units by
themselves are not all the " composition," we are forced to
recognize the existence of relations. But this does not stagger
us. We push on with the conceptions we have brought to the
work, and which of course can not be false, and we say, Oh
yes, we have here some more units, naturally not quite the
same as the others, and voila tout. But when a sceptical
reader, whose mind has been warped by a different education,
attempts to form an idea of what is meant, he is somewhat at
a loss. If units have to exist together, they must stand in
relation to one another; and, if these relations are also units,
it would seem that the second class must also stand in relation
to the first. If A and B are feelings, and if C their relation
is another feeling, you must either suppose that component
parts can exist without standing in relation with one another,
or else that there is a fresh relation between C and AB. Let this
be D, and once more we are launched on the infinite process of
finding a relation between D and C-AB ; and so on for ever. If
relations are facts that exist between facts, then what comes
between the relations and the other facts ? The real truth is
that the units on one side, and on the other side the rela
tion existing between them, are nothing actual. 50 They are
fictions of the mind, mere distinctions within a single reality,
which a common delusion erroneonsly takes for independent
facts. If we believe the assurance of a distinguished Pro
fessor^ this burning faith in the absurd and the impossible,
which was once the privilege and the boast of theology, can
now not be acquired anywhere outside the sacred precincts
of the laboratory. I am afraid it is difficult to adopt such an
optimistic conclusion.
66. And perhaps I may be pardoned if, by another illus-
IIl! 9 F r thC gCneral validity of Anal ysis and Abstraction see Book
fVid. Huxley, Hume, pp. 52, 69.
CHAP. II FORMS OF JUDGMENT 97
tration, I venture to show how entirely the mind which is
purified by science can think in accordance with orthodox
Christianity. 51 In the religious consciousness God and Man
are elements that are given to us in connection. But, reflect
ing on experience, we make distinctions, and proceed as above
to harden these results of analysis into units. We thus have
God as an unit on one side, and Man as an unit on the other:
and then we are puzzled about their relation. The relation
of course must be another unit, and we go on to find that we
should like something else, to mediate once more, and go be
tween this product and what we had at first. We fall at
once into the infinite process, and, having taken up with poly
theism, the length we go is not a matter of principle.
67. To return to the analytic judgment. When I say
" There is a wolf," the real fact is a particular wolf, not like
any other, in relation to this particular environment and to
my internal self, which is present in a particular condition of
feeling emotion and thought. Again, when I say " I have a
toothache," the fact once more is a particular ache in a certain
tooth, together with all my perceptions and feelings at that
given moment. The question is, when I take in my judg
ment one fragment of the whole, have I got the right to
predicate this of the real, and to assert " It, as it is, is a fact of
sense"? Now I am not urging that the analytic judgment is
in no sense true. I am saying that, if you take it as asserting
the existence of its content as given fact, your procedure is
unwarranted. And I ask, on what principle do you claim the
right of selecting what you please from the presented whole
and treating that fragment as an actual quality? It certainly
does not exist by itself, and how do you know that, when put
by itself, it could be a quality of this reality? The sensible
phenomenon is what it is, and is all that it is; and anything
less than itself must surely be something else. A fraction of
the truth, here as often elsewhere, becomes entire falsehood,
because it is used to qualify the whole.
68. The analytic judgment is not true per se. It can not
stand by itself. Asserting, as it does, of the particular
presentation, it must always suppose a further content, which
falls outside that fraction it affirms. What it says is true, if
98 THE PRINCIPLES OF LOGIC BOOK I
true at all, because of something else. The fact it states is
really fact only in relation to the rest of the context, and only
because of the rest of that context. It is not true except
under that condition. So we have a judgment which is really
conditioned, and which is false if you take it as categorical.
To make it both categorical and true, you must get the con
dition inside the judgment. You must take up the given
as it really appears, without omission, unaltered, and un-
mutilated. And this is impossible.
69. For ideas are not adequate to sensible perception,
and, beyond this obstacle, there are further difficulties. 52 The
real, which appears within the given, can not possibly be con
fined to it. Within the limit of its outer edges its character
gives rise to the infinite process in space and time. Seeking
there for the simple, at the end of our search we still are
confronted by the composite and relative. And the outer
edges themselves are fluent. They pass for ever in time and
space into that which is outside them. It is true that the
actual light we see falls only upon a limited area; but the
continuity of the element, the integrity of the context, forbids
us to say that this illuminated section by itself is real. The
reference of the content to something other than itself lies
deep within its internal nature. It proclaims itself to be
adjectival, to be relative to the outside; and we violate its
essence if we try to assert it as having existence entirely in
its own right. Space and time have been said to be " prin
ciples of individuation." It would be truer to say they are
principles of relativity. They extend the real just as much
as they confine it.
I do not mean that past and future are actually given, and
that they come within the circle of presentation. I mean that,
although they can not be given, the given would be de
stroyed by their absence. If real with them, it would not
be given; and, given without them, it is for ever incomplete
and therefore unreal. The presented content is, in short, not
compatible with its own presentation. It involves a contra
diction, and might at once on that ground be declared to be
unreal. But it is better here to allow it free course, and to
suffer it to develope by an impossible consequence its inherent
unsoundness.
CHAP. II FORMS OF JUDGMENT gg
70. We saw that you can not ascribe to the real one part
of what is given in present perception. And now we must
go further. Even if you could predicate the whole present
content, yet still you would fail unless you asserted also both
the past and the future. You can not assume (or I, at least,
do not know your right to assume) that the present exists
independent of the past, and that, taking up one fragment of
the whole extension, you may treat this part as self-subsistent,
as something that owes nothing to its connection with the
rest. If your judgment is to be true as well as categorical,
you must get the conditions entirely within it. And here the
conditions are the whole extent of spaces and times which
are required to make the given complete. The difficulty is
insuperable. It is not merely that ideas can not copy facts of
sense. It is not merely that our understandings are limited,
that we do not know the whole of the series, and that our
powers are inadequate to apprehend so large an object. No
possible mind could represent to itself the completed series of
space and time; since, for that to happen, the infinite process
must have come to an end, and be realized in a finite result.
And this can not be. It is not merely inconceivable psycho
logically ; it is metaphysically impossible.
71. Our analytical judgments are hence all either false or
conditioned. " But conditioned/ I may be told, " is a doubtful
phrase. After all it is not the same as hypothetical. A
thing is conditioned on account of a supposal, but on the
other hand it is conditioned by a fact. We have here the
difference between if and * because. 53 When a statement is
true in consequence of the truth of another statement, they
both are categorical." I quite admit the importance of the
distinction, and must recur to it hereafter (Chap. VII. 10).
But I deny its relevancy for our present purpose.
The objection rests on the following contention. " Ad
mitted that in the series of phenomena every element is
relative to the rest and is because of something else, yet for
all that the judgment may be categorical. The something
else, though we are unable to bring it within the judgment,
though we can not in the end ever know it at all and realize it
in thought, is, for all that, fact. And, this being so, the state
ment is true ; since it rests in the end, not at all on an if
IOO THE PRINCIPLES OF LOGIC BOOK I
but upon a because/ which, although unknown, is none the
less real. Let the analytic judgment admit its relativity, let
it own its adjectival and dependent character, and it surely
saves itself and remains categorical."
But even this claim it is impossible to admit. I will not
raise a difficulty about the " because " which is never realized,
and the fact which can never be brought before the mind.
My objection is more fatal. In the present case there is no
because, 54 and there is no fact.
We are fastened to a chain, and we wish to know if we
are really secure. What ought we to do? Is it of much use
to say, " This link we are tied to is certainly solid, and it is
fast to the next, which seems very strong and holds firmly to
the next; beyond this we can not see more than a certain
moderate distance, but, so far as we know, it all holds to
gether"? The practical man would first of all ask, "Where
can I find the last link of my chain? When I know that is
fast, and not hung in the air, it is time enough to inspect the
connection." But the chain is such that every link begets,
as soon as we come to it, a new one ; and, ascending in our
search, at each remove we are still no nearer the last link of
all, on which everything depends. The series of phenomena
is so infected with relativity, that, while it is itself, it can never
be made absolute. Its existence refers itself to what is be
yond, and, did it not do so, it would cease to exist. A last
fact, a final link, is not merely a thing which we can not
know, but a thing which could not possibly be real. Our
chain by its nature can not have a support. Its essence ex
cludes a fastening at the end. We do not merely fear that it
hangs in the air, but we know it must do so. And when the
end is unsupported, all the rest is unsupported. Hence our
condition*** truth is only conditional. It avowedly depends on
what is ^ not fact, and it is not categorically true. Not stand
ing by itself, it hangs from a supposition; or perhaps a still
worse destiny awaits it, it hangs from nothing and falls
altogether.
72- It will be said, of course, that this is mere meta
physics. Given is given, and fact is fact. Nay we ourselves
distinguished above the individual from the hypothetic judg
ment, on the ground that the former went to perception, and
CHAP. II FORMS OF JUDGMENT IOI
that we found there existing the elements it asserted. Such a
plain distinction should not be ignored, because it disappears
in an over-subtle atmosphere. But I do not wish to take
back this distinction. It is valid at a certain level of thought;
and, for the ordinary purposes of logical enquiry, individual
judgments, both synthetic and analytic, may conveniently be
taken as categorical, and in this sense opposed to universal
judgments.
But, when we go further into the principles of logic, and
are forced to consider how these classes of judgment stand to
one another, we are certain to go wrong, if we have not raised
such questions as the above. It is not enough to know that
we have a ground of distinction. We must ask if it is a true
ground. Is it anything more than a point to reckon from?
Is it also fact? Does the light of presence, which falls on
a content, guarantee its truthfulness even if we copy? Are
the presented phenomenon, and series of phenomena, actual
realities? And, we have seen, they are not so. The given in
sense, if we could seize it in judgment, would still disappoint
us. It is not self-existent and is therefore unreal, and the
reality transcends it, first in the infinite process of phenomena,
and then altogether. The real, 55 which (as we say) appears
in perception, is neither a phenomenon nor a series of
phenomena.
73. It may be said " This is only the product of reflec
tion. If we are content to take the facts as they come to us,
if we will only leave them just as we feel them, they never
disappoint us. They neither hang by these airy threads
from the past, nor perish internally in a vanishing network of
never-ending relations between illusory units. The real, as
it simply comes to us in sense, has nothing of all this. It
is one with itself, individual and complete, absolute and
categorical." We are not here concerned to controvert this
statement. We are not called on to ask if anything that is
given is given apart from intellectual modification, if there is
any product we can observe and watch, with which we have
not already interfered. We have no motive here to raise such
an issue; nor again do we rejoice in that infatuation for in
tellect, and contempt for feeling, which is supposed to qualify
the competent metaphysician. Nor will we pause to argue that
2321. I H
IO2 THE PRINCIPLES OF LOGIC BOOK I
frustrated feeling itself heads the revolt against the truth of
sense. It was a baffled heart that first raised the suspicion of
a cheated head.
You may say, if you like, that the real just as we feel it is
true. 56 But, if so, then all judgments are surely false, and
your singular judgment goes with the rest. For our present
purpose we may admit your assertion, but, if it is meant as an
objection, we answer it by asking the question, What then?
Who is it who says this? Who counts himself so free from
the sin of reflection as to throw this stone? Some man no
doubt who has not an idea of the consequences of his saying;
some writer whose pages are filled with bad analysis and
dogmatic metaphysics ; some thinker whose passion for " ex
perience " is mere prejudice in favour of his own one-sided
theory, and whose loyal regard for the sensible fact means
inability to distinguish it from that first result of a crude re
flection in which he sticks.
For the present we may assume, what metaphysics would
discuss, that phenomena are what we can not help thinking
them in the end, and that the last result of our thought is true,
or all the truth we have. It is not the beginning but the end
of reflection which is valid of the real ; or we are such at least
that our minds are unable to decide for aught else. And we
have seen that our thinking about the real, if we remain at
the level of the analytic judgment, will not stand criticism.
The result of our later and, we are forced to believe, our
better reflection is conviction that at least this judgment is
not true. To assert as a quality of the real either the whole
or part of the series of phenomena, 57 is to make a false
assertion.
74. The reality is given and is present to sense ; but you
can not, as we saw ( n), convert this proposition, and say
Whatever is present and given is, as such, real. The present 58
is not merely that section of the phenomena in space and time
which it manifests to us. It is not simply the same as its
appearance. Presence is our contact with actual reality; and
the reception of the elements of sensuous perception as exist
ing facts is one kind of contact, but it is not the only kind.
In hypothetical judgments there is a sense in which the
real is given; for we feel its presence in the connection of the
CHAP. II FORMS OF JUDGMENT IO3
elements, and we ascribe the ground to the real as its quality.
Hypothetical judgments in the end must rest on direct
presentation, though from that presentation we do not take
the elements and receive them as fact. It is merely their
synthesis which holds good of the real ( 50), and it is in our
perception of the ground of that synthesis that we come into
present contact with reality. I will not ask if this contact is
more direct than that which supports the analytical judgment.
But at all events we may say it is truer; since truth is what
is true of the ultimate real. A supersensible ultimate quality
is not much to assert, but at all events the assertion seems
not false. 59 On the other hand the categoric affirmation of
the analytic judgment of sense we know is not true. The
content it asserts we know is not real. And, taken in this
sense, there remains no hope for the individual judgment.
75. There is no hope for it at all, till it abates its pre
tensions, till it gives up its claims to superiority over the
hypothetic judgment, and is willing to allow that it itself is
no more than conditional. But it does not yet know the
degradation that awaits it. It may say, " It is true that I
am not categorical. My content is conditioned, and the be
cause has turned round in my hands into if/ But at least I
am superior to the abstract hypothetical. For in that the
elements are not even asserted to have reality, whereas, sub
ject to the condition of the rest of the series, I at least
assert my content to be fact. So far at least I affirm existence
and maintain my position."
But this claim is illusory, for if the individual judgment
becomes in this way hypothetical, it does not assert that its
content has any existence. If it did it would contradict itself,
and I will endeavour to explain this.
The content a-b in the categoric judgment was directly
ascribed to real existence. The abstract universal judgment
a-b does not ascribe either a or b or their connection to the
real; 60 it merely ascribes a quality x. The question now is
Can you save the categoric a-b by turning it into a hypo
thetical in which a-b is still asserted of existence, though
under a condition, or must it become the universal a-b
which ignores existence? In the latter case it would simply
mean, " Given a, then b." But in the former it would run,
IO4 THE PRINCIPLES OF LOGIC BOOK I
" Given something else, then a-b exists." This illusory claim
is not very pretentious, but I wish to show that it is suicidal.
Drobisch (Logik, 56), following Herbart (I. 106), trans
lates the judgment, " P exists," into " If anything exists any
where, then P exists." I consider this translation to be
incorrect; for it covertly assumes that something does exist,
and hence is in substance still categorical. And if we apply
this translation to the facts of sense, then what is really
supposed is the completed series of other phenomena, and
the translation must run thus, "If everything else exists, then
P exists." But the assertion is now suicidal, for " everything
else," we have seen above (70), can never be a real fact.
The hypothetical assertion of existence 61 is therefore made
dependent on a condition which can not exist. Now it is
not true that the consequence of a false hypothesis must
be false; but it certainly is true, when an impossible ground
is laid down as the sole condition of existence, that in a
roundabout way existence is denied. The individual judg
ment, we saw, was false when taken categorically. And now,
we see, when taken hypothetically, instead of asserting it
rather denies, or at least suggests that denial may be true.
76. The only hope for the singular judgment lies in
complete renunciation. It must admit that the abstract, al
though hypothetical, is more true than itself is. It must ask
for a place in the same class of judgment and be content
to take the lowest room there. It must cease to predicate
its elements of the real, 62 and must confine itself to asserting
their connection as adjectives generally, and apart from par
ticular existence. Instead of meaning by " Here is a wolf,"
or " This tree is green," that " wolf " and " green tree " are
real facts, it must affirm the general connection of wolf with
elements of the environment, and of " green " with " tree."
And it must do this in an abstract sense, without any reference
to the particular fact. In a low and rudimentary form it thus
tends to become a scientific law, and, entirely giving up its
original claims, it now sets its foot on the ladder of truth.
77- But it remains upon the very lowest round. Every
judgment of perception is in a sense universal, and, if it were
not so, it could never be used as the basis of inference. The
statement goes beyond the particular case, and involves a
CHAP. II FORMS OF JUDGMENT IO5
connection of adjectives which is true without respect to
"this" "here" and "now." If you take it as ascribing its
ideal content to this reality, it no doubt is singular, but, if you
take it as asserting a synthesis inside that ideal content, it
transcends perception; for anywhere else with the same
conditions the same result would hold. The synthesis is true,
not here and now, but universally.
And yet its truth remains most rudimentary, for the con
nection of adjectives is immersed in matter. 63 The content is
full of indefinite relations, and, in the first vague form which
our statements assume, we are sure on the one hand to take
into the assertion elements which have nothing to do with
the synthesis, and, on the other hand, to leave out something
which really helps to constitute its necessity. We say for
example, " This body putrefies ; " but it does not putrefy
because it is this body. The real connection is far more
abstract. And again on the other hand it would not putrefy
simply because of anything that it is, and without foreign
influence. In the one case we add irrelevant details, and in
the other we leave out an essential factor. In the one case
we say, " The real is such that, given abc, then d will follow,"
when the connection is really nothing but a-d. In the other
case we say, " The connection is a-b," when a is not enough to
necessitate b, and the true form of synthesis is a (c)-b.
Measured by a standard of scientific accuracy, the first forms
of our truths must always be false. They say too little, or
too much, or both; and our upward progress must consist in
correcting them by removing irrelevancies and filling up the
essential.*
78. The practice of science confirms the result to which
our long analysis has brought us; for what is once true for
science is true for ever. Its object is not to record that com
plex of sensible phenomena, which from moment to moment
perception presents to us. It desires to get a connection of
content, to be able to say, Given this or that element, and
something else universally holds good. It endeavours to dis
cover those abstract elements in their full completeness, and
to arrange the lower under the higher. Recurring to a term
* For explanation and illustration I must refer to Lotze s admirable
chapter cited above.
THE PRINCIPLES OF LOGIC BOOK I
we used before, we may say its aim is to purge out " thisness,"
to reconstruct the given as ideal syntheses of abstract ad
jectives. Science from the first is a process of idealization;
and experiment, Hegel has long ago told us, is an idealizing
instrument, for it sublimates fact into general truths.
Both in common life and in science alike, a judgment is at
once applied to fresh cases. It is from the first an universal
truth. If it really were particular and wholly confined to the
case it appears in, it might just as well have never existed,
for it could not be used. A mere particular judgment does
not really exist, and, if it did exist, would be utterly worth
less (cf. Chap. VI. and Book II.) .
79. It is time that we collected what result has come
from these painful enquiries. If we consider the ultimate
truth of assertions, then, so far as we have gone, the cate
gorical judgment in its first crude form has entirely dis
appeared. The distinction between individual and universal,
categorical and hypothetical, has been quite broken through.
All judgments are categorical, for they all do affirm about
the reality, and assert the existence of a quality in that. 64
Again, all are hypothetical, for not one of them can ascribe to
real existence its elements as such. All are individual, since
the real which supports that quality which forms the ground
of synthesis, is itself substantial. Again all are universal,
since the synthesis they affirm holds out of and beyond the
particular appearance. They are every one abstract, for they
disregard context, they leave out the environment of the
sensible complex, and they substantiate adjectives. And yet
all are concrete, for they none of them are true of any
thing else than that individual reality which appears in the
sensuous wealth of presentation.
80. But, if we remain at a lower point of view, if we
agree not to scrutinize the truth of judgments, and if we
allow assertions as to particular fact to remain in the character
which they claim for themselves, in that case our result will
be somewhat different. 65 Abstract judgments will all be hypo
thetical, but the judgments that analyze what is given in
perception will all be categorical. Synthetic judgments about
times or spaces beyond perception will come in the middle.
They involve an inference on the strength of an universal,
CHAP. II FORMS OF JUDGMENT 107
and so far they must have a hypothetical character. They
again involve an awkward assumption, for you can go to
them only through the identity of an element in the several
contents of a perception and an idea. As however, on the
strength of this assumption, the universal is brought into con
nection with the given, the " if " is so turned into a " be
cause," and the synthetic judgment may be called categorical.
The two classes, so far, will on one side be assertions about
particular fact and on the other side abstract or adjectival
assertions. The latter are hypothetical, and the first cate
gorical.
81 . We have all this time omitted to consider that class
of judgment which makes an assertion about an individual
which is not a phenomenon in space or time (41). Is it
possible that here we have at last a judgment which is not in
any sense hypothetical? Can one of these directly predicate
of the individual real an attribute which really and truly
belongs to it? May we find here a statement which asserts
the actual existence of its elements, and which is not false?
Can truth categorical be finally discovered in some such
judgment as " The self is real," or " Phenomena are nothing
beyond the appearance of soul to soul " ? 66 It would seem to
us strange indeed if this were so, and yet after all perhaps it
is our minds that are really estranged.
But we can not here attempt to answer these questions.
We can only reply when asked where truth categorical dwells,
" Either here or nowhere."
ADDITIONAL NOTES
i " S P." This form I found of course in use, and I employed
it in this volume where that seemed convenient. I neither did nor do
attach importance to its use. In I, par. 3, "is not our judgment"
should have been perhaps "need not be," and, lower down, after "was
not " might better have come " perhaps."
2 "Objectivity." What this means is that it is the object itself
which is this or that. The " subjective " = the irrelevant. See the
Index of this work. And cf. Appearance, p. 237, and Essays, the
Index.
3 " Existences of different orders." See here the Index, s. v. Ex-
I0 g THE PRINCIPLES OF LOGIC BOOK I
istence. And cf. Essays, Chap. Ill, and Index, s. v. real world.
"Existence" and "exist" (like "fact") are used in the present work
often in a wide sense. On the narrower sense, which limits " existence "
to the temporal series of my "real world," cf. Appearance, p. 317, and
Essays, Chap. XVI.
* Unfortunately in this work, with regard to "reality," neither
the view of Common Sense (whatever that is) nor any other view
has been kept to consistently. Cf. Chap. II. 72 and Bk. III. Pt. II.
Chap. IV.
5 " Altering the series of either space or time." But in what world?
In our own so-called "real world" only? Cf. Note 7.
6 " Images." But see Chap. I, Note 8. And (a few lines lower
down) " quite apart from " should certainly have been " without
regard to."
7 " Three great classes." These distinctions are all in the end
untenable. See Bosanquet, K & R, Chap. I. All judgments without
exception are conditional. See T. E. II, and cf. Appearance and
Essays, the Indexes. On class (ii), the words "some facts of time
or space " are of course qualified by the following words " which . . .
perceive." For the third class cf. 41. And, for a correction of the
footnote with regard to Kant, see the Note to Chap. VI, 28.
8 " Is false &c." It is false in the sense that its opposite also is
true. See the Index, s. v. Conditional. And cf. Essays, p. 232.
9 For references as to the "real" and "grammatical" subject see
Index, s. v. Subject. We must remember that there is no presump
tion anywhere that these two are identical. See Bosanquet, K & R,
163-4, 181 foil.
10 On the " present " &c. cf . 74, and see Appearance and Essays,
the Indexes s. v. Time. A view, such as that advocated, e.g., by Mr.
Russell, I take (i) to deny the reality of apparent change, and (ii) to
be incompatible with the fact of the appearance.
11 " The whole sensible reality." But at the same time there always
is selection. See the Index, s. v. Judgment. Cf. here Bosanquet,
K & R, 164 foil.
12 On proper names see Bosanquet, K & R, 73 foil., Logic y I, 47 foil.
13 "There is always an inference." How far the judgment itself
is here an inference is, however, a further question. See Essays,
p. 369, and Index, s. v. Memory.
14 " To attribute them" should have been "to attribute it or
them."
15 " The series itself," that is, as we have it before us.
16 " Content " or " quality " means here anything distinguishable
so as to be for us a content or quality. In saying that the " this "
does not fall within the " what," we must add that it does not fall in
the "that" either. For each of these is an abstraction. Again, where
a quality is unique, it ceases to be so if you take it as distinct from
its "that" for, if so, there may be another instar.ee. On Uniqueness
&c. see further T. E. IV and V.
CHAP. II FORMS OF JUDGMENT IOO,
17 On these important points see Essays, Chap. VI.
18 On the question raised here as to the idea of "this" see the
reference given in Note 16.
19 The one idea, so far as positive, is that of reality, or experience,
as immediate. Under this one main head of immediacy fall the " now,"
" here," and " mine." It is under the last of these that we are concerned
with Attention.
"Immediate contact with the presented reality" (24), if taken
as a definition, is, I think, wrong. " Contact " and " presentation "
are further aspects not, in my judgment, belonging essentially or
universally to immediate experience. See the references given in
Note 16. But in the present volume I certainly did not always mean
by " presentation " the outward or even the inward perception of
an object. The reader, I fear, must be on his guard throughout
against what is perhaps a careless use of this term.
20 " Former discussion." See 10 foil.
21 Reality is unique (a) negatively and (b) positively. The given
"this" also offers itself as unique. But an examination shows that we
here have but appearance. The "this," through its content, negates
itself as unique, and is seen to involve transcendence and ideality. On
these points see T. E. IV and V.
22 " A completed series &c." except (that is) when viewed in
relation to a limited purpose and idea which it realizes.
23 " Identity." Cf. 80, and see Bk. III. I. Chap. III. 2.
24 " Or has rather some point &c." But we must remember that
the "point" may be some quality of the whole. To the reference
given to Lotze should be added "and Med. Psych., p. 487 (published
in 1852)".
25 I had at this time, I think, no acquaintance, as yet, with Her-
bartian psychology, or I should have noticed the doctrine that percep
tions all survive below the conscious level, ready to emerge if and
when the conditions serve. But I should have added " However,
this problem of dispositions is solved ultimately (if it can be
solved), what stands in the text holds good. For it is in the end
only as an ideal construction that I can have before me the series
of events past and future &c." Cf. Mind, O. S., 47, p. 363. For
Memory, see Essays, the Index.
26 On Imagination see Bk. III. I. Chap. III. 23, and Essays, the
Index.
27 The false doctrine of "mere ideas" recurs in this section. See
Chap. I, Note 13. And, for " the image," see ibid., Note 8.
28 " If we actually &c." We do and must " attribute the series
to reality," though not to reality as present. If the reader will consult
the account of Uniqueness and of the idea of " This," in T. E. IV and
V, he will, I hope, see his way to correct the mistakes of the text.
29 " Implies the idea of a series." This is very doubtful.
30 See above, Note 7.
31 "If we take the soul to be eternal." I did not mean "ever
lasting." I was alluding to the yiew that the whole essence of the
HO THE PRINCIPLES OF LOGIC BOOK I
soul can not be identified with its appearance in one or more periods
of time.
32 " A mere serial character." The use of these words (I can now
recall nothing) seems careless. Probably I meant " a mere discreteness
in the events so that they do not exist in and by connection into one
whole."
33 42, 43. The division into (a) and (b), in 42, is clearly
wrong, if only because it omits all the worlds of events which fall
outside my " real " world. See Note 3.
We may perhaps distinguish "Singular" judgments (i) about my
" real " world, or (2) about some " imaginary " world of events.
(3) "General" judgments might perhaps be those referring to some,
if not all, of the above worlds. (4) Judgments become "abstract"
when this reference is struck out. Whether we have (5) to recognize
abstract worlds or regions, taken somehow to "exist," though sensible
existence in time and space is struck out, I will not offer to discuss.
There will remain (6) judgments taken otherwise than as falling
under the above heads. But, for myself, I attach little importance
to such distinctions, even if tenable. What is important is to keep in
mind that every judgment is, in various ways and degrees, conditioned
and conditional.
Instead of using " existence " as one with " reality," it is far better,
I think, to limit it to the sphere of events. But, if so, though all
judgments will be "real," certainly not all will be "existential." See
the Index.
54 The difficulty as to the "symbolic" use of such ideas as "this"
and " real " is dealt with in T. E. V.
3(5 " The particular thing " should be " the particular or individual
thing."
36 " Adjectivals." The words "even where these are not taken so
ostensibly " should have been added.
37 On the Collective Judgment (cf . Bk. II. II. Chap. III. 3) my
treatment is one-sided. It ignores the fact that this judgment asserts a
connection of content within an aggregate of individuals taken as
exhaustive. On the Collective and Generic Judgments the reader is
referred to Dr. Bosanquet s Logic, I, 152 foil., and 209 foil.
a8 " Collection of actual cases." "Actual" does not mean "given
as present."
s9 " Will be universal and abstract." This, I think, is wrong. See
Chap. VI, i.
40 " Ideal experiment." But (a) we must remember that there are
no mere ideas. Every idea is referred to its own world as there
real and true, and as, so far, not merely "in my head." And (b)
the " reality," to which my idea is opposed, is not necessarily " fact "
in the sense of belonging to my "real world." It itself may be
"imaginary," though here, as against my idea, it is taken as real.
Having then an idea, or rather a truth, holding in one region,
we may be said to apply this to another region of reality with a
view to observe the result. This other reality, as we have it, repels
CHAP. II FORMS OF JUDGMENT III
our idea, or admits its opposite, and hence, taken on one side, the
result is doubt. But on the other side it is a judgment made subject
to an x. We assert, that is, not S M P, but S(x) M P.
M p ? W e say, is true, but, as to S M, we have not got that
actually, and, further, we do not know what qualification of S is
involved in the reality of S M.
For the logical meaning of " If" the reader is referred to T. E. II,
and to Dr. Bosanquet s Logic, the Index, s. v. Hypothetical. We
can, I think, easily see its psychological nature and origin, if we take
the case of means (M) to an end desired, a certain alteration, that is,
of a given fact (S). I may have one or more ideas of these means,
but there is something in S, as I have it, which repels them all. I,
however, retain them because they are (a) relevant and interesting,
and also (b) possible. They contain, that is, some of the conditions
of S, as that is to be altered, and I do not know that there really are
counter-conditions in S itself. On the other side I do not know, and
I will not assume, that S does not contain these. Hence I refrain
from action, and assert S M P subject to a doubt as to S M.
I hold, in other words, S(x) M P as true. And here x means
(a) that further conditions are involved, and that (b) as to the nature
and effect of these I am more or less ignorant.
The supposed (to pass to another point) is in one aspect (M P)
quite certain and actual. It is in connection with S (as known) that
M P is but possible. And I may add that, where S itself is taken
as possible only, the supposed is here doubly possible. But, essentially
and always, what is supposed is taken as possible.
This statement may seem at first to be in conflict with plain facts,
such as the example given on p. 87 (cf. Essays, pp. 37-40). I ma Y
be told that possibility is here certainly excluded. I would on the other
side, however, ask the reader to reflect whether certainty is not
contrary to the very meaning of "If." And, since to my mind that
point is clear, I conclude that any appearance to the contrary rests
on what may be called linguistic or rhetorical artifice. I actually,
that is, assert or deny some real connection, and so far there is no
"If." But, for some unstated reason, I desire at the same time to
suggest that things throughout might have been otherwise. And I
convey at once my undoubting judgment and my doubtful suggestion
by licentiously applying " if" to the undiscriminated compound. "The
destruction of the barometer ( 50) caused the absence of warning
and it need not have been so." And " since you are well (which
you might not have been)" is the double meaning conveyed in "si
vales bene est." We may notice further in this connection that it
is common to refute an asserted S P by showing it as true only
if the impossible is supposed.
4 1 "The fact is the quality in the man s disposition." (i) It is
so here, but even here a " disposition " apart from any circumstances
is an impossible abstraction. Further (ii), if "disposition" is used
to explain "conditional," then obviously, since the very meaning of
H2 THE PRINCIPLES OF LOGIC BOOK I
" disposition " involves a standing " if," the explanation is circular
(see Appearance, Index, s. v. Dispositions), (iii) The objection to
"quality" is that it seems merely to repeat (what we knew before)
that things are so; and to admit (if we add "latent") that we do
not know how (Cf. Appearance, p. 362.).
42 " A quality which has appeared . . . experiment." This state
ment (see above) may involve a vicious abstraction.
43 There is much here that requires correction, (i) I surely, in
the case of every categorical judgment, am not forced to make it.
The " arbitrary " character of all judgment and inference is discussed
in T. E. I and II. (ii) Logical compulsion means merely that the
object is so, whatever else I am pleased to fancy. And if a hypotheti
cal judgment did not say that much, it would be no judgment at all.
(iii) And further, to make the result of the "experiment" disappear
from the reality is in principle vicious.
44 "Were very different." The "very" here is objectionable. See
Chap. Ill, 13.
45 With regard to the limits of explanation I will merely state
here that except in a relative sphere where assumptions are made
all judgments and all truth on my view involves what is inexplicable.
There is in every case a certain amount of unknown condition (x).
The question in any particular case will be as to the nature and amount
in the end of this x. See Appearance, p. 581 and its Index, and that
of Essays, s. v. Inexplicable.
46 The conclusion drawn in 53-56 is, I think, sound on the whole,
though in part perhaps inaccurate. Even in the case of a designated
particular we can hardly say broadly that this falls outside the sup-
posal. On the other hand certainly we fail to get this, as merely
designated, within the supposal and the judgment. The judgment
therefore will, more or less against our wish, turn out to be abstract
merely and only conditional though neither in form. See Essays, pp.
38-40, and the Index of that work, and of this, s. v. Designation.
47 " It does not assert the existence." Yes, it does assert this and
must do so. But what existence and where is in every case the ques
tion. See on 2 and Chap. I, 10.
48 For the doctrine that all judgments are conditional see Essays,
Index, s. v. Judgment.
49 Cf. T. E. I and IX, and Essays, pp. 299 foil.
50 The real truth . . . actual." This is the doctrine for which
I have now for so many years contended. See Appearance and Essays,
the Indexes. Relations exist only in and through a whole which
can not in the end be resolved into relations and terms. " And,"
"together" and "between," are all in the end senseless apart from
such a whole. The opposite view is maintained (as I understand)
by Mr. Russell, and was perhaps at last tacitly adopted by Prof.
Royce. But, for myself, I am unable to find that Mr. Russell has
ever really faced this question. See Essays, Index, s. v. Unity.
51 In "orthodox Christianity," the "orthodox" was meant to be
emphatic.
CHAP. 11 FORMS OF JUDGMENT 113
52 On the actual content of the " this " see T. E. IV and V, and
the Index.
53 On conditioned and conditional see T. E. II, and Essays, the
Index.
54 " There is no because," i.e. of the character which you assume
and require. The argument here is, in my opinion, sound, but it is
perhaps better put as follows. The condition, on which the judgment
holds, is unknown, and it admits also the opposite of what is asserted.
The judgment therefore, in its present form, is at once both true
and false. See Essays, Index, s. v. Conditional.
55 The "real." See on 4.
56 " You may say &c." It is of course the English empiricist of
1883 who is being addressed here. As to how far the criticism is now
out of date, the reader must judge for himself.
57 " The whole or part of the series of phenomena," i.e. as such.
ss " The present." Cf. ii foil.
59 " The assertion seems not false." On the other side, since it
depends on an unknown condition, and since therefore its opposite
also is possible, it has not absolute truth. In this point, and so far,
it is like the " analytical judgment of sense." On the other hand it is
higher and truer because, and so far as, its condition is less unknown
and less dependent on mere " matter of fact."
60 "Does not ascribe . . . real." This, we have seen (Note 3)
is wrong. But, if " existence " meant my " real world " of events, it
could stand. On the " quality " see Note 41.
61 If "existence" (Notes 3 and 33) means my " real world," then to
say of anything that its existence is implied in there being such a
world, is, so far, unconditional assertion. But on the other hand, so
far as this world itself is not absolutely real and true, the assertion
becomes, so far, merely relative, and dependent on an unknown con
dition. If you could say that P, as such, is implied in the real, that
would make P true absolutely.
To " the consequence of a false hypothesis &c.," we should, I think,
add "unless by an abstraction the hypothesis is taken as merely false."
62 It must cease to predicate real " should be " It must cease
to predicate its elements, as such, of the perceived real."
63 "Immersed in matter." For "matter of fact" see Essays, pp.
377-8o.
64 " Assert the existence . . . that " should be " assert their content
of that." And "can ascribe ... as such" should be changed to
"can ascribe to reality its content unconditionally."
65 The division made in 80 is (we have seen) indefensible, if only
because the "imaginary" is left out. See Note 33- And for the
" awkward assumption " cf. 32.
66 " Soul to soul." Cf. Note 31. And (lower down), to the question
raised by "Either here or nowhere," the answer, I think, must be
" in the end nowhere." But for the sense of this reply I must refer
to my Appearance and Essays.
CHAPTER III l
THE NEGATIVE JUDGMENT
I. After the long discussion of the preceding chapter,
we are so familiar with the general character of judgment that
we can afford to deal rapidly with particular applications.
Like every other variety, the negative judgment depends on
the real which appears in perception. In the end it consists
in the declared refusal of that subject 2 to accept an ideal
content. The suggestion of the real as qualified and deter
mined in a certain way, and the exclusion of that suggestion
by its application to actual reality, is the proper essence of
the negative judgment.
2. Though denial, as we shall see, can not be reduced to
or derived from affirmation, yet it would probably be wrong
to consider the two as co-ordinate species. It is not merely
as we shall see lower down (7), that negation presupposes
a positive ground. It stands at a different level of reflection.
For in affirmative judgment we are able to attribute the
content directly to the real itself. To have an idea, or a
synthesis of ideas, and to refer this as a quality to the fact
that appears in presentation, was all that we wanted. But,
in negative judgment, 3 this very reference of content to reality
must itself be an idea. Given X the fact, and an idea a b,
you may at once attribute a b to X ; but you can not deny
a b of X, so long as you have merely X and a b. For, in
order to deny, you must have the suggestion of an affirmative
relation. The idea of X, as qualified by a b, which we may
write x (a b), is the ideal content which X repels, and is
what we deny in our negative judgment.
It may be said, no doubt, that in affirmative judgment the
real subject is always idealized. We select from the whole
that appears in presentation, and mean an element that we do
not mention (Book III. I. Chap. VI. 12). When we point
to a tree and apply the word " green," it may be urged that the
subject is just as ideal as when the same object rejects the
114
CHAP. Ill THE NEGATIVE JUDGMENT HtJ
offered suggestion "yellow." But this would ignore an im
portant difference. The tree, in its presented unity with
reality, can accept at once the suggested quality. I am not
always forced to suspend my decision, to wait and consider
the whole as ideal, to ask in the first place, Is the tree green?
and then decide that the tree is a green tree. But in the nega
tive judgment where " yellow " is denied, the positive relation
of " yellow " to the tree must precede the exclusion of that
relation. The judgment can never anticipate the question.
I must always be placed at that stage of reflection which
sometimes I avoid in affirmative judgment.
3. And this distinction becomes obvious, if we go back
to origins and consider the early development of each kind.
The primitive basis of affirmation is the coalescence of idea
with perception. But mere non-coalescence of an idea with
perception is a good deal further removed from negation. It
is not the mere presence of an unreferred idea, nor its unob
served difference, but it is the failure to refer it, or identify
it, which is the foundation of our first denial. The exclu
sion by presented fact of an idea, which attempted to qualify
it, is what denial starts from. What negation must begin,
with is the attempt on reality, the baffled approach of a
qualification. And in the consciousness of this attempt is
implied not only the suggestion that is made, but the subject to
which that suggestion is offered. Thus in the scale of reflec
tion negation stands higher than mere affirmation. It is in
one sense more ideal, and it comes into existence at a later
stage of the development of the soul.*
4. But the perception of this truth must not lead us into
error. We must never say that negation is the denial of an
existing judgment. For judgment, as we know, implies belief;
and it is not the case that what we deny we must once have
believed. And again, since belief and disbelief are incom
patible, the negative judgment would in this way be made to
depend on an element which, alike by its existence or its
disappearance, would remove the negation itself. What we
deny is not the reference of the idea to actual fact. It is the
mere idea of the fact, as so qualified, which negation ex-
* Compare on this whole subject Sigwart, Logik, I. 119 and foil.
I do not, however, wholly accept his views.
!l6 THE PRINCIPLES OF LOGIC BOOK I
eludes; it repels the suggested synthesis, 4 not the real judg
ment.
5. From this we may pass to a counterpart error. If it
is a mistake to say that an affirmative judgment is presup
posed in denial, it is no less a mistake to hold that the predicate
alone is affected, and that negation itself is a kind of affirma
tion. We shall hereafter recognize the truth which this doc
trine embodies, but, in the form it here assumes, we can not
accept it. The exclusion by fact of an approaching quality is
a process which calls for its own special expression. And
when we are asked to simplify matters by substituting " A
is Not-B " for " A is not B," we find an obvious difficulty.
In order to know that A accepts Not-B, must we not al
ready have somehow learnt that A excludes B? And, if so,
we reduce negation to affirmation by first of all denying, and
then asserting that we have denied, a process which no doubt
is quite legitimate, but is scarcely reduction or simplification.
6. There is a further objection we shall state hereafter
( 16) to the use of Not-B as an independent predicate. But
at present we must turn to clear the ground of another error.
We may be told that negation " affects only the copula ; " and
it is necessary first to ask what this means. If it means what
it says, we may dismiss it at once, since the copula may be
wanting. If the copula is not there when I positively say
" Wolf," so also it is absent when I negatively say " No wolf."
But, if what is meant is that denial and assertion are two sorts
of judgment, which stand on a level, then the statement once
again needs correction. It is perfectly true that these two
different sorts of judgment exist. The affirmative judgment
qualifies a subject by the attribution of a quality, and the
negative judgment qualifies a subject by the explicit rejection
of that same quality. We have thus two kinds of asserted
relation. But the mistake arises when we place them on a
level. It is not only true that, as a condition of denial, we must
have already a suggested synthesis, but there is in addition
another objection. The truth of the negative may be seen in
the end to lie in the affirmation of a positive quality; and
hence assertion and denial cannot stand on one level. 5 In " A
is not B " the real fact is a character x belonging to A, and
which is incompatible with B. The basis of negation is really
CHAP. Ill THE NEGATIVE JUDGMENT 117
the assertion of a quality that excludes (#). It is not, as we
saw, the mere assertion of the quality of exclusion (Not-B).
7. Every negation must have a ground, and this ground
is positive. It is that quality x in the subject which is in
compatible with the suggested idea. A is not B because A
is such that, if it were B, it would cease to be itself. Its
quality would be altered if it accepted B ; and it is by virtue of
this quality, which B would destroy, that A maintains itself
and rejects the suggestion. In other words its quality x and B
are discrepant. And we can not deny B without affirming in A
the pre-existence of this discrepant quality. 6
But in negative judgment x is not made explicit. We do
not say what there is in A which makes B incompatible. We
often, if asked, should be unable to point out and to dis
tinguish this latent hindrance ; and in certain cases no effort we
could make would enable us to do this. If B is accepted, A
loses its character ; and in these cases we know no more. The
ground is not merely unstated but is unknown.
8. The distinctions of " privation " and " opposition "
(Sigwart, 128 foil.) do not alter the essence of what we have
laid down. In a privative judgment the predicate " red " would
be denied of the subject simply on the ground that red was
not there. The subject might be wholly colourless and dark. 7
But if " red " were denied on the ground that the subject was
coloured green, it would be the presence of an opposite quality
that would exclude, and the judgment would then be based on
positive opposition. This distinction we shall find in another
context to be most material (cf. Chap. VI. and Book III. II.
Chap. III. 20) ; but, for our present purpose, it may be called
irrelevant. In the one case as in the other, the subject is
taken with a certain character; and by addition as well as by
diminution that individual character may be destroyed. If
a body is not red because it is uncoloured, then the adding-on
cf colour would destroy that body as at present we regard it.
We may fairly say that, if the predicate were accepted, the
subject would no longer be the subject it is. And, if so, in
the end our denial in both cases will start from a discrepant
quality and character.
9. It may be answered, no doubt, that the subject, as it
is now and as we now regard it, is not the same thing as the
2321.1 i
Il8 THE PRINCIPLES OF LOGIC BOOK I
subject itself. In the one case, the subject rejects a sugges
tion through a quality of its own, in the other it may reject
on the strength of our failure. But I must persist in denying
that this objection is relevant. In both cases alike the subject
is taken as somehow determined; and it is this determination
which (whatever it comes from) does give the subject a
positive character, which in both cases lies at the base of the
denial. No subject could repel an offered suggestion simply
on the strength of what it was not. It is because the " not-
this " must mean " something else that we are able to make
absence a ground for denial. We shall all agree that the
nothing which is nothing can not possibly do anything, or be a
reason for aught. 8
These distinctions do not touch the principle we stand
upon, but I admit they give rise to most serious difficulties. 9
And, mainly for the sake of future chapters, it may be well if
we attempt here to clear our ideas. And (i) first, when we
have a case of " opposition," there the subject repels the offered
predicate because it has in its content a positive quality,
filling the space which the predicate would occupy, and so
expelling it. If a man has blue eyes, then that quality of
blueness is incompatible with the quality brown. But (ii),
when we come to privation, two cases are possible. In the
first of these (a) within the content of the subject there is
empty space where a quality should be. Thus, a man being
eyeless, in this actual content lies the place where his eyes
would be if he had them. And this void can not possibly be
a literal blank. You must represent the orbits as somehow
occupied, by peaceful eyelids, or unnatural appearance. And
so the content itself gets a quality, which, in contrast to the
presence of eyes, may be nothing,* but which by itself has a
positive character, which serves to repel the suggestion of
sight.
10. But privation can rest on another basis (&). The
*I may mention that, though contrast can not always be taken
as holding true of the things contrasted, yet for all that it may rest
n a positive quality. Thus, even in the case of a word like blind
ness we should be wrong if we assumed that the blind man is
qualified simply by the absence of sight from the part which should
furnish vision. His mind, we can not doubt, has a positive character
which it would lose if another sense were added.
CHAP. Ill THE NEGATIVE JUDGMENT 1 19
content of the subject may contain no space which could pos
sibly be qualified by the presence of the predicate. What
rejects the predicate is no other determination of the con
tent itself, but is, so far as that content itself is concerned,
an absolute blank. It is difficult to find illustrations of this
instance. If I say "A stone does not feel or see," it may
rightly be urged " Yes, because it is a stone, and not simply
because it is nothing else." But we can find an example of
the privation we want in the abstract universal. The univer
sal idea (cf. Sigwart, 130), if you keep it in abstraction,
repels every possible extension of its character. Thus " tri
angle," if you mean by it the mere abstraction, can neither
be isosceles nor scalene nor rectangular; for, if it were, it
would cease to be undetermined. We may invent a stupid
reductio ad absurdum: This isosceles figure is certainly a
triangle, but a triangle is certainly not isosceles, therefore .
If we release the universal from this unnatural abstraction,
and use it as an attribute of real existence, then it can not sup
port such a privative judgment. For, when referred to reality,
we know it must be qualified, though we perhaps can not state
its qualification. Once predicate triangle of any figure, and
we no longer can deny every other quality. The triangle is
determinate, though we are not able to say how. It is only
the triangle as we happen not to know it, which repels the
suggestion of offered predicates. It is our ignorance, in short,
and not the idea, which supports our exclusion of every sug
gestion.
ii. In a judgment of this kind the base of denial is
neither the content of the subject itself, nor is it that content
plus a simple absence; for a simple absence is nothing at all.
The genuine subject is the content of the idea plus my psycho
logical state of mind. The universal abstraction, ostensibly
unqualified, is determined by my mental repulsion of qualities.
And the positive area which excludes the predicate really lies
in that mental condition of mine. My ignorance, or again my
wilful abstraction, is never a bare defect of knowledge. It is
a positive psychological state. And it is by virtue of relation
to this state, which is used as content to qualify the subject,
that the abstraction, or the ignorance, is able to become a
subject of privation. We shall see that, in this form, the
120
THE PRINCIPLES OF LOGIC BOOK I
universal may more truly be called particular (Chap. VI.
35) ; for it is determined and qualified, not by any develop
ment of the content, but simply by extraneous psychological
relation. 10
12. The various kinds of negative judgment follow
closely the varieties of affirmation. The immediate subject
may be part of the content of present perception (" This stone
is not wet ") ; or it may be found in some part of the series of
space, or again of time, which we do not perceive (" Marseilles
is not the capital of France," " It did not freeze last night ").
Again what is denied may be a general connection ("A metal
need not be heavier than water"). In this last case it is of
course the unexpressed quality at the base of the hypothesis
(Chap. II. 50) which the real excludes. 11 But, in all negative
judgment, the ultimate subject is the reality that comes to us
in presentation. We affirm in all alike that the quality of
the real excludes an ideal content that is offered. And so
every judgment, positive or negative, is in the end existential.
In existential judgment, as we saw before (Chap. II. 42),
the apparent is not the actual subject. Let us take such a
denial as " Chimaeras are non-existent." " Chimaeras " is here
ostensibly the subject, but is really the predicate. It is the
quality of harbouring chimaeras which is denied of the nature
of things. And we deny this because, if chimaeras existed,
we should have to alter our view of the world. In some
cases that view, no doubt, can be altered, but, so long as
we hold it, we are bound to refuse all predicates it excludes.
The positive quality of the ultimate reality may remain occult
or be made explicit, but this, and nothing else, lies always at
the base of a negative judgment.
13. For logical negation can not be so directly related to
fact as is logical assertion. 12 We might say that, as such and
in its own strict character, it is simply " subjective : " it does
not hold good outside my thinking. The reality repels the sug
gested alteration; but the suggestion is not any movement of
the fact, nor in fact does the given subject maintain itself
against the actual attack of a discrepant quality. The process
takes place in the unsubstantial region of ideal experiment.
And the steps of that experiment are not even asserted to
exist in the world outside our heads. The result remains, and
CHAP. Ill THE NEGATIVE JUDGMENT 121
is true of the real, but its truth, as we have seen, is something
other than its first appearance.
The reality is determined by negative judgments, but it
can not be said to be directly determined. The exclusion, as
such, can not be ascribed to it, and hence a variety of ex
clusions may be based on one single quality. The soul is not
an elephant, nor a ship in full sail, nor a colour, nor a fire-
shovel; and, in all these negations, we do make an assertion
about the soul. But you can hardly say that the subject is
determined by these exclusions as such, unless you will main
tain that, after the first, the remainder must yield some fresh
piece of knowledge. You may hold that " all negation is deter
mination," if you are prepared to argue that, in the rejection
of each new absurd suggestion, the soul exhibits a fresh side
of its being, and in each case performs the special exclusion
by means of a new quality. But it seems better to say that
nothing is added by additional exclusions. 13 The develop
ment and application of these may proceed ad infinitum, but
the process is arbitrary and, in the end, unreal. The same
quality of the soul which repels one predicate, repels here all
the rest, and the exclusion itself takes place only in our heads.
I do not mean to deny that a thing may be qualified by
the exclusion of others, that the real character of a fact may
depend on what may be called a negative relation. What I
mean to say is that the negative judgment will not express
this. It asserts that a predicate is incompatible, but it does
not say that either the predicate, or the incompatibility, are
real facts. If you wish to say this you must transcend the
sphere of the negative judgment.
14. We must not, if we can help it, introduce into logic
the problems of the " dialectical " view. 14 It may be, after all,
that everything is just so far as it is not, and again is not just
so far as it is. Everything is determined by all negation ; for
it is what it is as a member of the whole, and its relation to all
other members is negative. Each element in the whole, itself
the whole ideally while actually finite, transcends itself by
mere self-assertion, and by mere self-emphasis brings forth
the other that characterizes and negates it. If everything thus
has its discrepant in itself, then everything in a sense must be
its own discrepancy. Negation is not only one side of reality,
I2 2 THE PRINCIPLES OF LOGIC BOOK I
but in the end it is either side we please. On this view it
would be doubtful if even the whole is positive ; for it is just
so far as by position it disperses itself in its own negation, and
begets from its dispersion the opposite extreme. It is doubt
ful if we may not transform the saying that " Everything is
nothing except by position," into " Everything by position is
its proper contrary, and nothing by position is all and every
thing."
If this is so, there would remain no quality which is
simply positive; and logical negation, in another sense than
we have given it above, becomes the soul and, we sometimes
are inclined to think, the body of the real world. But we are
not called upon to discuss this view (cf. Chap. V.), for our
result will stand in any case, I think, in its principal outline.
A mere logical negation, 15 it is fully admitted by the dia
lectical method, need not express a real relation. And, this
being so, it seems the better course to consider it by itself
as merely subjective, and to express the real implication of
exclusives by an affirmative judgment, which sets forth that
fact. What denial tells us is merely this, that, when we bring
the discrepant up, it is rejected. Whether what repels it is
entirely independent, or whether it has itself produced or
solicited what it excludes, is quite irrelevant. And it is still
more irrelevant to ask the question if the first rejection is
merely coquettish, and will lead in the end to a deeper sur
render. This all goes beyond what denial expresses, for that,
merely by itself, is not asserted beyond our minds.
The dialectical method, in its unmodified form, may be
untenable. It has, however, made a serious attempt to deal
with the relation of thought to reality. We can hardly say
that of those eminent writers who are sure that logic is the
counterpart of things, and have never so much as asked them
selves the question, if the difference and identity, with which
logic operates, are existing relations between actual phenomena.
15. To resume, logical negation always contradicts, but
never asserts the existence of the contradictory. To say " A
is not B " is merely the same as to deny that " A is B," or
to assert that " A is B " is false. And, since it can not go
beyond this result, a mere denial of B can never assert that
the contradictory Not-B is real. The fact it does assert is the
CHAP. Ill THE NEGATIVE JUDGMENT 123
existence of an opposite incompatible quality,* either in the
immediate or ultimate subject. This is the reason why the sug
gested A B is contradicted ; and it is only because this
something else is true, that the statement A B is rejected
as false. But then this positive ground, which is the basis of
negation, is not contradictory. It is merely discrepant, oppo
site, incompatible. It is only contrary. In logical negation the
denial and the fact can never be the same.
1 6. The contradictory idea, if we take it in a merely
negative form, must be banished from logic. If Not- A
were solely the negation of A, it would be an assertion with
out a quality, and would be a denial without anything positive
to serve as its ground. A something that is only not some
thing else, is a relation that terminates in an impalpable void,
a reflection thrown upon empty space. It is a mere nonentity
which can not be real. And, if such were the sense of the
dialectical method (as it must be confessed its detractors have
had much cause to suppose), 18 that sense would, strictly
speaking, be nonsense. It is impossible for anything to be
only Not-A. It is impossible to realize Not-A in thought.
It is less than nothing, for nothing itself is not wholly negative.
Nothing at least is empty thought, and that means at least my
thinking emptily. Nothing means nothing else but failure.
And failure is impossible unless something fails; but Not-A
would be impersonal failure itself ( n).
Not-A must be more than a bare negation. It must also
be positive. It is a general name for any quality which, when
you make it a predicate of A, or joint predicate with A, 17
removes A from existence. The contradictory idea is the
universal idea of the discrepant or contrary. In this form it
must keep its place in logic. It is a general name for any
hypothetical discrepant; but we must never for a moment
allow ourselves to think of it as the collection of discrepants.
17. Denial or contradiction is not the same thing as
the assertion of the contrary; but in the end it can rest on
nothing else. 18 The contrary however which denial asserts,
is never explicit. In " A is not B " the discrepant ground is
wholly unspecified. The basis of contradiction may be the
assertion A-C or A-D, C and D being contraries of B. But
*0n the nature of incompatibility see more, Chap. V.
I2 4 THE PRINCIPLES OF LOGIC BOOK I
again it may perhaps be nothing of the sort. We may reject
A-B, not in the least on the ground of A, but because A
itself is excluded from reality. The ultimate real may be
the subject which has some quality discrepant with A-B. For
contradiction rests on an undetermined contrary. It does not
tell us what quality of the subject excludes the predicate.
It leaves us in doubt if the subject itself is not excluded.
Something there is which repels the suggestion; and that is
all we know. Sokrates may be not sick because he is well, or
because there is now no such thing as Sokrates.
18. Between acceptance and rejection there is no middle-
point, and so contradiction is always dual. There is but one
Not-B. But contrary opposition is indefinitely plural. The
number of qualities that are discrepant or incompatible with
A, can not be determined by a general rule. It is possible of
course to define a contrary in some sense which will limit the
use of the term; but for logical purposes this customary
restriction is nothing but lumber. In logic the contrary should
be simply the discrepant. Nothing is gained by trying to
keep up an effete tradition. If a technical distinction can
not be called necessary, it is better to have done with it.
19. Contradiction is thus a " subjective " process, which
rests on an unnamed discrepant quality. It can not claim
"objective" reality; and since its base is undetermined, it is
hopelessly involved in ambiguity. In " A is not B " you know
indeed what it is you deny, but you do not say what it is you
affirm. It may be a quality in the nature of things which is
incompatible with A, or again with B. Or again it may be
either a general character of A itself which makes B impos
sible, or it may be some particular predicate C. That "a
round square is three-cornered," or that " happiness lies in
an infinite quantity," may at once be denied. We know a
round square, or an infinite number, are not in accordance
with the nature of things. But " virtue is quadrangular," or
" is mere self-seeking," we deny again because virtue has no
existence in space, and has another quality which is opposite
to selfishness.
" The King of Utopia died on Tuesday " may be safely
contradicted. And yet the denial must remain ambiguous.
The ground may be that there is no such place, or it never
CHAP. Ill THE NEGATIVE JUDGMENT 125
had a king, or he still is living, or, though he is dead, yet he
died on Monday. This doubtful character can never be re
moved from the contradiction. It is the rejection of an idea,
on account of some side of real fact which is implied but
occult.
20. We may conclude this chapter by setting before our
selves a useful rule. I think most of us know that one can
not affirm without also in effect denying something. In a
complex universe the predicate you assert is certain to exclude
some other quality, and this you may fairly be taken to deny.
But another pitfall, if not so open, yet no less real, I think
that some of us are quite unaware of. Our sober thinkers,
our discreet Agnostics, our diffident admirers of the phenome
nal region I wonder if ever any of them see how they com
promise themselves with that little word " only." How is it
that they dream there is something else underneath appear
ance, and first suspect that what meets the eye veils some
thing hidden? But our survey of negation has taught us the
secret, that nothing in the world can ever be denied except on
the strength of positive knowledge. I hardly know if I am
right in introducing suggestive ideas into simple minds; but
yet I must end with the rule I spoke of. We can not deny
without also affirming; and it is of the very last importance,
whenever we deny, to get as clear an idea as we can of the
positive ground our denial rests on.
ADDITIONAL NOTES
1 This chapter contains some serious erors. I have since accepted
in the main Dr. Bosanquet s account of negation. See his K & R and
Logic. I have briefly discussed the whole matter in T. E. VI.
2 "That subject," i.e., as in one with a selected determination. See
Chap. !,ii and 12.
s The abstraction of the idea from all " reference " is not defensible.
See on Chap. I, 10. There is always some region in which an idea is
real. It is only where the perceived world is taken as the one real
object, that other worlds are merely subjective" (13).
As to whether affirmation and denial are co-ordinate, we ^may
say that in the end they are so, because the conscious use of ideas
as ideas implies both a positive and negative aspect. But denial can
be called more "reflective," in the sense that we become aware of
it later. We must retain an excluded idea before we can know it
126 THE PRINCIPLES OF LOGIC BOOK I
as excluded. The beginning of affirmation, we may say, is an object
before me changed ideally so as to lead to action. The beginning
of negation is the exclusion of an ideal change in the object this
exclusion not being retained by the mind, though action is thereby
prevented. By "action" (I should add) is not meant necessarily
action which is "practical." Thus it is not true that we have a
separate suggestion and then consciously apply it. The attempt to
identify may at first appear to us not as an attempt, but simply as
the actual exclusion, where not the actual qualification. It is when we
hold the suggestion, while excluding it from our perceived and selected
object, that we first have denial in the proper sense of the word.
4 The " suggested synthesis " (here and lower down) needs correc
tion in the sense of the foregoing Note.
5 It is true that a excludes b because it is a. It is true that there
is a ground and a Why, and that in the end you can not make this
Why explicit. But the same holds good also of b, as distinct from
and so as negative of a. On the other hand this two-sided negation
is at first implicit only and does not appear. You begin positively
(as we saw above) with a designated object (Ro) qualified further
ideally. It is only later and through reflection that, instead of such
an object, Ro (ab), we arrive at a world qualified everywhere by
distinctions, at once connected with and opposed to one another, and
R
so can write our object as / \
a b
6 1 have, here and everywhere, altered " disparate " where in the
original text it was used wrongly for " discrepant." I am quite unable
to account for this mistaken use, which, I am sorry to add, recurs
frequently, and for the sake of the reader has been now throughout
corrected.
7 "Colourless and dark." If "dark" meant "visibly dark"
which I do not think it did mean there would be a mistake here. See
Bosanquet K & R, p. 247.
8 On the subject of Incompatibility the reader is referred to Ap
pearance, Appendix, Note A, and to Bosanquet s Logic.
9 These distinctions are (i) exclusion by a specified incompatible;
(ii) exclusion of a quality from a space in a subject where that
quality is looked for; (iii) exclusion from an assumed space taken
as empty on the ground of absence, i.e. of my failure to find the
quality there. If you were to drop the assumption made here, and
were to reject the empty space, as being either meaningless or itself
for some known reason excluded, the above exclusion would become
sound. But at the same time it would cease to rest upon failure
and mere privation. What on the other hand damns the privative
judgment, as ultimate, is its assumption, based on mere ignorance,
of an empty space in the character of the Universe. Where however
you know positively that the Universe is in a certain respect deter-
minable further, there your failure to find a particular qualification
CHAP. Ill THE NEGATIVE JUDGMENT 127
(a) is a ground for denial, just so far as you have reason to think
your knowledge complete. But see the Notes on Chap. VII, 13 and
28, and see T. E. VII. And cf. Appearance and Essays, the Indexes,
s. v. Privation.
10 " Extraneous psychological relation " should be perhaps " a dis
tinction turned into a separation and made an exclusion on a mere
extraneous psychological ground."
11 " The unexpressed quality." See on Chap. II, 50.
12 " Fact " here should be " perceived fact." And negation is " sub
jective " in the sense that mere negation, mere exclusion, is an ab
straction and is by itself really nothing at all. Cf. 15-19. Otherwise
negation is not "subjective," though it is more "reflective" than is
affirmation (2).
13 " Nothing is added by additional exclusions." It is true that the
abstract negation takes no account of the " how," which therefore,
so far, may be the same. But to go beyond this is wrong (Chap. I,
52). SeeT. E. VI.
14 " Dialectical view." But, apart from this, in logic we may and
must insist that Reality has to be regarded as a disjunctive totality,
as the positive unity of diversities each of which is one and is not
the others. In our intellectual world we must take every element as
within a whole, and as qualified by its relations in that whole, and,
further, as qualified by them internally. By "internally" is meant
that the element itself, and not merely something else, is qualified.
Hence everything will imply its relations both positive and negative.
On the other hand we must not say of anything that it is nothing
beyond its implications even though what else it is we are unable
in the end to state. The problem of identity and diversity is, I agree,
not in the end soluble (see Essays, pp. 240, 264). And our whole
world, as merely intellectual, is not ultimately real.
15 " A mere logical negation." The mere must be emphasized.
16 " Much cause " should perhaps be " some cause."
17 "Or joint predicate." In a sense it never is anything but a joint
predicate. See Appearance, Appendix, Note A.
18 The main point is this, that denial means exclusion from and
by the real. Mere denial, however, rests on abstract exclusion, which,
as abstract, is really nothing. Actually the real excludes because the
real is qualified incompatibly, and may be so in a variety of senses, the
whole of which variety is ignored by the abstract denial. See on 13.
CHAPTER IV
THE DISJUNCTIVE JUDGMENT *
I. The disjunctive judgment may fairly complain that
by most logicians it is hardly dealt with. It is often taken
as a simple application of the hypothetical, and receives the
treatment of a mere appendage. It is wonderful in how many
respectable treatises not the smallest attempt is made to
understand the meanings of " if " and of " either or."
The commonest way of regarding disjunction is to take it
as a combination of hypotheses. This view in itself is some
what superficial, and it is possible even to state it incorrectly. 2
" Either A is B or C is D " means, we are told, that if A is
not B then C is D, and if C is not D then A is B. But a
moment s reflection shows us that here two cases are omitted.
Supposing, in the one case, that A is B, and supposing, in the
other, that C is D, are we able in these cases to say nothing
at all ? Our " either or " can certainly assure us that, if A is
B, C-D must be false, and that, if C is D, then A-B is false.
We have not exhausted the disjunctive statement, until we have
provided for four possibilities, B and not-B, C and not-C.
2. But however complete may be the cases supposed,
disjunctive judgments can not really be reduced to hypothet
ical. Their meaning, no doubt, can be given hypothetically ;
but we must not go on to argue from this that they are
hypothetical. The man who illustrated everything else has
touched this point too in the Gentlemen of Verona:
Speed. But tell me true, will t be a match?
Launce. Ask my dog: if he say, ay, it will; if he say, no, it will;
he shake his tail and say nothing, it will.
Speed. The conclusion is then that it will.
Launce. Thou shalt never get such a secret from me but by a
parable (Act II. Scene v.).
It is indeed by an indirect process, and by making secret
a categorical judgment, that hypothetical can express dis
junction.
128
CHAP, IV THE DISJUNCTIVE JUDGMENT I2Q
I do not mean that the " either or " is purely categorical.
I mean that to some extent at least it is categorical, and
declares a fact without any supposition. In " A is b or c "
some part of the statement is quite unconditional. It asserts
a fact without any " if " at all. And when pressed with the
objection, " But you can not deny that it is reduced to a com
bination of supposals," we need not take long to practise an
answer. A combination of hypothetical surely does not lie
in the hypothetical themselves. It lies in the mind which
combines them together, and surveys the field which together
they exhaust. It is nonsense to say you are able to " reduce "
a statement to elements of a certain character, when these
elements, if taken merely by themselves and without a
peculiar mode of union, are able to express nothing like the
statement. 3 The basis of disjunction, the ground and founda
tion of your hypotheticals, is categorical. 4
3. There is, no doubt, some difficulty about the categor
ical nature of disjunctive judgments. " A is b or c; " but this
mode of speech can not possibly answer to real fact. No real
fact can be " either or." It is both or one, and between the
two there is nothing actual. We can hardly mean to say that
in fact A is b or c. On the other hand, we are far from
expressing simple ignorance. If we merely said " I do not
know if A is b, and I do not know if A is c" that would not
be equivalent to the original statement. And that we make
an assertion can be shown in this way. If the subject of our
predicate " either or " were proved not to exist, our state
ment would be false. It is clear not only that the subject
has existence, but that it also possesses some further
quality. 5
The distinction of the apparent and the ultimate subject,
which we had to make in our former discussions, must not
here be forgotten. " A is either b or c " need not always imply
that A is a fact. For example, I may say that "either A
exists or does not exist." The subject here is the nature of
things, and this either repels the content A or is qualified by
it. But still the assertion remains categorical. Throughout
the rest of the chapter I shall take A to stand for the real
subject, and the reader must remember that in every case
the apparent subject may belong to the predicate, and that what
130 THE PRINCIPLES OF LOGIC BOOK I
is asserted respecting A may only be true of the ultimate sub
ject.
And the same remark applies to such examples as " Either
A is B or C is D." The subject in this case is not A or B or
again C or D. The subject is the real, which is qualified by
the predicate A-B or the predicate C D.
4. The assertion in " A is b or c " is not that A is b or c.
What then do we affirm? We say in the first place that A
exists. In the next place we certainly give it some quality. 6
What quality do we give it? If it can not be either b or c,
can it possibly be something that falls between them ? No, for
that would be neither. For instance, grey is not white or
black, and it excludes both colours. The predicate of A, while
neither b nor c, must not be a quality exclusive of either. It
must then be a quality common to both, which is not yet
either, but is further determinable as one or the other.
5. If we like to call this basis x, then "A is x " is
categorically true. We may in some cases have distinguished
x and given it a name, but in other cases it is unnamed and
implicit. " Man, woman, and child," have a common basis in
" human being." In " white or black " the quality " coloured,
and coloured so as to exclude other hues," is the attribute
asserted. " In England or America," " alive or dead," com
mit us to the statements " somewhere not elsewhere " and
" organized being." And so, if we call a man " bad or good,"
we say at least he is a moral agent. There is no exception to
the truth of this rule. Even existence and non-existence have
so much in common that, in any sense in which we can use
them, they imply some kind of contact with my mind. We
have seen (Chap. III.) that there is no pure negation. So,
in every disjunction and as the ground of it, there must be
the assertion of a common quality, the sphere within which
the disjunction is affirmed.
6. But x is not any universal whatever which happens to
be common to b and c. It is particularized further. It excludes
the opposite of each of these qualities, and can not be the nega
tive of " b or c" It is affirmed as fully determined not outside
the region which is covered by be. But since b and c, as
predicates of A, are incompatible, it can not be both of them.
The conclusion remains that it must be one. " One single
CHAP. IV THE DISJUNCTIVE JUDGMENT 13!
element of the region enclosed by be " is the predicate common
to b and c. And this predicate it is which, in disjunction, we
categorically assert of A.
So much is fact and no hypothesis ; but this by itself would
not be the assertion " b or c." The disjunctive judgment is
not wholly categoric. Being sure of our basis, the quality x t
upon this universal we erect hypotheses. We know that b
and c are discrepant. We know that A is particularized
within b and c, and therefore as one of b and c. It can not be
both, and it must be some one. 7 So much is the fact. To
complete the disjunction we add the supposal, "If it is not
one it must be the other." If A is not b, it must be c; and it
must be b, if it is not c. This supposal completes the " either
or." Disjunctive judgment is the union of hypotheticals on
a categoric basis.
7. We shall return to consider this process further, but
at present we may pause to correct a mistake. It has been
doubted if alternatives are always exclusive. 8 " A is b or c"
it is said, may be taken to admit that A is possibly both. It
may either be be or b or c. And, no doubt, in our ordinary
disjunctive statements we either leave the meaning to be
gathered from the context, or really may not know what it is
that we mean. But our slovenly habits of expression and
thought are no real evidence against the exclusive character
of disjunction. " A is b or c " does strictly exclude " A is both
b and c." When a speaker asserts that a given person is a
fool or a rogue, he may not mean to deny that he is both. But,
having no interest in showing that he is both, being perfectly
satisfied provided he is one, either b or c, the speaker has not
the possibility be in his mind. Ignoring it as irrelevant, he
argues as if it did not exist. And thus he may practically be
right in what he says, though formally his statement is down
right false ; for he has excluded the alternative be. 9
And it is not always safe to be slovenly. It may be a
matter of vital moment to make our disjunction accurate and
complete, and to know if we mean " A is b or c" or " A is
be or b or c." About the commonest mistake in metaphysics
is the setting up of false alternatives. If we either admit be
as a predicate when b and c are discrepant, or exclude be
when b and c are compatible, we are liable to come to most
132 THE PRINCIPLES OF LOGIC BOOK I
false conclusions. And the very instance we have quoted above
should read us a lesson. It is false that the alternative
" either rogue or fool " does never exclude the possibility of
both. It is a common thing to make this mistake. When
we try to guess a man s line of conduct, we first lay it down
he is fool or rogue, and then afterwards, arguing that he is
certainly a rogue, we conclude that his conduct will be de
liberately selfish. But unfortunately the man has been a fool
as well, and was not in any way to be relied on. It is often im
possible to speak by the card, but still inaccuracy remains
inaccuracy. And, if we do not mention the alternative " or
both," when held to our words we certainly exclude it.
If we mean to say " A is b or c or again be" the process
of the judgment is very simple. A exists and is further
determined. It is determined within the region be. A ex
cludes all qualities which are incompatible with b and c and
again with be. Within be fall b and c and again be, and
nothing else falls there. And since these are discrepant, A
is but one of them. So far the fact, and then come the
hypotheses. If A as determined excludes b and c it must be
be; if it excludes c and be it is b; if it excludes b and be it is c.
The number of discrepants is of course irrelevant to the
nature of the process.
8. But the inaccuracy we have noticed has a natural
foundation. We are accustomed to use " or " with an impli
cation, and at times we forget whether " or " stands alone or
must be taken as so qualified. I will briefly illustrate. If, in
drawing up a rule, I lay down that " the number of tickets
being limited, each person shall be entitled to a red ticket or
a white one," it is at once understood that the alternatives are
incompatible. A ticket means here obviously one at most.
But, if I say " No one shall be entitled to pass within this
enclosure except the possessor of a white or red ticket," I
should hardly be taken to exclude the man who was qualified
by both. A ticket means here one at least. And it becomes
very easy to misunderstand, and to suppose that " or " in each
of these cases has a different force.
But in both cases " or " means precisely the same. In the
second, as in the first, it is rigidly disjunctive. But in the
second of our instances "or" does not stand alone. It is
CHAP. IV THE DISJUNCTIVE JUDGMENT j^
qualified by an unexpressed " if not " or " failing that." And
this implication makes a vital difference.
9. The alternatives which are offered are not red and
white. I am not to be admitted, given white or red. The
entitling conditions (so far as they are contemplated) are
firstly " white," and then " red, white failing " or " red with
out white ; " and it can hardly be maintained that these con
ditions are compatible. For, if white is there, then red can not
make good the failure of white, and the red, that is specified
as excluding white, can not by any means admit its presence.
What you mean to say is, Suppose white is there, then cadit
quastio; but, if white is not there, red will answer the pur
pose. And you express your meaning by assigning two
alternatives, " white present " on the one hand, and, on the
other hand, " red coupled with the absence of white." And
this practically provides for every possibility.
The logical objection which may be raised against it is not
that its "or " is partly conjunctive, for this, as we have seen, is
a pure mistake. The disjunction is faulty not because it is
conjunctive, but because it is incomplete. It ignores the
possibility of the co-existence of red and white, and in form
it might be construed as excluding it. But the reason is
obvious. You are never forced to consider separately this
individual possibility, since you can always treat it as a
simple case of the presence of white. If "white" really
means " white with or without red," and " red " means " red
on the failure of white," and if the absence of both is fully
provided for, then the disjunction is absolutely complete and
exhaustive. And these alternatives (i) white with or without
red, (ii) red without white, and (iii) failure of both, are
absolutely incompatible.
10. And this I think is the answer to an argument
brought forward by Professor Jevons (Principles, p. 73).
Against the exclusive character of alternatives he urges an
indirect argument. If that were so, he objects, the negative
of such a term as " malleable-dense-metal " could not be
" not-malleable or not-dense or not-metallic." There would be
seven distinct alternatives, and this would be absurd.
I must remark, in the first place, that I wholly fail to see
the absurdity. If you mean to exhaust the cases which ex-
2321.1 K
134 THE PRINCIPLES OF LOGIC BOOK I
elude the term " malleable-dense-metal," the absurdity would
lie in their number being less than what follows from the
number of possible combinations. But if you mean to say
that, if "or " is exclusive, you can not deny the term which is
offered unless you set out all the cases which exclude it, then
this is just the mistake we have been considering. In " not-
malleable or not-dense or not-metallic" the disjoined are in
compatible, but the full possibilities are not set out. You
must understand with each " or " the implication of " failing
that." " Not malleable " does not mean the isolated presence
of non-malleability. It is not one possibility: it is a class
that covers several. It means the absence of malleability,
whether the subject is metallic or not-metallic, dense or not-
dense. You may fairly object that combinations are ignored,
or else that the term " not-malleable " is ambiguous, since it is
used to cover a number of cases. But these technical objec
tions would have little importance, and they do nothing to
show that " or " does anything but rigidly disjoin.
ii. Despite my respect for Professor Jevons, I can not
admit any possible instance in which alternatives are not
exclusive. I confess I should despair of human language, if
such distinctions as separate " and " from " or " could be
broken down. And, when I examine the further evidence
produced, it either turns on the inaccurate modes of expres
sion we have lately discussed, or consists in what I must be
allowed to call a most simple confusion. We are told that
the expressions " wreath or anadem," or again " unstain d by
gold or fee " (Jevons, p. 70), show that " or " may sometimes
be non-exclusive. But this is quite erroneous. The alterna
tives are meant to be rigidly incompatible. The distinction is
however not applied to the thing, but simply to the names. If
we suppose that the terms are quite synonymous, then " wreath
or anadem" means "you may call it by either name you
please." The thing has two titles, one of which is at your
service. I hardly think Professor Jevons would assert that we
are asked to use both names at once. So, if " fee " is not
meant to be distinct from " gold," the assertion is that there is
no stain arising from the thing you may term indifferently
gold or fee. The idea of your wanting to say both at once is
quite ignored.
CHAP. IV THE DISJUNCTIVE JUDGMENT 135
I will try to make the matter clearer by inventing a piece
of imaginary dialogue. A. Who is the greatest Roman poet?
B. His name is Virgil. A. What, not Vergilius? B. Yes,
Virgil or Vergilius. A. I understand : he has two names. I
will call him henceforth " Vergilius- Virgil," and then I shall be
safe. B. Excuse me: in that case you must be wrong. You
may call him by either of the names you please, but not by
both of them at once.
It is not worth while to multiply illustrations. In every
instance that can be produced, we have either a loose mode of
common speech, or else the " or " denotes incompatibility,
whether that lie in the simultaneous use of alternative names,
or in the facts themselves.
12. The mere statement, of course, may fail to tell us
which of these incompatibilities is before us. And no one can
deny that alternatives are often presented in a very inac
curate way. It is an excellent thing in all these questions
to refer to the common usages of language, but we must
remember that in those usages, besides what one calls " un
conscious logic," there also may lurk mere looseness and care
lessness. It may not be amiss to illustrate the mistake we
have just been discussing, by a parallel ambiguity in the
hypothetical judgment. It is, of course, the established doc
trine that, while you may argue from ground to consequence,
you can not demonstrate from consequence to ground. 10 And,
although from a metaphysical point of view this doctrine is
certainly open to doubt, still for logical purposes it is suffi
ciently valid. But yet, by appealing to loose expressions,
we might show that the ground is the only ground, and can
therefore be inferred from the presence of the consequence.
Sigwart has called attention to these cases (Logik, I. 243 ; and
Beitrage, 59). "If you run hard you will catch him," is
often an indirect way of saying, " You will not catch him
unless you run hard." But such mere loose phrases are no
valid reason for impugning the doctrine that, unless this fact is
specially stated, the condition is not given as a sine qua non.
When the context shows that our expressions are not to be
strictly interpreted, we are at liberty to take " eitheror " as
compatible, and " if " may be the same as " not unless." But
136 THE PRINCIPLES OF LOGIC BOOK I
we should remember that what a thing can pass for may differ
widely from what it really is.
13. It is time we left these misleading errors to return to
the discussion of the matter itself. The detail of the process
in disjunctive judgments can not fully be dealt with till we
come to inference. But here we may partly prepare the
ground.
In the first place, as we shall see in the following chapter,
disjunction does not rest on Excluded Middle. The latter is
merely a case of disjunction.
" A is b or c " asserts, as we saw, that A exists and pos
sesses a quality. That quality, further, falls within be. It is
affirmed to be what is common to both, and it is stated also to
be further determinable within be. In other words, it excludes
all discrepant with both b and c.
We have seen this above, and the point I wish here to
bring forward is the following. How do we know, and how
can we know, that there is not something discrepant with be
and yet compatible with A? All rests upon this; and what
does this rest on?
We must answer, for the present, that it rests on our
impotence. 11 There is no great principle on which we can
stand. We can not find any opposite of b or opposite of c
which is not also an opposite of A; and we boldly assume
that, because we find none, therefore there is none. The con
clusion from impotence may itself seem impotent, but, as
we shall hereafter see, there remains some doubt if it may not
in the end be taken as the ground and the sole ground we have
for believing anything (Book III. II. Chapter III.).
14. We may state the whole matter once more thus. " A
is b or c" may be expressed by (i) If A is b it is not c, and
If A is c it is not b, (ii) If A is not b then it is c, and If A
is not c then it must be b. The first two hypothetical state
ments are erected on the knowledge that b and c as predicates
of A are incompatible, or that Abe can not possibly exist.
The second pair are based on the assumption that, because
we do not find a predicate of A which excludes b or c, there
fore there is none. Every opposite of b or of c, that we find,
is an opposite of A. Hence there remains this result; within
the limit of A there is no not-fc but c, and no not-c but b: and
CHAP. IV THE DISJUNCTIVE JUDGMENT 137
A must have some further quality. This is the ground for our
second two hypotheticals.
So we see the essence of disjunctive judgment is not got
by calling it a combination of supposals. It has a distinctive
character of its own. It first takes a predicate known within
limits, and defined by exclusion, and then further defines it
by hypothetical exclusion. It rests on the assumption that we
have the whole field, and by removing parts can determine
the residue. It supposes in short a kind of omniscience. Its
assertion again, if not quite categorical, is certainly not quite
hypothetical. It involves both these elements. And it implies,
in addition, a process of inference which will give us cause
for reflection in the future.
ADDITIONAL NOTES
1 On the subject of Disjunction the reader is referred to Dr.
Bosanquet s Logic. I fully accept his main view; but, before pro
ceeding in consequence to point out some errors made in this volume,
I will add a few remarks which may perhaps assist the reader.
Disjunction means "or," and, viewed psychologically, "or" stands
for Choice. Hence it may be useful to consider here how choice
arises. Where something is desired, where there are various ways
of realizing this end, and where I find that I can not have all of
these as a whole and at once and where, by this negation, action
has been suspended the result may be choice. And, in choosing, I
accept one way while rejecting the rest. Or, again, I foresee, let us
say, that an event affecting me must actually happen, and that, so far,
there are no two ways, but that, as to how the event will happen and
affect me, the ways are various. And let us add that I perceive that
these diverse modifications, while impossible all at once, are otherwise,
each of them, more or less in my power. Here, as above, after suspend
ing action I identify myself in choice with one of these modes, while
rejecting the rest. And obviously the "or" thus contained in choice
is exclusive; and any other view as to "or" would, here at least,
conflict with plain fact.
We may note further that in choice the alternative need not
merely be dual. The incompatibles that are each possible may be
clearly more than two. And this plurality in the " or " holds, I would
add, not merely psychologically and in choice, but equally belongs to
the "or" of logical disjunction. The necessary duality of disjunction
in the sense that the incompatibles, which are each possible, can not
be taken as more than two is to my mind a view which, so far, is
contrary to fact.
THE PRINCIPLES OF LOGIC BOOK I
What is true here is that when, and so far as, in choice or other
wise, you identify yourself with one possibility, the residue tends to
be regarded or at least treated, so far, as not even possible. It is
taken for our purpose, we may say, in the lump and as all one, and
so, we may add, is taken but as one only. But in the above attitude
(to speak strictly) there is really no question of number, since what
is rejected is viewed merely from the side of its general quality.
Having now noticed the character of " or " as we find it in choice,
I will go on to deal briefly with the origin and nature of logical dis
junction. Before this arises we have found that Reality, as this or
that recognizable object, has various qualities. We have passed, that
is, beyond the stage of an immediate unity of one and many. We
have reached a level where the distinguished many are recognized as
diverse, and yet, as each and also the rest, belonging somehow to the
one object. And the object possesses this diversity, so far, all together
and at once. The qualities thus seem simply conjoined and are called
compatible. But we go on to discover, in the same or in some other
object, qualities not found thus together, and we call these, so far,
incompatible. The object may have now one and now another, but
never has at once both or all. On the other side (here is the point)
the object has these qualities. It has them, now one and now
another, according to the conditions. It has them, that is, not simply,
but according as it itself is made diverse, so as itself to enter into
and become this one qualification while rejecting the others. And,
since we find that this holds good also with regard to these other
incompatibles, the object is now qualified by them all, but qualified
disjunctively. While on one hand the object is all, it is on the other
hand each singly and each exclusively according to the diverse con
ditions.
Such in outline, we may say, is the origin of Disjunction, and its
intellectual importance and necessity can not well be overestimated.
But we are led none the less to look beyond it to a higher and more
ultimate stage, where we return to Conjunction in a different sense
and at a higher level. In a complete and perfect system, where all
conditions were filled in, the real Universe would have all its de
terminations at once, all as connected and each as qualifying the others
and the whole. And here negation would disappear except as one
aspect of positive and complementary distinction. But for us this
ultimate stage of the intellect remains an ideal, in the sense that it
can not in detail and everywhere be attained completely.
This ideal, I must add, in no way justifies the doctrine that in
logic " or " can anywhere have a sense which is not exclusive. In
other words so far as " or " ceases to exclude both " or," and
disjunction with it, have so far ceased as such to exist. See below,
on 7.
2 " To state it incorrectly." I can not now recall the origin of this
remark, which seems at best negligible. For the possibility of reduc
tion to two hypothetical see Bosanquet, K & R, p. 208.
CHAP. IV THE DISJUNCTIVE JUDGMENT 139
31 " It is nonsense." Certainly (I must insist) it is so. We may
illustrate by the attempt to reduce relational wholes, and even per
haps all facts, to relations and terms.
4 "The basis ... is categorical." This, however, is subject to a
qualification, for which see Bosanquet, Logic (Ed. II), I, 328.
5 It is of course not true that disjunction assumes the existence
of its subject (cf. Chap. V, 23), if that means "existence in my real
world." The subject may be hypothetical or otherwise "imaginary."
But there is in the end an Ultimate within which all disjunction falls
and which has no negative.
6 The use of "quality" here is objectionable. See on Chap. II, 50.
7 " It can not be both and it must be some one." If " some one "
means " one only," this would anticipate the disjunction. It should
mean " must be, so far, within the field of both while not both." The
disjunction implied in "one only" requires hypothetical to complete
it and make it explicit. The same requirement, though not in the
same sense, holds, I think, of our knowledge that b and c are in
compatible.
8 I am more than ever convinced that the view which takes " or "
as not always exclusive is utterly untenable, except perhaps by way of
of a mere convenient artifice. On the whole question, and for a refuta
tion of technical objections, see Bosanquet, Logic (Ed. II), Vol. I,
pp. 355 foil. The subject is now perhaps exhausted, but I will allow
myself to add one or two remarks.
(i) The evidence from psychology seems to me to be all on one
side. " Or " answers to choice, and choice seems nonsense if it means
that you can have all at once. And this consideration ought, I submit,
to carry great weight.
(ii) The fallacy of " false alternative," I would further remind
the reader, may be said perhaps to dominate our lives. But how could
this be so, if "or" were not taken instinctively as everywhere exclu
sive? And the fallacy does not lie in our assuming this as true. It
lies, on the other hand, in our forgetting constantly the actual nature of
our subject. We may say that (apart from exceptional cases) in every
judgment made in life the real subject is other than that which is
formulated. It is really that which is "understood" for the purpose
in hand, which limited purpose, not being made explicit, is easily
ignored or forgotten. Thus, in " A is b or c," the A which we mean
is A qualified and limited by our special object and interest. It is of
and within this qualified A that our " b or c " holds. And it is when
we ignore or forget this, and when we go on to take A simply and
unrestrictedly in the sense of " A anyhow," that the fallacy everywhere
tends to arise. But this tendency, with its false result, points, I submit,
to our unfailing reliance on the exclusiveness of "or."
The arguments against its exclusiveness seem to me plausible only
when this unexpressed qualification of A is ignored. In our actual
use of " or," A means an A not only where the possibility of Abe is
excluded, but also where it is tacitly set aside as irrelevant to our
I4O THE PRINCIPLES OF LOGIC BOOK I
purpose. And, when we remember this, the case against exclusiveness,
to my mind, disappears.
(iii) If we keep to mere "or," then "or" is both exhaustive and
exclusive; and, if we are to argue against the second of these characters,
we must also argue against the first. After stating that A is & or c, we
may receive the answer "yes or both" without any feeling that our
statement has been denied. But, on just the same principle, we may
accept a suggested addition of "or d" not as a correction but as a
complement. And yet to argue from this that disjunction is not taken
as exhaustive would, if plausible, be erroneous. The " or d " is ac
cepted because, and so far as, A did not mean "A pure and simple."
It in fact meant, for our purpose, something like " A, whatever else A
elsewhere may be." Hence a correction and a replacement of A by
a wider subject is (we feel) not called for here by the addition of
"or d." And thus the actual disjunction is really exhaustive, just as
on the same principle (we saw above) it was really exclusive unless,
that is, the disjunction in both cases has ceased, as such, to exist, and
has really given way to some lower or higher mode of assertion.
9 " His statement is ... false." And it therefore, I presume, can
lead formally to the equally false result " He is either wise or honest "
(Keynes, Formal Logic, p. 280, note). This, if correct, I take to
confirm the doctrine of my text, which doctrine, I venture to think,
here and elsewhere, Dr. Keynes has failed to understand.
10 "The established doctrine." The doctrine is, however, in the
end untenable. See Bosanquet, Logic I, Chap. VI. I have fully
accepted his view; see Appearance, Index, s. v. Cause, and T. E. X.
Apart from this, the instance in the text may serve to illustrate the
ambiguity of ordinary language.
11 For privation and impotence as a ground of knowledge see on
Chap. Ill, 9. So far as our knowledge is completely systematized,
privation, of course, so far ceases to exist.
CHAPTER V
THE PRINCIPLES OF IDENTITY, CONTRADICTION, EXCLUDED
MIDDLE, AND DOUBLE NEGATION.
i. After discussing negative and disjunctive judgments,
we may deal at once with the so-called " Principles " of Iden
tity, Contradiction, and Excluded Middle; and we will add
some remarks on Double Negation.
The principle of Identity is often stated in the form of a
tautology, " A is A." If this really means that no difference
exists on the two sides of the judgment, we may dismiss it
at once. It is no judgment at all. As Hegel tells us, it sins
against the very form of judgment; for, while professing to
say something, it really says nothing. It does not even assert
identity. For identity without difference is nothing at all.
It takes two to make the same, and the least we can have is
some change of event in a self -same thing, or the return to
that thing from some suggested difference. For, otherwise, to
say " It is the same as itself " would be quite unmeaning. We
could not even have the appearance of judgment in " A is A,"
if we had not at least the difference of position in the different
A s ; and we can not have the reality of judgment, unless some
difference actually enters into the content of what we assert.
2. We never at any time wish to use tautologies. No
one is so foolish in ordinary life as to try to assert without
some difference. We say indeed " I am myself," and " Man is
man and master of his fate." But such sayings as these are
no tautologies. 1 They emphasize an attribute of the subject
which some consideration, or passing change, may have
threatened to obscure ; and to understand them rightly we
must always supply " for all that," " notwithstanding," or
again, " once more." It is a mere mistake to confuse what
Kant calls " analytical judgments " * with tautologous state
ments. In the former the predicate is part of the content of
the conception A, which stands in the place of, and appears as,
*This is not the sense in which I have used "analytical." p. 48.
141
!42 THE PRINCIPLES OF LOGIC BOOK I
the subject. But in every judgment of every kind a synthesis
is asserted. The synthesis in Kant s analytical judgment holds
good within the sphere of the conception ; and the real subject
is not the whole of A, but is certain other attributes of A
which are not the attribute asserted in the predicate. In " All
bodies are extended " what we mean to assert is the connection,
within the subject "bodies," of extension with some other
property of bodies. And even if " extended " and " body "
were synonymous, we still might be very far from tautology.
As against some incompatible suggestion, we might mean to
assert that, after all misapprehension and improper treatment,
the extended is none the less the extended. And, again, we
might be making a real assertion of a verbal nature. We
might mean that, despite their difference as words, the mean
ing of " body " and " extended " was the same. But mere
tautology with deliberate purpose we never commit. Every
judgment is essentially synthetical.
3. The axiom of Identity, if we take it in the sense of a
principle of tautology, is no more than the explicit statement
of an error. And the question is, would it not be better to
banish irrevocably from the field of logic such a source of
mistake? If the axiom of Identity is not just as much an
axiom of Difference, then, whatever shape we like to give it,
it is not a principle of analytical judgments or of any other
judgments at all. On the other hand, perhaps something may
be gained if a traditional form can get a meaning which con
veys vital truth. Let us try to interpret the principle of Iden
tity in such a way that it may really be an axiom.
4. We might take it to mean that in every judgment we
assert the identity of subject and predicate. Every connection
of elements we affirm, in short all relations and every differ
ence, holds good only within a whole of fact. 2 All attributes
imply the identity of a subject. And taken in this sense the
principle of Identity would certainly be true. But this perhaps
is not the meaning which, for logical purposes, it is best to
mark specially.
5. There remains a most important principle which,
whether it be true or open to criticism, is at least the sine qua
non of inference. And we can not do better than give this the
name of principle of Identity, since its essence is to emphasize
CHAP. V THE PRINCIPLE OF IDENTITY 143
sameness in despite of difference. What is this principle? It
runs thus : " Truth is at all times true," or, " Once true always
true, once false always false. Truth is not only independent
of me, but it does not depend upon change and chance. No
alteration in space or time, no possible difference of any event
or context, can make truth falsehood. If that which I say is
really true, then it stands for ever."
So stated the principle is not very clear, but perhaps it
will find acceptance with most readers. What it means, how
ever, is much more definite, and will be much less welcome.
The real axiom of Identity is this : What is true in one context
is true in another. 5 Or, If any truth is stated so that a change
in events will make it false, then it is not a genuine truth at all.
6. To most readers this axiom, I have little doubt, will
seem a false statement. For the present it may stand to serve
as a test if our previous discussions (Chap. II.) have been
understood. If every judgment in the end is hypothetical,
except those not directly concerned with phenomena if each
merely asserts a connection of adjectives, in this sense that
given A then B must follow we see at once that under any
conditions it will always be true. And we shall see here
after that in every inference this result is assumed as a prin
ciple of reasoning, and that we can not argue one step with
out it.
7. We saw that such judgments as " I have a toothache,"
in their sensuous form, are not really true. They fail and
come short of categorical truth, and they hardly have attained
to hypothetical. To make them true we should have to give
the conditions of the toothache, in such a way that the con
nection would hold beyond the present case. When the judg
ment gave the toothache as the consequent coming according
to law from the ground, when the judgment had thus become
universal, and, becoming this, had become hypothetical, then
at last it would be really true, and its truth would be uncondi
tional and eternal.
I know how absurd such a statement sounds. It is impos
sible, I admit, however much we believe it, not to find it in a
certain respect ridiculous. That I do not complain of, for it
is not our fault. But it is our fault if the common view does
not seem more ridiculous. I say that " I have a toothache "
144 THE PRINCIPLES OF LOGIC BOOK I
to-day. It is gone to-morrow. Has my former judgment
become therefore false? The popular view would loudly pro
test that it still is true, for I had a toothache, and the judg
ment now holds good of the past. But what that comes to is
simply this. The judgment is true because answering to fact.
The fact alters so that it does not answer; and yet the judg
ment is still called true, because of something that does not
exist. Can anything be more inconsistent and absurd? If the
change of circumstance and change of day is not a fresh con
text which falsifies this truth, why should any change of
context falsify any truth? And if changed conditions make
any truth false, why should not all truth be in perpetual flux,
and be true or false with the fashion of the moment ?
8. We shall discuss this question more fully hereafter
(Bk. II. Part I.), but may here anticipate a misunderstanding.
To ask " Does space or time make no difference " is wholly to
ignore the meaning of our principle. We ask in reply, " Does
this difference enter into the content of A? If it does, then
A becomes perceptibly diverse, and we confessedly have left
the sphere of our principle. But, if it does not so enter, then
the truth of A is considered in abstraction from spaces and
times, and their differences are confessedly irrelevant to its
truth. We thus meet the objection by offering a dilemma.
You have abstracted from the differences of space and time,
or you have not done so. In the latter case your subject itself
is different; in the former case it is you yourself who have
excluded the difference.
We may indeed on the other side be assailed with an ob
jection. We may be asked, "What now has become of the
identity? Has it not disappeared together with the differ
ences? For if the different contexts are not allowed to enter
into the subject, how then can we say what is true in one con
text is true in another? It will not be true in any context at
all." But we answer, The identity is not contained in the judg
ment " S P," since that takes no kind of account of the dif
ferences. 4 The identity lies in the judgment, " S P is true
everywhere and always." It is this "everywhere" and "al
ways " that supply the difference against which S P becomes
an identity. The predicate attributed to the real belongs to it
despite the difference of its diverse appearances. We do not say
CHAP. V THE PRINCIPLE OF CONTRADICTION 145
the appearances are always the same, but the quality keeps its
nature throughout the appearances. And with this reply we
must here content ourselves.
9. When we come to discuss the nature of inference we
shall see more fully the bearing of the principle. It stands
here on the result of our former enquiries, that every judg
ment, if it really is true, asserts some quality of that ultimate
real which is not altered by the flux of events. This is not the
place for metaphysical discussion, or we might be tempted to
ask if identity was not implied in our view of the real. For if
anything is individual it is self -same throughout, and in all
diversity must maintain its character.
THE PRINCIPLE OF CONTRADICTION.
10. Like the principle of Identity, the principle of Con
tradiction has been often misunderstood. And in the end it
must always touch on a field of metaphysical debate. But, for
logical purposes, I think it is easy to formulate it in a satisfac
tory way.
It is necessary before all things to bear in mind that the
axiom does not in any way explain, that it can not and must
not attempt to account for the existence of opposites. 5 That
discrepants or incompatibles or contraries exist, is the fact it is
based on. It takes for granted the nature of things in which
certain elements are exclusive of others, and it gives not the
smallest reason for the world being such in nature and not
quite otherwise. If we ever forget this, the Law of Contra
diction will become a copious source of illusion.
II. If the principle of Contradiction states a fact, it says
no more than that the discrepant is discrepant, that the exclu
sive, despite all attempts to persuade it, remains incompatible.
Again, if we take it as laying down a rule, all it says is, " Do
not try to combine in thought what is really contrary. When
you add any quality to any subject, do not treat the subject
as if it were not altered. When you add a quality, which not
only removes the subject as it was, but removes it altogether,
then do not treat it as if it remained." This is all the meaning
it is safe to give to the axiom of Contradiction; and this
meaning, I think, will at once be clear, if we bear in mind our
former discussions. The contrary is always the base of the
146 THE PRINCIPLES OF LOGIC BOOK I
contradictory, and the latter is the general idea of the contrary.
Not-A for example is any and every possible contrary of A
(Chap. III. 16).
12. We have to avoid, in dealing with Contradiction, the
same mistake that we found had obscured the nature of Iden
tity. We there were told to produce tautologies, and here
we are by certain persons forbidden to produce anything else.
" A is not not-A " may be taken to mean that A can be nothing
but what is simply A. This is, once again, the erroneous asser
tion of mere abstract identity without any difference. It is
ordering us to deny as a quality of A everything that is differ
ent from A, and in this sense not-A. But differents and dis-
crepants should never be confused. The former do not exclude
one another; they only exclude the denial of their difference.
The discrepant with A can never be found together with A in
any possible subject, or be joined to it in the relation of subject
and attribute. 6 The different from A does not exclude, unless
you attempt to identify it with A. It is not A generally, but
one single relation to A, which it repels.
As we saw before, there is no logical principle which will
tell us what qualities are really discrepant. Metaphysics, in
deed, must ask itself the question if any further account can
be given of incompatibility. It must recognize the problem,
if it can not solve it. We might remark that no thing excludes
any other so long as they are able to remain side by side, that
incompatibility begins when you occupy the same area; and
we might be tempted to conclude that in space would be found
the key of our puzzle. But such other experiences as that
assertion and denial, or pain and pleasure, are incompatible,
would soon force us to see that our explanation is insufficient.
But in logic we are not called upon to discuss the principle,
but rest upon the fact. Certain elements we find are incom
patible; and, where they are so, we must treat them as such.
13. There is no real question of principle involved in
such different ways of stating the axiom as " A is not not-A,"
" A is not both b and not-b" " A can not at once both be and
not be." For if A were not-A, it would be so because it had
some quality contrary to A. So also, if A has a quality b, it
could only be not-b by virtue of a quality discrepant with b.
And again, if A both were and were not, that would be be-
CHAP. V THE PRINCIPLE OF CONTRADICTION 147
cause the ultimate reality had contrary qualities. The charac
ter in which it accepted A, would be opposite to the quality
which excluded A from existence. Under varieties of detail
we find the same basis, repulsion of discrepants.
A simple method of stating the principle is to say, " Denial
and affirmation of the self -same judgment is wholly inad
missible." And this does not mean that if a miracle in psy
chology were brought about, and the mind did judge both
affirmatively and negatively, both judgments might be true.
It means that, if at once you affirm and deny, you must be
speaking falsely. For denial asserts the positive contrary of
affirmation. 7 In the nature of things (this is what it all comes
to) there are certain elements which either can not be con
joined at all, or can not be conjoined in some special way;
and the nature of things must be respected by logic.
14. If we wish to show that our axiom is only the other
side of the Law of Identity, we may state it thus, " Truth is
unchangeable, and, as discrepant assertions alter one another,
they can not be true." And again, if we desire to glance in
passing at the metaphysical side of the matter, we may remind
ourselves that the real is individual, and the individual is har
monious and self-consistent. It does not fly apart, as it would
if its qualities were internally discrepant.
15. Having now said all that I desire to say, I would
gladly pass on. For, notwithstanding the metaphysics into
which we have dipped, I am anxious to keep logic, so far as is
possible, clear of first principles. But in the present instance
the law of Contradiction has had the misfortune to be flatly
denied from 8 a certain theory of the nature of things. So far
is that law (it has been contended) from being the truth, that
in the nature of things contradiction exists. It is the fact that
opposites are conjoined, and they are to be found as discrepant
moments of a single identity.
I need hardly say that it is not my intention compendiously
to dispose in a single paragraph of a system which, with all its
shortcomings, has been worked over as wide an area of ex
perience as any system offered in its place. My one idea here
is to disarm opposition to the axiom of contradiction, as it
stands above. 9 But I clearly recognize that, if not-A were
148 THE PRINCIPLES OF LOGIC BOOK I
taken as a pure negation, no compromise would be possible.
You would then have to choose between the axiom of contra
diction and the dialectical method.
I will say, in the first place, that whatever is conjoined is
therefore ipso facto shown not to be discrepant. If the ele
ments co-exist, cadit qucestio; there is no contradiction, for
there can be no contraries. And, saying so much, I feel
tempted to retire. But yet with so much I shall hardly escape.
" Have not we got," I hear the words called after me, " have
we not got elements which any one can see negate one another,
so that, while one is, the other can not be; and yet have we
not got very many conceptions in which these discrepants
somehow co-exist ? It is all very well to say, * then not con
trary ; but try them, and see if they are not exclusive."
It is plain that I must stand and say something in reply.
But I think I shall hardly be so foolish as to answer, " These
conceptions of yours are merely phenomenal. Come to us and
learn that knowledge is relative, and with us give up the
Thing-in-itself." For without knowing all that would be
poured on my head, I can guess some part of what I should
provoke. " You say give up the Thing-in-itself ? Why that
is all that you have not given up. You profess that your
knowledge is only phenomenal, and then you make the law of
Contradiction valid of the Absolute, so that what it excludes
you are able to know is not the Absolute. That is surely in
consistent. And then, for the sake of saving from contradic
tion this wretched ghost of a Thing-in-itself, you are ready to
plunge the whole world of phenomena, everything you know
or can know, into utter confusion. You are willing to turn
every fact into nonsense, so long as this Thing-in-itself is
saved. It is plain, then, for which you really care most. And
as for * relativity/ it is you yourselves who violate that prin
ciple. Your turning of the relative into hard and fast con
traries is just what has brought you to your miserable pass."
I confess I should hardly care to subject myself to all these
insults; and I had rather Mr. Spencer, or some other great
authority whoever may feel himself able to bear them, or
unable to understand them should take them on himself.
If I chose to turn and provoke a contest, I know of
another weapon I might use. I might say, " Your conceptions
CHAP. V THE PRINCIPLE OF CONTRADICTION 149
4-
are partial illusions. They are crude popular modes of repre
senting a reality whose nature can not be so portrayed. And
the business of philosophy is to purify these ideas, and never
to leave them until, by removal of their contradictions, they
are made quite adequate to the actual fact." But, after all,
perhaps I could only say this for the sake of controversy, and
controversy is what I am anxious to avoid. And for this end
I think that some compromise may perhaps be come to. With
out calling in question the reality of negation, and the identity
of opposites, are we sure that we can not understand that
doctrine in a sense which will bear with the axiom of Contra
diction? This axiom is not like the principle of Identity. It
is a very old and most harmless veteran; and for myself I
should never have the heart to attack it, unless with a view
to astonish common-sense and petrify my enemies. And in
metaphysics we can always do that in many other ways.
What I mean is this. 10 Supposing that, in such a case as
continuity, we seem to find contradictions united, and A to be
b and not-b at once, this may yet be reconciled with the axiom
of Contradiction. A we say is composed of b and not-b; for,
dissecting A, we arrive at these elements, and, uniting these,
we get A once more. But the question is, while these elements
are in A, can they be said, while there, to exist in their fully
discrepant character of b and not-b? I do not mean to sug
gest that the union of contraries may be that misunderstanding
of the fact which is our only way to understand it. For, if I
felt sure myself that this were true, I know it is a heresy too
painful to be borne. But, in the object and within the whole,
the truth may be that we never really do have these discrep-
ants. We only have moments which would be incompatible if
they really were separate, but, conjoined together, have been
subdued into something within the character of the whole. If
we so can understand the identity of opposites and I am not
sure that we may not do so then the law of Contradiction
flourishes untouched. If, in coming into one, the contraries
as such no longer exist, then where is the contradiction?
But, I fear, I shall be told that the struggle of negatives is
the soul of the world, and that it is precisely because of their
identity that we have their contradiction. It is true that the
opposition which for ever breaks out leads to higher unity in
2321. x L
I5O THE PRINCIPLES OF LOGIC BOOK I
which it is resolved ; but still the process of negation is there.
It is one side of the world which can not be got rid of, and it is
irreconcileable with the non-existence of discrepants in a single
subject. Each element of the whole, without the other, is
incompatible with itself ; but it is none the less incompatible
with the other, which for ever it produces or rather becomes.
I am after all not quite convinced. If the law of Contra
diction is objected against because, in isolating and fixing the
discrepant, it becomes one-sided, is it not quite possible that,
in denying the law, we have become one-sided in another
way? If the negation itself, while negative on one side, is on
the other side the return from itself to a higher harmony if,
that is to say, the elements are not discrepant without each at
once, by virtue of its discrepancy and so far as it is discrepant,
thereby ipso facto ceasing to be discrepant, then surely, in
denying the law of Contradiction, we ourselves have fixed one
side of the process, and have treated the contrary as simply
contrary. The contrary which the law has got in its head, is
the contrary that entirely kills its opposite, and remains tri
umphant on the field of battle. It is not the contrary whose
blows are suicidal, and whose defeat must always be the doom
of its adversary. It is incompatibles fixed as such, it is dis
crepants which wholly exclude one another and have no other
side, that the axiom speaks of. But dialectical contraries are
only partially contrary and it is our mistake if we keep back
the other side. And if an opponent of the law reminds me
that the existence of these two sides within one element is just
the contradiction, that in the b which is contrary to not-&
the implication of not-b makes it self-contradictory, then I
must be allowed to say in reply that I think my objector has
not learnt his lesson. The not-& in b is itself self-discrepant,
and is just as much b: and so on for ever. We never have
a mere one-sided contrary.
But it is one-sided and stationary contraries that the axiom
contemplates. It says that they are found, 11 and no sober
man could contend that they are not found. No one ever
did maintain that the dialectical implication of opposites could
be set going in the case of every conjunction that we deny.
It can hardly be maintained that there are no discrepants,
except these contraries which at the same time imply each
CHAP. V THE PRINCIPLE OF EXCLUDED MIDDLE 151
other. And the law of Contradiction does not say any more
than that, when such sheer incompatibles are found, we must
not conjoin them.
Its claims, if we consider them, are so absurdly feeble, it is
itself so weak and perfectly inoffensive, that it can not quarrel,
for it has not a tooth with which to bite any one. The
controversy, first as to our actual ability to think in the way
recommended by Hegel, and secondly as to the extent to which
his dialectic is found in fact, can not only not be settled by an
appeal to the axiom, but falls entirely outside its sphere.
Starting from the fact of the absolute refusal of certain ele
ments to come together, and wholly dependent upon that fact,
so soon as these elements do come together the axiom ceases
forthwith to be applicable. It is based upon the self-con
sistency of the real, but it has no right to represent that con
sistency except as against one kind of discrepancy. So that, if
we conclude that the dialectic of the real would in the end
destroy its unity, that has nothing to do with the axiom of
Contradiction. Like every other question of the kind, the
validity of dialectic is a question of fact, to be discussed and
settled upon its own merits, and not by an appeal to so-
called " principles." And I think I may venture to hazard the
remark, that one must not first take up from uncritical
views certain elements in the form of incompatible discrepants,
and then, because we find they are conjoined, fling out against
the laws of Contradiction and Excluded Middle. They, such
as they are, can be no one s enemy; and since no one in the
end can perhaps disbelieve in them, it is better on all ac
counts to let them alone.
PRINCIPLE OF EXCLUDED MIDDLE. 12
1 6. The axiom that every possible judgment must be
true or false, 13 we shall see is based on what may be called a
principle. It is however doubtful if the axiom itself should
receive that title, since it comes under the head of disjunctive
judgment. We must not imagine that our axiom supplies the
principle of disjunction. It is merely one instance and applica
tion of that principle.
17. If we recall the character of the disjunctive judg
ment, we shall remember that there we had a real, known to
152 THE PRINCIPLES OF LOGIC BOOK I
be further determined. Its quality fell (i) within a certain
area; and (ii) since that area was a region of discrepants, the
real was determined as one single member. On this basis 1 *
we erected our hypotheticals, and so the " either or " was
completed.
Excluded Middle shows all these characteristics. In it we
affirm (i) that any subject A, when the relation to any
quality is suggested, is determined at once with respect to
that predicate within the area of position and negation, and
by no relation which is incompatible with both. And (ii) we
assert that, within this area, the subject is qualified as one
single member. And then we proceed to our " either or."
18. Excluded Middle is one case of disjunction: it can
not be considered co-extensive with it. Its dual and con
tradictory alternative rests on the existence of contrary
opposites. The existence of exclusives without reference to
their number is the ground of disjunction, and the special case
of assertion and denial is developed from that basis in the
way in which contradiction is developed from exclusion.
Common discrepant disjunction is the base, and the dual
alternative of b and not-b rests entirely upon this.
19. Excluded Middle is one kind of disjunction : and we
must proceed to investigate the nature of that kind, (i) Dis
junction asserts a common quality. In "b or not-b" the
common quality asserted of A is that of general relation to b.
(ii) Disjunction asserts an area of incompatibles. Affirmation
or denial of b is here the area within which A falls. The
evidence that it does not fall outside and that all the dis
crepants are completely given, may be called my impotence
to find any other. 15 (iii) Disjunction attributes to the subject
A one single element of the area. And this part of the process
does not call here for any special remark.
20. We find however, when we investigate further, a
point in which the axiom of Excluded Middle goes beyond
the limits of disjunctive judgment. It contains a further
principle, since it asserts a common quality of all possible
existence. It says, Every real has got a character which
determines it in judgment with reference to every possible
predicate. That character furnishes the ground of some
judgment in respect of every suggested relation to every
CHAP. V THE PRINCIPLE OF EXCLUDED MIDDLE 153
object. Or, to put the same more generally still, Every element
of the Cosmos possesses a quality, which can determine it
logically in relation to every other element.
21. This principle is prior to the actual disjunction. It
says beforehand that there is a ground of relation, though it
does not know what the relation is. The disjunction proceeds
from the further result that the relation falls within a dis
crepant sphere. We thus see that, on the one hand, Excluded
Middle transcends disjunction, since it possesses a self-de
termining principle which disjunction has not got. On the
other hand, in its further development, it is nothing what
ever but a case of disjunction, and must wait for the sphere
of discrepant predicates to be given it as a fact. 16
22. The disjunction is completed by the fact that, when
any predicate is suggested, the quality of every element is a
ground of either the affirmation or the denial of the predicate.
It compels us to one and to one alone ; for no other alternative
can possibly be found.
And here the opposition, directed before against the axiom
of Contradiction, must again be confronted. It is false, we
are told, that A must either be c or not-c. We have often to
say " both," and sometimes " neither." But I think perhaps
the discussion at the end of the foregoing chapter will have
strengthened us to persist. I fully admit that often, when
challenged to reply Yes or No, it is necessary to answer " Yes
and No" or "Neither." But, I venture to think, that is
always because the question is ambiguous, and is asked from
the standpoint of a false alternative. 17 " Is motion continuous?
Yes or no." I decline to answer until you tell me if, by saying
Yes, I am taken to deny that it is also discrete. In that case
perhaps, instead of saying Yes, I should go so far as to
answer No. There may be a middle between continuity and
discretion; there can be none between continuous and not-
continuous.
The ground of the objection to the Excluded Middle is,
I am bold enough to think, fallacious. Given not fixed dis-
crepants but dialectical opposites, the existence of these
together in one single subject does not give us the right to a
negative judgment. One can not be made use of as the
positive ground on which to build the denial of the other.
154
THE PRINCIPLES OF LOGIC BOOK I
One does not wholly remove the other, and, failing to do so,
it is not qualified as a logical contrary. For it is only the
discrepant which destroys its opposite that can serve as the
base of a negative judgment. And, failing the denial of one
quality through the other, the answer must be that both are
present, and the denial of either is wholly excluded. But I
fear it is hard altogether on this point to effect a compromise.
If the negative of b is ever simply not-&, and if this is the
other which is implicated with b in one subject A, then I
grant the Excluded Middle disappears. But, I think, in this
case it will carry along with it enough to ruin what is left
behind. And I must leave the matter so.
23. The Excluded Middle, as we saw before, is a
peculiar case of the disjunctive judgment; and I think this
insight may serve us further to dispel some illusions which
have gathered round it.
In the first place we must not think it is a formula, by
applying which we can magically conjure elements of know
ledge from the unknown deep. It is nonsense to say that it
gives us a revelation that any subject must have one of two
predicates. For, even if we do not make a logical mistake and
really have got contradictory qualities, that is still not the
right way to put the matter. Denial is not the predication of
a contradictory ; and all that Excluded Middle tells us is that,
given any possible element of knowledge, you must be right in
either affirming or denying any suggestion that is made about
that.
We learnt, in our chapter on the Disjunctive Judgment,
that this judgment must assume the existence of its subject, 18
though that subject may not be the grammatical subject. And
when, in the case of Excluded Middle, we are told it will
guarantee us the truth of either b or not-& as a predicate of A,
we naturally ask, " But what guarantees to us the existence of
A ? " And we get no answer. Things in themselves either
are b or are not b. Undoubtedly so, but what is the real sub
ject of this statement? It perhaps after all is not " Things-in-
themselves," but is ultimate reality, which may totally reject
the whole offered synthesis. In this case we shall at once be
able to say that Things-in-themselves are not anything at all
in the real world, though, considered as illusions, they no doubt
CHAP. V THE PRINCIPLE OF EXCLUDED MIDDLE 155
have qualities. On the other hand, if Things-in-themselves
are taken as such to have existence, then that is not proved
by our Excluded Middle, but is a sheer assumption on which
we base it and which it presupposes.
24. But when we are told, " Between the true and the
false there is a third possibility, the Unmeaning" 19 (Mill,
Logic, II. vii. 5), we must answer, " Yes, an unmeaning pos
sibility, and therefore none at all." The doctrine that proposi
tions need neither be true nor yet be false because they may be
senseless, would introduce, I agree, " a large qualification "
into the doctrine of the Excluded Middle. But I am inclined
to think that this " qualification " might be larger than it seems
to be, and might be operative perhaps beyond the limits so
sparingly assigned to it. But surely, on the one hand, it is
clear that a proposition which has no meaning is no proposi
tion ; and surely again, on the other hand, it is clear that, if it
does mean anything, it is either true or else false. And when
a predicate is really known not to be " one which can in any
intelligible sense be attributed to the subject " is not that
itself ground enough for denial ? 20 But logicians who actually
(Mill, loc. cit.) are ready to take divisible finitely and divisible
infinitely as contradictories, are justified in expecting extra
ordinary events. Suppose these terms to be absolutely incom
patible, that would hardly bring them under Excluded Middle,
unless we are prepared to formulate the axiom thus: When
ever predicates are incompatible, then, although there be three
or more possibilities, it is certain that one of these two possi
bilities must always be true. But perhaps this " qualification "
might tend to create more difficulties than it solves.
25. If we turn from these somewhat elementary mis
takes, and consider the amount of actual knowledge vouch
safed to us by the Excluded Middle, I hardly think we shall
be much puffed up. We must remember that, even if we are
able to assert about such a subject as Things-in-themselves,
we must always be on our guard against an error. We may
be affirming about the meaning of a word, or about a mere
idea in our heads, and may confuse these facts with another
kind of fact (p. 42). But, even supposing we keep quite
clear of this mistake, yet when we come to negative judgments
THE PRINCIPLES OF LOGIC BOOK I
there is ambiguity, unavoidable and ceaseless, about the
positive ground of the denial. We may penetrate so far into
hidden mysteries as perhaps to be privileged solemnly to avouch
that Things-in-themselves are not three-cornered, nor coloured
rose-red, nor pock-marked nor dyspeptic. But what does this
tell us? What more should we know, if we spent our breath
and wasted our days in endless denials of senseless sugges
tions? If the ground of negation remains the same, 21 each
particular denial asserts nothing in particular (Chap. III. pp.
121, 124).
26. 22 Confined to its limits the Excluded Middle is
rigidly true. But you may easily assert it in a shape which
would exhibit a parallel falsehood to those we considered in
examining the Principles of Identity and Contradiction.
" Everything," we might say, " is either simply the same as
any other, or else has nothing whatever to do with it."
Once again, in conclusion, I must call attention to the
positive principle which underlies the Excluded Middle. We
assume that every element of knowledge can stand in some
relation with every other element. And we may give this, if
we please, a metaphysical turn, though in doing so we go
beyond the equivalent of the Excluded Middle. We may say,
If the real is harmonious and individual, it must exist in its
members and must inter-relate them.
27. I may notice by way of appendix to this subject a
somewhat subtle argument of Professor Jevons, which I regret
to state I am unable to understand. He argues * that to say
" A = B or b " must be incorrect. For the negative of " B or
b " will be Bb, and by consequence a, the negative of A, must
itself be Bb. And the objection to this is that Bb = o. But
because " every term has its negative in thought," therefore the
negative of A can not be = o, and the premise " A = B or b "
is thus indirectly proved false. Professor Jevons proceeds to
draw from this a general conclusion that any judgment, in the
form " A = B or b" is necessarily erroneous, and that we
must write instead of it " A = AB or A&."
Though I fully agree with this last result, yet Professor
Jevons reasoning, as I understand it, appears to me unsound,
* Principles, p. 74. For the meaning of Professor Jevons sym
bols I must refer to his work.
CHAP. V THE PRINCIPLE OF EXCLUDED MIDDLE 157
and I can not reconcile his conclusion with his process. I will
take the latter point first. It appears to be right to judge
" A = AB or Ab" But what is the negative ? I suppose the
negative is AbE, and we must conclude that a = AbE. But
the term AbE most clearly = o. So that, after all, we are
left with a conclusion which proves the falsity of our
premise.
The result is thus out of harmony with the argument, but
for all that the result is perfectly true. It is true that we can
not say " A = B or b" and I will proceed to show why this
must be true. We must take it that A has a determinate
quality; but what is merely B or & is anything whatever. Eb
being nothing, what is simply not-Eb will therefore be any
thing. And, as A is something definite, " A = anything " will
of course be false. The sphere " B or b " is wholly un
limited.
This confirms the doctrine we have above adopted (p. 123).
If you take not-B as the bare and simple negation of B, it is
nothing at all. And if you keep to this sense, then " A =
not-B " could not be true. The true meaning of not-B is any
indefinite general quality which does exclude B. And, so
long as A is something definite, A can not be this. I am
inclined to think from the presence of x (Principles, pp. 94,
95) that Professor Jevons would agree with this doctrine.
But the conclusion, which Professor Jevons uses as false,
is not only quite true, but is the necessary result of the true
doctrine he accepts. Taking A as the genuine subject 23 that
lies at the base of the disjunction, then " a = nothing " must
follow at once, since " A is B or not-B " does assume and
postulate that A is real. If a were anything but non-existent,
you could not use A as the base of a disjunction. What is
wrong is not this conclusion or its premises, but the mistaken
idea about the negative which Professor Jevons has em
braced.
I confess I am not sure if I apprehend him rightly, but he
seems to argue that the non-existent is not thinkable, and
hence, because the negative of everything is thinkable, you
must never have a negative which is non-existent. Now I
admit that, if " existence " is used in the widest possible sense,
this argument is tenable. The unreal, the impossible, and
158 THE PRINCIPLES OF LOGIC BOOK I
the non-existent will every one of them exist, provided they
are thinkable. And, since even nothing itself 24 in this sense
exists, it is obvious the whole argument thus disappears.
But, if it does not disappear, and if existence be taken
in anything like the sense of reality, the argument becomes
vicious. We have no right to assume that the contradictory
of an idea which is true, must itself be real. Take for in
stance the idea of " reality " itself. I could not even admit that
in thought all ideas are qualified by their negations. I should
doubt if the highest term we arrive at can be said to have an
opposite even in thought, although by an error we are given
to think so. But to hold that what contradicts the real must
be real, is a logical mistake which I cannot venture to attribute
to Prof. Jevons.
I may end with the remark that it would be entertaining
and an irony of fate, if the school of " Experience " fell into
the cardinal mistake of Hegel. Prof. Bain s " Law of Rela
tivity," approved by J. S. Mill, has at least shown a tendency
to drift in that direction. " Our cognition, as it stands, is
explained as a mutual negation of the two properties. Each
has a positive existence because of the presence of the other
as its negative" (Emotions, p. 571). I do not suggest that
Prof. Bain in this ominous utterance really means what he
says, but he means quite enough to be on the edge of a preci
pice. If the school of " Experience " had any knowledge of
the facts, they would know that the sin of Hegel consists, not
at all in the defect, but in the excess of " Relativity." Once
say with Prof. Bain that " we know only relations " ; once
mean (what he says) that those relations hold between posi
tives and negatives, and you have accepted the main prin
ciple of orthodox Hegelianism.
28. It is obvious that duplex negatio affirmat. To say
" It is false that A is not B " is equivalent to the positive
assertion, " A is B." But this is not because the added negation
barely negates the original judgment. For if that were all, we
should be left with nothing. If mere not-A is simply zero,
then not-not-A is, if possible, less. And we must not say that
CHAP. V DOUBLE NEGATION 159
negation presupposes a positive judgment, which is left in pos
session when the negative is negated. For we saw before
(Chap. III. 4) that this positive judgment is not presup
posed.
29. The real reason why denial of denial is affirmation,
is merely this. In all denial we must have the assertion of a
positive ground; and the positive ground of the second denial
can be nothing but the predicate denied by the first. I can
not say " It is false that A is not b" unless I already possess
the positive knowledge that A is b. 2Q And the reason of
my incapacity is that no other knowledge is a sufficient
ground.
30. I will briefly explain. We know well by this time
that, in judging A not to be b, I presuppose a quality in A
which is exclusive of b. Let us call this y. I now desire to
deny my judgment, and need, as before, some quality as the
ground of my new denial. Let us take some quality other
than b. Let this quality s be exclusive of y, and let us see
what we have. We have now A^ with the exclusion of y which
excluded b. But that leaves us nowhere. We can not tell
now if A is b, or is not b, because z itself, for anything we
know, may also exclude b f just as much as y did. What, in
short, we have got is our own private impotence to deny " A
is b " ; but what we want is an objective ground for declaring
such a denial to be false.
The same result holds good with any other quality we
can take, excepting b itself. The only certainty that b is not
absent is got by showing that b is present. For the possible
grounds of the exclusion of b being quite indefinite, you can
not get rid of them by trying to exhaust the negations of b.
You could only do that if the number of possibilities with
respect to A had already been limited by a disjunctive judg
ment. And this is not here the case.
Suppose, for instance, we have the judgment that " Ulti
mate reality is not knowable," and we wish to assert that this
judgment is false. We expose the ground on which it is based,
and go on to show that this ground is not valid. Our pro
ceeding, no doubt, may be perfectly admirable, but all that it
gives us is the right to doubt the original judgment, and to
deny the truth of the basis it stands on. If we wish to deny
I6O THE PRINCIPLES OF LOGIC BOOK I
the original judgment, we can not do that by refuting our
antagonists. We must show ourselves that reality is know-
able. The ground for the denial of " A is not b" must lie in
"Aw b." 27
31. I will endeavour to remove a possible source of mis
apprehension. It might be urged that in practice the denial
of a judgment can always be denied by something other than
the judgment itself. Thus, for instance, " It did rain yes
terday," may be false, because it snowed or because it was
fine. But each of these can be denied on the ground of the
other. The result of our double negation of " it rained,"
might be either " it snowed," or again " it was fine " : and we
might return to " it rained," by virtue not of a double but of a
triple denial.
But this objection would rest on a misunderstanding. It
is perfectly true that, in denying " it rained," I must imply
and make use of some discrepant quality. It is, once more,
true that what I have in my mind, and should assign as my
reason, may be either " it snowed " or again " it was fine."
But it is a mistake to conclude that the denial really rests upon
either the one of these or the other. Whatever you might
have had in your mind, no logic could force you to allow that
your denial had committed you to either " it snowed " or " it
was fine." What we use in denial is not the whole discrepant :
it is that part of the discrepant which answers our purpose.
The denial asserts no more than the existence of so much
quality as is enough to exclude the judgment " it rained."
This universal " so much " is possessed by either " it
snowed " or " it was fine," and this you can not banish by
anything short of the judgment " it rained." In other words,
if you say " it did not rain," you are at once committed to a
positive " because," but you are committed to nothing but
an unspecified quality. The evidence for this quality no doubt
in the end must be found in the presence of a contrary asser
tion, but the mere contradiction does not affirm this or any
particular contrary. It affirms merely some contrary, and you
get rid of this only by the judgment " it did rain." We find
here once more the constant ambiguity, which we have seen
(Chap. III. 19) makes the use of negation so precarious.
It is so difficult to work with double denial that I hardly can
CHAP. V DOUBLE NEGATION l6l
expect in the present volume to have supplied no example of
the error I condemn.*
* Mr. Venn, I think, has certainly done so. 28 When I had the
pleasure of reading his Symbolic Logic, I congratulated myself on the
fact that I had already written the present and all the preceding
chapters. I have not found occasion in consequence to alter anything
of what I had written, but I should like to use one of his principal
doctrines to exemplify the fallacious use of the negative. I have added
this discussion as a mere appendix, for it hardly carries the subject
further. It is due to myself to defend my own views against a counter
theory from a writer of established and merited reputation.
After calling attention to the ambiguity of affirmative universals,
the doubt, that is, if they affirm the existence of their grammatical
subject, Mr. Venn, if I understand him rightly, asserts that at all
events the negative is not ambiguous (p. 141). I will not here enquire
if in other places he is compelled to recognize that the opposite of this
assumption is true. At all events the foundation he here seems to
build on is the assertion that negatives have only one meaning. " It
comes to this therefore that in respect of what such a proposition
affirms it can only be regarded as conditional, but that in respect of
what it denies it may be regarded as absolute" (142). The affirmation
of xy is always ambiguous, since x may not be actual; but the denial of
x not-y is perfectly clear. And upon this basis he seems to build his
doctrine.
Now the reader of this volume will know that a negation is always
ambiguous. We may consider this as settled, and I will not re-discuss
the general question. I will first call attention to the seeming absurdity
of Mr. Venn s doctrine. He teaches in effect that, although you do not
know what a statement means, you can always tell what you mean by
denying it. And he ought to hold that the ambiguity of a judgment at
once disappears, if you deny it and then deny your denial. This course
has not generally been found so successful.
But it is better to show the actual mistake. And we will preface our
criticism by setting down some elementary truths. You can not argue
from the assertion of possibility to the assertion of actuality, but you
can always argue from the denial of possibility to the denial of actual
ity. To deny possible x (you must of course not take "possible" as
"merely possible") is by implication to deny actual x. Now the simple
application of this commonplace doctrine is that, if you are given a
connection xy and do not know whether it is possible or actual, at all
events, if you deny its possibility, you may be very sure that you also,
and as well, have denied its actuality. This is literally (unless I mis
understand him) the whole principle which Mr. Venn unconsciously
proceeds upon, and the idea that it could lead to any great result, or
to a better understanding of hypothetical, seems somewhat strange.^
I can not be quite sure of his exact procedure, but I think it is this.
l62 THE PRINCIPLES OF LOGIC BOOK I
The affirmative judgment both affirms and denies. Mr. Venn will not
say that what it affirms is mere possibility, but he quietly assumes that
what it denies is impossibility. (If he does not do this, he makes a
simpler mistake to which I will return.) That is to say, he tacitly and
without any justification assumes that x not-;y asserts the impossibility
of xy; and it is solely by denying this arbitrary fixture that the positive
xy becomes unambiguous. But if he wishes to restrict the affirmative
judgment to the minimum sufficient to deny the denial of possibility,
surely it would be better to say at once, "The affirmative judgment
does not assert more than bare possibility." He would so have done
openly and in an intelligible manner the very thing he has in effect
done, indirectly and most objectionably, by going round through two
denials. The procedure could in no case have become more arbitrary.
I will put the same thing otherwise. With affirmative judgments
possibility is the minimum: with negative judgments impossibility is
the maximum. Now it is uncertain (we may so interpret Mr. Venn)
if the affirmative xy asserts the maximum (actuality) or the minimum
(possibility), but it is certain that it unambiguously denies the nega
tive. But, if the negative becomes unambiguous because it is arbi
trarily fixed at its maximum degree (impossibility), then surely it is
clear that we thereby, and ipso facto, are fixing the affirmative at its
minimum degree. For so far at least as the affirmative denies and is
not ambiguous, it is so because its minimum is enough. And the
fallacy is simple. This minimum is not enough unless the negative is
fixed at the maximum. Suppose not-xy to mean " xy does not exist,"
then " xy is possible" ceases to deny this: for, although xy may not
exist, it still can be possible. Again if xy meant " xy is actual," then
"xy is impossible" (or, again, "if x then no y") is not its contra
dictory, and goes a long way beyond its denial. In short, since not-*y
means either d-e facto non-existence or else impossibility, it seems
absurd to assert that the denial of this is not ambiguous. And if you
mean to fix the meaning of the negative arbitrarily, it seems absurd
to shrink from doing the same by the positive.
In conclusion, if we suppose that not-;ry is really meant to assert
non-existence, that is to deny the actuality of xy, then the error is
palpable. You first say you do not know whether xy asserts existence
or possibility, and yet you say it denies the non-existence of xy. But
possibility, not affirming existence, of course can not deny non-exist
ence, and the whole process disappears unless you rapidly shuffle from
one term to the other.
This hidden equivocation soon begins to bear fruit in the curious
reasoning which immediately follows (p. 143). If I do not misappre
hend Mr. Venn, he tries to make a passage from bare possibilities to
a positive existential judgment. I confess his metaphysics take away
my breath ; and I am bound the more to admire his audacity as he
somewhat poses as abjuring "transcendentalism," and likes to take
things " in a perfectly matter of fact way." But let us see what this
way is. We suppose four possibilities, (i) x with y, (ii) x not-y, (iii)
CHAP. V DOUBLE NEGATION 163
y not-*, and (iv) not-* not-y. We have first a conditional assertion
of xy, and this destroys (ii). We have next a similar assertion of yx,
and this destroys (iii). We have therefore, after this second asser
tion, but two possibilities, (i) and (iv).
" Before, the positive possibilities were three in number, now they
are reduced to two ; for it is implied that everything must be either
both x and y or neither of the two. Carrying this process one step
further, we see that three such " [i.e. conditional] " propositions would
be requisite to establish unequivocally the existence of any one of
the four classes. If we expunge xy" [i.e. not-* not-;y] "also, we are
then reduced at last to an assertion of existence, for we have now
declared that xy is all, viz. that within the sphere of our discussion
everything is both * and y" (p. 143).
Now, so far as I can see, we may understand this process in two
different ways, but on either understanding the argument is vicious.
The first way is to take our possibilities as holding within an exhaus
tive disjunction. As Mr. Venn says, we know " that everything must
be either xy, or * not-y, or y not-*, or not-* not-;y" (142). The
disjunction will rest here on a positive existential proposition, and
the inference will be quite correct. But the objection is that, on
Mr. Venn s theory, we can hardly assume that we have such a dis
junction. At least I do not understand why the assertion, Everything
is one of four possibilities, should be able to be taken in its positive
meaning. We surely are bound, if we wish to be unambiguous, to
take it as denying. And if you take it as denying, it does not prove the
conclusion. It asserts that what is not one of four possibilities is non
existent (or impossible), but it does not say that anything exists.
The possibility of everything is all that is asserted, and from this the
argument will not take you to more than the sole possibility of xy.
If you start with nothing but possibilities, you can not cross from a
bare possibility to actual existence simply on the ground that the other
possibilities have sunk into nothingness. At least I am sure " tran-
scendentalists " especially would be interested in learning Mr. Venn s
"matter of fact way" of accomplishing this exploit.
We thus see that the reasoning can not be based on an affirmative
existential disjunction. And without this foundation it is thoroughly
unsound. Not-* not-y is to be suppressed by a conditional judg
ment, and in its dying struggles is to establish xy as "an assertion of
existence." I will not ask what the conditional proposition could be.
"If anything exists then xy exists" might answer the purpose; but
it would not do so unless it were really unconditional, and covertly
contained the very assertion that " xy is actual." And this I think
is the alternative to which we are brought: we either completely
abandon and throw over our doctrine of the superiority of the nega
tive, and avowedly start with an affirmation of existence; or else
we prove the existence of xy through a double denial which assumes
the conclusion in order to extract it.
We may verify the presence of the same ambiguity in the ex-
164 THE PRINCIPLES OF LOGIC BOOK I
traordinary assertion that contrary judgments, such as "All x is y"
and "No x is y," can be compatible (145). It is not worth while to
enter into a discussion of this matter. They are of course compatible
if you allow yourself to play on their ambiguity; but how in that case
they can be said to be contrary I have no conception. " The interest
ing and unexpected application" is to me, I confess, not anything
beyond a confused example of a well known doctrine concerning the
relations of possibility and existence. But I confess besides that, I
have never been much used " to discuss the question in a perfectly
matter of fact way."
I need not mention what seem to me other mistakes of much the
same kind. And, beside these, there are some statements in connection
with the hypothetical judgment with which I do not agree, but for
which, I think, my treatment of the subject has provided sufficiently.
I am sorry to be forced, both here and again (Chap. VII.), to empha
size my difference with Mr. Venn. And by way of compensation I
should like, if he will allow me, to offer a suggestion. If Mr. Venn
had not such a horror of "metaphysics" and "transcendentalism," if
he was a little less resolved to be " matter of fact," and " discuss the
question entirely on scientific or logical ground," I fancy he would
have come somewhat nearer a solution of the problems it is his merit
to have undertaken. At any rate I suspect his idea of science might
have been expanded, and some prejudices as to "matter of fact"
have been somewhat loosened. He would certainly have imbibed a dis
like for artifices, and such a scruple against entertaining commodious
fictions, as in itself would have saved him from a succession of serious
logical mistakes.
ADDITIONAL NOTES
1 On the idea of a term being related to itself see Essays, Index,
s. v. Terms.
2 "Within a whole of fact." "Fact" is of course to be under
stood here in the widest sense.
a All truth must abstract, and, so far as it is truth, it can not
be made false from the outside. How far any truth which abstracts
can be wholly true, I have discussed elsewhere. See Appearance and
Essays f the Indexes.
4 "In the judgment S P." Add "of which we were speaking."
And, after "becomes an identity," add "and so enters as an element
into a fresh S P." In the next sentence the "it" (in "belongs to
it") is to be emphasized.
5 What the reader should keep in mind is the following. Differ
ences are all incompatible if you attempt simply to identify them.
They are again all compatible if and so far as they are merely con
joined. Wherever there is conjunction there is something more in
the conjoined whole than mere identity, so that here the whole, as
CHAP. V DOUBLE NEGATION
simply identical, does not attempt to enter into each diversity. The
whole, however, if it is to be made intelligible, must become dis
junctive. The aim of disjunction (see Chap. IV, i) is to replace the
conjunctive unity by the discovery and statement of conditions. As
to why certain conjunctions are possible in fact, while others are not
so logic does not enquire. The question of detail belongs here
mainly, I think, to psychology. On the above see Appearance, Appen
dix, Note A, and Bosanquet s Logic, II, Chap. VII.
6 "The discrepant with A ... attribute." This sentence should
run, "The incompatible with A is what is not a mere joint predicate
with A in any subject, nor is joined to it ... attribute."
7 " For denial . . . affirmation." In this sentence " the " should
be " a."
8 " From a certain theory." " From " is here, I think, rightly used
in contradistinction to " by."
9 The main point here is as follows, Incompatibles exist, and no
one denies this fact. And, so far as they exist, the Law of Con
tradiction holds. The real question is as to the limits within which,
and the conditions under which, incompatibles are found and can
be justified. How far in other words is the truth of contradiction,
as such, only relative and more or less of an appearance? What,
as I understand it, the Dialectical Method is concerned to deny is
merely the absolute, utter and final, truth of fixed incompatibles. On
the whole matter see my Appearance, Index, s. v. Contradiction.
10 " What I mean, &c." The point here is that, where you have
differences in A, A is never mere and bare A. Cf. on 10.
11 " Stationary contraries " . . . " are found." Yes, but as an
appearance only. See Note 9.
12 On the principle of Excluded Middle, while once more referring
the reader to Bosanquet s Logic, I will add a few words. This prin
ciple presupposes a disjoined world of incompatibles, and its truth
is but relative and limited to Reality taken in the character of such
a world. So far as the real is otherwise, as being either below or,
again, above the level of disjunction, the principle does not hold.
If we accept the view that no truth is quite true and no error merely
false a view advocated in my Essays and Appearance we must admit
that Excluded Middle, however necessary and important, is not true
absolutely.
In rejecting it as the principle of disjunction, I meant to deny that
disjunction stands upon it in the shape of a ready-made base. We
may on the other hand take it as containing the abstract form of
disjunction. It is disjunction made all-embracing and dual by group
ing all the incompatibles, save only one, under their negative aspect,
with the result that nothing is left beyond assertion or denial. The
leaving the other members of the whole thus artificially blank, is of
course a grave shortcoming. For, merely in the shape of such an
abstraction, these other members are not real positively, and so are
not real at all. Knowledge is not advanced by the exhaustiveness
2321. i M
1 66 THE PRINCIPLES OF LOGIC BOOK I
of disjunction effected formally through an artificial duality. Its real
object is to discover in concrete detail the full connection of its
elements.
Excluded Middle is, however, in a sense more fundamental, and
goes, we may say, further than mere disjunction. For it asserts the
actual being of the disjunctive world. We affirm in it that Reality
is a region where "either or" holds, and that everything is so de
termined as to fall within this sphere everything, that is, so far as
it is not self -contradictory or otherwise senseless. (For the connec
tion between these two ideas see T. E. VIII.) But, as was remarked
above, we have here a relative truth which is taken wrongly if made
absolute.
I may add that the principle that every idea is attributed to Reality,
and is therefore in some sense real, has no special connection with
Excluded Middle. And the same thing holds again of the corollary
that, where all possibles but one are excluded, the one left is actually
real.
13 " True or false." See, however, the preceding Note.
14 "On this basis." But see on Chap. IV, 6.
15 " My impotence." See on Chap. Ill, 9.
16 "Must wait" . . . fact." But it is better, I think, to take
Excluded Middle as assuming, not only connection everywhere through
out the Universe, but also that special kind of connection which
holds between incompatibles. See Note 12.
17 " False alternative." But, if we say this, surely we must mean
that Excluded Middle has been assumed to hold outside its own lim
ited sphere, and that hence it does not hold everywhere. Again, in
the next paragraph, " fallacious " can not, I think, stand. But I agree
that it is certainly possible, and sometimes easy, to object wrongly to
the legitimate and necessary use of Excluded Middle.
18 "The existence of its subject." But see on Chap. IV, 3.
19 Mill s misuse of " contradictories " can be excused, I presume,
as a mere slip; but his doctrine of a "third possibility" seems really
something worse. He takes the possibility with regard to an offered
judgment that it is senseless, and therefore no actual judgment; and
he then places this itself as a possibility under the judgment as actual,
and as itself falling between the two other possibilities of truth and
falsehood. Cf. Bosanquet, Logic, I, 352 (Ed. II).
Conceivably all that Mill meant was to warn us that an unmeaning
idea or judgment is none, and so must not be used. But, if so, his
meaning, I submit, was expressed by a serious blunder. The writer
whom he criticizes, we may also do well to remind ourselves, made
use of the word "judgment" rather than "proposition."
20 "Ground enough for denial." It would be better, for "denial,"
to substitute "rejection with a denial of possibility."
21 " Ground of negation remains the same." We should add " or
at least is not known." See on Chap. Ill, 13.
22 For this section, as also for 20, see Note 12.
CHAP. V DOUBLE NEGATION 167
23 Taking A as the genuine subject." "Genuine" is to be em
phasized. See on Chap. IV, 3. And, again, for " reality " and " exist
ence," see on Chap. II, 2.
2 * "Even nothing itself." For "nothing" see Essays, the Index,
and T. E. VII.
25 " Double Negation." There is a serious mistake in these pages.
The whole subject has, I think, been made clear in Bosanquet s Logic,
I, PP. 302-7. Cf. his K & R, pp. 230 foil.
The main point here is this. Double negation holds where the
alternatives are limited to two, and it does not hold otherwise. And
in denial we have always this dual alternative.
The error in my treatment is as follows. I did not see that (as
Dr. Bosanquet has shown) all denial sets up an exhaustive dual dis
junction (Cf. T. E. VI). Judgment divides the world, we may say,
into the selected and the residual Reality, and in denial what is ex
cluded must qualify the latter. Having so an " either or "when
we have denied our denial the affirmative only is left.
So much for my mistake; but, apart from this, my discussion did
well, I think, to insist on an important truth. Since all denial rests
on a positive ground, though this is not stated in and by the denial,
we may hence be led into error. We may make the ground of
negation, as we happen to have that in our minds, an essential part
of the denial. We covertly, that is, in "A (x) is not b" explicate
the x, and treat this, in the form e.g. of c, as being the sole ground
of our denial. We thus turn " A (x) is not b " into " A (c) is not b,"
and so without right come back from the denied absence of b to the
presence of c. For instance, having decided to wait because the
ground will not be dry, and, having then the denial that there has
been rain, I may rush to the conclusion that the ground will be ({ drv
forgetting snow or dew. I have turned " not after rain," into " dry,"
by taking wrongly the simple denial as qualified.
26 " Positive knowledge." We must add " direct or indirect." " It
is false that the ground will not be dry " rests on the exclusion, how
ever arrived at, of every state incompatible with dryness.
27 " A is b." " Or " (we should add) " in the knowledge that what
excludes b does not belong to A, but is (where it is anything) some
thing merely accidental.
28 I now regret the asperity of this criticism. Dr. Venn probably
had no idea of his challenge and of the provocation which he gave.
And how far he ought to have been aware of this, I have now
certainly no wish to discuss.
CHAPTER VI
THE QUANTITY OF JUDGMENTS
I. If in considering an idea you attend to its content, 1
you have its intension or comprehension. Its extension may be
taken in two different senses. It is an instance or instances,
ideal or actual. 2 It refers ultimately to the real, but it may
directly signify (a) any other more concrete idea which con
tains the intension, or (b) any individual of which the inten
sion can be predicated. Thus if " horse " signifies the attributes
possessed by a horse, it is taken in intension. If it signifies any
other idea which includes " horse," e.g. cart-horse or race-horse,
it is taken in extension. And again, it is otherwise taken in
extension if it is used for individual horses.*
2. We have come again upon a distinction which is now
familiar. An idea is symbolic, and in every symbol we sepa
rate what it means from that which it stands for. A sign
indicates or points to something other than itself ; and it does
this by conveying, artificially or naturally, those attributes of
the thing by which we recognize it. A word, we may say, never
quite means what it stands for or stands for what it means.
For the qualities of the fact, by which it is recognized and
which correspond to the content of the sign, are not the fact
itself. Even with abstracts the actual case of the quality is
hardly nothing but the quality itself. The idea and the reality
are presumed to be different.
It is perhaps an ideal we secretly cherish, that words
should mean what they stand for and stand for what they
mean. And in metaphysics we should be forced to consider
seriously the claim of this ideal. But for logical purposes it
is better to ignore it. It is better to assume that the meaning
is other than the fact of which the meaning is true. The fact
is an individual or individuals, 3 and the idea itself is an univer
sal. The extension can not be reduced to intension.
* If it were used for possible horses, it would be taken in sense (a).
Cf. pp. 171, 179, 186.
168
CHAP. VI THE QUANTITY OF JUDGMENTS 169
3. The difference may be expressed by the terms " de
notation " and " connotation." These phrases have found
favour with the English public, and the indiscriminate use of
" connotation " marks one kind of superior person. 4 But they
serve no useful purpose in logic. They are unnecessary and
objectionable. 5 They have no advantage over the terms in
general use, and they have in addition a positive vice. To
" connote " is to " imply " ; and the meaning of a word is not
its implication. With the names of individuals the meaning
may perhaps be said to be " connoted," but with adjectives
such as " red," and abstracts such as " redness," what is
" connoted " is clearly not at all the attributes but the indi
vidual reality. Nothing but ambiguity can arise from such
perversions. If you will use a word which signifies implica
tion, to convey what more usually is the direct meaning, you
must expect the confusion which your unfortunate choice has
already to some extent occasioned.
4. Hand in hand with this slovenly terminology there
goes a superstition we have in part refuted (Chap. II. 17).
We are told that words may be " non-connotative." They
may signify, we are told, a subject only or only an attribute.
Both of these assertions must be rejected. No word such as
" whiteness " stands simply and solely for the abstract quality.*
It means this directly; but it indirectly points to an implied
individual, an actual case of whiteness. And still less can be
said for the doctrine we have already refuted. The name of
an individual must carry with it and imply certain attributes,
or else its attachment to that individual becomes a psycho
logical impossibility. It is mere want of thought which allows
us to suppose that a sign can mean nothing and yet stand for
something.
5. It would be as easy to prove that a word may mean
nothing and may also stand for nothing. And it may be
useful, perhaps, at this point to digress. We have seen that
all propositions are "real" (p. 42). Verbal propositions be
come manifestly real, if you write them " The meaning of S is
P." But there is a class of judgments where the subject has
*A11 ideas imply a reference of their content to the real (p. 3),
and hence to the individual. We may notice besides that abstracts
imply within their content a supporting subject. They are doubly
adjectival. 6
170 THE PRINCIPLES OF LOGIC BOOK I
got no definite meaning, and is not a perfect sign. If we take
such a statement as " magistri is the genitive case of magister"
we might be tempted to assert that some words are devoid of
both extension and intension.
"Theophilus is Greek," " Theophilus is dear to God,"
" Theophilus has the measles." The last of these informs us
of the disease of a man. The second tells us the meaning of
a name. The first assures us that a word is a member in a
system of signs, but it seems to give us nothing which that
word stands for and nothing that it means. If a sign were
something with a definite signification, then we could not say
that all words are signs. We may know of a sound no more
than this, that it is a sign. It stands for something, but we
do not know what ; and it means something also, but what we
do not know.
And we are not at the end. This last remnant of ordinary
extension and intension is doomed to vanish. I may treat the
word as a common noise. " Why did you make that noise
Theophilus when you saw that man? Theophilus is not a
pleasant sound." We have here no signification and no
meaning, nor have we any longer a word. But even here
in a rudimentary form we have the sides of extension and
intension. We may distinguish two elements that are blended
in Theophilus. Even here it is universal, and is the product
of abstraction and generalization. The sound that I should
know under all its differences, of varying tone, of the person
uttering, and of places and times, is one side of the whole.
The other is this particular utterance and other possible par
ticular utterances. The elements still co-exist at this early
stage of their evolution. We can never separate the one from
the other except by a mistake.
6. Let us dismiss for ever the term " connotation," and
try to keep clear of the errors it beacons. We may pass to a
doctrine of another kind, not so misleading but equally idle.
Extension and intension, we are told, are related and must be
related in a certain way. The less you happen to have of
the one, the more you therefore must have of the other.
This statement has often passed itself off as both true and
important. 1 confess that to me it has always seemed either
false or frivolous. 7
CHAP. VI THE QUANTITY OF JUDGMENTS 17!
(a) If we take extension to mean that number of real
individuals of which the meaning is true, then it is ludicrously
false that an increase of the extension is a decrease of the
meaning. The logician who, impelled by the practical syl
logism, begets a child, does not find his doctrine verified by
the fact. The conclusion, which appears from the union of
the premises, no doubt may surprise him and add to his
experiences, but it may not diminish the " comprehension "
with which he hears the word child. His new-born instance
may destroy his definition of the genus homo as animal risibile,
but the content it shears off will be largely made good by
other attributes. He may say, what he never thought to
have said, All children are scourges.
It is obvious that fresh instances may increase the inten
sion by the discovery of attributes essential but overlooked.
The doctrine understood in this sense is false. And if you
write " possible " for " actual " individuals, still diminution of
the meaning need not add to the number. If possible means
that which is presumed to exist, we may remark that the com
plex may be possible in fact just as much as the simple; the
simple indeed by itself may be impossible. But if possible
means what can be produced by artificial and arbitrary think
ing (p. 203), we have now obviously left the sense of exten
sion we have been dealing with. The extension has ceased to
lie in the individuals ; 8 it has become those groups of attributes
in which analysis can find the meaning.
7. But (b) even if we give this sense to extension, the
doctrine is not true. If you compare ideas, the narrower mean
ing does not always have the wider application. Take a
simple instance. The idea of the visible has, we may all
admit, a fuller meaning than the ideas of that which can be
tasted or smelt. But the latter have not got any greater
extension. Everywhere, if you take adjectives or combina
tions of adjectives, which are co-ordinate and which can not be
subsumed the one under the other, the doctrine ceases to have
any bearing. Since the greater emptiness has not been got by
further abstraction, there is no reason why the adjective which
has less content should be predicable of a greater number of
kinds.
And if for marks and combinations of marks we sub-
1/2 THE PRINCIPLES OF LOGIC BOOK I
stitute laws or modes of combination, the same thing holds
good. If these laws do not stand the one under the other,
but simply fall under a common head, then you have no right,
on comparing these laws, to expect the emptier to be the more
wide and the wider to be more empty.
8. There undoubtedly is some truth in the doctrine, but
that truth does not come to much more than this. If you take
adjectival marks or laws, and choose to arrange them in the
form of a pyramid; if you place at the bottom, and as the
stones of your lowest layer, all those ideas which have noth
ing subordinate; if you form the second and superimposed
layer by subtracting the differences from two of these stones,
and by placing the residue left by the operation on the top of
the pair; and if you so proceed to pile layer upon layer, so
as to form a mass which grows narrower with each tier if all
this is done, then it is geometrically true that the higher you
go up the fewer stones you will find, and the lower you go
down the more stones you will have. And since you have
gone up by leaving out differences, it is obvious that the nar
rower the pyramid becomes the more stones will each single
stone have to stand upon, and the more there will be of which
it can be predicated. This is undeniable, but what does it come
to? It comes to this, that if you arrange your material in a
certain geometrical figure, then it will have certain geometrical
properties. That is true, but it seems to me quite frivolous.
9. It is true, I admit, that if B must be C, then, sup
posing A should ever be B, it will also be C. But, if you offer
me this as a truth about A, I can hardly affect to feel very
grateful. It looks to me more like a truth about B. You
begin to establish a claim to gratitude when you show me also
that A is B, or is likely to become so. And this is the real
question at issue. If you arrange ideas in a certain way they
will have the qualities of that arrangement. Who doubts it?
What first may be doubted is the possibility of so arranging
all ideas ; and what may next be doubted is the wisdom of the
arrangement. If it is not the natural relation of the material,
if it is forced and arbitrary, then the truth you offer me may
after all be sterile. It may have little or nothing to do with
the actual matter in hand.
If you confine yourself to the ideas of adjectivals, then
CHAP. VI THE QUANTITY OF JUDGMENTS 173
(though I will not undertake to maintain it) I think that with
more or less of regularity you may effect your pyramidal
arrangement; but I think you much over-estimate its value.
If reasoning were always the subsumption of a stone on a
lower tier under a stone belonging to a higher layer, then
your construction would begin to serve as a machine and
would even live; your ladder would grow green and blossom
as the tree, not of pedantry, but of knowledge. But reasoning
is really not always subsumption, and with the cutting off that
root of delusion your tree shows dead, and breaks before the
breath of actual existence. The importance ascribed to your
arrangement of ideas comes from a fundamental mistake
(See Book II. Part I. Chap. II.).
10. And there remains an objection we can not discuss
but must not pass over. If you do not confine yourself to
the ideas of adjectives and their combinations, what then?
Take ideas of individuals. If you have ideas of smaller
wholes, enclosed in and subordinated to larger wholes, will
it there be true that the wider the synthesis the emptier it
becomes? Are universals always more abstract than particu
lars? Is it certain that the idea of a state has less content
than the idea of any one of its citizens? Are we sure that
the soul is more of an abstraction than any particular psychical
event? Is the idea of God assuredly less full than the idea
of a molecule? And if we consider the idea of synthetical
unity, it does not appear that the higher and wider function
of synthesis need have less attributes than a subordinate func
tion. If we entertain the belief that syntheses are possible
which are not the abstraction from lower syntheses, but are
the individuations of these lower abstractions, then the doc
trine which has showed itself to be idle once more becomes a
positive error.
This objection, I am aware, will not press very heavily.
There are few readers not so wise in their own esteem as to
convict this suggestion of folly or madness. 9 It would belong
to metaphysics to lay folly at the door of its true possessors. It
is sufficient here for our logical purpose to have pointed out an
objection, disregarded and despised, but in itself not despicable.
Apart from this possible ground of dissent, and confining
ourselves to the consideration of marks and the modes of
174 THE PRINCIPLES OF LOGIC BOOK I
their union, we may sum the matter so. The law of the
relation of extent to intent is not a law of ideas themselves;
it is a law of pyramidal arrangement; and that arrangement
in the case of ideas, where it is possible, is not of importance.
It may fairly be relegated to our logical lumber-room.
ii. The question which is next to claim our notice is
still concerned with Extension and Intension. 10 If we leave
mere ideas and go on to judgments, it has been asked whether
these make a statement in respect of the extension of their
elements, or the intension, or both. And this is a topic we
can not quite pass over, as it presents us with several dangerous
illusions. I will begin by the assertion that every proposition
can be read in whichever of these ways we prefer. I will then
show, in the first place, how all can be interpreted in extension,
and will prove the same, secondly, with respect to intension.
12. Every judgment makes a double affirmation, or a
single affirmation which has two sides. It asserts a connec
tion of different attributes, with an indirect reference to an
identical subject; or it directly asserts the identity of the
subject, with an implication of the difference of its attributes.
If you prefer to consider the identity of the subject (im
mediate or ultimate), you read the judgment in extension.
If again you emphasize the connection of the differences, you
take the judgment intensionally. It is not true that every
judgment is naturally read in both of these ways. It is true
that all judgments can be read correctly in either manner, and
read legitimately.
If you take the proposition " Dogs are mammals," then
this means either that, where anything is a dog, the same
individual thing will be a mammal ; or that, given in anything
the attribute dog, you will certainly have with it the at
tribute mammal. And it is possible to interpret every judg
ment in this self -same way.
13. Dismissing for the present the intensional reading,
let us consider interpretation in Extension. We find here the
presence of misleading errors. It is a common doctrine that
when we read in extension we assert inclusion in a class or
collection. We are told that in " Dogs are mammals " no
attribute is really affirmed of dogs; the assertion is that the
CHAP. VI THE QUANTITY OF JUDGMENTS 175
things called dogs are included within the class of mammals.
I can discover little in this current theory but error and
confusion.
It sounds at least palpable, when we hear of enclosing
within a class. But try to handle it, and at once your grasp
is closed upon mist and unreality. The class, if it is to be
real at all, must be, I presume, an aggregate or collection of
individuals; and this must exist either in my head or else
outside it. The latter alternative can hardly be meant. There
is no actual physical aggregation which answers to every
general name. For every single mark would be the ground of
such an aggregate, and I can not suppose that any one believes
that these strange complications of groups or herds actually
exist in rerum natura.
14. " The class is mental. It is no group of things. It
is our own private way of putting images together within our
own minds." But, at the risk of seeming to affect singularity,
I am bound to assert that within my own mind I can not find
these classes. By a class I suppose you mean a group of
images which actually exist; but when I come to the facts
and look into my mind, and survey what is there when I hear
the word " mammals " or " triangles " or " cats," I scarcely ever
am able to find an actual group. The idea that " mammals "
is the name of a flock of mammal-images, herded together in
my mental field, and that among these I can see the little
pack of dogs, and all the cats sitting together, and the rats,
and the rabbits, as well as the elephants, all marked with
curious references and cross-references to heads " quadruped "
and " carnivorous " and " placental " and Heaven knows what
else I do not think that this looks like the fact.
15. These flocks and herds are pure mythology, they are
nothing real. But let us suppose that they really exist. Enter
taining fables, we may unawares embrace a truth. Let
" mammals " be a group of mammal-images ; and let " dogs "
be a mental pack of dog-images ; and let the judgment " Dogs
are mammals " be the inclusion of the former within the
latter. But what does this mean?
If I look at the mammals I either know which mammals
are dogs, or this is hid from me. (a) Suppose that I know it.
The inclusion then means that a certain definite number of
176 THE PRINCIPLES OF LOGIC BOOK I
my present mammal-images are also dogs, and that these are
surrounded or mixed up with the residue of mammal-images
which are not dogs. The judgment asserts a spatial relation
in my mind of the dog-mammals to the mammals which are
rats and cats and rabbits and the rest. But such juxta
position, let it be ever so actual in my imagination, is clearly
not what we meant by our judgment. I wanted to say some
thing real about dogs ; but this local relation fabled in my head
does not even pretend to represent external existence.
(b) And if I do not know which mammals are dogs, the
case is not altered. I regard my mental conglomeration of
mammals, and fail to distinguish the dogs from the cats. I
can not say which image is a dog-image, but I know that the
dogs are every one there. They are inside the mammal-fold
and not outside. The mammals range over a mental park, and
all the dogs are on this side of the paling. But that again
is not what I meant to assert. The local position of my canine
images with respect to the enclosure which bounds my mam
mals, is not the idea which I meant to convey by " Dogs are
mammals."
1 6. These interpretations are fictions that is one objec
tion. But it is followed by another they are unprofitable
fictions. They are not only baseless: they also are useless.
They do not read the whole proposition in extension. If the
extension means the objects called mammals, then in neither
case is " mammals," in this sense, the predicate. In saying
" Dogs are enclosed by mammals," I do not say that " Dogs
are mammals." A group of objects is one thing; a spatial
relation, indefinite or definite, to that group of objects is
clearly another thing. And, what is more, that relation is an
attribute of dogs. The local relation is not the things them
selves, and it certainly is predicated as qualifying dogs.* If
the ostensible predicate has been taken in extension, the propo
sition has in part been read intensionally ; for it has asserted
an attribute of the subject. The inclusion within the class
has no meaning, if the class is the mere individuals themselves,
and the copula simply asserts them of the subject. But if the
judgment affirms a spatial relation to some of those individuals,
* I do not say the spatial relation of A to B is nothing but an
attribute of A. Still it is such an attribute.
CHAP. VI THE QUANTITY OF JUDGMENTS 177
or the area they all occupy, or the fence that confines them,
then what the judgment really affirms is an attribute.
17. If we keep to extension we must keep to the ob
jects, and it is these we must try to predicate of the subject.
In " Dogs are mammals " we must try to assert " some mam
mals " of dogs. What is affirmed must be identity. The
dogs and dog-mammals are all the same thing. (Cf. Chap
I- 17.)
If they were wholly the same there would be no difference.
They could not then be at all distinguished, and both sides
of the judgment would fall together. The judgment would
disappear. Hence a difference must exist ; and what we mean
to say must come to this, that, Though the dogs and dog-
mammals are the same, yet for all that what? Here we have
to join issue.
For all that, we may say, they are sometimes inside the
mammal-enclosure and sometimes outside, and that is the
difference. The dog-mammals sometimes are packed by
themselves, and go wandering off in the mental distance, and
at other times their images, compelled by some secret influ
ence, consort with all whose blood flows warmly. But this
strange mythology would not answer to our meaning. We
never intended to say that the dogs could exist indifferently
on each side of a hedge which grows in our minds.
1 8. " The dog-mammals and the dogs are all the same,
and yet for all that their names are different. You have a
set of individuals which obviously in themselves are simply
themselves. The difference asserted is the difference of their
two signs * mammal and dog. That surely is a very pal
pable thing, and, in saying Dogs are mammals/ we mean to
assert that certain definite indivisible objects have got two
names. It happens that they have been christened twice, or
christened with two names, and this is the real heart of your
mystery."
The explanation possesses the merit of simplicity. It is
perhaps too simple for sophisticated mortals. Belief in it will
not " come with observation," but demands a new birth from
the world of fact into the world of faith. Philosophy has not
revealed it, and not many wise are likely to accept it. The
creed of nominalism is no theme for argument. To those
178 THE PRINCIPLES OF LOGIC BOOK I
who believe that assertions about things assert nothing but
names, the universe has long ago given up its secrets, and
given up everything.
19. The first interpretation asserts that the individuals,
notwithstanding their sameness, cross and recross the mam
mal-fence. The second asserts that, although they are the
same, their names are different. The first interpretation is a
fiction ; the second ignores the fact to be interpreted. Neither
expresses the meaning of the judgment; and both in the end
do predicate attributes. The change of position with respect
to a herd or the pale that encloses it, is a spatial attribute.
The possession of one or two or three names is again an
attribute. The subject is not two different names; it has
them. One name is not the other; it co-exists with it. One
thing as distinguished is not the other thing; both have a
quality which is the same. On the nominalist interpretation
the actual predicate is not taken in extension. The interpre
tation is not only ludicrously false, but, if we take it as true, it
still asserts an attribute of the subject.
The natural and the true interpretation of " Dogs are
mammals " is that dog and mammal are different attributes,
and that these differences co-exist within the same things ; or
again, that, though the things are certainly the same, for all
that they possess two different attributes, dog and mammal.
But this natural interpretation involves the abandonment of
the theory of inclusion within the predicate.
20. And if you understand extension in a different sense,
the result is the same. The class of mammal may be taken
to contain, not only the collection of individuals which are
mammals, but also the kinds of thing which are mammal.
" Dog is one kind, and the judgment includes it among all the
other kinds." It is doubtful what this means, but, whatever
it means, the extension is not affirmed as a predicate. If I
have in my mind a known or unknown aggregate of kinds,
and say that dog is in the midst of this aggregate, then I
assert of dog a spatial relation to a set of elements or the area
they occupy. But this relation is surely an attribute. If
again I mean that dog is an unit which, taken in addition
with other units, amounts to the sum which I call " mammal,"
then I assert a relation to the other units, and a further
CHAP. VI THE QUANTITY OF JUDGMENTS 179
attribute that results from this relation. If I mean that dog
possesses mammal, and that other kinds, known or unknown,
do so, or that dog is like these other kinds in possessing
mammal, then again I assert an attribute of dog, the having
an attribute, and the identity in this respect with some other
kinds.
These interpretations are all forced and unnatural. They
none of them are really what I have in my mind when I say
" Dogs are mammals." Inclusion is not what I mean to
assert. But, if I assert it, then my predicate is an attribute.
The whole or part of the extension of mammals is not the
real predicate. The predicate is that which I either affirm or
deny of the subject, and a thing is not the same as a relation
between itself and something else.
21. If you say, " The dogs, with other things, make up a
certain amount we know as mammals," then this contribution
to a certain number is an undeniable attribute. If you say,
" The dogs share a quality mammal with a heap of other
things," this again is an attribute. If you suppose dogs and
mammals to be two different lots in two adjoining folds, and
if you pull up the mental hurdles which separate them, then
you can not say, " The dogs are in the mammals," unless you
are prepared to embrace a marsupial or some other such
hypothesis. They are related locally to the other mammals or
to the area or fence within which all mammals are circum
scribed. And this local relation is an attributive predicate.
The mythology you invoke is not strong enough to save
you, and, if you throw yourself into the arms of Nominalism,
then you have not only an account of the fact which is
absurdly insufficient, but the difference of names is still an
attribute.
And if, in the end, to escape from your difficulties, you say
"The class is no real collection in my head or out of it. It
is a name that stands for the possible objects that have a
certain attribute," then the answer is simple. If the class is no
longer an aggregate or collection, it has become little else than
a mere description. " Dogs are included in a possible group of
things which are mammals," " Dogs are of the description
mammal," " Dogs possess the attribute mammal " what is
the difference between these three assertions? I ask you, is
ISO THE PRINCIPLES OF LOGIC BOOK I
there any, and if so, what? To include real dogs among mere
possibilities can hardly be the end you have in view. 11 You
must mean, " The dogs possess this attribute, and by virtue of
this attribute are related to other possible mammals." The
last part of the sentence calls for interpretation. " Dogs," we
must read it, "are not only mammals but, supposing anything
else to be mammal, then we may argue a relation between this
thing and dogs." What relation? Surely not juxtaposition;
that is too preposterous. The relation meant must surely rest
on nothing whatever but the joint possession of the attribute.
The inclusion in the class of possible mammals means nothing
but the having the attribute mammal, and in addition, a
hypothetical relation of identity with anything else of the
same description. We predicate two things, in the first place
a quality, and then a relation to possible objects supposed to
have the same quality. Both of these predicates are attributes,
and the last is an addition which may be superfluous. It is
a mistake to think that the phrase " possible " will help us
anywhere into anything but bad metaphysics. And the fa
vourite prey of this delusion is the men who think themselves
above metaphysics.
We may briefly sum up this matter thus. The only way
to read the whole judgment in extension 12 is to take it as
asserting a relation of identity between different individuals.
Two individuals are one though their attributes differ. 13 This is
simply the other side of the judgment that different attributes
are interrelated within the same individual. To take the sub
ject as included in the predicate is in the first place to sub
stitute fiction for fact, and in the next place is to predicate
an attribute and is not to read the whole judgment in ex
tension. But if the subject alone be taken in its extension,
then what is asserted is obviously a connection of attributes
within an individual or individuals.
22. 14 Every judgment can be read in extension. Al
though some present two or more subjects in relation, yet all
can be reduced to the affirmation of a connection of content
within one subject. In " A is to the right of B," the whole
presentation is the subject, and the spatial relation of A to B
is an attribute of that. In " Caesar is sick," the same person is
CHAP. VI THE QUANTITY OF JUDGMENTS l8l
said to be sick as well as Caesar. And in " Dogs are mam
mals," there are certain things which are declared to be both.
In this sense of extension every proposition can be read ex-
tensionally.
We have now to ask if every judgment can be taken in
intension. Can not only the predicate, but also the subject be
reduced to mere content? Do they all assert a connection of
attributes? And this question at first sight may be answered
in the negative. In " Caesar is sick," we certainly have a
junction of adjectives, but it will be said, " We have some
thing else beside. There is the individual of whom these
qualities are predicated ; and. this individual is finite and deter
mined. Admitted that in every intensional judgment you have
a reference to the ultimate reality, and that this reality is
individual, yet the ultimate subject does not affect the judg
ment. 15 It is given undetermined except so far as it is deter
mined by the judgment : and hence it does not interfere with
the connection of the adjectives. But when you have a finite
subject, then that subject interferes. In Caesar is sick, the
judgment is not true unless you make it of this one Caesar.
You can not get rid of the individual person, and, while he
remains, he prevents your reading the judgment in intension."
23. We have already cut the ground from under this
objection by proving that every such judgment is hypothetical
and strictly universal (Chap. II.). If the subject is taken as an
existing individual or set of individuals, then no doubt the
judgment is categorical, and can not possibly be read inten-
sionally. " All these six sheep have got the rot," " William
invaded England," " I have a headache " : if " these sheep," or
" William," or " I," are taken as sensible individuals in the
series of time, then that character enters into the assertion,
and we can not reduce it to a hypothetical synthesis of ad
jectives. But then our analysis in Chapter II. has shown us
that the reduction is demanded. When we press for the final
truth of the judgment, the particular subject becomes an
unspecified condition of the content. The Assertion is thus
hypothetical. It conjoins mere adjectives, though what it
conjoins is vague and undetermined. The true subject of
the judgment is, not this or that finite person or thing, but
the ultimate reality. All the qualities of the ostensible sub-
2321.1 N
l82 THE PRINCIPLES OF LOGIC BOOK I
ject pass into the condition of a universal connection of
attributes. It would be idle to repeat the painful enquiries
which have established this result. It stands or falls with our
second chapter, and while it stands it carries the conclusion
that every judgment can be read in intension.
24. Thus, when the ostensible subject is a particular
phenomenon 16 or collection of phenomena, no ordinary means
will reduce the judgment. To take it in intension we must
apply the drastic treatment we discussed in Chapter II. But
in other instances the remedy is more obvious, and is easier
to administer. " Some trespassers must be prosecuted,"
" Some English citizens are to be hung," " In some impossible
cases right would be wrong." These assertions would, I pre
sume, be called particular, but none of them need refer to
this or that phenomenon. The " some " may mean " under
some condition." It may describe the attribute, not point to
the individuals.
There are cases where " some " most clearly does not
indicate this or that particular or set of particulars. " Some
crimes are deserving of capital punishment," " In some dis
eases the patient should be secluded " : we mean here that,
given a crime or disease of a certain sort which we do not
specify, then something else would in that case follow. The
judgment couples mere attributes with attributes. It does not
assert the existence of this or that crime or disease. It is
hypothetical, and is naturally read at once in intension. 17
25. " Some " again may mean an unknown number.
" Some English citizens will be hung next year," may mean,
not one sort, but one unspecified quantity of English citizens
will suffer this fate. A particular event is here asserted, and
the proposition must in the end be reduced by the method
laid down in Chapter II. But the event it foretells has al
ready in part been stripped of particularity. The forming a
number, or contributing to an amount, is an universal at
tribute : it is a general adjective, and to this extent the subject
has been already purified. When read in intension the judg
ment runs thus, " Given certain conditions, part unspecified,
part specified as the attribute of English citizen and the at
tribute of amounting to a certain number, then" etc.
It is an elementary mistake to suppose that number 18
CHAP. VI THE QUANTITY OF JUDGMENTS 183
confers particularity and destroys intension. And the error
reveals a deep foundation of bad metaphysics. Number is
surely nothing but an attribute. And how can the addition
of an universal quality force us to take a judgment merely in
extension? How can it even help towards such a result?
You may say, perhaps, that nothing is numbered save actual
phenomena, but such an assertion would be incompatible with
fact. " In the single case of two men being three men, four
men would be six men" this is, I presume, an hypothetical
judgment. Not only can you take it as connecting attributes,
but I do not see how you can take it otherwise. 19 It is idle to
object that the subject is really the imagined example, where
two is three, and that this example is a particular event. For
it is nothing of the sort. It is a supposed condition which,
if it existed, would really be single, but does not exist and
will never be anything real at all.
26. The idea that a numerical subject is particular van
ishes as soon as we confront it with facts. The numerical
character is nothing but a character. It is nothing but an
adjective, and no adjective or accumulation of adjectives will
make anything else than an abstract universal. Suppose that
a phenomenon is capable of division in fact or in idea. Its
divisibility is a general quality, which other phenomena might
also possess, and which would not difference one from the
other. To be regarded as a collection of units summed by
means of addition to a certain quantity, is an attribute not
special to any single phenomenon: it can in no sense bestow
uniqueness. And again, if the subject is taken as a quan
tity which stands in a certain fractional relation to another
quantity, it is absurd to think that, on the strength of these
mere qualities, you leave universals and get to existence. 20
" If a penny is thrown one thousand times, half the number of
throws will most probably give head " : we have here a purely
intensional judgment. There is nothing contained in it but
bare universals: there is nothing but hypothetical junctions of
adjectives. Of course, if you say, " This penny in half its
throws will now give heads," the case is altered : but the num
bers have not changed it. The subject is particular, not be
cause it is numerical, but because it is not so, because over
and above it has now been taken as a particular fact. It must
184 THE PRINCIPLES OF LOGIC BOOK I
be reduced by the method laid down in Chapter II. But so far
as it is numerical it is already reduced, and is already nothing
whatever but attributes.
27. We may pass on to consider another superstition.
If the intension signifies the meaning of a word, and the ex
tension is the number of actual objects of which the meaning
can be truly predicated, then both extension and intension
are relative to our knowledge, and naturally fluctuate with
altering experience. For instance, " mammal " is a term whose
meaning has changed and will change. We can fix no limit
to the possible information the word may convey, for we do
not know how many attributes in the end may be found to
be implied in the quality of giving suck. And the number of
objects we denominate " mammal " is of course not stationary.
Such considerations may seem too obvious to be ignored, but
their neglect has given rise to a serious mistake.
In certain judgments, where the predicate is not of the
" essence " of the subject, we are warned that an intensional
reading is impossible. " All American citizens know the name
of their President," is, we are told, to be taken in extension
(Venn, Symbolic Logic, p. 395 ). 21 It can not connect one set
of attributes with another set of attributes, because the con
nection it asserts is accidental. But the mistake here is
obvious. If I know every single American citizen, so as on
this knowledge to make my assertion, I surely must know by
the selfsame process that the attribute I assert exists in each.
After I have noticed each single citizen, it is one of his at
tributes and part of his meaning to know the name of his
President, and, before I have done so, I can say nothing at
all. If the extension is increased, so also is the meaning. And
the objection that, if the mark were part of the intension of
" American," we should assert it of American citizens in the
future as well as at present, may at once be dismissed. If
the subject stands also for " all Americans in the future," then
the attribute becomes at once part of their meaning. But,
if the subject is confined to the present time, then the mark is
the meaning of "present Americans," and you have no right
to apply it beyond.
The judgment is particular, not in the least because it is
" accidental," but because American citizens are facts in time.
CHAP. VI THE QUANTITY OF JUDGMENTS 185
It would be just as particular if I changed it into " American
citizens are Americans." And of course if the citizens meant
by the subject are neither real men, nor real images, but mere
possibilities, the judgment is hypothetical at once, and we
need not have recourse to Chapter II. to effect its reduction.
28. This same mistake lay at the foundation of the doc
trine (4) that proper names have no " connotation." 22 The
meaning is not fixed, and this leads to the idea that no mean
ing exists. The simple enquiry "Is the denotation fixed?"
leads at once to the result that, here as everywhere, intension
and extension fluctuate together.
Both are relative to our knowledge. And the perception
of this truth is fatal to a well-known Kantian distinction. A
judgment is not fixed as " synthetic " or " analytic " : its
character varies with the knowledge possessed by various
persons, and at different times. If the meaning of a word
were confined to that attribute or group of attributes with
which it set out, we could distinguish those judgments which
assert within the whole one part of its contents from those
which add an element from outside (p. 142) ; and the distinc
tion thus made would remain valid for ever. But in actual prac
tice the meaning itself is enlarged by synthesis. What is added
to-day is implied to-morrow. We may even say that a synthetic
judgment, so soon as it is made, is at once analytic. Kant
has really no need of this unfortunate division, which he
seems to have inherited. The real question which he means
to ask is, What kind of synthesis does each judgment contain,
and what in each synthesis is the principle of unity? 23
29. To sum up the result 24 a proposition is read in-
tensionally, when both subject and predicate are taken as
attributes hypothetically related. Whenever the ostensible
subject is no individual or collection of individuals the
judgment is naturally understood in intension. Where the
subject is one or more actual phenomena, the judgment can
not be interpreted naturally as a hypothetical connection of
attributes. But although not natural, this interpretation is
legitimate, and is also necessary. When we leave first appear
ances and ask for truth, we find that any phenomenal judg
ment, whose subject refuses to be taken as content, is a
judgment which is false (Chapter II.).
l86 THE PRINCIPLES OF LOGIC BOOK I
The error we must avoid is the idea that a class is a
mere aggregate of individuals. 25 Such aggregates in my head
or outside my head are barren mythology : they do not really
exist. And if we mean by a class a possible aggregate of
possible * individuals, we have no longer any collection. For
possibilities occupy no place in the series of events connected
with perception. They are not actual individuals, but merely
ideal. A possible horse is anything which might conceivably
possess the qualities, first of general uniqueness, and then of
equine nature (Chap. VII.). Thus if the class means the
attribute with reference to a hypothetical collection, to in
clude in the class is to predicate an adjective. It is to assert
an attribute, and through that attribute to assert a relation of
identity and difference with any other instance.
30. We have by this time had perhaps more than enough
of the quantity of judgments, and yet there is a question we
have not fully cleared up. The distinctions " universal,"
" particular," and " singular," fall under quantity, and it may
be well that we should more definitely state here the meaning
in which we take these terms. The common logic, we shall
all remember, ranks singular and universal judgments to
gether, and opposes the particular to both of these. A par
ticular judgment is a judgment which fails to take the subject
explicitly and avowedly in the whole of its extension; and
other judgments are considered universal because in them you
have all of the subject. This arrangement we shall not pro
ceed to discuss. It is sufficient for the technical use of the
syllogism, and it is perhaps in itself not so foolish as it seems
to be. We need not however pause to examine it. We may be
satisfied if we succeed in making clear our own interpretation.
31. The subject is not only beset with ambiguities, but
it tends at each moment to cross the border and to enter the
field of metaphysics. I am afraid it is impossible for me here
to defend the interpretation which I have adopted. I must
content myself with trying to exhibit clearly the doctrine which
seems metaphysically true, and which agrees with the logical
results we have arrived at.
*I suppose we do not always mean "judged possible." Cf. p. 4
note.
CHAP. VI THE QUANTITY OF JUDGMENTS 187
We may realize some difficulties which obscure the sub
ject, if we state them in the form of thesis and antithesis.
(i) Nothing that is real is universal, (ii) All that is real is
universal, (iii) Nothing that is real is particular, (iv) Most
that is real is particular. I believe in the truth of all these
propositions, and will endeavour to show that they are not in
conflict. But first it is better to advocate each.
32. (i) Nothing that is real is universal. Indeed, how
should it be? What is real is substantial and exists by itself:
it is individual. But the universal is nothing whatever but an
adjective. It is an epithet divorced, a shadow which apart
from its body is nothing, and can not exist.
(ii) Everything that is real is universal. How can it be
otherwise? For what exists must be individual, and the indi
vidual is no atom. It has an internal diversity of content.
It has a change of appearance in time, and this change brings
with it a plurality of attributes. But amid its manyness it
still remains one. It is the identity of differences, and there
fore universal.
(iii) And so we see that No real is particular. For if
particular, then not individual, and if not individual, then
non-existent. The particular is atomic. It excludes all dif
ference. It is itself and nothing beyond itself. And that self
is simple : it is so far as it is nothing else. The true particular
in respect of quality is shut up in one quality; relations it
can not be said to have; in respect of time it has no con
tinuance, and in space it can not occupy extension. Its exist
ence in space is nothing but a point, in other words, is nothing
spatial. Such a particular is of course not to be verified in
experience. It is a metaphysical ens rationis, an abstract
universal 26 which can not be real.
(iv) And it can not be real because, if not all, at least
Most reality must be particular. 27 For in existence the indi
viduals which are real are finite. To some extent at least
they are defined by their limits. It is because they repel
other things that they are what they are. Exclusion by
others, and exclusion of others, enters into their substance;
and where this is there is particularity.
33. It is obvious here that in thesis and antithesis words
have been used with different meanings. And this result we
l88 THE PRINCIPLES OF LOGIC BOOK I
desired to establish. The abstract universal and the abstract
particular are what does not exist. The concrete particular
and the concrete universal both have reality, and they are
different names for the individual.
What is real is the individual; and this individual, though
one and the same, has internal differences. You may hence
regard it in two opposite ways. So far as it is one against
other individuals, it is particular. So far as it is the same
throughout its diversity, it is universal. They are two dis
tinctions we make within it. It has two characters, or aspects,
or sides, or moments. And you consider it from whichever
side you please, or from the side which happens for the pur
pose of the context to be the emphatic or essential side. Thus
a man is particular by virtue of his limiting and exclusive rela
tions to other phenomena. He is universal because he is one
throughout all his different attributes. You may call him
particular, or again universal, because, being individual, he
actually is both, and you wish to emphasize one aspect or
side of his individuality. The individual is both a concrete
particular and a concrete universal ; and, as names of the whole
from different points of view, these both are names of real
existence.
34. The abstract universal and abstract particular are
both unreal, because neither are names for the individual.
They take the two aspects or characters of the whole, and,
turning them into independent existences, then assert their
reality. But one side of a whole can not stand by itself
except in our heads. It is nothing but an adjective, an internal
distinction which we try to take as substantial fact. We can
all see that this holds good of abstract universals. The
oneness or identity of a man, we know, is not found when we
search the series of mental phenomena. But the same is true
of the abstract particular. If you take atoms seriously, and
deny their extension, you find at once you are dealing with
something which can not be fact. Mere exclusion in space of
other spaces is nothing real. A reality in space must have
spatial diversity, internal to itself, and which it does not ex
clude. And this holds again with psychical atoms. For, as
observed, they have internal multiplicity, duration in time,
quality, and degree; and as anything else they could not be
CHAP. VI THE QUANTITY OF JUDGMENTS 189
observed. An atom which really was particular, which was
not divisible at least in idea, could not possibly be fact. It is
one aspect of fact torn away from the rest, and is nothing in
itself and apart from the act which tears it away.
35. The abstract particular and the abstract universal are
mental creations, which, if taken as fact outside our heads,
are different examples of the same mistake. Both are dis
tinctions within a whole, hardened into units that stand by
themselves. And not only do they spring from the same
mistake, but we may even say that they are the same error.
The abstract triangle in and by itself is found to exclude all
further predicates (cf. p. 119). Determined by that division
and consequent exclusion which gave it its origin, it has be
come particular. And the particular itself, because produced
by mental separation, is really no more than an adjective
divorced, or abstract universal. The dialectical method has
laboured to show that, here as everywhere, insistence upon a
onesided view brings out by negation the opposite onesided-
ness. The universal, the more we emphasize its character,
divides itself the more from the whole. We make its being
depend on exclusion, and it turns in our hand into its logical
contrary. The particular again, excluding others, and being
so far as it merely excludes, is its own negative relation to
other particulars. It falls beyond itself into a series of units
pervaded by an universal identity, and itself has there become
its own opposite. In this speculative movement, if we take it
in the character it claims for itself, 28 I neither myself profess
belief nor ask it from the reader. But I think we may go so
far as this, that in the end the individual is real, and that ab
stract universal and abstract particular are distinctions taken
within that reality, which a mistake has afterwards turned into
divisions and hardened into units. If we do not admit that
each is a moment which, by negation of itself, affirms the other
and begets the whole, we may certainly say that each has
sprung from the same mistake, and is an illusion of the
self-same kind. And we may muster courage, perhaps, to
profess that the individual is the identity of universal and
particular.
36. We must keep in view the following distinctions.
We have first the abstract universal and particular, and
IQO THE PRINCIPLES OF LOGIC BOOK I
neither of these can exist in nature. 29 On the other side we
have the individual, and the individual is the only thing which
is real. But where this real is finite it may be taken from two
points of view : it is concrete particular or concrete universal.
In so far as it is a finite individual which excludes all others,
so far it is a relative particular. But because it includes a
diversity of content, it is therefore also a relative universal.
There is here, I confess, a doubtful point I am forced to
.leave doubtful. It might be urged that, if you press the
enquiry, you will be left alone with but a single individual.
An individual which is finite or relative turns out in the end
to be no individual; individual and infinite are inseparable
characters. Or again, it might be said, the individual is
finite, and there can not be an absolute individual. Meta
physics, it is clear, would have to take up these questions, and
in any case to revise the account which is given in this chapter.
But that revision must be left to metaphysics ; and for the pur
poses of logic we may keep the distinctions already laid down.
We have (i) the real, supposed to fall into (a) absolute indi
vidual or concrete universal, (b) relative individual or con
crete universal or concrete particular; and (ii) the unreal, con
sisting (a) of the abstract universal, and (b) of the abstract
or absolute particular.
37- We may now attempt to lay down what we mean by
universal judgments. Such a judgment is one whose subject
is universal. And it is obvious that here we have more than
one meaning. An universal judgment may be (i) absolute,
or (ii) relative.
(i) In the first case we have again two divisions. Such a
judgment may (a) be abstract, or again (b) may be concrete.
If (a) the judgment is abstract, the ostensible subject will of
course be an attribute. The statement will truly be hypo
thetical, 30 since the actual subject is non-phenomenal reality.
The ordinary kind of universal judgment such as " The angles
of a triangle are equal to two right angles " is, as we have seen
(Chap. II.), of this description. And it is universal for two
reasons. The grammatical subject is an abstract universal:
while the actual subject, the ultimate reality, is a concrete uni
versal and is also absolute. This is the first and more ordi
nary kind of judgment which we are able to call absolutely
CHAP. VI THE QUANTITY OF JUDGMENTS IQI
universal. But (b) it is necessary to mention another sort.
Any statement made concerning a reality which is not con
sidered finite will also be an absolute universal judgment.
Nothing will fall outside the subject, and the predication will
be categorical. I do not say that such judgments are prac
ticable; but they are logically possible, 31 and must be provided
for.
38. (ii) A judgment is relatively universal where the
subject is a finite individual or collection of individuals. It is
universal, because the subject is the identity of its own internal
diversity. In " Caesar is sick," Caesar is not affirmed to be
nothing but sick: he is a common bond of many attributes,
and is therefore universal. But this judgment is relative,
because Caesar is one man among other men ; and, if you take
him so, he himself is particular.
39. 32 A judgment which is absolutely particular can not
exist. It would have a subject completely shut up and con
fined in the predicate. And such a judgment, if it came
into being, would not be a judgment. For it obviously would
say nothing else of the subject or predicate than themselves.
" This is this " may be taken as the nearest example.
A relative particular judgment is one where the subject
is this or that singular or collection. It is the same as the
relative universal judgment, but is taken from another side of
its nature. The subject excludes all other individuals, and so
is particular; but within itself it has a diversity, and so is
universal. It possesses attributes other than the predicate,
and may be taken within another context. It thus serves as a
middle term in reasoning, as is shown in the third of the
syllogistic figures.
40. We have seen before (Chap. II. 45) that no logical
difference separates the singular and collective judgments. 33
It is ridiculous to think that if one individual is not universal,
you reach universality by adding on others. The number
of units is quite irrelevant, since, however many they become,
each remains a singular. And this or that collection of indi
viduals is as hard a particular as any individual found in the
collection. Nay, from this point of view, the single individual
himself turns out to be a mere collection. Considered logi
cally they are both alike. Excluding others, they are relative
IQ2 THE PRINCIPLES OF LOGIC BOOK I
particulars. Common to all their internal diversity and iden
tical throughout it, they both alike are relative universals.
41. No judgment has or can have a subject shut up
within the limits of one single predicate. If we remain at the
popular point of view, and admit those judgments where the
subject is nothing but a finite phenomenon or set of phenomena,
yet even these judgments are universal relatively. The sub
ject will serve as a middle in reasoning. It is hence the iden
tity of differences, and it could not be that if it were only
particular. Every judgment is thus universal, and in the end
they all may be said to be universal absolutely. For, if we
exclude the possibility of non-phenomenal finite individuals,
we have shown (Chap. II.) that every judgment to be true
must predicate of the absolute individual, either hypothetically
or categorically. And the former of these cases must, in the
end, be reduced to the latter. The finite subject changes in
our hands into a heap of mere adjectival conditions, and, since
these conditions can never be complete, the statement loses its
categorical force. But becoming hypothetical it predicates
indirectly a latent quality 3 * of the ultimate reality, and so once
more is categorical, true categorically of the absolute
subject.
42. All judgments are thus alike universal, but it can
not be said they are universal equally. If the subject of one
judgment is a whole which includes the subject of another,
the first is certainly the more universal. And again, if we take
two abstract judgments, they are both hypothetical, but the
one may assert a more abstract connection than is affirmed in
the other. The purer hypothesis, the one most set free from
irrelevant conditions, will be also more true. It will predicate
in a higher sense of the universal subject, and therefore may
be called the more universal. But if the connection, although
less concrete, is not more pure, we must then not call one
judgment more universal than the other, unless we qualify uni
versal by abstract. 35
43. I will repeat in conclusion the distinctions it is right
we should keep in mind. The real is individual. The merely
universal or merely particular are unreal abstractions. Con
crete universal and concrete particular are the individual from
different points of view. But we could not say that an abso-
CHAP. VI THE QUANTITY OF JUDGMENTS IQ3
lute individual was really particular, since it would have no
relation to anything outside.
Particular judgments, if taken categorically, are precisely
the same as relative universal. The phenomenal individual,
or collection of individuals, is the identity of diverse relations
and qualities. Universal judgments are relative or absolute.
If relative, they are the same as particular judgments. If
absolute, they are either hypothetical or categorical. In the
first the ostensible subject is an abstraction: in the second it
must be the ultimate reality. Particular categorical judgments
may all be reduced to abstract or hypothetical universals, and
these again to categorical universals. In the end all truth, if
really true, is true of the ultimate non-phenomenal fact.
ADDITIONAL NOTES
1 " Its content," i.e. in abstraction from its reference.
2 " Ideal or actual." By "actual " I evidently meant here " existing
in our " real world." But the " ideal " instance, though not in this
sense " real," must be taken as an individual or particular. The ex
tension always means the particular object or objects to which the
meaning is applicable. We may note that the word " any " implies
always, if strictly used, a number of individuals (Cf. Essays, p. 286).
The statement, in the footnote to this page, as to "possible horses"
is wrong. It forgets that the " imaginary " also is " real " and can
be individual. Cf. on Chap. II, 45, note.
3 " The fact is &c." The " fact," however, may be " imaginary."
* "The indiscriminate use person." This detestable misuse as
well as that of "distinctly" for "clearly" or " undoubtedly "seems
now gone out of fashion.
5 " Unnecessary and objectionable." Dr. Keynes (Formal Logic)
has not induced me to alter my opinion. He is, I presume, right in
saying that what Mill meant by "connotation" was merely "conven
tional meaning"; and I very possibly also in some other point may
not have represented Mill s view fairly. But that his innovation was
useless and objectionable I remain convinced, and why it should
not be quietly buried, Dr. Keynes, I think, has failed to show. For
the meaning of Proper Names I refer the reader to Bosanquet s
Logic, I, pp. 50-1.
6 Cf . here Bosanquet, Logic, I, 47.
7 "False or frivolous." Cf. p. 486. The doctrine clearly, except
within certain limits, is false. But to call it everywhere worthless is,
on the other hand, to fall into error. Subsumption (9) has its own
value. See Bosanquet, Logic I. 55 foil.
194 THE PRINCIPLES OF LOGIC BOOK I
8 " Has ceased to lie in the individuals." But see Note 2.
9 " There are few readers." This perhaps, even in 1883, was an
exaggeration.
10 On the subject of 11-29 see further T. E. III.
11 " To include real dogs &c." should be " to include dogs, perhaps
real, &c."
12 " The only way . . . extension." I do not, by " in extension,"
mean " merely in extension " ; for this on my view is not possible.
13 "Two individuals . . . differ." We should add, "And, where
you have only one individual, you can still, by more or less of vio
lence, bring it under the above head. For, dividing it by a distinction,
you can so make the one individual into two."
14 Sections 22 foil, require correction. No judgment can on my
view be read merely in intension (see Note 10). Any passage in the
text therefore, which seems to imply that possibility, should be
amended. In 22, par. 2, the words " reduced to mere content " are
ambiguous and misleading. Though nothing but " content " enters into
a judgment, the question as to the reference and the extension remains
(cf. Notes i and 2).
15 How far and in what sense "the ultimate subject" does, and
does not, enter into the judgment is discussed elsewhere (see on
Chap. I, 12). It is true that, so far as the judgment depends
on Designation, it remains conditional (see Index, s. v. Designation).
But to pass from this to the assertion of a mere conjunction of ad
jectives is at least misleading. What in the text I really was
attacking is the position of any one who takes the content of the
judgment as depending on individuals or particulars, known merely
by Designation so as to preclude an intensional reading of the
judgment. Anything beyond this was to overshoot the mark, if not
to fall into error. On Designation see the Index, s. v., and Appear
ance and Essays, the Indexes. On "the ultimate subject" see on
Chap. I, 12.
16 " A particular phenomenon " should have been " a merely par
ticular &c."
17 " Naturally read at once in intension," but not merely inten-
sionally, however much the emphasis falls on the intension. The
words " It is hypothetical " are again misleading here, as is also the
reference to " existence," if that means " existence in my real world."
18 " Number." The mark here is once again overshot. I was really
concerned to deny that mere "numerical" sameness and difference
is possible, and that particulars, diverse in this sense, and so unique,
can enter into a judgment and so exclude an intensional reading.
19 "How you can take it otherwise." (Cf. the "impossible cases"
of 24.) These words should be corrected in accordance with what
has been laid down in previous Notes. And so again with "nothing
of the sort." There is aways an extensional side in judgment, how
ever much this side may be wrongly emphasized or misinterpreted.
20 "And get to existence," i.e. in such a sense as to exclude an
intensional reading.
CHAP. VI THE QUANTITY OF JUDGMENTS 195
21 It is, I think, unnecessary to ask if I here represent Dr. Venn s
contention fairly. If "all American citizens" means "all that now
exist," the extensional aspect, I can agree, is naturally emphasized,
though the statement becomes, I presume, obviously false. But in any
case the intensional aspect of the judgment is there. I would add
that the use of " hypothetical " and " hypothetically " (in 27 and 29)
would better have been here avoided. Cf. Note 17.
22 " Proper Names." See Note 5.
23 Kant is not a writer whom I can suppose myself to understand,
but my criticism seems, at least in part, to be unfair both in the foot
note to Chap. I, 7 and also here. However insufficient his answer,
Kant did not, I presume, neglect " the real question " as to the nature of
the synthesis within the idea, and as to how far, and by what right,
this limited synthesis can be transcended.
On the real importance of the distinction between the essential
and the accidental, see Bosanquet, K & R, pp. 59 foil.
24 The statement here is far less correct than that in 12. After
"actual phenomena" add "real or imaginary." And, after "judg
ment which is false," add " In any case, even where we refer to one
or more particulars and the emphasis is on the extension, the inten
sional aspect is still there."
25 On Class see Essays, pp. 283 foil. A class is an aggregate, but
is also more. The mere aggregate is that which here and everywhere
is mythical.
" Possible individuals." The statement here is, at the least, mis
leading. Possible horses, as actually imagined, are real individuals,
though, except as psychical events, they do not enter into my "real"
world. The footnote here repeats an error for which see Note 2.
" Possible horses," again, are not the same as the possibility of horses,
which latter is, itself as such, hardly a particular fact, except, once
more, in the sense of a psychical event.
"A relation of identity, &c.," should have been "a relation of
identity with, and difference from, every &c." For the Collective
Judgment see Chap. II, 45.
26 " An abstract universal." Though this statement is correct, it
might have been better to have said merely " an abstraction."
2. 7 "Most reality." All reality, that is, except the Universe itself.
In the next sentence, and again lower down, "existence" is not to
be confined merely to " my real world." See Chap. II, Note 3. And
(in 33, line 4) to "what does not exist" we should add "as such."
For everything conceivable has existence in some sense.
2 " Character it claims for itself," should be, I think, " character
so often claimed for it."
29 "Exist in nature" should be "as such be real." And, in the
following paragraph, "as such" should again be added to "and (ii)
the unreal."
so " Hypothetical." Here (in 37 (0, and again in 41) "con
ditional " would be a better term to use, if either term is required.
IQ6 THE PRINCIPLES OF LOGIC BOOK I
31 "Logically possible." But even here the judgment will be sub
ject to a condition. See Essays, pp. 228 foil., and T. E. II.
32 1 have in 39-41 assumed that merely external relations are
impossible or at least would be useless.
33 " No logical difference." This seems to be unnecessary, and is
incorrect (see on Chap. I, 45). And the sentence "Nay . . . collec
tion," though true, seems to be here more or less parenthetical.
34 " A latent quality." See on Chap. I, 50.
35 This 42 seems wanting in clearness, and I can not recall what
exactly was in my mind when I wrote it. It appears to contemplate
first (i) the case of two concrete wholes, and to lay down that the
one which includes the other, or (we should add) is, generally, the
more inclusive, is the more universal. We have next (2) the case
of two abstract judgments, one of which is higher than the other
(as being more general, and also "purer," in the sense of containing
fewer unanalyzed, and perhaps irrelevant, conditions. The former
judgment is therefore more universal as really covering and including
more ground. Then we have (3) apparently two cases. In one of
these (a) the judgment should be more universal in the sense of No. 2,
but fails really to be so, because, though in a more general sphere
and, in this sense, more abstract it contains as much or even more
internal irrelevancy than is found in the other. Or (b) we have
the case of a judgment which holds in a narrow, and so abstract,
region, and therefore does not really cover more or even as much
ground as is covered by a less " pure " and more concrete, but in
effect wider, judgment.
We should here remember that, if our knowledge were completely
systematic, these distinctions, at least in part, would cease to hold.
But, as things are, our pure and abstract knowledge is really, though
not ostensibly, conditioned by that enormous mass which it fails to
explain and comprehend, and so really to include. Hence the knowl
edge (say) of a mathematician may in one sense be far narrower
and less universal than the knowledge (say) of a biologist. The
above remarks may perhaps serve to explain, and, where necessary,
to correct the text of 42 in detail. The subject is perhaps too difficult
to admit of any brief statement.
CHAPTER VII
THE MODALITY OF JUDGMENTS*
i. Modality is not an alluring theme. I should be glad
to plead the fragmentary nature of the present work as an
excuse for passing it by in silence. But for the sake of clear
ness it is necessary to make an excursion into the subject,
neglecting those parts of it which do not seem to concern us
here.
We must begin by stating an erroneous view. Modality
may be supposed to affect the assertion in its formal character,
and without regard to that which is asserted. We may take
for instance a content S P, not yet asserted, and may claim
for modality the power of affirming this content S P, un
altered and unqualified, in several ways. S P, it is sup
posed, may be asserted, for instance, either simply or prob
lematically or apodeiktically, and may yet remain throughout
S P : and thus, though the content is unmodified, the asser
tion is modal.
2. This doctrine rests on a misunderstanding. There
are no degrees of truth and falsehood. 1 If S P is fact, it
can not be more than fact : if it is less than fact, it is nothing
at all. The dilemma is simple. S P is affirmed or it is not
affirmed. If it is not affirmed, it is not judged true at all. If
it is affirmed, it is declared to be fact, and it can not be more
or less of a fact. There clearly can be but one kind of judg
ment, the assertorical. Modality affects not the affirmation,
but what is affirmed. It is not mere S P that is asserted
modally : it is another content, a modified S P. In other
words, you do not say that the mere idea S P holds good
in fact ; you first say something else about S P, and it is
then this new and different idea which really is asserted.
3. Modality in this sense, it has been rightly observed,
has no natural limits. There are endless ways of modifying a
judgment so as to make a fresh judgment. You may take
* Cf. Sigwart, Logik, pp. 189 and following.
2321.1 W
198 THE PRINCIPLES OF LOGIC BOOK I
the idea of a judgment S P and express any attitude of
your mind towards it. You may say " I make it," or " wish to
make it," or " fear to make it," or " can not make it," or " am
inclined to make it," or " am forced to make it." All these are
simple assertorical statements about my condition of mind.
They have a psychological not a logical bearing, and may at
once be dismissed.
4. The different ways in which we can stand to a judg
ment S P are a matter for psychology rather than for logic.
Logical modality must be limited to that which seems to affect
the idea S P, and to affect it in its relation to the world of
reality. If we say, " I wish S P were a fact," this once
more is a psychological mode. The content S P is not
here first modified and then attributed to the ultimate subject.
Neither itself nor anything we can call a modification of itself,
pretends to be either true or false. The judgment in fact is
concerned with nothing but my mental attitude.
Either logic has nothing to do with modality, or modality
affects S P from the side of truth and falsehood. The ideal
content must be referred to or else denied of reality. But the
reference or denial itself is simple, and can not be modified. 2
What therefore must in some way be modified is the content
itself. Not S P but a transformed and conditioned S P
is the assertion made by logical modality.
5. The modes of S P which logic has to consider are
three in number. In each case we assert, we refer some idea
to ultimate fact, we begin the judgment by saying, " It is true,"
but we go on to fill up the blank in each case by a different
idea. It is true that S P is actual, or is possible, or again
is necessary. The idea pronounced true is " actual S P," or
"possible S P," or "necessary S P." These modes we
retain for consideration, dismissing all others. But our choice
is not really so arbitrary as it seems. We have here in a
veiled and hidden shape the distinction of categorical and
hypothetical assertion. The possible and the necessary are
special forms of the hypothetical ; and between the assertorical
and the categorical there is no difference whatever. 3
I shall begin by asking (i) the general meaning which in
logic we assign to the predicates possible, necessary, and real.
I shall then point out (ii) that the possible and the necessary
CHAP. VII THE MODALITY OF JUDGMENTS 199
have no real existence. But on the other hand I shall show
(iii) that these modal assertions, though as such and in them
selves they are not true of fact, must always rest on a basis of
assertion which is true or false of actual reality.
6. (i) We need not ask what we mean by (a) asser-
torical judgment. It is judgment categorical or unconditioned.
" S P is real," attributes S P, directly or indirectly, to the
ultimate reality. And on this point we have nothing to add
to the explanations already given in Chapter II. The asser-
torical judgment may be dismissed from our thoughts. To
draw a difference between a categorical judgment on the one
hand, and on the other a judgment which asserts reality, is
plainly impossible. The assertorical is simply the categorical,
taken in contrast with the possible and the necessary.
7. And these are nothing but phases of the hypothetical.
What may be and what must be involve a supposition. Neither
is declared to be actual fact: they both are inferred on the
strength of a condition, and subject to a condition.
(b) It is easy to give the general sense in which we use the
term necessity. A thing is necessary if it is taken not simply
in and by itself, but by virtue of something else and because
of something else. Necessity carries with it the idea of media
tion, of dependency, of inadequacy to maintain an isolated
position and to stand and act alone and self-supported. A
thing is not necessary when it simply is; it is necessary when
it is, or is said to be, because of something else.
And where necessity is " internal," this meaning is re
tained. 4 For it is not the totality which in this case is necessi
tated. There is a diversity of elements contained in the whole,
and these elements are divided into that which constrains and
that which follows. In an unseparated world there could be no
necessity.
8. In a work on metaphysics the word " because " 5 would
lead us straight to some fundamental difficulties, which will
meet us again in our concluding Book. Is there any because
outside of our heads ? Is it true that one thing is by means
of another, and because of another? Or are we forced to
admit that every fact, while it is no doubt and is also perhaps
together with others, is not an adjective depending on these
others, has no real bond that fastens it to its environment,
2OO THE PRINCIPLES OF LOGIC BOOK I
nor is subject to any alien influence? The objection would
assail us : " One fact is and another fact is/ so much is true ;
but One fact is and so another fact is/ must always be false.
It is giving reality to mere ideal connections." And, if we
escaped this objection, we should find another lying in wait for
us. " You may say that one reality is the cause of another,
and you may, if you please, add to this that the second is
because of the first. But, if you venture to convert this asser
tion, and assume that whenever you have a because you have
also a cause, you fall into error of the worst description. A
cause is real, a because is ideal; you may have the one and
do often have it, where the other is impossible. They do not
always co-exist; and where they do co-exist, they do not
always coincide; and where they coincide, they are not identi
cal. They are not the same thing: they are not even two
different faces of the same thing. They are nothing but coun
terparts, two parallel series which have no common points
but possess some terms which have a constant relation "
(Book III.).
9. In a work of this kind we can not grapple with the
problems offered us. We must here admit the objection and
retire before it. We must admit that in logic " because " does
not stand for a real connection in actual fact ; 6 we must allow
that necessity is not a bond between existing things. For
logic what is necessary is nothing beyond a logical conse
quence. Necessity is here the force which compels us to go
to a conclusion, if we start from premises. The " because "
expresses an ideal process of mental experiment, which gives
as its result a certain judgment. It does not guarantee the
truth of this judgment, if you take it by itself. It does not
guarantee the truth of the data which the process starts from,
and on which it operates. A necessary truth may be, and
commonly is, categorical, but, so far as its necessity goes, it is
hypothetical. It ceases to be hypothetical only when it ceases
to be merely necessary. 7
10. I admit it is not the same thing to affirm " // M is P
then S is P," and " Since M is P therefore S is P." 8 And the
difference is obvious. In the latter case the antecedent is a
fact, and the consequent is a fact: they are both categorical
(Chap. II. 71). In the former case the antecedent may be
CHAP. VII THE MODALITY OF JUDGMENTS 2OI
false and the consequent impossible. But the necessity in each
case is one and the same. S P must be true, if you take
M P, and take S M, and draw the conclusion. That
is all the necessity it is possible to find. The knowledge that
S M M P are both true, and that S P is a statement
which holds of fact, falls outside the necessity and does not
increase it. The hypothetical result becomes categorical by
an implied addition. And the hypothetical connection may
not even then become categorical. The bond of necessity is a
logical passage, and to say that this logical passage itself exists
in fact demands an assumption which can not be hazarded in
the face of objections. In logic we must be content to say
that, if the premises are categorical, the result is categorical.
We can not add that this result is necessary, unless for a
moment we treat the data as hypotheses, and mean no more
than // S MM P are given, then S P must follow.
ii. We are able to urge a two-fold argument to show
that necessity is hypothetical. We can reason from principle,
and again from usage. The argument from principle 9 we may
repeat as follows. Logical necessity is an ideal process, and
you can not assume that either ideas or process are facts.
Even if the ideas exist in fact, and exist in corresponding
sequence, you can not assume that in this sequence your process
exists. Your ideal operation works with ideas, and, so far
as you know, it works only with ideas. The idea may be more
than a mere idea, but it is as an idea that it goes into the
experiment. And a mere idea is no more than a mere sup-
posal. The result, so far as necessitated, is therefore so far
not categorical. This we may call the argument a priori.
And we have in addition an argument from usage. A
necessary judgment, a statement introduced with " It must be
so," may assert what not only fails to be actual but is plainly
impossible. " If two were three then four must be six " pre
sents us with a truth which is compulsory. The result must
follow ; it is necessary truth ; but it does not follow in actual
existence, and could not follow there, since both antecedent
and consequence, and their actual junction, are impossibilities.
It is not true that apodeiktic modality strengthens our asser
tions. It serves rather to weaken them.. If S is P, there
is an end of doubt. If S must be P, we know indeed that,
2O2 THE PRINCIPLES OF LOGIC BOOK I
given something else, we can be sure of S P, but we are
certain of no more. The apodeiktic mode either leaves our
doubts, or removes them only by the covert assertion of the
condition of S P. Where the necessary asserts strongly
it borrows its strength from a concealed assertorical. I will
conclude this section in Sigwart s words. " There is a common
idea that the apodeiktic judgment stands for something higher
than the assertorical. It is believed that, if we start from the
problematic judgment and ascend to the apodeiktic, we steadily
increase the certainty of our knowledge, and add to the worth
and dignity of our assertions. This idea must be relinquished.
All mediate certainty must stand in the end on immediate
knowledge: the ultimate premises of every proof can not be
proved. The usages of life stand in comic discrepancy with
the emphasis we lay upon apodeiktic certainty. The sayings
1 It must be so/ It must have so happened, are judgments
apodeiktic: but the confidence they express has most modest
limits." (Logik, I. 195.)
12. (c) A necessary truth is a truth which results from
assumed conditions. 10 If we imply, as we very commonly do,
that those conditions are actual, then the result is categorical.
But, though the necessary may be real, its necessity is hypo
thetical. What have we now to say about possibility? When
S P is possible, does that mean that S P would exist as
fact, if something else were fact? Is possibility in short a
form of hypothetical necessity?
It sounds strange when we hear that the possible falls
under the head of the necessary. But it is at least as surpris
ing to learn that the necessary may be impossible or non
existent; and this we already know to "be the case. On such
subjects as these our first impressions may be worth very little.
The possible is that which is known or assumed to be the
consequence of certain conditions. So far the possible is one
with the necessary, where it is implied that the antecedent is
real. But it differs in this point ; for S P to be possible
all the conditions which make S P necessary must be sup
posed, but only a part of them need be assumed to exist. It
is implied that a part of the antecedent exists, but as to the
other part we are left in ignorance. Thus the partial existence
of the conditions of S P is the differentia which separates
CHAP. VII THE MODALITY OF JUDGMENTS 203
the species " possible " from the genus " necessary." Take
a judgment such as this, Given abed then E must follow.
Add to it the judgment, or the supposition ( 15), that ab
exists, while cd is not known to exist, and we get the possible.
E is now a possibility. We have an assumed fact ab, we also
have ideal conditions c and d, assumed to be compatible with
ofc/ 1 but not taken to exist. We have a hypothetical judgment,
Given abed, we should have E. And from this, by the as
sumption that ab exists, we pass to " We may in fact have E."
In other words, ab is the " real possibility " of the possible E.
It is known to be real, or at least is treated as if it were so
known ( 15).
13. Everything possible must be really possible. It must
stand on a reality assumed to exist, and taken as part of that
sum of conditions which would make S P an actual fact.
Possibility apart from or antecedent to the real world is utter
nonsense.
But the basis of fact may vary indefinitely. S P is
possible in the highest sense when the detailed conditions
which make it necessary are fully known, and a part of these
detailed conditions is also taken to exist. 12 This highest sense
sinks by slow degrees to the lowest of all, where " possible "
stands for "not known to be impossible." Here we do not
know what special conditions give S P. Our basis of fact
is nothing but the assumption that the nature of the world
admits S P. 13 Because reality does not in our knowledge
exclude S P, we take reality as one existing condition of
S P, and we assume not only that the rest may be found,
but also that they are compatible with reality. In this lowest
and barest sense of possibility it is really wrong to call S P
possible. It is better to say, We do not know that S P is
impossible.*
Between these extremes come many degrees. In the hypo
thetical judgment about S P we may not know the special
conditions of S P, but we may know a smaller or greater
amount of them, and, where we are ignorant, we may have
more or less reason to make an assumption. And in respect to
the partial existence of these conditions, our knowledge admits
*We rest our assertion on a privative judgment. Cf. Chap. IIL
8, and p. 213.
2O4 THE PRINCIPLES OF LOGIC BOOK I
of many stages, and we make assumptions with grounds that
may vary almost indefinitely. We should gain nothing here
by dwelling on these varieties, and prefer to give some simple
illustrations.
14. Are disembodied spirits possible? Let us agree to
take the most unfavourable view for the sake of argument.
We have no direct experience of the existence of such spirits,
and the question is whether we can call them possible. We
know no conditions which would give the result. We have no
reason to think such imagined conditions compatible with the
real nature of things. 14 On the other hand we can not reject
the idea as impossible, since we have no right to affirm " It is
incompatible with the nature of things." We should content
ourselves with saying, " Your proposed assertion is not cer
tainly false, but there is no ground for thinking it true. Our
ignorance is forced to admit a * bare possibility/ but it gives
not the very smallest reason for entertaining that idea as real.
And such bare possibilities, we have seen, are none; they
are * idle frivolities, that have no place in the minds of reason
able men/ "
The case we have given is, as we have given it, an ex
ample of the lowest sense of " possible." Let us go a step
higher. " It is possible that some of the planets are inhabited."
We have here the hypothetical judgment that under certain
conditions life would result ; and to some extent we know these
conditions, while we supplement our ignorance by assumptions
for which we have reasonable ground. These special condi
tions again are in various planets known to exist in part and in
different amounts. Our judgment that this or that planet may
be tenanted thus varies through different degrees of possibility,
according to the amount of this partial existence.
But now take the assertion " That coin may have given
head." Here we know, on the one hand, special conditions
which must exhibit head, and we know on the other hand that
part of these conditions really exists. This is possibility in its
highest form.
15. We have noticed that possibility may stand not on
fact but on supposition. If a coin had three sides, then it
would be possible that neither head nor tail should be upper
most. There is here no vital change in the meaning of
CHAP. VII THE MODALITY OF JUDGMENTS 2O5
" possible." For the real basis is supposed to exist, and the
possible is subject to the supposition. But we should not here
say that S P is possible ; we can not strictly go beyond " It
would be possible." It is possible, if by a fiction of thought
you treat the unreal as if it were real, or the unknown as if
it were known. We must distinguish such hypothetical from
actual possibility. For, just as we more commonly imply that
the necessary exists, so we imply and must ordinarily even be
taken to assume that the ground of the possible is actual fact
and not merely supposed. 15
1 6. We have now discussed the meanings of " possible "
and " necessary," so far as to see that both are forms of the
hypothetical. And with this conclusion we have anticipated
the result of our second enquiry, Does logical modality exist
in fact? 16
(ii) We saw long ago that hypothetical judgments, as such,
are not true in rerum natura. Neither the subject, nor the
predicate, nor again the connection, need exist in fact. What
is true of fact is the quality that forms the base of that con
nection. The junction itself may be non-existent and even
impossible. We shall verify this result in the possible and the
necessary.
17. (a) We have seen that what must be is never neces
sary save on the hypothesis of some condition. We have seen
that this antecedent, and the consequence which follows, may
claim no existence and may have no possibility. 17 The neces
sity in these cases, if we mean the necessary connection of the
elements, does not exist outside our ideas; it is not true of
fact.
And again, when the antecedent and with it the conse
quence have actual existence, and appear in a relation which
is clearly the counterpart of logical necessity, the same result
holds. We saw that the difference between the cause of
knowledge and the cause of existence staggers our assump
tions. And even when the two seem to us to coincide, how
can we assume that they are ever identical ? It is a great thing
to say that what is true in thought must hold in fact. But
it is something more to maintain that thinking and existence
appear as two sides of a single reality, and to insist that every
logical process must be found in fact, and that all real con-
2C>6 THE PRINCIPLES OF LOGIC BOOK I
nection is, if we could see it, a logical process. We shall recur
to these questions in a later Book. For the present we may
repeat that, if such a doctrine is tenable in metaphysics, it
can not be supported in a logical treatise. The objections it
calls forth, if they could be disposed of, could be disposed of
only by a complete revolution of our current doctrine as to
mind and things. 18
For logic the necessary must remain the hypothetical.
Facts for logic must be facts that are and that never must be.
The real connection which seems the counterpart of our logical
sequence, is in itself not necessary. It is necessary for us,
when in ideal experiment we retrace the process of actual fact.
But, at least in logic, we must not assume that our ideal rela
tion is the bond of existence. The ideal compulsion of logical
necessity is as strong where the premises are known to be
false, and the antecedent can not be believed to exist, as where
we start from categorical truths and pass from them to a cate
gorical conclusion. If in both these cases there is logical
necessity, how can we ever be safe in assuming that such
necessity is found in existence?
1 8. (b) And when we pass from the necessary to the
possible, our conclusion remains. The possible, as such, exists
nowhere at all but in the heads of men. 19 The real is not
possible unless for a moment you think of it as unreal. When
the possible becomes real it ceases at once to be a mere possi
bility. For metaphysics I will not deny that the possible might
bear another meaning. But for logic, wherever a fact appears,
a possibility vanishes. It is not merely that the possible is
confined within the limits of human thinking. It can not
exist outside the domain of human doubt and human ignorance.
We have seen that to say " S P is possible," means,
" S P would follow under certain conditions, some at least
of which are not known to be present." And at this stage of
our enquiry, we may say at once that the sequel of such a
hypothetical judgment can not be taken to have actual exist
ence. The antecedent is not fact, the connection is not fact,
and the consequence is not fact. Or, if they are fact, their
" factual " character must be either unknown or put out of
our minds, when we treat them as possible. If we knew the
reality we should make no supposals; or, if we made them,
CHAP. VII THE MODALITY OF JUDGMENTS 2O?
we should know that they were made and, as such, did not
exist.
19. Common usage enforces our conclusion. The accused
obviously is guilty or is not guilty (Sigwart, 228). But we
say " It is possible he may be either." That is grossly false,
if you take it as asserting about the fact. A fact is not and
can not be an alternative. The possible existence of both
guilt and innocence is relative to our knowledge ; it exists only
in our heads, and outside them has no meaning. A ship has
sailed from Liverpool for America, and we say " It may have
arrived in New York, or again it may be at the bottom of the
sea." If you make this statement of the actual fact, it can not
be true. It is not possible that a ship should be in two places
at once. It must actually be somewhere; and, being actually
there, it is not possibly elsewhere, nor even possibly where it
is. The possibility is nothing beyond a supposition founded
on our real or hypothetical ignorance. Outside that ignorance
and that supposition it is not anything at all.
20. 20 We have now shown in the first place that
" necessary " and " possible " are both hypothetical. We have
seen in the second place that, at least for logic, they do not
exist, as such, in the world of fact. It remains to show that,
although " subjective," they must rest on a basis of categorical
assertion about reality.
(iii) We have only to recall the doctrine we reached in
our Second Chapter, to perceive at once the truth of this con
clusion. We saw there that all judgment in the end was
categorical. The basis of the hypothetical must be fact, and
without that basis the judgment would be false.
(a) We need give ourselves no pains to verify this result
in the case of necessity. We have seen that " S P is a
necessary truth" means "S P follows from something
else." This something else need not be fact, and, where it is
fact, that can not be assumed to make any difference to the
ideal connection. We can not say " In fact S P really is a
necessary consequence as such." But, the connection being
hypothetical, it on the other hand demands a basis which is
categorical. All necessity affirms a real ground explicit or
implicit. It thus so far has actual existence, not in itself, but
indirectly and simply in its ground (Chap. II.).
2O8 THE PRINCIPLES OF LOGIC BOOK I
21. When we come (b) to the possible, we are tempted
to think it has less actuality than belongs to the necessary, 21
since a part of its conditions remains unspecified. But, un
less we imply that the antecedent of the necessary exists in
fact, such a comparison would be illusory. In neither case can
we assume that antecedent or consequent exists; and when
we pass from what must be to what only may be, the ground
of the judgment seems in either case to be equally real.
In the merest hypothetical possibility we have an assertion
about actual fact. We affirm the necessity of S P following
from abed, conditions a part of which is supposed. And in
this we attribute the base of that connection to ultimate reality.
But in an ordinary assertion of possibility we imply the exist
ence of a part of abed, and thus make another statement about
fact. What we do in a case of so-called bare possibility again
is this. We first, on the strength of a privative judgment 22
( 13), conclude that the conditions are compatible with
reality. We then get the existence of a part of these unspeci
fied conditions by taking the real (because it is compatible)
as a joint condition. Thus reality, taken in some unknown
character and passing into the conditions, gives partial exist
ence unknown to the antecedent; while the same reality, in
another character, then guarantees the hypothetical sequence
of S P. We thus in the end (whatever we may think of
them) have two categorical assertions.
In " A disembodied spirit is possible " we start by denying
that it is impossible. This judgment rests, first, on the as
sumption that the real has an actual unknown quality, which,
in the second place, if you take it together with other unspeci
fied conditions, makes a hypothetical antecedent from which
" disembodied spirit " follows as a consequence. As the
ground of this second judgment we have to attribute another
unknown quality to the real to serve as the basis of the hypo
thetical connection. We have thus two assertions about the
nature of things.
22. Let us now take an instance of rational possibility.
If we say " It is possible A holds the ace of trumps," we know
there are conditions which would give this result. Such or
such an arrangement of the pack, such or such adjustments of
the muscles in the person who cuts and the person who deals,
CHAP. VII THE MODALITY OF JUDGMENTS 2OO,
must give the ace to A. The ground of this judgment consists
in mechanical and other laws, in accordance with which the
result would follow. These laws we regard as qualities of the
real, and this is one of our assertions. We next affirm that
an event has happened, viz. the dealing of the pack, which
presents in fact a certain part of our antecedent; in other
words, which gives reality to our supposed conditions to a
certain point and within a limit. The antecedent is not actual
in that full and especial form which gives the ace to A, but
it is there in that outlined and partial character which gives
the ace to some one player.
Everywhere, where we say that S P is possible, we
assert a real possibility of S P. We must assume a fact
which actually is, though it is not S P. And we assume that
this fact would under some conditions give us S P. That
is, we categorically assert the ground of an hypothetical judg
ment; and again we categorically assert the existence of a
fact which forms part of the antecedent. These two positive
assertions can everywhere be found in the most guarded state
ment about an actual possibility; and the former is required
for mere hypothetical possibility.
We have now accomplished the third task we set before us.
We have shown that the necessary as well as the possible has
a basis in fact and depends upon experience. A modal judg
ment has to make an assertion about reality. But the judg
ment itself expresses a truth which is not a fact. Modality is
but hypothetical, and hypothetical connections exist only in
our thoughts.
23. There are various points in connection with the sub
ject which claim our attention. We are accustomed to hear
of " capacities " and " faculties," and to use such phrases as
"potential energy," with but little regard for their actual
meaning. The "potential" is regarded as something real,
stored up outside existence, which hereafter may emerge in
the world of fact. This deplorable piece of effete metaphysics
takes a leading place in popular versions of the truths^ of
physics. Potential energy of course as such has no real exist
ence. It is merely the consequence in a hypothetical judgment
where the conditions are not all taken as actual. It would-be
better to say, " Though there is no energy, there is something
210 THE PRINCIPLES OF LOGIC BOOK I
actual which exists as the real possibility of energy." But
even this correction leaves a residue of error.
In strictness of speech a real possibility of S P can not
exist as such. 23 It should mean that reality which, if you
place it in an ideal construction, developes S P as a conse
quence. Itself is fact, and the attribute at the base of the
hypothetical judgment again is fact: but that judgment with
its elements can not be taken as fact. We are met by this
dilemma. Apart from the judgment the real is mere fact and
has no potentiality ; but within the judgment the reality itself
has ceased to be real. It has taken its place in a mental con
struction. Unless you are prepared to make ideal elements
determining forces in the processes of nature, you can not
properly believe in real possibilities. And I think, upon any
metaphysical theory, it would be better to find some other
expression.
24. But I shall hear : " Conditions are surely real. 24
Before life began its conditions could be present. And the
real possibility being a condition, as such you must allow it to
exist." In the above I see nothing but the same mistake. A
condition as such can not be said to exist. A condition is an
element in a hypothetical judgment and, outside that judgment,
it is no condition. If you say, " A exists and is an actual
condition of B," you are speaking inaccurately. What real
bond corresponds to your phrase? B is not in existence, and
if the other conditions do not appear, it will not exist. And
yet you say, " A is one of its conditions." If you wish to be
accurate you should say, " A is something which, if taken from
existence and placed within an ideal construction, mentally
gives rise to B." All beyond is unwarranted.
A condition ex vi termini does not as such exist; and to
define the cause as " the sum of the conditions " is to commit
a serious metaphysical mistake. It is saying, " The reality
which gives rise to reality is made up by adding mere ideas
together." * But the cause must be fact, and its effect must
* Of course the word sum again is open to criticism. It implies a
theory of the union of the elements, which certainly can not be taken
for granted. But to clear up this point a long digression would be
wanted. There are some remarks on causation in Book III. II.
Chap. II.
CHAP. VII THE MODALITY OF JUDGMENTS 211
be fact. We should do better to call the cause the meeting of
elements which, in the moment of their union, begin a process
which issues in the change we call the effect. An actual union
of actual elements is the cause. Each element by itself and
apart from this union is not even a condition. It becomes a
condition when you place it ideally in union with others. But,
in order to do that, you must make it an idea. In its character
of condition it must so far cease to be fact.
I am far from suggesting that the want of accuracy I have
just been noticing is always error. The phrases " potential "
and " condition " and " possibility " may be harmless and
useful. We ought all to be able to employ them safely. But
I fear that too often the case is otherwise. Too often they
prove mere engines of illusion, drowsy sops thrown down to
make reason slumber. If we believe in something that neither
is nor is not, but rules some strange middle-space between
existence and nothingness, let us at least have courage to
profess our opinion. Do not let us use words in using which
we take refuge from doubt in blind ambiguity.
25. It was blind ambiguity and little beside that lay at
the root of a controversy we remember. Amongst those who
vexed themselves and others with disputes on the " Perma
nent Possibilities of Sensation," 25 how many adopted the
obvious course of asking what lay hid in this spell ? We know
now that a real possibility means something which, in itself
and in fact, is no possibility, but must be something actual.
It is a veritable fact which actually exists; and to this we
must add here the idea of permanence. I suppose this means
that our actual fact has, against something else, at least a
relative duration and freedom from change. But now what is
this real or, I should say, these reals, which do not change, and
which an attribute of the reality guarantees to produce the
consequence of sensation, so soon, that is, as you have trans
formed them into ideas, and placed them within ideal con
structions? Are they real things, as distinct from sensations,
or, if not, what are they? I do not say that the asking this
question is enough to explode the theory of J. S. Mill. I will
say that the answer to it, however it is answered, must alter
at least the statement of that theory, and change at least some
of the points in dispute.
212 THE PRINCIPLES OF LOGIC BOOK I
I must be pardoned for seeing in another use of this delu
sive phrase an ambiguity which threatens the conclusion. If
there are difficulties in the way of making pleasure, in the
sense of atomic and momentary feelings, the end of life, can
we be said to escape them if we say Happiness is the end, and
if Happiness is defined as a permanent possibility of pleasant
feeling? We are met by the objection, If the end is pleasure
then it surely must lie in actual pleasure. But if it lies in
actual pleasure, it can hardly lie in mere possible pleasure.
Either the end is pleasure present and actual, such pleasure
again as has a quality (itself also pleasure) which guarantees
a hypothetical result of ideal pleasure, and this present pleasure
is also permanent either this, I say, or Hedonism is given up,
for something not pleasure is made the end. Here again I
must venture to make the remark that the answer to the objec
tion must modify at least the statement of the doctrine. 26
26. We may turn from these criticisms to a positive
result laid down by Sigwart (182, 227), and which our dis
cussion of possibility should have served to make clear. The
particular judgment, in the end and really, we found to be
nothing but a hypothetical in which the conditions remained
imperfect (Chap. II.). In the problematic form of judgment
we once again encounter the particular. The one is the other
under a disguise which disappears before our scrutiny. The
particular judgment " Some S is P " is the same as the judg
ment " S may be P." The assertion that S does actually exist
is not contained in the particular judgment, 27 any more than
it is in the problematic. " Some S is P " asserts no more than
that, S being given in ideal connection with other conditions,
of which conditions some part is assumed or supposed to be
actual, then P will follow. And this is precisely the sense of
" S may be P." Both are imperfect hypothetical judgments,
and both are founded on a basis of fact believed in or sup
posed ( 15).
27. Reality in itself is neither necessary, nor possible,
nor again impossible. These predicates (we must suppose in
logic) are not found as such outside our reflection. 28 And to
a knowledge and reflection that had command of the facts
nothing ever would be possible. The real would seem neces
sary, the unreal would seem impossible.
CHAP. VII THE MODALITY OF JUDGMENTS 213
The impossible is that which must be unreal. 29 We might
call it, if we chose, one kind of the necessary. When we say
of S P that it can not exist, we do not merely mean that in
ideal experiment the suggestion of S P directly vanishes.
We suppose for a moment that S P is real. Then on that
hypothesis we see that the conditions from which alone S P
would follow are directly or indirectly incompatible with the
real. The real, if changed in ideal construction so as to afford
the conditions of S P, is changed in such a way as to cease
to be itself. The alteration removes some attribute that we
assign to the real ; and this attribute, in our reflection, by means
of its exclusion of other possibilities, thus generates the im
possible and becomes the necessary.
Impossibility and necessity are correlative ideas. They
emerge together. The real does not seem necessary until it
has excluded what is incompatible, and reasserted the attribute
which is the ground of the exclusion. 30 Because of this attri
bute nothing else can be, and the attribute must be because
nothing else is. The unreal again is not impossible until we
have seen, not merely that it fails, but that its supposed success
would destroy what is, and what must be because its opposite
is excluded.
28. These ideas suggest a number of difficulties. In a
later book we must return to one of them, and may content
ourselves here with a brief indication. The impossible we see
must always imply a positive quality, known or assumed to
belong to the real. If X is impossible, this means and must
mean that an actual X would remove by its presence some
positive attribute we take to be real.
This bears on a point which already has engaged us
( 13, 21). The possible may be taken as anything whatever
which is not real nor yet impossible. 31 We objected to this
process, as frivolous in its result and insecure in its method.
The method is insecure, since it passes from the absence of
known incompatibility to the assumption of compatibility.
We take X to be compatible, if the real, as we know it, will
pass unabridged into a set of conditions which give X as a
consequence. Again, so far as we know, X is not incompatible,
when the suggestion of X as an attribute of the real calls
forth no answer affirmative or negative. And the doctrine
2321. I p
214 THE PRINCIPLES OF LOGIC BOOK I
we object to passes direct from want of incompatibility to
compatibility. In the one case X is possible, since it follows
from conditions a part of which is supplied by the real. But
in the other case we can say nothing about reality, unless we
make an enormous assumption.
29. We offer our suggested X to the real, and the real
is passive: X is not excluded. This privative judgment, if
we wish to understand it, must be reduced to an ordinary
negative where a positive quality in the subject rejects. What
is the positive quality here? It is the mental presence of the
real with such and such attributes. Now even the smallest
addition to these present attributes is an alteration of the real,
as we have it in our minds, against which it asserts itself in
the character it bears at the actual moment. In other words,
the base of our assertion that X is not rejected by the real, is
the assumption that the real differs in no point from the real
as at this moment it is present.
Now it is one thing to say " Whatever I judge true holds
good of reality," and another thing to say " What I fail to
judge true is absent from reality." And there is this very
great difference between them. In the first case we assume
that, whatever else may be, at least so much is true. In the
second we go so far as to say that what we have in our minds
is co-extensive with reality. But, if we hold to this, we ought
to go further. What the real does not exclude is not possible,
it is actual and necessary (pp. 118-19). And if we shrink
from this assertion, ought we to maintain that X is even
possible ?
30. The mistake is apparent. A privative judgment (as
we saw in Chapter III.) is not true of a subject, if that subject
is confined to something without the sphere of the predicate.
It then becomes obviously frustrate and unmeaning. You can
not predicate absence unless you predicate the positive space
from which the absent is lacking (Chap. III.). We shall find
that this holds good of ultimate reality. To say of it, " It is
without the rejection of X," is to say of it something which
has no meaning unless, so to speak, the place left empty by
this mere privation is occupied by a positive attribute. We
ought to be able to say There is a quality the presence of
which guarantees, or goes to guarantee, the absence of the
CHAP. VII THE MODALITY OF JUDGMENTS 215
exclusion of X. But this quality would obviously be either
the presence or compatibility of X. It is on the ground of this
presence or compatibility that we ought to assert the possibility
of X. For otherwise we fall into circular argument.
I will give an illustration. Suppose I were to say that an
isosceles triangle with three unequal angles is certainly pos
sible, and possible because it is not impossible. The universal
triangle, so far as I am supposed to know it, tells me nothing
about the nature of the isosceles. 32 On the privative judgment
that the universal triangle does not reject my idea,, I call it
possible. Is not this absurd ? It is absurd, because a privative
judgment, where the subject is left entirely undetermined in
respect of the suggestion, has no kind of meaning. Privation
gets a meaning, where the subject is determined by a quality
or an environment which we have reason to think would give
either the acceptance or the rejection of X. But, if we keep
entirely to the bare universal, we can not predicate absence,
since the space we call empty has no existence.
31. Or if our privative judgment has a meaning, then it
has a false meaning (Chap. III.). It rests on a confusion
between the universal and its psychological existence. We
take the idea, as we find it existing within our minds as a
psychical event, and then confound the determination it so gets
with its logical qualities. We say Here is a fact, and we can
not find that it does reject X. But the answer is simple. In
the first place we have the reductio ad absurdum. Since the
real has a quality on the ground of which it must accept or
decline every possible suggestion (Chap. V.) ; and since the
real here ex hyp. does not decline, it therefore must accept.
X is not possible, it is actual and necessary. In the next place
we directly deny the premise. In your experiment you have
not got the reality, and you ought to know that you have not
got it. If you wish to determine your empty universal so as
to get an answer in regard to X, you have nothing to do with
the psychological setting of this universal. The psychical
environment is not the space which, in respect to X, must be
full or empty. It is quite irrelevant and must be discarded.
You must fill out your idea by adding to its content. When
the content is supplied to such an extent that, in saying, " Re
jection of X is still absent/* you mean that some of the condi-
2l6 THE PRINCIPLES OF LOGIC BOOK I
tions of X are already present when you mean that there are
qualities which do affect the prospects of X, that a part of that
attribute, which when complete will accept or reject X, is
already there and that part is favourable then I admit you
may found possibility on your privative judgment. 33 The com
plaint I make is that your proceeding is frivolous. You have
in your hands the positive ground on which your judgment is
based directly, and you choose to proceed in a way which is
indirect and in this case circular (Chap. V. 28).
We should never trust a privative judgment until we have
seen its negative form. We should never trust a negative
judgment until we have seen its affirmative ground. We
should not take our impotence as a test of truth, until we at
least have tried to discover the positive counterpart of that
failure. The observance of these rules might preserve us from
errors which sometimes are dangerous.
The relation of necessity and impossibility to our mental
impotence is a subject which would carry us beyond the present
volume. We shall add some remarks in our concluding Book.
In the present chapter we have yet to see how modality is the
passage from judgment to reasoning. But, before we indicate
that transition, we must rapidly deal with a most important
application of modality, so far at least as to show its connec
tion with our general view.
32. If Logic professed to supply a method for the dis
covery of truth, the logician could not mention the theory of
Probability 34 without shame and confusion. The fruitful
results of the modern rival would offer themselves in damag
ing contrast with the sterility of the old and privileged veteran.
And, where a true view of the claims of logic makes this con
trast impossible, the logician, it may seem, has no right to
trespass within the limits of another science. The objection
is heightened when the writer on logic confesses himself un
acquainted with mathematics. He may appear in this case to
be talking about things of which he knows nothing.
But the objection rests on a misunderstanding. The prin
ciples on which probabilities are reckoned, the actual basis and
foundation of the theory, are not themselves mathematical.
Before mathematics can deal with the subject some assump-
CHAP. VII THE MODALITY OF JUDGMENTS 2I/
tions are necessary; and, though these assumptions can be
justified by their results, it is desirable to examine them simply
by themselves, to see what they are and whether they are true.
An enquiry of this sort, by whomsoever it is made, is a logical
enquiry.
33. Probability, we know, has to do with possibilities.
And starting from this, at the point we have reached, we
can go at once to an important result. No statement we make
about probabilities can, as such, be true of the actual facts.
This is half the truth, and we must not forget it. But it is not
more than half, nor is it even the half best worth remembering.
It is just as true that an assertion about chances does make an
affirmation about reality. Every hypothetical judgment, we
have seen, must rest upon some categorical basis. The con
clusions we have adopted enable us to say without further
enquiry, Any theory which calls the doctrine of chances merely
" objective," or merely " subjective," is certainly false. It
is a vicious alternative which, if it were sound, would upset
general results we have found to be true, and which is con
trary to the special facts of the case.
34. I shall return hereafter to the consideration of this
root-mistake, but it is better to begin with a statement of the
truth. We are to omit the subject of probability in general,
and confine ourselves to the particular instance of that which
is called mathematical probability. And the point which first
presents itself to our notice, is the necessity of limiting the
possibilities. Before we can advance a single step we must
have the whole of the chances before us. This exhaustive
survey may rest on knowledge or on arbitrary assumption, but
it is always presupposed. The calculation of chances, in a
word, must be based on a disjunctive judgment, and the hypo
thetical assertions, which represent the chances, take place
within the bounds of that judgment. But disjunction, as we
know (Chap. IV.), implies a categorical foundation. This
basis of fact is the condition of our assertions about the
chances.
35. Take a simple instance. A die has been thrown
without our knowledge, or is now about to be thrown before
us. As a previous step to reckoning the chances we must
make some categoric statements. We must be able to say,
2l8 THE PRINCIPLES OF LOGIC BOOK I
The die will fall (or has fallen), and will fall beside in a
certain way. It must have one side up, and this, whatever else
it is, will at least be not other than all these six sides. It must
have a quality determined as what is common to the six, and
not determined as what will be none of them. On this cate
gorical foundation all the rest is based, and without it there is
no possibility of advance.
This result has a most important application. There is no
probability before all reality. There is none which does not
stand on a basis of fact assumed or actual, and which is not a
further development of that basis.
36. We have seen the foundation of our disjunctive
judgment. What is it that completes it? It is of course the
setting out of exclusive alternatives. These alternative possi
bilities are given us in the various hypothetical judgments
which we are able to make as to the number on the face which
we know is lying uppermost, or which will so lie. We have
now a disjunctive judgment, enclosing an exhaustive statement
of exclusive possibilities. But we have not yet got to mathe
matical probability. To reach this a further step is to be made.
We must take the possibilities all to be equal, or, if they are
not equal, we must make them comparable.
37. The possibilities must all be equally probable. What
does this mean? It means that there is no more to be said
for one than there is for another. The possibilities are
each a hypothetical result from certain conditions ; and these
results are equal, when, in the first place, they follow each
from no more than one single set of conditions, and when
in the second place, I attach no more weight to any one
set than I do to the others. When, in short, I have no more
reason for making one hypothetical judgment than I have
for making any other, they are possible alike and equally
probable.
X must be a or b or c. X qualified by certain conditions
would be a, if qualified by other conditions would be b f and so
with c. If in my knowledge I have any ground 35 for taking X
in one set of conditions rather than in another, then a, b, and c
are not equally likely. If such a ground is absent, then they
are equal. Again, if X will give a with a single set of con
ditions, and b or c with more than one set, the chances are
CHAP. VII THE MODALITY OF JUDGMENTS 219
different in the different cases. 36 Otherwise they are the
same.
38. If the separate alternatives are not found equal, then
we must either give up our attempt to reckon chances, or must
find some common unit of value. We must analyze one possi
bility, and find, perhaps, that its final result is really two; or
that, though the final result is one, it will follow from two or
three sets of conditions, and hence can stand for two or three
units. In these cases there were two hypothetical judgments
which we joined in one. Again, if we can not divide the
greater, we may join the smaller. By considering two or
more alternatives as one, we raise the whole to a unit of
higher value.
39- Where we have a disjunction the alternatives of
which are equally likely, or are reduced to alternatives which
are equally likely, we can state the chances. Since we have
the same ground to think every possibility true, the probability
of each is just the same quantity. In our knowledge they
divide the actual fact between them equally. The reality then
we represent as unity, and each alternative possibility we
represent by a fraction, of which the denominator is the number
of equal alternatives, and the numerator is one. Against our
belief in the general fact we have nothing to set. Against
any one of its developments we have to set the whole of the
others.
40. Take the instance of the die. We know it will fall
in a certain way. So much is categorical, and we have now to
determine the further possibilities. What are the conditions
from which in each case our hypothetical results proceed?
They are first the general character of the fall, those positive
and negative general conditions from which comes a fall with
one of the six faces up, and no more than one. Do these
furnish a ground for making one fall more likely than others?
Clearly they do not.
The general conditions, which we have considered so far,
are known to exist. The fact must take place in such a way
that these conditions will be realized. But, beside this known
* Wolff has expressed the principle very well, " Probabilior est pro-
positio, si subjecto predicatum tribuitur ob plura requisita ad veritatem,
quam si tribuitur ob pauciora."
22O THE PRINCIPLES OF LOGIC BOOK I
element, there are a number of circumstances about which we
are in doubt. The particular throw must be the result of one
particular position of the die, the contraction of particular
muscles in the thrower, and the character of the surface which
receives the fall. The number of different sets of conditions
which would lead to the result, is very great, and in part per
haps unknown. 37 Still this makes no difference. They are all
at least known or assumed to be compatible with the reality,
and they lead indifferently to any one of the six results.
With respect to each face we have exactly as much reason
to think it uppermost, as we have to think any other face
uppermost. The chances are equal; and since they are six,
and since they divide the sphere of a single unity, they are
each one-sixth. We have a certain reason to expect one face,
say for instance four, but we have the same reason five times
over not to look for four.
41. Now suppose one face loaded. The final possibilities
are still six in number, but their value is not equal. There are
more sets of conditions, which would lead to the loaded face
being downwards, than sets which would bring the opposite
face into the same position. I have thus more reason to look
for one than I have to expect the rest. My task is now
to get a fresh unit by breaking up some or all of the
possibilities. If I succeed in this, the whole will again be
divided into fractions expressing the respective chances, but
these fractions will be unequal. The units of reason to
look for each face will be more in one case and less in
another.
42. The above is, I think, the entire foundation of
the doctrine of chances. It is perfectly simple and entirely
rational. It need not appeal as a warrant for its existence to
those splendid successes which make it indispensable. Rightly
understood its principles by themselves are abundantly clear
and beyond all controversy.
We have no cause and no right to follow the theory even
into its first and most simple applications, but we can not
pass over an important point. Where we can not determine
numerically the conditions of different possibilities in a way
that is direct, we can proceed indirectly. For example, in
the case of a loaded die, I may have no data for calculating
CHAP. VII THE MODALITY OF JUDGMENTS 221
the chances, since I may not have accurate knowledge of the
conditions. But I can go to the result in another way. I
can throw the die a number of times, and, setting down the
numbers for every face, can then in view of an unknown throw
state the fractions in accordance with the relations of these
numbers. But this inverse process implies no appeal to a
different principle.
Let us perceive its nature. I assume that I have no reason
whatever to think the unknown throw, which I wish to deter
mine, different from the rest. I therefore take it as simply the
same. But I can not take it as the same as any one, 38 for then
it must be different from others. It is therefore the same in
its general character, with possible alternatives which fall
within the data supplied by the actual series. It remains to
reduce these possibilities to fractions.
We are obliged to reason from effect to cause. If a known
cause A would produce a given effect, and if we have no
reason whatever to believe in any other cause, 39 we assume we
can go from the effect to A. The effect we are considering is
a certain series, and the question is, Do we know the one cause
which would produce that series?
I hardly think we do. However long and however regular
the series may be, we can never say that there is one and but
one disposition of elements, which leads and must lead to the
series we have seen. And if we could say this, and assume
beside that the unknown throw will follow from this deter
minate cause, then there would no longer be any probability
in the case. The whole thing would be understood and cer
tain. But we obviously do not know this one special cause
which would produce our series. We can determine no more
than its general character. It must be such a cause as would
give a series possessing certain numerical relations. And we
assume that an arrangement of which we can say, " It is the
real possibility, with respect to any throw, of chances disposed
in those numerical relations," is such a cause. It is therefore
probable that the series is the effect of this cause. And since
(by another assumption) we have no reason to believe in any
other cause, it is certain that the series has resulted from this
cause. And since again we assume that the unknown throw
has a general character the same as that possessed by the
222 THE PRINCIPLES OF LOGIC BOOK I
series, we proceed without any further hesitation to reckon its
chances directly.
43. We may notice in passing that, if we had to suppose
that the series might arise from some other cause, beside the
one we have already mentioned, a further complication would
be at once introduced. 40 But this we need not consider; for
the most simple case of inverse or inductive probable reasoning
proceeds as above, and is sufficient to show the principle
employed. And we may notice again that there are assump
tions involved, which we shall have to discuss in a following
section. We may here remark that, if we are not satisfied
with a probable conclusion, if we go on to assert that the series
has actually been produced by a cause of a certain character,
which will operate again in the unknown throw, our assump
tion is doubtful, if it is not false. But, to resume, however
this point may be decided hereafter, the nature of our reason
ing on chances is the same in inductive as it is in deductive
probability. The chances of the new throw represent the pro
portion of our grounds for belief. The fact that these grounds
have been supplied by a series, and the reduction of that
series to its actual or probable cause, makes no difference to
the principle. What grounds have we got for determining the
throw that is to take place? Those grounds which as causes
have determined the known series. What are those grounds?
They are those from which we go to the series in hypothetical
judgments. What is the nature of these? We do not know
them exactly, but, so far as known, we can arrange them as
units, and groups of units, which stand to one another in
certain relations. But grounds for belief, which stand to one
another in numerical relations, are what we mean by the
chances of the throw.
44. From this hurried account of the general nature of
what has been called the Logic of Chance, we pass to the
removal of erroneous ideas. It is evident, in the first place,
that probability does not affirm about the fact as such. The
event may be past and absolutely fixed, but our alternatives
continue to be truly asserted. But, on the other hand, if the
chances are not facts, are they nothing at all but our belief
about facts? Is probability simply the quantity of the belief
we happen to possess? No, that once more would be in-
CHAP. VII THE MODALITY OF JUDGMENTS 223
correct. We need not trouble ourselves to discuss the mean
ing assignable to "quantity of belief," for the whole idea
must be banished at once. The amount of our belief is
psychological, the probability of a fact is always logical. No
matter what it is we happen to believe in, whether it exist or
do not exist, our belief itself is unaffected. But an asser
tion about chances must be true or false. It depends on fact
and refers to that, though it is not true or false of the special
fact in question.
45. We have not contradicted ourselves. Probability
tells us what we ought to believe, what we ought to believe on
certain data. These data are assertions about reality, and the
conclusion as to what we ought to believe results from a com
parison of our grounds for belief. Since these grounds are
the conditions of hypothetical judgments, the judgments again
must be true or false, and they rest upon categorical bases.
In these two points, (i) the general ground of the disjunction,
and (ii) the special grounds of the alternatives, probability is
true or false of reality. We call it " objective."
On the other hand probability is " subjective." If I say
"The probability of S P is y 1 ^," this may be true although
S P is impossible. It is true to-day, and to-morrow it is
true that the chance is -jfo, and the next day |. The belief
must change with my varying information, and it is true
throughout these variations, and is true though every one of
them is an error. How can this be " objective "? It seems to
lack the very differentia of truth.
The solution is obvious. Within the probability 41 what is
true or false is not the premises but the conclusion I draw
from them. Given certain assumptions, there is only one way
of stating the chances. Given certain grounds for belief or
disbelief, there is only one correct inference to the fractional
result. This result is neither " subjective " nor " relative,"
if those phrases mean that it might be different with different
men. From certain data there is but one conclusion, and, if
this is different in different heads, then one or both of these
heads is mistaken. Probability is no more " relative " and
" subjective " than is any other act of logical inference from
hypothetical premises. It is relative to the data with which
it has to deal, and is not relative in any other sense. It starts
224 THE PRINCIPLES OF LOGIC BOOK I
with certain assumptions about the nature of the fact, and it
tells us what, if we are ready to take these assumptions as
true, we ought to believe in consequence. If this is not to
be " objective " and necessary, then farewell for ever to both
these phrases.
Probability as such is not true of the fact, but it always
has a reference to fact. It is concerned with certain special
deductions from the basis of propositions which are true or
false in fact. 42 It certainly is confined to those deductions.
But it possesses, when kept within its own limits, truth abso
lute and unquestionable and that never can vary.
46. Probability is neither simply " subjective " nbr yet
simply " objective." This vicious alternative is the first of
the errors we have to dismiss. It is allied to another elemen
tary mistake, which must next engage us.
It is mere misunderstanding which supposes that chance
involves a series, and that the logic of probability is essentially
concerned with statistical frequency. It is mere error which
finds the necessary meaning of " The probability of S P is
i," in " Once in a series of four events S P will be true."
This mistaken theory contains some truth, but has taken one
part of the truth for the whole.
47. Is the series real or is it imaginary? Let us first take
it as real, as something that exists, has existed, or will exist.
Must the judgment " The chance of S P is J," refer always
and essentially to an actual series? The assertion would be
preposterous. The event S P may be hypothetical. It may
have a probability of J on the ground of assumptions which
we know are not true. Where is then the real series? The
event again may be unique. The chance of my dying before
I am forty is, say, ^. Does this mean that if I die three
times, one case will realize the possibility? The event once
more need not be an event. It need be nothing which ever
could happen in time, and we should deceive ourselves if we
gave it that name. " It is even chances that the soul is noth
ing but a function of the body " : the probability is J. " It is
one to two that God is a person " : the probability is -J-. " It is
one to ninety-nine that the will is free " : the probability is you-*
* Of course I do not mean these fractions as an expression of my
opinion.
CHAP. VII THE MODALITY OF JUDGMENTS 225
It may be said, no doubt, that the figures are illusory, and that
we can not find any unit of value; but I hardly think this
objection can stand. Admit that the case is highly improbable,
it still is possible that in the mind of some man the grounds,
present for and against such judgments as these, might be
reduced to a common denominator. How can we deny it ? and,
if we do not deny it, what becomes of our series?
48. The series clearly can not be real. Let us take it as
imaginary. The question is then, Is such a fictitious imagi
nary series the proper way in which to represent probability?
Can we say, It is my meaning, or the only true way in which
to render my meaning? This, I think, would be an absurdity.
It will not stand a serious examination.
Probability can indeed be always represented by a fictitious
series. " It is two to one he is guilty " may be rendered by
saying, " Two times out of three a verdict on such evidence as
this would be right." Even when the possibility is unique, we
yet can abstract from that quality and say, " Men such as I am
would die before forty two times out of three." Nay, even
when we leave events altogether behind us, we still can keep
up this mode of expression by a fictitious series. Imaginary
judgments here become the events. " It is even chances the
soul is a bodily function " may be translated by " In making
such judgments as this a man would be wrong through one
half of the series and right through the other half."
But is such a way of putting our meaning the real and
essential idea we entertain ? When we wish to be correct, are
we forced so to speak? It always is possible, but is it always
necessary? Is it always even natural? And then there re
mains a question in reserve, Is it not incorrect?
49. Let us begin with its possibility. Why can we
always express the chances by making use of a fictitious series?
For this reason. When the grounds from which we reckon
are considered as causes, we are accustomed to suppose that
their issue in a series of phenomena will exhibit the same
numerical proportions that our fractions possess. If so, then
on one side the causes (or cause) of the series and, on the
other side, the series itself will answer to each other. We say
what we have to say of the cause, indifferently, either by
stating its effects, or by setting out the reasons it gives us to
226 THE PRINCIPLES OF LOGIC BOOK I
expect one effect and not another. This is natural enough
where the fictitious series is imagined to be real. It is not so
natural with unique events, where the series strikes us as
specially manufactured to express the chance. It is still less
natural where the possibility itself is not an event, and the
series is nothing but the series of judgments. But even here
it still is possible. Since psychologically the grounds are
causes (p. 545), since, in other words, the logical reasons
which necessitate the result are what produces the fact of the
judgment, I can imagine, if I please, a series of judgments, and
say, Since these numerically answer to the reasons I have,
therefore such a numerical part will be true. The expression
by a series is here quite unnatural, but it still is possible.
50. The issuing of a certain series is only one way of
putting probability. It is sometimes a natural way; it is
sometimes a not unnatural way; it is sometimes most un
natural. But it is never the right way ; it is never more than
a manner of statement; it is never the real meaning and in
tent. Even when I start from an actual series, I must leave
it before I can get to probability. I must go to its cause by
what is called a method of reduction, by an inductive hy
pothesis. And I can not simply define this cause as that which
either has issued, or will issue, in a certain series. I can not
do the first, for that would be certainty and not probability.
And I can not do the second without an assumption which I
am unable to justify.
It is obvious, in the first place, that to take a series, and
to say " The cause which has produced this series has pro
duced this series " is merely frivolous. On the other hand, if I
add " will produce this very same series on other occasions,"
that is not frivolous, but is either irrelevant or else unjustifi
able. If it means " In another case where the conditions are
not discrepant, the same cause will be followed by the same
effect," that assertion is true but is quite irrelevant, because
merely hypothetical. For in an actual fresh case I do not
know the fresh conditions, and, if I did, I do not know what
the old cause specially is. I do not know the actual cause (or
causes) of the former series. I do not know that these are
present again in the unknown case. I do not know what
conditions the fresh case brings ; and, if I did, I might be
CHAP. VII THE MODALITY OF JUDGMENTS 227
unable to deduce the result from the complication of elements.
In short I can not go from a given series to an unknown
series or an unknown case. To reason directly is of course
impossible, and I can not reason indirectly through the cause,
because I do not know the actual cause in one case or the
other. Its general character, to a certain limit, I do know in
one case, and assume in the other, but this general character
does not imply a series, and the individual cause itself I do
not know and so can not use.
The upshot of this is that within probability you really
have not got the effects on one side and the cause on the other.
If then you give as the essence of probability the produc
tion of a series with certain marks, you go beyond what your
data will warrant. For your actual series has now 43 ceased to
be taken as a series of events produced in time. It has degene
rated into a set of conflicting reasons, possibilities as to an
event of a certain sort, which in default of detailed information
I use in order to determine my judgment. My probabilities
do not represent a series as such. I now have nothing what
ever but conflicting grounds for belief and expectation, grounds
for belief as to any fresh case or number of cases that have the
general character of my series. And these fractional reasons,
which are all I can work with, are the same in any one new
instance as in any number of new instances. Thus the sup
posed differentia of an imagined series, in the first place,
would add nothing to the probability which already exists apart
from the idea of any series. But, in the second place, if it
does add, and if it goes on to say that the series must have a
character answering to the expectation, then it adds what is
false.
51. And with this we come to an obstinate illusion.
There is a common idea that, if you know the chances of any
set of events, you really know the character of the actual events
which are to take place. It is supposed that the series will
correspond to the fractions. For instance, if we take the case
of a die, the chance of any one face is J-, and from this we
argue, " In a series of throws each face will be seen in one-
sixth of the run." But we have no right to any such assertion.
Not knowing the cause, knowing only a part while part is
hidden, we can say no more than that onr information leads
228 THE PRINCIPLES OF LOGIC BOOK I
us to expect a certain result. It is monstrous to argue that
therefore that certain result must happen. It is false reason
ing a priori, and a posteriori the facts confute it. It is not
found in experiment that actual runs do always, or often, 44
correspond exactly to the fractions of the chances. That cor
respondence is after all the most probable event, but to make
it more is a fundamental error.
52. I shall return to the truth contained in this error,
but at present we must try to get rid, if we can, of the error
itself. We may expect an objection. " Experiment," it will
be said, " does not disprove the assertion that is made. That
assertion is not that in a finite series the numbers will come
right. They will come right only if we go on long enough,
and in the long run." But what is this " long run " ? It is
an ambiguity or else a fiction. Does it mean a finite time?
Then the assertion is false. Does it mean a time which has
no end, an infinite time? Then the assertion is nonsense. An
infinite series is of course not possible. It is self-contradic
tory; it could not be real. And to say that something will
certainly happen under impossible conditions, is far removed
from asserting its reality. The affirmation that an event may
be assumed to take place in an infinite series, and not outside
it, would, in the mouth of any one who knew what he meant,
be a suggestion that the event may not take place at all. 45
53. I hope I need not protest that I am hardly so foolish
as to attempt to offer an ignorant objection to the use of
infinities and infinitesimals within the sphere of mathematics. 40
I would rather say nothing at all on this matter than appear
as presuming to doubt the validity of processes employed
by the greatest men in the exactest of sciences. But I shall
not so be misunderstood. An objection to the use within cer
tain sciences of certain ideas must be taken within the limits
of those sciences. But the use of these ideas outside their
science carries with it no authority, and, so long as the general
meaning is understood, may be criticized by men who are igno
rant of the science in which the ideas give brilliant results. It
is so with infinity. Outside mathematics an infinite number
is an idea that attempts to solder elements which are abso
lutely discrepant. It could not exist until the world, as known
in our experience, was utterly shattered and transmuted from
CHAP. VII THE MODALITY OF JUDGMENTS 22Q
the roots. I could not find an illustration I would sooner
use to express impossibility. And it is this idea which, out
side mathematics, is presented to us in the error we are
combating. Mr. Venn, for whose powers I feel great respect,
and from whose Logic of Chance we all can learn, holds that
in the long run every chance will be realized. This " long
run," he tells us, is an infinite series (p. 146), and (unless I
very much misunderstand him) he goes on to call it a " physi
cal fact" (p. 163). His book is much injured by this terrible
piece of bad metaphysics. He has translated a mathematical
idea into a world where it becomes an absurdity.
54. We must everywhere protest against the introduction
of such fictions into logic, and protest especially where the
ideas are not offered in the shape of fictions. The formula
of the " long run " must be banished from logic, and must
carry with it a kindred illusion in the imbecile phrase, " if
you go on long enough." " The event," we are told, " will
answer to the chances." But it does not answer. "Oh, it
will, if you only will go on long enough. You toss a coin
and, the chances being equal, if you only go on long enough,
the number of heads and tails will be the same." But this is
ridiculous. If I toss the coin until the numbers are equal, of
course they will be equal. If I toss it once more then, by the
hypothesis, they become unequal I might just as well say,
" If I only go on long enough the events will certainly not
answer to the chances." 4T Your formula is false or else tauto-
logous. If it means " Suppose the numbers are equal, and sup
pose I then stop, the numbers will be equal," that is surely
tautologous. But if it means the numbers will turn out equal
in an infinite series, then that is false, for such a series is im
possible.*
55. But let us turn from the error and see the truth
which lies hid beneath it. It is false that the chances must
be realized in a series. It is however true that they most
probably will be, and true again that this probability is in
creased, the greater the length we give to our series. What
* Cf. Lotze, Logik, 437. I may remark that if the formula meant,
" The series is sure to cross and re-cross the point of equality," then,
in the first place it would be false, since there is no certainty; and, in
the second place, such an oscillation is not equality.
2321. i Q
23O THE PRINCIPLES OF LOGIC BOOK I
reason have we for holding these two beliefs? (i) Why do
we think that the series will probably answer to the fractions ?
(ii) Why do we think that in a longer series the correspondence
is more likely?
(i) Probability, we have seen, is not essentially concerned
with any series. It is based upon grounds which, even if we
consider them as real, may not be causal in the sense of pro
ductive of events in time. They may be causes cognoscendi
and not essendi. 48 It is when our grounds are grounds for
belief as to the nature of an agency, which is to produce events
in time, that we are able to consider them as causal elements.
And this is the case we have to suppose.
We know that a series is to be thrown with a single die.
Let us first take one throw. That will have a cause, and the
cause is only partially known. We know that it is complex
and consists of many elements. Of these elements, so far as
they are distinctly known, five parts are hostile to any single
face and but one part favourable. The unknown residue, so
far as it determines the case, is quite unknown; and, though
it is not indifferent and though it can not be so, yet within
our knowledge we must take it as indifferent. In the cause
of the single throw there are therefore, beside the unknown
factors, one sixth part of the agencies favourable to each face.
Now take the whole series. That series, before I throw it,
is as certain and fixed as though I had thrown it already.
But here again I do not know the causes. About one part I
know nothing in detail, and so I must take it as being in
different, although I am sure it is not so in reality. Of the
rest of the agencies, which I suppose, one sixth is favourable
to each face, and five sixths hostile. What conclusion can I
draw as to the nature of the series? Will one agency pro
duce that result which we suppose it would produce, did the
others not intervene? Will in each case of the series the sup
posed majority of agents prevail? We have no means of
knowing. The series, absolutely fixed, is fixed by what we
do not comprehend. We must take the possibilities, and
the possibility for which there is most ground is the likeliest.
There is less ground to think that in a series of six throws
one face will be absent, and one twice present, than that
all should show once. 49 In the latter case we do but make
CHAP. VII THE MODALITY OF JUDGMENTS 231
ignorance a ground for complete indifference. In the former
case we give a preference without any kind of warrant. It is
not that each face has any sort of claim to come uppermost
once. It is that no face has more claim than another to show
itself twice. This is why we think the most likely series, or
the least unlikely, will be that which corresponds to our
fractions.
56. (ii) But why, it may be asked, does the length of
the series increase this probability? Does the greater length
add any new ground to those we have for believing in the
correspondence of the events with the chances? No, it does
not add any. Does it decrease any ground we had before for
thinking the opposite? Yes, it does do that; and it does it, I
think, in the following way. The unknown residuum in the
cause of each throw was assumed to be indifferent. But it was
not at all assumed to be passive. It supplies the determining
element in the cause. It decides for one face, though we do
not know for which face it decides. Now how does it de
cide? Does it act regularly and in strict rotation, or is it ir
regular? That we do not know; but, taking the possibilities,
we believe that those in favour of irregularity are more than
those in favour of rotation. It is therefore most probable that
our series will turn out to be irregular. But, since we know no
reason to prefer any one face, we can not say that any pro
portion other than strict equality is the most probable. How
are these assertions to be reconciled? Very easily in this
way. Owing to the assumed indifference of the causal residue
the faces will probably appear in their right numbers; but,
because of its irregularity, their appearance will probably be
irregular, and irregular to an extent to which we can assign
no limit. To combine these attributes it is necessary to sup
pose that the whole series will be most probably regular, but
will contain periodic irregularities. The greater the irregu
larity becomes, the less grows the chance of a final regu
larity, unless the series is proportionately lengthened. There
fore, since we can fix no limit to the irregular sequence of the
faces, we conclude that, the longer the series becomes, the
greater becomes the probability of a regular result. And this
is a rational, and necessary conclusion from our imperfect
data.
232 THE PRINCIPLES OF LOGIC BOOK I
57. It is true that, if you make a series longer, you de
crease the chance of irregularity. It is true that, if per
impossibile the series were so long that, in comparison with
its length, every possible abnormal run was a period which
other periods might easily balance in the completed cycle if,
I say, per impossibile this phantom could be real, it is true
that the above chance of irregularity would vanish. If we as
sume that what we do know gives us reason to believe in a
series correspondent to our fractions; if we next assume, by
virtue of a fiction, that the unknown residue gives no reason
to believe in an unbalanced irregularity, then on these assump
tions we may go to a conclusion, and we have no ground to
disbelieve the statement that the series will exhibit the relations
of the chances. But the first assumption is based on ignorance,
and the second is based on a known impossibility. 50 If we
mean to speak about a series of events that could ever happen,
we can say but this. It is certain there will be a series, each
throw of which will give a single face. It is possible that in
a series of any length but one single face should appear
throughout. No arrangement is impossible. It is most prob
able that the events will answer to the fractions, but against
that probability there still remains another consideration, the
chance arising from the possible irregularity of one part of the
causal elements. This fraction is diminished by each increase
of the series, but it does not disappear and it can not disappear.
58. We do not know that in the long run the events
will correspond to the probabilities. We do not know that,
if we go on long enough, every chance will be realized. It is
mere superstition which leads us to believe in the reality of
the fiction which gives birth to these chimaeras. When I see
the demonstrations, offered to gamblers against a bank, which
prove to them that in the long run they can not but lose, I say
to myself, On which side do I see the darker illusion? And I
answer, On both sides the illusion is the same. For what is
the root of the gambler s " system "? Is it not his belief that
independent events are affected by each other? But this
belief is a strict deduction from the premises offered him. If
he really must lose, if there really is a cycle in which the
chances must all be realized, then, let him observe the begin
ning of the cycle, and mark the irregularities, and he surely
CHAP. VII THE MODALITY OF JUDGMENTS 233
must win. Since to equalize the numbers the end of the
cycle must balance the beginning, he can speculate on that
balance and his " system " is right. " Oh, but it is wrong, for
the series is not finite. It is only after an infinite duration of
play that the balance is struck. It is absurd to say he can be
sure of winning." But is it not then equally absurd to say
that he is sure to lose? If you mean he must have lost by the
end of his life, you have just admitted your assertion to be
false. If you mean he must have lost when he has got to the
end of infinite time, confess that your meaning is something
like nonsense, and that the gambler is right in imagining that
you, as a rational man, must mean something else. The
truth is that your common assumption is false. There is no
must about it. The chances consist of grounds for belief in
the nature of a series no event of which is known. And all
they tell us is this: that we have more reason to expect one
thing than we have to expect another, and that the increased
length of the series proportionately decreases a reason for
doubt, which never quite vanishes.
5Q. 51 I must not be suspected of a desire to intrude into
mathematics if, in this connection, I venture to remark on a
well-known paradox. I am to toss a coin, and to go on toss
ing so long as I throw heads and nothing but heads. I am to
receive 2 if I throw head once ; if I throw head twice I am
to win 4; for three successive heads I get 8, and so on
accordingly. The series is supposed to have no limit except
the appearance of a tail. And the question arises, how much
am I to pay for the privilege of one single trial ? The answer
given is, An infinite sum; for it is possible I may throw an
infinite series of nothing but heads (vid. De Morgan, Proba
bilities, p. 99). The reasoning on which this conclusion seems
to rest is exceedingly simple, and I need hardly say that I do
not doubt its perfect validity within mathematics. And I think
I see that no other answer can possibly be given. Unless an
arbitrary limit is fixed, I may be allowed to say in all humility
that I think I understand that, if this possibility has any
value at all, then the worth of my chance is either incalculable
or else is infinite. If this answer is given me by a special
science, I dutifully receive it as true within that science.
But if I am told that in actual fact the result is true, I
234 THE PRINCIPLES OF LOGIC BOOK I
must be allowed to protest. I must be permitted to remark
that the reasoning is absurd and the result is nonsense. I do
not mean merely that it is absurd if we take it as a practical
precept, because a man can not live for ever, and all the
money in the world is finite. I mean that it is a theoretical
absurdity. It is not true ideally any more than really. Since
an infinite sum is an impossibility, the infinite series can not
possibly be thrown. There is no chance whatever. There is
no fraction at all. It is nothing I could win. It is nothing
I can expect. It is nothing for which I can reasonably pay.
The result is a deduction from premises known to be false
and impossible.
It is idle to answer that the problem is " stated in the
ideal form " (Venn, ibid. p. 137). There is a difference surely
between ideals which as such do not exist, because they are
abstractions, and ideals which are downright self-contradic
tions. It is one thing to say, " There is a connection between
abstract elements, so that when one of these is found as a
real quality we shall have the other," and another thing to
continue this assertion, when we know that the first of these
elements is self-contradictory and could not possibly be any
quality of reality. In this latter case what is true of fact can
not be the consequence of an impossibility, but only the basis
of the hypothetical judgment. Neither antecedent nor con
sequent is taken as real or even as possible. But in a com
mon abstract judgment the antecedent is taken as at least
a possible quality of the world. 52 Mr. Venn perhaps would
question this difference between an abstraction and an im
possibility, and would perhaps assert that an infinite series is
really possible. In any case I must be allowed to protest
against the invasion of logical reason by mathematical fic
tions. If an infinite series is thought possible, we should be
told how it can be possible. If it is not thought possible, it
should not be offered us as if it were.
60. There are other points in the theory of chances
which have logical interest, but we have no space to discuss
them here. We have said enough to make clear the relation
in which that theory stands to our general principles. We
have to avoid the fiction of the infinite long run, and the
vicious alternative of " objective " and " subjective," and the
CHAP. VII THE MODALITY OF JUDGMENTS 235
false assumption that the essence of chance involves a series
of events in time. If we keep clear of these pitfalls, the truth
is by no means difficult to reach, and we hope above to have
stated it clearly in its general form.*
61. There is an aspect of modality we have neglected
to notice. The omission was intentional, and the mention of
this aspect has been reserved for the present place. There is
an old doctrine which connects universality with necessity,
and that doctrine is true. The necessary we saw was the
ideal consequent, and such a consequent can not come except
from an ideal antecedent. You never can say " B follows
from A," " is because of A," " must be, given A," unless A is
present in a determinate form. A must be a content without
any mixture of mere sensuous conditions. 53 It must be
ideal, abstract, and so universal. If the ancient doctrine on its
logical side may suffer some loss, since necessity becomes for
logic hypothetical, yet it stands all the firmer. The " because "
can not couple anything but universals.
62. We may notice an error which creeps in with this
truth. 5 * The antecedent in necessity must be universal, but it
need not be more universal than the consequent. Where we
say " because " we do not always appeal to anything more
abstractly general than that which follows from our reason.
" A must be equal to B, because C is equal to both B and A,"
" A must be removed by one foot from C, since B, which
touches both in a certain manner, is one foot long." The
consequence is not less general than the antecedent, and we
deceive ourselves in thinking it always must be so.
No doubt in the cases where you say " because " you may
find what we call the principle of the sequence, and that of
course must be more abstract than the actual consequent.
But the principle is not the antecedent itself. It is the base
of the general connection, not the sufficient reason of the
particular consequent. There is no more need for the con
sequent to be more concrete than the antecedent, than there is
for the effect to be more special than the cause. These ideas
are nothing but kindred illusions (Book III. Chap. II.).
*The books from which on this subject I have learnt most are
Lotze, Logik; Sigwart, Logik; Wundt, Logik; Jevons, Principles of
Science; Venn, Logic of Chance; De Morgan, Probabilities.
236 THE PRINCIPLES OF LOGIC BOOK I
63. We shall have to return hereafter to this point, but
have been right to anticipate here the conclusion. We have
indeed begun some time back to anticipate the conclusions we
have to reach in the following Books, since already unaware
we have entered their territory. Silently before in the second
Chapter, and now almost explicitly we have made the transi
tion from judgment to inference. In both the latter kinds
of modality we reason openly. The possible is that which
we argue would follow from certain premises, part of which
are taken as true. The necessary is that which we infer must
follow, if its grounds are premised. It was in this sense
that possibility was one kind of necessity. In both alike we
deal with conclusions, reasoned results from given data. In
logic we find that a necessary truth is really an inference, and
an inference is nothing but a necessary truth. This is the
secret which we hardly have kept, and with the discovery of
which we may pass at once to our Second Book.
ADDITIONAL NOTES
doctrine . . . falsehood." This statement needs correc
tion. It is true that there are no degrees of the fact of logical
assertion (cf. Chap. I, 15 (rf)). It is true that you can not alter the
logical mode of asserting S P without altering S P itself. On the
other hand it is not true that you can abstract the assertion from the
asserted content See Bosanquet, Logic, I, 363 foil. On the doctrine of
degrees of truth I may refer the reader to my Appearance and Essays.
2 " The reference or the denial itself," i.e. taken in abstraction as
a mental fact.
3 " The possible . . . whatever." This sentence must be corrected.
It is better, once more here, to substitute " conditional " for " hypo
thetical." Further, both " conditional " and " categorical " should be
taken as falling under " necessary." The merely categorical is the
lowest form of necessary (Chap. II, 75 foil.) On the whole subject
see Bosanquet, Logic (loc. cit.), and K & R, pp. 114 foil.
4 "Where necessity is internal &c." So far as the totality is a
system which is because of its internal necessity, and is viewed in
that character, the above statement will not hold.
5 " Because." On " because " see T. E. II.
6 " We must admit fact." This, I think, is wrong. Logic, I agree,
should abstain from dealing with the ultimate problem. But on the
other hand logic most certainly should not admit and assume that its
"because" is not real. To regard logical implication as merely
CHAP. VII THE MODALITY OF JUDGMENTS 237
" ideal " is an error. See T. E. I. And we must remember that " fact,"
like "existence," is ambiguous. See on Chap. II, 2 and 4.
7 " When it ceases to be merely necessary." " Merely " here seems
misleading. The "necessity" itself is in any case not hypothetical.
Cf. 12.
8 On the difference between " if " and " because " see T. E. II.
This 10 is largely erroneous. It wrongly identifies " reality " and
" fact," and it wrongly assumes the existence of judgments which really
are not mediated. See ibid.
9 " The argument from principle." This surely is vicious. There
are no "mere ideas" (see on Chap. I, 10). Logic must assume that
the ideal is real somehow and somewhere. The idea that did not
qualify Reality would certainly fail to be an idea.
As to the " argument from usage " I agree that " must " can be
used to weaken an assertion. But this is where we have an implica
tion that our " because " is only partial and is so defective. In an
immediate certainty (e.g.) we are sure that we are right somehow
though the " how " is not specified. At times, again, we specify the
"how" in order to throw doubt on it. We mean that we have this
reason, and no more than this. Cf. Bosanquet, Logic I, 379, and
K & R, pp. 122 foil. As to the " ultimate premises " which are
known immediately, such things I consider to be illusions.
10 F or " conditions " see on 24.
11 "Assumed to be compatible." These words (Cf. 13, 14, and
21 ) were overlooked by some critics, who in consequence objected to
my account on the ground that I had overlooked the possibility of
incompatible conditions. But on the contrary my account assumes,
not only that I have all the conditions, one part of which is taken
as actual, but also that the rest are, in my knowledge, not incom
patible. This point, however, should have been brought out more
clearly, as it was later in Appearance, Index, s. v. Possible.
12 " Taken to exist " should be " taken to be actual."
13 "Our basis of fact &c." But we must remember that, for an
idea to be an idea at all, it can not, so far, be unmeaning. We have
therefore with every idea an assertion that it possesses, so far, the
character of Reality, and further is real somehow. No possibility
can rest fundamentally on mere privation. The assumption that, be
yond the above, an idea is possible further, may, however, in a sense,
be so grounded. Cf . on Chap. Ill, 9- What is certainly wrong is to
use " possible," where we are simply ignorant as to impossibility abso
lute or relative. See Appearance, Chaps. XXIV and XXVII. For the
meaning of "possible" cf. T. E. XI and the Index of the present
volume.
14 "We have no reason &c." This must be corrected. For in the
first place (i) if the idea has a meaning it, so far, is real. And (ii),
if there are any facts which suggest a further reality, we have in these
surely an additional ground. The "most unfavourable view," to be
rational, would have, I think, to rest on the positive knowledge that
238 THE PRINCIPLES OF LOGIC BOOK I
body and mind are in themselves, directly or indirectly, inseparable.
The following words, " are idle frivolities . . . men," are almost
certainly a quotation, and are so marked. But I can not recall the
source.
15 ]7 or t m m supposed." This statement goes too far. The cor
rect account of " hypothetical possibility " is, I think, as follows. If
you take the actual (or fully grounded), to which the possible is
anywhere opposed, and degrade this actual to possible your first
possibility becomes then possible at a further remove. Or (it is the
same thing) take a possibility as actual and then, in consequence,
(on and against this) an even less grounded possibility may be
doubly or possibly possible. Cf. T. E. XI.
16 For this question see Note 6.
17 " May claim no existence . . . possibility." But, since it must
be thinkable, it must also to a certain point be real and possible.
See preceding Notes.
18 " Complete revolution," which revolution I consider necessary.
19 By " men " I meant here " finite beings." And the same remark
applies lower down to " human." In 18 foil, we should bear in mind
the following. The ordinary abstract judgment does not deal ostensibly
with possibles, since it assumes a world in which these are actual.
And it is better not to call it "hypothetical," since the attitude of
supposal is not there. We need not, again, take the supposed as
possible, though clearly, if in no sense it were so logically for us,
we could not in fact suppose it.
The possible, as the partly grounded, is negative of a limited
known reality, in the sense that not all of the possible is there. A
part falls beyond and is actual only in another world. Thus the
possible belongs to both of these worlds at once. But it is not
a member of the first limited world, because it is only that in part
and also is more. And hence alternative possibilities (r 1 , r 2 , r 3 ) are
all possible, though they can not all at once simply qualify our limited
reality. Thus the possible and the actual may or may not exclude
one another. The assertion, e.g. that the actual Universe is not possible
is ambiguous. And it is false if it means to go beyond the denial of
mere possibility, and to suggest that the "more" must, in every sense
and everywhere, exclude the " less." Cf. T. E. XL
I shall return ( 28) to the dangerous error which takes " possible "
as the contradictory of "impossible." Cf. ibid.
20 Sections 20 foil, need correction throughout, but I need not
repeat everywhere in detail what has now been laid down in general.
21 " Less actuality than . . . the necessary." But obviously, if and
so far as the " necessary " is taken as the " fully grounded," this is the
case.
22 "Privative judgment." This must be corrected. See above on
13, 14. " Bare possibility " is that which is general as against that
which is possible here or there. Or it is that which possesses no more
than the least amount of the character required for possibility.
CHAP. VII THE MODALITY OF JUDGMENTS 239
23 On " real possibility," and on the " potential " see Appearance
and Essays (the Indexes), and cf. the Index of this work.
24 On Ground and Conditions cf. T. E. II. This section (24) is
in part wrong because it once more ignores the various orders of
reality (see Chap. II, Note 3). The conditions are the diverse elements
of a grounded whole, and therefore are, in some sense and somewhere,
actually real. Where in a limited "actual" you have a part of the
above totality taken as there present this limited reality is the "real
possibility "of the rest, though the rest is not actually there present,
or at least is not taken as being so. In what follows, on "the
cause," I had in mind, I presume, the cause taken as mere existing
fact. But some correction is required here. See Bosanquet K & R,
pp. 20-1.
25 " Permanent Possibilities." Cf. Appearance, pp. 124-5.
26 I was not denying here that the Hedonistic End can be formu
lated correctly. I was merely giving another instance where the use
of the same delusive phrase takes the place of thought.
27 " The assertion &c.," that is, " apart from designation." See
the Index, s. v. Designation.
28 "These predicates reflection." But see Note 6. Further, with
regard to the statement, "And to a knowledge . . . possible," we
must ask, How far and in what sense would perfect knowledge
contemplate unreality at all? It would do so, I presume, only so far as
it remained discursive knowledge, and then only so far as the un
reality is relative.
In the next paragraph for "directly vanishes" "simply and
directly" would, I think, be better.
29 "On the Impossible see Appearance (Index), and T. E. VII.
The impossible must of course have enough meaning to be what
might perhaps be called " possibly possible."
30 " The real does not ... incompatible." Under " incompatible "
here will fall the case of the absence of some predicate. In the next
sentence the words "Because . . . else is" go, I think, certainly
beyond the first appearance of necessary impossibility. All that, so
far, is present there, seems to be re-assertion with an exclusion on the
ground of a " must."
si On Privation cf. Note 13. And see T. E. VII and VIII and
Appearance (Index). The main point here is this that a mere
absence or exclusion is nothing at all. " Possible " and " impossible "
are hence not mere contradictories. If the impossible is not possible
enough to have a meaning, it is logically nought. Total absence of
compatibility with the Real means sheer nothingness. The real ques
tion is as to further compatibility, and whether we have positive
reason, and if so, how much, to assume that, if there were "incom
patibility," that would appear. In other words a mere failure to
exclude is logically nothing, and so again is all mere exclusion whether
of what has sense or is senseless.
The doctrine of 28-9 is, I think, right in the main though some
24O THE PRINCIPLES OF LOGIC BOOK I
correction is needed. For "pass unabridged" (28) see Note n.
For the rest, no suggestion, if it is a logical suggestion, can be
meaningless and elicit no answer at all from Reality. Whether an
utterly meaningless suggestion is possible as a psychological fact it
would be idle here to ask. In logic the suggested must have a
meaning, and must to some extent be real, and the question will be
as to its further reality. Here, if we have but one possibility, that
is real. If, on the other hand, we have counter-possibilities, the
question will be as to the value to be attached to each of these upon
positive grounds.
Apart from this, the doctrine of 29 seems correct. We have a
vicious identification of the real, as it is, with the real as we find
it now mentally present; and we have a vicious conclusion that, if
there were incompatibility, I should know of it. The reductio ad
absurdum seems also correct. If anything is possible, then, if there
is no counter-possibility, it is necessary and real.
32 " The universal . . . nothing." " Nothing " here should be
" nothing special." And, in the next sentence, " The universal tri
angle " should be qualified by "thus held in abstraction." Cf. Chap.
Ill, 10.
33 On the doctrine of 31 see above, Note 31. The statement " then,
I admit . . . judgment" is, we have seen, incorrect, unless we under
stand what follows to deny the privative character of the foundation.
34 On Probability cf. Bosanquet, Logic, Chap. VIII. 2.
35 Instead of " any ground " " any further ground " would be
more accurate.
36 The reason of course is that in the latter case b (for instance)
becomes a common heading of b 1 b 2 &c.
37 1 think that " perhaps " should here be omitted.
38 " The same as any one " would better have been " the same
as any particular one."
ao " Cause" is taken here not as pure cause (where there is
reciprocity between cause and effect), but in that looser sense which
admits " plurality of causes." See T. E. X and Index s. v. Cause.
40 The " other cause " might, e.g. be loaded dice or some art in
the thrower. The question thus raised is answered by considering
the comparative probability of each " cause " ; and no new principle
is involved here.
41 i n " Within the probability " " within " is to be emphasized.
42 In " true or false in fact " we must here, once more, give a wide
sense to "fact" (see Chap. II, Note 3). What in probability is "sub
jective" is in short merely the amount of my ignorance and knowledge.
43 The word " now " should be omitted, as it might be wrongly
taken in reference to "go beyond."
44 The words " or often " can not, I think, stand. For, even if they
were true, they would be superfluous.
45 By " be a suggestion " what I meant was " be at least a sugges
tion.
CHAP. VII THE MODALITY OF JUDGMENTS 24!
46 Cf . 59. I should also have said that I do not pretend to
know the sense in which within mathematics the word "infinite" is
taken. But, so far as I have been able to understand the meanings
in which, outside mathematics, some mathematicians wish to use
the term I am clear that these are self-contradictory.
With regard to " an infinite number," see Bosanquet, Logic, II,
pp. 161 foil. He points out that it involves the fallacy of counting
where you have nothing in particular to count, where, that is, you
count in abstraction from any presupposed whole. This objection
is in principle the same as that usually urged, which insists on the
necessary external determination, and consequent internal incomplete
ness, of any mere counted sum. If you are led in principle beyond
any whole which you take, that is really the same thing as counting
without any whole.
If I may be permitted a word of criticism on the later work of
Prof. Royce, I would add that whether by the study of mathematics
he really was carried over to a better world of ideas I am quite
unable to judge. But the passage by that Lethe, where he crossed,
led him (so far as I see), here and elsewhere, simply to forget that
way of understanding (good or bad) which he once shared with those
who still are able to remember what they learnt.
47 By aiming at an unnecessary reductio ad absurdum, and also
perhaps by a misunderstanding of Lotze, I was led here to injure a
good case by a superfluous and serious blunder. This was noticed
by Dr. Bosanquet, K & R, pp. 108 foil., and Logic, I, 108 foil. If
the series is broken off at such a point that it can not exactly coincide
with the ratio, to take this as being in any sense a deviation is plainly
wrong. See Bosanquet, Logic I, 350.
48 Essendi should have been fiendi.
49 The statement here seems at least wanting in clearness. It would
be better after "all should show once" to proceed as follows. "It
is not that each face has a claim to show itself once, or that no face
has a claim to appear twice. It is that there is less ground for the
presence than for the absence of deviation from the ratio. This is why
we think &c."
50 The words "But the first assumption . . . impossibility" need
some correction. They should, I think, have been "But the first
assumption is based on partial ignorance, and the second, as to the
unknown residue, is not true. We have some reason here to expect
irregularity, and we find nothing here about a balance."
51 On 59 cf. the Note on 53-
62 The sentences " But ... the world," and the two preceding
sentences are partly incorrect (see on 17). But, since the ques
tion here is as to existence in fact, the conclusion remains unaffected
53 "Without any mixture of" should be "freed, so far, from."
And, in the next sentence, for "so universal," it would be better to
write "in this sense universal." I should have added here that
242 THE PRINCIPLES OF LOGIC BOOK I
necessity has no meaning outside a whole which is a concrete universal.
Lower down " hypothetical " should, once more, be " conditional."
54 1 am unable to remember against what doctrine or writer I
was arguing here, and I can not even say that the error noticed
exists outside of some misapprehension of my own. See Bosanquet,
K 6- R, pp. 209 foil.
BOOK II I NFERENCE
AT the end of our First Book we made a transition to the
subject of our Second. Modality took us from judgment to
reasoning. An inference is either a result or a process. If
we take it as a result, we saw that it is the apprehension of a
necessary truth. If we take it as a process, it is simply the
operation which leads to that result. A truth judged true
because of something else, and the going to a truth from
the ground of a judgment or supposition x are what we mean
by conclusion and reasoning. And this starting-place being
reached, our right course may seem plain. We should first
make quite clear the general character of inference, and should
exemplify this by the necessary detail. And then we might
proceed at our ease to remove the erroneous doctrines which
cumber the ground.
There is an objection to this way of dealing with the sub
ject. The reader would find his difficulties increased. I do
not indeed know, after my first Book, if at this stage I have
any actual reader ; but I am sure, if I have one, that he is not
eager to make a great effort. We have perhaps nothing in
front of us so hard to cross as what we have passed over, and
yet we shall find there are obstacles enough. It is better to
make a gradual advance. Instead of going at once from the
facts to the truth, and from that to the removal of erroneous
theories, I shall aim at reaching an easy vantage-ground, from
which we may disperse the mass of mistakes which bar our
progress and harass each movement. This will be the object
we shall try to gain first. Secure in our rear, we may then
proceed upon the final position.
243
244 THE PRINCIPLES OF LOGIC BOOK II
We must therefore in the first of the two following Books
be content with a truth which is only partial. We must
assume that in every valid inference no less than three terms
are given to the reasoner. We shall hereafter see that this
assumption is not tenable, but it will serve as a basis from
which to operate. It may be a high thing to have no order
of convenience, to follow the development of the subject
matter, and to let the reader follow if he can. But it is an
end more possible, and perhaps not much lower, to help the
reader by any means whatever to a better understanding.
The arrangement of this Book as well as its basis must be
considered arbitrary. I shall begin by setting down some
characteristics of inference which perhaps are likely to be
accepted by all. And to these I shall add a few examples of
actual reasoning. I shall then proceed to deal with some
mistakes, confining myself in the main to the syllogism. In
the next place I will point out that inference consists in an
ideal construction. And fourthly I will state some principles
of synthesis by which we operate to effect that construction.
One essential factor in valid inference will then be indicated,
and will be seen to rest on a serious assumption ; and we shall
further show that in every inference at least one premise must
be universal. Having reached this point we shall conclude our
First Part, and take a fresh departure; and throughout the
rest of this Second Book we shall be engaged in the work of
clearing the ground. We shall have to criticize in general
the alleged Association of Ideas, and especially the Associa
tion of Similars. We shall briefly dispose of the supposed
way of arguing from particulars to particulars ; and shall show
by an examination of J. S. Mill s Canons that his Inductive
Logic is theoretically invalid. After this, having declined to
enter on a discussion of Mr. Spencer s doctrine, we shall end
with a review of Professor Jevons theory of Equational Logic.
The position we shall have reached, and the negative results
we shall have been forced to gain, will have served to prepare
us for a completer view.
ADDITIONAL NOTE
!" Judgment or supposition." Cf. p. 245, footnote. But to take
"supposition" as excluding "judgment" is wrong. There are no
"mere ideas." See on p. 4.
PART I
THE GENERAL NATURE OF INFERENCE
CHAPTER I
SOME CHARACTERISTICS OF REASONING
i. When we first consider the subject of reasoning we
seem to have nothing but a conflict of opinion. But a second
glance reveals some agreement. There are three characteristic
features of inference as to which in our hearts we are really
at one. I do not mean that we should not deny them if our
theories required it, but we should do so unwillingly and with
a sense of compulsion. The first of these is a negative mark.
There is a difference between reasoning and mere observa
tion ; if a truth is inferred it is not simply seen, and a conclu
sion is never a mere perception. The latter may seem to be
given to us bodily, but the former involves some other ele
ment. It may indeed be thrust upon us, we may be compelled
and constrained to make it, but we can not passively take it in.
The fancies we cherish in respect of perception desert us as
soon as we come to inference. The external fact or the reflec
tion it throws off can violently break into and enter our minds,
or the reality can stamp our yielding substance with its image
and superscription. But we can hardly apply these ideas to
a conclusion, for we feel that in this there is something that
repels them. An inference can not wholly come in from with
out or be passively received. It is not mere vision, it is more
than observation.
2. There is another mark which a conclusion possesses.
It is not a mere fragment or isolated unit; it does not exist
in and by itself, but is the result of a process. It rests upon
a basis, and that basis is something we already know.* In
inference we advance from truth possessed to a further truth ;
* For the sake of clearness I here ignore the hypothetical character
of inference.
2321.1 245
THE PRINCIPLES OF LOGIC BOOK II. Pi. I
and the conclusion would never be reached at all if it were
not for knowledge already attained. It is therefore dependent
and in a sense adjectival.
3. But there is another attribute which a conclusion has
got. It must convey some piece of information, and must tell
us something else than the truths it depends upon. We have
no inference at all, we have simply a frivolous show and
pretence, if taking something we already know we assert the
whole or part of this once more, and then say, " I have rea
soned and got to a conclusion." An inference must be more
than a vain repetition, and its result is no echo of senseless
iteration. It is not mere observation yet it gives us something
new. Though not self-existent it is more than a shadow.
To those who delight in discrepant metaphors we may bring
conviction when we so express ourselves : The truth which is
seen in the mirror of inference has not wandered in through
the window-pane of sense, nor yet is it merely a reflection
cast by an article of furniture already in the mind.
4. Except in the interest of a preconceived theory, I
think that these statements, at least so far, will not be denied.
But I can hardly hope that the examples of reasoning I am
about to produce will all escape unchallenged. Yet I shall not
defend them, for I do not know how. They are palpable
inferences, and the fact that they are so is much stronger than
any theory of logic.
(i) A is to the right of B, B is to the right of C, therefore
A is to the right of C. (ii) A is due north of B, B due west
of C, therefore A is north-west of C. (iii) A is equal to
(greater or less than) B, B is equal to (greater or less than) C,
therefore &c. (iv) A is in tune with B, and B with C, there
fore A with C. (v) A is prior to (after, simultaneous with)
B, B to C, therefore A to C. (vi) Heat lengthens the
pendulum, what lengthens the pendulum, makes it go slower,
therefore heat makes it go slower, (vii) Charles I. was a
king; he was beheaded, and so a king may be beheaded, (viii)
Man is mortal, John is man, therefore John is mortal. We
shall go from these facts to ask how far certain theories
square with them.
CHAPTER II
SOME ERRONEOUS VIEWS
i. The task before us in the present chapter is the re
moval of certain mistaken ideas. And the first to go must
be the major premise. We saw, at the end of the foregoing
Book, that the necessary truth need be no more particular
than the truth it depends on, and that logical necessity does
not always come from the application of universals * to some
thing less universal. But if so, there need not be always a
major; and the examples we have given put this beyond
doubt.
In (viii) our old friend is still to be found, but in (vi) and
in (vii) you will hardly be able to distinguish him from the
minor, and in all the rest he has totally vanished. You may
say that in (iii) we really argue from " Things equal to the
same are equal to each other," and I do not doubt you will
find believers. But if such reasoning is reasoning from an
axiom, how did people reason before axioms were invented?
And if without axioms it is impossible to infer, I wonder
where all the axioms can have come from (cf. Book II. Part
II. Chap. I.). But if we take an example like number (i), will
any one show me the major there? "A body is to the right
of that which that, which it is to the right of, is to the right
of." I know this major, because I have just manufactured
it; but you who believe in major premises and who scores of
times must have made the inference, confess that you never
saw this premise before.
We must either admit that a major is not necessary, or
else we must say that my examples are not inferences because
they have no major. In either case an effete superstition will
be doomed.
Begotten by an old metaphysical blunder, nourished by a
senseless choice of examples, fostered by the stupid conserva
tism of logicians, and protected by the impotence of younger
247
248 THE PRINCIPLES OF LOGIC BOOK II. PT. I
rivals, this chimaera has had a good deal more than its day.
Really dead long since I can hardly believe that it stands
out for more than decent burial. And decent burial has not
yet been offered it. Its ghost may lie quiet when it sees that
the truth, which lent it life, can flourish alone (cf. Book III.).
2. The major premise, we have seen, is a delusion, and
this augurs ill we may think for the syllogism. Our suspicion
is well founded, for the syllogism itself, like the major premise,
is a mere superstition. It is possible, no doubt, as in our
seventh example, to have a syllogism which has either no
major premise, or at all events no minor. And it is unques
tionably true that in many arguments a major premise is
actually used. Nor will I deny that some three fourths of our
valid arguments can be got within the forms of Barbara
Celarent. But yet after all the syllogism is a chimsera, for it
professes to be the model of reasoning, and there are reason
ings which can not by any fair means be conformed to its
pattern. In whatever sense you interpret it, it turns out
insufficient; and in certain cases it will turn out worse. Let
us examine the principles of reasoning it lays down.
3. If we take first the axiom of inclusion in extension as
it finds expression in the maxim De omni &c., we are forced to
say that this principle is unsound. It sins against the third
characteristic of inference (Chap. I. 3), for it does not really
give us any new information. And, as has been long ago
remarked, it embodies a petitio; for if, asserting the premise
" All men are mortal," I understand by the subject each
single man, then I either am aware that John is mortal, or if
not my major must be withdrawn. The major premise has
asserted something of each member of a collection, and the
minor and conclusion do but feebly re-echo one part of this
statement. But that is no inference.
We might try to understand the assertion differently. We
might say that what " All men " really means is the collection
or class and not each one member. But, if so, we fall blindly
into a second pitfall. John s personality perhaps has no unity,
but he can hardly be called a collection of men, and our
syllogism now fails through quaternio terminorum. It per
haps fails too through falsity of the major. 2
The dictum de omni thus turns out vicious. But if it were
CHAP. II, SOME ERRONEOUS VIEWS 249
sound it would not be sufficient, for it does not cover all valid
reasonings.
4. There is another mode of interpreting the major.
" All men are mortal " may be said to assert the identity of
the subjects in " men " and " some mortals ; " and " John is
man and therefore mortal " assures us that the subject, which
we distinguish as John, is identical with a member of the class
of men and also of mortals. But we know already how this is
to be read. 3 The identity of the subject is another way of
affirming the conjunction of diverse attributes. The fact we
have got is either the co-existence in one single subject of the
attribute mortal with the rest of John s attributes, or else the
possession by a single thing of the several names " John,"
" man," and " mortal " (cf. Book I. Chaps. I. and VI.). And
interpreted in this way, though the inference is valid, it will
not fall under the dictum de omul.
5. We may illustrate the above from complete induction.
I may show that all planets move in an ellipse by counting
and observing each single planet. But in what sense am I
then said to perform an inference? I say "therefore all
planets move in an ellipse," but I know already that every
single planet does so move. If there were any planet which I
could not so qualify I could not go on to therefore all planets.
Does the " therefore " simply reiterate the " because "? Then
there is clearly no inference. Does the conclusion assert that
the collection, or class, itself moves through space in an
elliptical manner? If this were true the premises would not
prove it. But perhaps it means that, if anything is a known
planet, it must have a course which will be found elliptical.
We are free to forget that the individuals we know do move
in ellipses. We have firmly established a connection of at
tributes, so that hereafter, given any single individual which
we barely perceive to be a known planet, we can go at once
from the base of that attribute to elliptical movement. But
the conclusion here does not rest on enumeration complete or
otherwise; it proceeds from and rests upon a distinguished
connection of attributes (Book I. Chap. VI. and Bk. II. II.
Chap. III. 3)- , <T7 .
We may sum up the matter thus. If you say Each
individual has a certain attribute and therefore each has it,
250 THE PRINCIPLES OF LOGIC BOOK II. PT. I
that is absurd. If you say " therefore the collection has it,"
that is invalid. If you say " Anything belonging to the col
lection has it and therefore this has it," then that is valid, but
the " anything belonging " stands for an attribute. Com
plete induction shares the fortunes of the syllogism.
6. The principle of inclusion within class extension is not
merely insufficient, but unless we interpret it as a connection of
attributes it is intrinsically vicious. Let us see if we can find
any other view which will come to the rescue and will save
the syllogism. " What stands," says Kant, " under the condi
tion of a rule stands under the rule." It is thus he interprets
" nota notes est nota rei ipsius" If you have an universal
connection of two attributes, then, given one in a subject, you
must also have the other.
It is evident that this principle of reasoning is valid, but it
will not cover the whole of the ground; for, confined to the
category of subject and attribute, it fails wherever you pass
beyond. The subject no doubt is in some way qualified by
whatever can be asserted about any of its attributes, but it is
idle to expect a result from this where we are not concerned
with subject and attributes. " A is prior to B and B to C, and
therefore A is prior to C," but what here am I to call the
"condition of the rule" or the "nota" or "attribute"? I
can not take B as the attribute of A, and if I look for that
attribute in " prior to B," I fall at once into quaternio termi-
norum, since the second premise has got B simply.
And even when we keep to subjects and qualities, there
are inferences which the principle will not justify. The syllo
gistic third figure can hardly be supposed to exemplify the
axiom which Kant has adopted. Not only is the category
of subject and attribute (as commonly applied) unable to
cover the whole field of reasoning, but within that category it
is a further mistake to insist on the necessity of a major
premise.
7. It is evident that the syllogism can not be saved or
can only be saved in such a way as to be syllogism no longer.
The one chance there is of preserving the syllogism is for us
to take our stand upon the third figure. c< The attributes of
one subject are interrelated " will then become the axiom of
inference. We have seen (4) that all syllogisms in exten-
CHAP. II SOME ERRONEOUS VIEWS 251
sion can be interpreted according to this axiom, since the
identity of the subject was the other side of that relation of
attributes which we wished to assert. And it is evident again
that all relations of attributes can be regarded as based in a
subject. We shall see hereafter (Part II. Chap. IV) that Sub
stitution of Similars can be taken as syllogism within the third
figure; and I will go yet further. There is and there can be
no inference whatever which may not be reduced under the
head of the axiom, since everything which in any way is con
joined can be taken as related within some subject (Book III.
Chap. VI. 33,34). "
We may see hereafter how this reduction is effected. For
our present purpose it is enough to remark that in many cases
it can not be performed without processes which would hor
rify the conservative logician, and which gain no end worth the
violence they use. Unless " subject and attribute" are used
in a way which is quite unknown to the traditional logic, the
axiom fails of universal validity, for it does not apply to any
of those relations which two or more subjects bear to each
other. " Two pianos are in tune with one fork and therefore
the one is in tune with the other." But in this instance, unless
the terms are manipulated freely, you will not show one sub
ject with its attributes.
8. It is obvious, if we fairly consider the examples which
have been adduced at the end of Chapter I., that the syllogism,
if it keep its traditional form, is in great part impotent. And
I confess I do not know what policy will seem good to the
friends of the syllogism. They may boldly accept the violent
alternative of excluding all examples which they can not deal
with. But I think we may say that such a course as this
would be nothing short of a confession of bankruptcy. If a
savage may know the road that will take him from A to B,
and the road that will take him from B to C, and yet may not
know, and may be unable to find out, the way he should go
from A to C (cf. Spencer, Sociology, I. 91), I do not see bow
it can be denied that he is ignorant because he is incapable of
an operation. 5 And if that operation is not an inference, I can
not see why anything else should be inference. The plain and
palpable facts of the case will, I think, be too hard for the
friends of the syllogism. And if they embrace another alterna-
252 THE PRINCIPLES OF LOGIC BOOK II. PT. I
tive, and find their amusement in the manufacture of majors,
which would never have been seen if the arguments had not
come first, then I think once more that the end must be near.
So barren a shift will be the dying effort of a hard-run and
well-nigh spent chimsera.
But there is, as we saw, another alternative; it may per
haps be thought possible to save the syllogism by first reform
ing it. Throw the major premise overboard, and call anything
a syllogism which can be brought into the form of elements
related within one whole. But if the friends of the syllogism
resolve on this policy, I think they are friends it might pray
to be saved from. It is better to bury a delusion and forget
it than to insult its memory by retaining the name when the
thing has perished. And it is better to profess that delusion
openly than ostensibly to abandon all but the name, and then
covertly to re-instate the errors it once stood for. When a
mistake has lasted some two thousand years I am ready to
believe that it must contain truth, but I must believe too that
the time is come when that truth should be able to stand by
itself. We can not for ever with eyes fast closed swallow
down the mass of orthodox rubbish in which that truth has
wrapped itself up. And if the time has not come for extracting
the kernel, the time has come for rejecting the shell.
9. But if the principle of the syllogism is not the axiom
of reasoning, can we find any other which will stand the test?
We shall see hereafter that the logic of " Induction " is no
more satisfactory. We shall allude to the doctrine of Mr.
Spencer, and review the theory of Substitution which has
found an advocate in Professor Jevons. For the present it
will suffice to mention a principle adduced by Mr. Spencer,
and which has succeeded in gaining the authority of Wundt.
" Things related to the same are related to each other " is
the axiom, we are told, of all valid reasoning. " Where judg
ments are placed in relation to one another by means of con
ceptions they possess in common, the other conceptions, which
the judgments possess but do not possess in common, must
stand themselves too in relation to one another, and that rela
tion is expressed in a new judgment." (Wundt, Logik, I.
282.)
We may confine ourselves to the simpler formula.
CHAP. II SOME ERRONEOUS VIEWS 253
" Related to the same are related to each other " is wide
enough to cover the examples we have given. We shall cer
tainly hereafter have occasion to question if it is wide enough
to cover all possible examples (Book III. Part I. Chap. I.).
But though I may object to it hereafter as being too narrow,
I must object to it here because it is too wide. It is a principle
of falsehood as well as of truth ; " A runs faster than B and
B keeps a dog (C)," "A is heavier than B and B precedes
C," " A is worth more than B and B is on the table (C)," or
" A is like B and B is like C." You may doubtless extract
some kind of inference out of these premises, but you can
hardly go from them to any definite and immediate relation
between A and C. 6
10. It is true no doubt that, if A and C are both related
to a common term B, we know that some relation must exist
between them, since both must be elements in one world of
knowledge. But unfortunately we knew thus much before,
and independent of the relation of both in particular to B. 7
And again in defence of the axiom it may be said, In " A is
like B and B is like C " the terms are not related to a common
third term. B resembles A perhaps in one point and resembles
C in another different one, and so it is with the other examples.
It is not in so far as B keeps a dog that A outstrips him, it is
not the B which has a place in time which is heavier than A,
B is on the table in one capacity and is worth more than A in
an other and different one. Thus the terms related are not
related to the same, and, if they were, they would be related
to each other.
The defence I have invented points towards the truth, and
yet it is vitiated by a fatal mistake. It is true to say that in
every relation there must always be an underlying identity;
that relations, such as those of space and time, presuppose a
common character in the things they conjoin. And it is there
fore true that, if a third term C stands first in spatial relation
with A and again in temporal relation with B, its character in
those two relations is different. Hence, if two relations are
of different classes, the term common to each will so far not
be the same.
But this line of argument, if we follow it out, will make an
end of all kinds of relation (cf. Chap. VI. 6). To say that,
254 THE PRINCIPLES OF LOGIC BOOK II. PT. I
when A is related to B, it is related so far as B is nought else
but its relation to A, is quite suicidal. And, if we will not say
that, and if already B is something different from its relation
to A, on what ground can we refuse it a right to another
relation with C, when at all events it has one point in which
it differs from A? Let us try to see clearly; the terms of
a relation must always be more than the relation between
them, and, if it were not so, the relation would vanish. "A
is equal to B," but if B were mere quantitative identity with
A, we should have no equality ; there would be nothing but A.
" A is the same as B or different in quality," but if A and B
were not both different and the same, then the terms and the
relation would all disappear together. " A is north of B or
prior to C ; " but if A, B, and C were no more than mere
naked positions in space or time, they would not be even that,
and their relations would sink to utter nothingness. There
always must enter into the relation something more than the
actual relation itself. And this being admitted, if you deny
that the B, which for instance is spatially related to C, is the
same as the B which has a relation in time with A, you must
be taken to assert that in the relation A B the character of
B is perfectly simple, and that B is nothing but that which
constitutes its relation in time. But, if so, it is nothing which
can be related, and the axiom can find no possible application.
The mistakes, which arise from a too wide axiom, may
indicate the truth that related to the same are not related to
each other unless they are related under certain conditions.
We shall return to this point in Chapter IV., and the following
Chapter will endeavour to convey some general idea of the
nature of inference.
ADDITIONAL NOTES
1 " Given universals " would be better here than " universals."
2 On the "Collective Judgment" and on "Class" see the Index.
The "falsity of the major" refers to the ambiguity involved in the
above ideas. On Complete Induction and Counting see Bk. II. II.
HI. 3.
3 " But we know . . . read." It would be better to say " But we
CHAP. II SOME ERRONEOUS VIEWS 255
know already how this identity of diverse subjects is here to be read."
See on Bk. I. VI. n.
4 See i of the next Chapter.
5 " If a savage &c." The case, as stated, is so extreme as to be
perhaps abnormal, but as an illustration it may stand.
6 " Definite and immediate " should be " fresh and special." See
again as in Note 4.
7 After " in particular to B " add as follows. " Further, when
we have got to know that A and B, B and C, are related in a par
ticular whole which is before us this mere knowledge, that A and
C are both together as members of that whole, will not be the con
clusion that we seek We presumably are looking for some further
and special relation between A and C, other than their mere co-pres-
ence within one subject."
CHAPTER III
A GENERAL IDEA OF INFERENCE L
I. Every inference combines two elements; it is in the
first place a process, and in the second place a result. The
process is an operation of synthesis; it takes its data and by
ideal construction combines them into a whole.* The result
is the perception of a new relation within that unity. We start
with certain relations of elements; by virtue of the sameness
of two or more of these elements we unite their relations in
one single construction, and in that we perceive a fresh rela
tion of these elements. What is given to us is terms conjoined ;
we operate on these conjunctions and put them together into
a whole ; 2 and the conclusion is the perception of two terms in
relation, which were not related before the operation. Thus
the process is a construction and the result an intuition, while
the union of both is logical demonstration.
2. Demonstration in logic is not totally different from
demonstration elsewhere ; proof is only one kind of demon
stration. Logicians however seem generally not to be aware
of this fact. When the mathematician " demonstrates " a
conclusion the logician feels uneasy, though he can not deny
that the conclusion is proved. But uneasiness becomes protest
and open renunciation when he attends at the " demonstra
tions " of the anatomist. He shudders internally at the blas
phemous assertion that " this which I hold in my hand " is
" demonstrated." But his trials are not over ; the illiterate
lecturer on cookery overwhelms him by publicly announcing
the " demonstration " of an omelette to the eyes of females.
But I think the logician has no real cause of quarrel even
with the cook. For demonstration is merely pointing out or
showing ; 3 and if the conclusion of an inference is seen and
thus may be shown, so also may a nerve or again an omelette.
*As we remarked before, the statements in this Book are subject
to correction by the Book that follows.
256
CHAP. Ill A GENERAL IDEA OF INFERENCE 257
It is useless to deny this, and the task of the logician is to
distinguish inference from other kinds of demonstration.
3. When in ordinary fact some result can be seen and is
pointed out, perhaps no one would wish to call this " demon
stration." It is mere perceiving or observation. It is called
demonstration when, to see the result, it is necessary for us
first to manipulate the facts; when you show within and by
virtue of a preparation you are said to demonstrate. But if
the preparation experiments outwardly, if it alters and ar
ranges the external facts, then the demonstration is not an
inference. It is inference where the preparation is ideal,
where the rearrangement which displays the unknown fact is
an operation in our heads. To see and, if it pleases us, also to
show a new relation of elements in a logical construction, 4 is
demonstration in the sense of reasoning.
4. In what does this mental preparation consist ? We
have seen in our account of the synthetic judgment its general
character. It demands in the first place certain data; 5 it
must have two or more connections of elements, as A B
B C C D ; and these are the premises. It is necessary
again that these premises should be judgments actual or sug
gested, 6 and what they assert or suppose must consist in logical
connections of content. For if the data consisted of unrefined
sensuous material, or were mere imaginations, the result would
be sensuous or merely imaginary; it would be a psychological
effect and not a logical consequence. The premises are thus
so far two or more judgments, and the operation on these
data will consist in joining them into a whole. We must
fasten them together, so that they cease to be several and are
one construction, one individual whole. Thus instead of
A B B C we must have A B C.
Now if this were done arbitrarily it would not be done
logically, and we should have no reason to think the result
true. If we took A B and C D and joined them together
as A B C D, our procedure would be as futile as if in
anatomy we showed connections by manufacturing them, or
as if in order to clear a preparation, we employed some agent
which radically changed it. In relation to fact our results in
this case would be invalid.*
*A11 this is subject to correction by Book III. 7
258 THE PRINCIPLES OF LOGIC BOOK II. Pi. I
We can not logically join our premises into a whole unless
they offer us points of connection. But if the terms between
which the relations subsist are all of them different, 8 we are
perfectly helpless, for we can not make an arch without a
key-stone. Hence, if we are to construct, we must have an
identity of the terminal points. Thus, in A B B C, B is
the same and we connect A B C; in A B C and
C D, C is the same and we connect A B C D. The
operation consists in the extension and enlargement of one
datum by others, by means of the identity of common links.
And because these links of union were given us, therefore we
assume that our construction is true; although we have made
it, yet it answers to facts.
Having thus turned our premises into one whole, we pro
ceed to our conclusion by mere inspection.* If A B
C D is true of reality, then in that we can see A C or
A D, or again B D, relations which previously we did
not know. Then, leaving out of view those parts of our
construction in which we are not interested, we extract the
conclusion we desire to assert. We first do a certain work
on our data; and this work is the construction. We then
by inspection discover and select a new relation, and this
intuition is the conclusion. 10
5. I will illustrate the above by several examples. Take
three pictures on a wall A, B, and C; if I see them all at
once as A B C there seems so far no inference, 11 for my
mere analytic judgment will give me A C (Book I. Chap.
II.). But suppose I see first A B, and then afterwards
B C, no mere analysis will give me A C. I must first
put them together as A B C, and this is the construction
of a synthetic judgment. I then perceive A C, and this is
the conclusion, which is inferred not because it is seen in fact,
but seen in my head.
Let us take an instance from geographical position. A is
ten miles north of B, B is ten miles east of C, D is ten miles
north of C; what is the relation of A to D? If I draw the
figure on a piece of paper that relation is not inferred ; 12 but
if I draw the lines in my head, in that case I reason. In
* I omit to consider here the selective action. That is not of the
essence of all inference. 9 Vid. Book III. Part I. Chap. I.
CHAP. Ill A GENERAL IDEA OF INFERENCE 259
either case we employ " demonstration," but only in the latter
do we demonstrate logically.
" A = B and B C therefore A = C." In this argument
there is no demonstration to sense, for the showing is ideal.
The terms are put together through the sameness of B, and
are combined into a whole united by the relation of quan
titative identity. The whole is a series united by that charac
ter, and here is the construction. We then inspecting the
series find a new relation A C, and here is the conclusion.
Take an example we have given in Chapter I. ; if three
strings A, B, and C are struck together and we hear that they
all produce the same note, we hardly infer 13 that they are in
tune with one another. But first strike A and B, and then
strike B and C ; on this, if A and B have no difference in note,
and B and C have no difference in note, I proceed to construct
the ideal group of ABC united throughout by sameness of
note. This is a mental synthesis ; and a mere analytical percep
tion then adds that A and C are in tune with one another.
We may see this again in an ordinary syllogism. We
must not state it so as to beg the question, or to have no com
mon term, but may state it thus, " Man is mortal and Caesar
is man and therefore Caesar is mortal." There is first a
construction as Csesar-man-mortal, and then by inspection we
get Caesar-mortal.
6. It is useless to attempt to lay down rules for either
part of this process. It is the man who perceives the points
of union within his premises who can put (as the saying is)
two and two together who is able to reason. And so long
as he secures the unity of his construction he has reasoned
rightly. In the next Chapter we shall see that no models for
construction can possibly be invented. And for the process
of inspection one wants a good eye; for there are no rules
which can tell you what to perceive.
We must free ourselves from these superstitions, if we can,
and there are others beside which have oppressed us too long.
It is ridiculous for instance to think about the order of our
premises. The construction when made need have no order
in time, and the order of its making may be left entirely to
private convenience or else to chance.
And there is another superstition we may here dispose
26O THE PRINCIPLES OF LOGIC BOOK II. PT. I
of. 14 The number of terms is not limited to three. In the
geographical example of the previous section we certainly
A A Dl /A D A
do not argue thus
C-
B*
, and
D
C
but we first complete our construction
C
A
, and then
go to D A. It is true no doubt that in making a con
struction we are forced to establish one link at a time; but
it is wholly false that we are compelled to conclude before
we take in another premise. Logic sets no limit to the number
of premises which may precede the conclusion, and it is
the weakness of our heads which narrows our constructions
and narrows them sometimes to the prejudice of our inference.
There is no branch of science where constructive power is
wholly uncalled for, and certainly some where it is of the
first importance. And perhaps we may say without exaggera
tion that a man, who can not use more than three terms in
reasoning, is unlikely to do much in any subject. But, how
ever that may be, the limit is psychological and is not logicaL
ADDITIONAL NOTES
^This chapter must be taken as no more than a provisional
clearing of the ground. Not only is the warning in the footnote to
i to be borne in mind, but, in addition, the chapter contains
serious errors the correction of which can only be indicated in
passing.
2 " Into a whole" should be "into a connected whole," and (in the
next line) " not related " should be " not so related."
3 " Demonstration is merely pointing out." This is a grave mis
take, and the term is, I think, nowhere so used in practice. It every
where and always means showing the necessary and ideal connection
and sequence. Whether and how far you have before you external
fact and its alteration, or deal merely with what is "in your head,"
is utterly irrelevant. The " demonstration " in every case has to
bring out not the fact but the ideal bond and process. Cf. on Bk.
III. I. II. 5, and T. E. I.
4 " In a logical construction " should be " in and as the result
of &c."
5 On " data " and " premisses " see Index, s. v. Premisses, and cf .
Bosanquet, Logic, II, pp. 12 and 203.
CHAP. Ill A GENERAL IDEA OF INFERENCE 26l
6 The words " actual or suggested " should be omitted. See the
first Note on Book II. And (at the end of this paragraph) it would
be better to insert " new " before " individual," in the words " one
individual whole."
7 " All this " should have been " Much of this."
8 " Different " should have been " merely different."
9 The " selective action " is really quite essential. See the Index
s. v. Selection. What I meant here was merely that "elimination" is
not always necessary. You do not always in the conclusion omit part
of the construction. See Bk. III. I. I. 2.
10 " This intuition is the conclusion." Certainly not so, unless the
new relation appears in it as " following." The " conclusion " means
seeing as part of the whole and because of the whole. See Note 4.
11 " So far no inference" except so far as the analytic judgment
itself involves inference. See Index, s. v. Analysis.
12 " If I draw the figure &c." This and what follows is seriously
wrong. See Note 3.
13 "We hardly infer, etc." Yes, but how far the "we hear" is
already itself inferential, still remains a question. See Note II.
14 "And there is another &c." On this see Bosanquet, K & R,
p. 307, and Logic, II, pp. 12 foil. My statement here was wrong in
forgetting that the necessary establishment by synthetic construction
of each link, one at a time, itself is inference. On the other side I
was right in insisting that in the final conclusion there is an inference
from the whole construction without regard to the number of terms
contained in that. Cf. Bk. Ill, I. II. 5.
2321.1
CHAPTER IV
THE PRINCIPLES OF REASONING 1
I. We have seen in outline the main character of infer
ence and we naturally recur to a former question, Is there
any axiom or principle of reasoning? The result of our
enquiry in the Second Chapter was that we could find nothing
quite satisfactory. The syllogistic maxims were all too nar
row, and the axiom that " Things which are related to the
same are related to each other," we found on the other hand
was much too wide. It may serve us however as a point of
departure. When properly restricted it will express the truth,
so far as is required by the present Book. 2
I will repeat the result we arrived at before. The principle
that elements which stand in relation to a common point are
themselves related, is not the actual principle that operates in
any given special inference. 3 In its abstract form it is useless
for the purpose of getting a conclusion. It assures us, before
any construction is made, that anything which we have as an
element of knowledge stands in some relation with every other
element. But it will not enable us to go beyond this, and
by combining our premises to get a definite relation. If A
is prior to B in time, and B is west of C in space, then on
the strength of B we can put these together, but we can not
by means of our combination get a definite relation of A to
C. We knew long ago that A and C po-existed as members
within the universe of knowledge, and we desire to learn now
not that general connection, but some special attitude of A to
C. But in order to get this, and to be able so to speak to
draw a new line from A to C, it is necessary first to connect
A and C in a special manner. They must be interrelated not
generally and in the universe at large, but in some special
world. If one is merely in time and the other merely in space,
they have so far not got any binding centre. To be specially
related they must be related to the same, and under conditions
which secure an unity of construction.
262
CHAP. IV THE PRINCIPLES OF REASONING 263
If what operates in inference is the principle of the indi
viduality of synthesis, the axiom of that operation must not
be taken too widely, and at the cost of clumsiness we must
state it in two pieces. " Where elements A and C are related
homogeneously to a common B, A and C are related within
the same genus. Or where one relation only (either A B
or B C) is within the category of subject and attribute,
there is a valid conclusion within the category of either A B
or B C." To express the same otherwise, " There is no
conclusion where the relations are heterogeneous unless one
of the two joins an attribute to a subject. In the latter case
an inference is possible even outside the category of subject
and attribute."
2. We found first in our examination of the syllogism
that there were inferences which fell outside its single cate
gory of subject and attribute. We found again that if we
kept outside all special categories, mere interrelation was
much too vague to form a bond. The conclusion, which in
the next place naturally offers itself, is that inference must
take place within several special categories (such as time,
space, subject and attribute, &c.), but must always be confined
in each case to one category. To get a relation of time in
the conclusion you would have to keep in your premises to
time-relations, and the same thing again with other kinds of
relation. And, if this were true, the axiom would run, " Things
related to the same within one kind will be interrelated within
that kind."
But there are inferences which will not submit to this
principle. " Gold is heavier than lead and lead is a metal,"
" A runs faster than B and B is twice as tall," " A is stronger
than B and B is full grown," " A is equal to B in weight and
B is moved with such or such velocity " are premises which
certainly will yield conclusions, and yet their relations are
heterogeneous. And this shows that we may cross from cate
gory to category. On the other hand we are unable to do
this unless there exists a special condition ; one relation must
be that of attribute to subject. From " A is equal to B and
B has such velocity " we have seen you can not get to the
conclusion " A has such velocity." You can not do so till
you predicate of A that point in B which brought it into
264 THE PRINCIPLES OF LOGIC BOOK II. PT. I
relation with the other element (C). And from "A is equal
to B and B is in my pocket " you can not infer that A is in
my pocket, since the spatial relation which is affirmed of B
is not true of B as equal to A. You can not argue to a relation
of A to my pocket, but your conclusion must be " A is equal
to something which is in my pocket." We have still the old
relation of A to B, but qualified by the addition of an ad
jective of B. And it is true, I think, in all possible cases that
the relation between a subject and attribute is the only one
which, if used with another category, is able to give us a new
relation.*
The remarks we let fall in a previous chapter (II. 7)
may have prepared the reader for our result. The categories
do not stand on one and the same footing. 5 It is possible
after all to express unconditionally the principle of inference,
and it is possible to do this within the one category of subject
and attribute (p. 296). But we are not yet arrived at the
stage where this is possible, and must content ourselves here
with the formula that ended the foregoing section, " Related
to the same within the same kind are interrelated within that
kind," with a further axiom of possible inference where one
relation is that of subject to attribute.
3. Our main principle, it is obvious, will have as many
forms as there happen to be categories or kinds of relation.
It is not the business of this work to elaborate any theory as
to how these kinds are connected or are subordinated. It is
again not our purpose to draw out and defend a complete
enumeration or scheme of such classes. But in order to make
clear the general result, I will state and illustrate four or five
main principles which operate in inference. We may call
them the principles (i) of the synthesis of subject and attri
bute, (ii) of identity, (iii) of degree, (iv) of space, and (v)
of time.
I. Principle of synthesis of subject and attribute.
* Other examples are "A has a voice (B), that voice overpowers
Z s voice (C), therefore A overpowers C." "A has a voice (B) which
is in tune with C, therefore A has something in tune with C." In the
first of these the relation of the conclusion is hardly between a subject
and attribute. 4 A by virtue of its attribute, which attribute acquired
a momentary independence, has got a new relation to another subject.
CHAP. IV THE PRINCIPLES OF REASONING 265
(a) The attributes of one subject are interrelated.
(/3) Where two subjects have the same or a different attri
bute they are alike or different.
(y) (i) Where the attribute is not taken as distinct from
every subject, what is asserted of the attribute is asserted of
its subject, (ii) Where the subject is not taken as distinct
from every attribute, what is affirmed of the subject is affirmed
of any attribute considered as its attribute.
Examples, (a) This man is a logician, this man is a fool,
therefore a logician may be * (under some conditions is) a
fool.
(13) This dog is white, this horse is white (or brown), this
dog and this horse are alike (or different) .
(y) (i) This figure is a triangle, a triangle has the angles
equal to two right angles, this figure has the angles equal to
two right angles, (ii) Gold is heavier than lead; lead is a
metal. Therefore lead-metal (or some metal) is lighter than
gold, or metal may be lighter than gold.
I may remark on (y) that, if we were to say " What is
true of the attribute is true of the subject, and what is true of
the subject is true of the attribute," we should fall into an
error. The subject qua subject and the attribute qua attribute
have each predicates which can not be applied to the other.
Thus " Iron is heavy, heavy is a quality " is no ground for the
assertion " Iron is a quality," nor from " Iron is heavy, iron
is a substance," can you go to the conclusion " Heavy may be
a substance" (cf. Book I. Chap. III. 10). If on the other
hand we laid down as a condition of the inference that this
attribute and this subject must be taken together, we should
then have become circular. 6
II. Synthesis of Identity.
Where one term has one and the same point in common
with two or more terms, there these others have the same
point in common.
Examples. " Coin A has the same inscription as coin B,
and coin B as coin C, therefore A as C; " " Instrument A is
in tune with my tuning-fork (B), and so too are instruments
C and D, therefore they are all in tune with one another;"
*May be because, the subject being undefined, the conditions are
partly unknown. Vid. Book I. Chap. VII. 26.
266 THE PRINCIPLES OF LOGIC BOOK II. Px. I
" If A is the brother of B, and B of C, and C is the sister of
D, then A is the brother of D."
III. Synthesis of Degree.
When one term does, by virtue of one and the same point
in it, stand in a relation of degree with two or more other
terms, then these others also are related in degree.
Examples. " A is hotter than B and B than C, therefore A
than C ; " " Colour A is brighter than B and B than C, there
fore A than C ; " " Sound A is lower in tone than B and B
than C, therefore A than C." I will not enquire here whether
" A = B and B = C, therefore A = C," falls under this head
or under the previous head of the synthesis of identity.
IV. and V. Synthesis of Time and Space. 7
Where one and the same term stands to two or more other
terms in any relation of time or space, there we must have a
relation of time or space between these others.
Examples. " A is north of B and B west of C, therefore C
south-east of A ; " "A is a day before B, B contemporary
with C, therefore C a day after A."
This list, as we have said, does not pretend to be complete,
and it would not be possible for us here to discuss the ques
tions which any such pretence would at once give rise to.
Take for instance the synthesis of cause and effect. Does
this fall entirely under the head of time? Does it fall under
the head of subject and attribute? Does it fall under both
or again under neither ? The answers to these questions would
be hard to get, and, if we got them, they would be of no use
to us here. They would not much serve to confirm the result
we already have reached ; they would possibly supply one more
illustration, where I hope enough have already been given.
4. But there is another question which can not be
passed by. We have called these syntheses Principles of
inference, and have ejected the syllogism to enthrone them in
its stead. But how are we to understand the title they lay
claim to? We know what the syllogism tried to accomplish,
for it professed to control from a central office every possible
event in all parts of its kingdom. It issued some two dozen
forms of reasoning, to which all inference was expected to
conform. Thus you had always some model with relations
ready drawn between all the terms both in premises and con-
CHAP. IV THE PRINCIPLES OF REASONING 267
elusion, and no liberty was left you save to fill up the blanks
with terms of your own. The moods and figures were a bed
of Procrustes into which all arguments had somehow to be
forced, and they were therefore not merely principles of rea
soning, but actual canons and tests of inference. Within
this pale you were secure of salvation, and on the outside it
was heresy to doubt you were lost. Such was the claim
which the syllogism put forth, and enforced as long as it had
any strength.
Like some other chimseras that have had their day, the
syllogism is effete and its realm is masterless ; and the question
for us who aspire to the inheritance is to know in what charac
ter we mean to succeed. Do we wish to substitute one des
potism for another? Are our principles of inference to be
tests and canons? Most assuredly not; for if the thing were
desirable, and I am much too staunch a Protestant to desire
it, it is at all events thoroughly impossible.
5. Our principles give us under each head of inference
the general and abstract form of the operation. They do not
profess in all cases to give us the individual operation itself
which is necessary. It is not merely that the terms are left
blank, for the special relations of the premises and conclusion
are also left blank. The kind of construction is indicated
generally, and the kind of conclusion you will find within it;
but the actual construction, and the actual new relation to
which that will give rise, are left entirely to private judgment. 8
From such premises as " A to the right of B and B to the
right of C," there is and there can be no form of reasoning
which will give you the conclusion. It is true that the axiom
goes so far as to assure you that A and C must be related in
space, for 9 you do not know that unless you know that the
two space-relations belong to one world. And you do not
know this unless you are sure that they have a common
meeting-point in space (Book I. Chap. II. 21). But the
axiom will not tell you anything beyond. It will neither give
you the definite relation, nor even assure you that you will be
able to attain to any such relation. A is greater than B, and
C is greater than B, therefore (if the point in B is the same)
A and C must certainly be related in degree ; but you do not
know how. B is south of both A and C, therefore A and C are
268 THE PRINCIPLES OF LOGIC BOOK II. PT. I
related in space ; but you have no means of getting to know
their particular relation. For the individual construction can
not here be drawn, and it is that alone which can supply the
conclusion.
Where the inference is valid, the special operation by which
it is performed falls outside the axiom, and it is impossible
therefore that the axiom can supply any test of validity.
Where the inference is invalid, what makes it invalid may
fall without the axiom, and the axiom is therefore no test of
invalidity. If I like to argue that, because A and C are both
greater than B, they are equal to one another, the principle
has nothing to say against it. If I choose to go from " B is
south of both A and C " to, " therefore A and C lie east and
west," again the principle is perfectly satisfied. It can no more
tell me that here I am wrong than that I am right if I say,
" A is due north-west of C, because B is five miles south of
A and again the same distance west of C." The general form
is valid in either case, but the actual operation, whether
erroneous or correct, is in either case beyond the scope of the
principle. It is not a matter for superior direction; it is a
matter for private inspiration and insight.
6. It is impossible that there should be fixed models for
reasoning; you can not draw out exhaustive schemata of valid
inference. There are principles which are tests of the general
possibility of making a construction: but of the actual con
struction there can be no canons. The attempt to manufacture
them would lead to the search for a completed infinity; for
the number of special relations has no end, and the possible
connections in time, space, and degree are indefinite and inex
haustible. To find the canons of valid inference you must
first make a list of valid inferences. You will manufacture a
major premise for each, and that major premise derived from
each operation will appear as its canon. Your success, if you
succeeded, would be the capture of a phantasm, but in the
endlessness of the field you would be for ever eluded, No
canon will fix for us the pale of orthodoxy, until that day
comes when the nature of things will change itself to gratify
our stubborn illusions.
7. The popular belief in logic endows it with ability to
test all reasonings offered it. In a given case of given premises
CHAP. IV THE PRINCIPLES OF REASONING 269
the logician is thought to be a spiritual Director who, if he
can not supply, at least tests right and wrong. Thus, if logic
is no art which provides us with arguments, yet, once give
it the premises, and it is both the art of extracting conclusions
and of assaying all those which amateurs have extracted with
out its authority. But, understood in this sense, logic has no
existence, for there is and there can be no art of reasoning.
Logic has to lay down a general theory of reasoning, which is
true in general and in the abstract. But when it goes beyond
that, it ceases to be a science, it ceases to be logic, and it
becomes, what too much of it has already become, an effete
chimsera which cries out for burial.
8. It should not lie alone. There is another false science
more unlovely in life and more unpleasant in decay, from
which I myself should be loath to divide it. 10 Just as Logic
has been perverted into the art of reasoning, so Ethics has been
perverted into the art of morality. They are twin delusions
we shall consign, if we are wise, to a common grave.
But I would not grudge Casuistry a Christian burial. I
should be glad to see it dead and done with on any terms ; and
then, if all the truth must be spoken, in its later years it has
suffered much wrong. That it became odious beyond parallel
and in parts most filthy, is not to be denied ; but it ill becomes
the parents of a monster, who have begotten it and nourished
it, to cry out when it follows the laws of its nature. And, if I
am to say what I think, I must express my conviction that it
is not only the Catholic priest, but it also is our Utilitarian
moralist, who embraces the delusion which has borne such a
progeny. If you believe, as our Utilitarian believes, that the
philosopher should know the reason why each action is to be
judged moral or immoral; if you believe that he at least
should guide his action reflectively by an ethical code, which
provides an universal rule and canon for every possible case,
and should enlighten his more uninitiated fellows, then it seems
to me you have wedded the mistake from which this offensive
offspring has issued. It may be true that the office of pro
fessional confessor has made necessary a completer codifi
cation of offences, and has joined doctrinal vagaries to ethica
blunders. We may allow that it was the lust for spiritual
tyranny which choked the last whisper of the unsanctified
27O THE PRINCIPLES OF LOGIC BOOK II. PT. I
conscience. It may be true that, in his effort theoretically to
exhaust the possibilities of human depravity, the celibate priest
dwelt with curious refinement on the morbid subject of sexual
transgression. But unless his principle is wholly unsound I
confess that I can hardly find fault with his practice; for if
there is to be an art and a code of morality, I do not see how
we can narrow its scope beforehand. The field is not limited
by our dislikes, and whoever works at the disgusting parts, is
surely deserving not of blame but of gratitude. Hence if the
Utilitarian has declined to follow the priest, he has also de
clined to follow his own principles; he has stopped short not
from logical reasons but from psychological causes.
9. It is natural to think that logic has to tell us how we
are to reason from special premises ; and it is natural to think
that ethics must inform us how we are to act in particular
cases. Our uncritical logic and our uncritical ethics naturally
assume these doctrines as self-evident. But the mistake, if
natural, is in both cases palpable. Unless you artificially limit
the facts, then models of reasoning can not be procured, since
you would need in the end an infinitude of schemes to parallel
the infinitude of possible relations. And a code of morality
is no less impossible. To anticipate the conclusion in each
special case you would have to anticipate all possible cases;
for the particular condition which makes this conduct right
here and wrong elsewhere, will fall outside the abstractions of
the code. You are thus committed to a dilemma : at a certain
point you must cease to profess to go right by rule, or else,
anticipating all possible combinations of circumstances, you
must succeed in manufacturing countless major premises.
The second alternative is in the first place illusory, since the
principle is really got from the intuition, and in the next place
it is impossible, since the number of principles will be limitless
and endless. But if you accept the first alternative, and admit
that only in certain cases it is possible to deduce the conclusion
from a principle, you have given up the hope of your " prac
tical reason," and denied the axiom from which you set out.
The syllogistic logic possesses one merit. If its basis is
mistaken and its conclusion false, at least it has not stopped
short of its goal. In Barbara Celarent its code is perfected,
and it has carried out the purpose with which it began. We
CHAP. IV THE PRINCIPLES OF REASONING 271
can not say so much of the Casuistry of Hedonism. The con
fident dogmatism of its setting-out has been lost in vagueness
and in hesitation. It flies to ambiguities it does not venture
to analyze, and sighs faintly to a Deity which it dares not
invoke. But if the principle of our most fashionable Ethics
is true, then an art of Casuistry and a Science of Sin are the
goal of that Ethics, and the non-recognition of this evident
result, if creditable to the heart, does no honour to the head.
If the popular moralist will not declare for a thorough-going
Casuistry, if he retires in confusion from the breath of its
impurity, he should at least take courage to put away the prin
ciples which have given it life. We may apply to him as he
stands a saying of Strauss, " He partly does not know what
he wants, and partly does not want what he knows." *
10. If we return to the subject of the syllogistic logic, we
may see on the one hand that its moods and figures will not
take in any one of our syntheses except the synthesis of subject
and attribute. The fifth, the fourth, the third, and the second,
refuse to enter the traditional limits. On the other hand the
first of our syntheses covers every argument of the syllogistic
logic. An inspection of the figures would at once assure us
that with positive reasoning this assertion holds good, and we
must now proceed to test our conclusion by applying it to the
subject of negative inference.
* Compare on the subject of Casuistry my pamphlet, Mr. Sidgwick s
Hedonism, 8, and Ethical Studies, pp. 142, 174, foil (Ed. II. pp. IS7,
193, foil.)-
ADDITIONAL NOTES
i There is a main point in this Chapter where, if not correction,
at least some explanation seems necessary. All inference depends on
the unbroken individuality of a single subject; and in this sense all
inference may be said to fall under the category of subject and
attribute (Bk. II. I. VI. 13). But, so understood, this category must
not be taken as merely one among others. It is pre-supposed through
out as the condition of the rest, which, as against it, will be subordinate
and special. On the other hand there are inferences which are made
simply under and by the use of the above category in an individual
case. This will be true, for instance, of the entire syllogistic logic.
Hence to say that on my view logic is confined to the sphere of sub
ject and attribute, or substantive and adjective, would be true or false
272 THE PRINCIPLES OF LOGIC BOOK II. PT. I
according to the sense given to such a statement. Everything, I
agree, must with me fall under this main principle, and I know of
no other main principle which to myself is intelligible. But to add
that on my view the other special categories are not necessary, and
that the conclusions got under these categories could, so far as
correct, be got without them, would, I submit, be untrue. And I am
bound to claim whatever merit is due to me for having insisted
on the opposite. But this double sense in which, in this Chapter and
elsewhere, the category of subject and attribute may be said at once
to preside and yet to be co-ordinate, is, I admit, misleading. And
this double sense, if borne in mind throughout these pages, tends,
I think, to make part of the detail superfluous.
The reader should further keep in view the following distinctions.
We have, first, the knowledge that everything falls within and qualifies
one individual Universe. We next, in any particular case, have to
do also with some subordinate individual whole. Now, so far as
this whole is not taken as known immediately, all the elements
within it must be somehow interrelated. They all are at least related
among themselves as common adjectives. Further, having distin
guished the adjectives within the whole, you can go on to qualify
this whole by what beyond it is true of any of these adjectives so
long, that is, as you do not, by a further abstraction, set free and
substantiate this adjective. And so again, subject to the same con
dition, you can infer similarity (3).
But the knowledge you so far possess does not enable you to
draw conclusions under the more special categories such as Space
or Time or Degree. These have powers and rights of their own,
though, while acting by and under these, you can, at the same time
and concurrently, make use in addition of your power under the
more general category of subject and attribute. But, so long as we
remain clear in principle, the effort to distinguish in detail the pre
cise limits as to where, in this or that case, the above concurrent
use comes in, seems really superfluous.
2 " So far as is required &c." Cf. Bk. II. I. II. 9.
3 " Is not the actual &c." " Is not by itself the actual &c.," would
have been better. And (lower down) "anything which we shall
have" is better, I think, than "anything which we have." Again
lower down, for "get a definite relation" substitute (in the first
sentence) "a more definite relation," and (in the second sentence)
substitute "a new direct relation." And (still lower down) after
"not that general connection" add "nor even anything that follows
from the mere co-inlierence of A, B, and C in a new apprehended
whole."
4 The statement "in the first of these &c.," seems clearly wrong.
And, otherwise, the conclusion would become illegitimate.
5 " The categories . . . footing." See i. And cf. the Index.
6 To " We should then have become circular " add " or should
have failed altogether." So far, that is, as you take this attribute and
CHAP. IV THE PRINCIPLES OF REASONING 273
this subject as immediately one, you remain within one individual
whole of immediate qualification.
7 Here Nos. IV and V must be corrected by the insertion of
" within one world of time or space " after " Where one and the
same term." We can not assume the spatial or temporal unity of
all spaces or times. (See Appearance, the Index.) Whether a similar
correction should be made in No. Ill will depend on the sense which
there is given to " by virtue of one and the same point."
The real question everywhere is whether the consequence is the
self -development of that which we take as the subject, or whether,
by the intrusion of something foreign, the identity of the subject
is broken. When we are asked by a writer in Mind (I regret to
have lost the reference), whether in "A cheats B, B cheats C, and
therefore A cheats C," we have a valid inference the answer is easy.
We have here a good inference if we take the action of A on B as
itself developing itself, without loss of identity, through B into action
on C. On the other hand the inference is vitiated, so far as we
suppose a foreign condition to be necessary, such as to destroy the
process when viewed as the self-development of A s action.
In connection with the Synthesis of Degree I may remark that,
though I failed in this volume to notice what is called the argument
a fortiori, I should at once have placed it under the above head.
The argument obviously depends on the comparative amount of
ground.
s "Private judgment" should be "individual judgment"; and a
similar correction should be made in the last words of this section.
9 " For you do not know, etc." The " for " seems here to involve
some confusion. When (see Note 7) the axiom has been corrected,
it would be better to substitute for " the two space-relations belong to
one world " the words " the premises fall under the axiom."
10 It would, I think, have been better if this attack upon Casuistry
and Hedonism had been shortened, if not omitted.
CHAPTER V
NEGATIVE REASONING 1
i. The general nature of negative reasoning does not
vitally differ from that of positive. We have, given us in the
premises, two or more relations presenting us with certain
identical points, and on the basis of these points we combine
the relations into an individual whole. We then by inspection
find a new relation within that whole. The conclusion rnay
connect two terms directly, as in A B C . * . A C, or it
may connect them indirectly, as A B C . . A (B)C, or
A(B) C. 2 The new line that is drawn may fall clear of the
middle-point of the construction, or may pass through it on the
line of the old relations. Negative reasoning and positive have
all these qualities in common. It is true that in a negative
inference the line that connects the terms of one relation is a
line of denial; one part of the figure, which ideally we con
struct, consists of a repulsion; and the fresh connection we
draw from that construction is a connection by exclusion. But
these differences are varieties within the same main principle.
2. It might seem as if nothing remained for us to do but
to state and illustrate those negative formulae which corre
spond to the axioms of affirmative reasoning. And to this we
shall at once proceed to address ourselves; but it is right to
premise that there are further difficulties which lie in wait for
us at the end of this section.
In negative reasoning we may so state the principle, 3 " If
B is related within one genus positively to A and negatively to
C, then A and C are negatively related within that genus. And
if the affirmative and negative relations (A B, B C) are
heterogeneous, yet, if one is in the category of subject and
attribute, there is a negative inference within one or both of
the two categories which have appeared in the premises."
Unless A B B C are within the same genus, or unless one
is a relation of subject and attribute, there is no connection
at all.
274
CHAP. V NEGATIVE REASONING 275
I. Synthesis of subject and attribute.
(a) Where the attribute is not taken as distinct from every
subject, what is denied of the attribute is denied of the subject,
and where the attribute is denied the subject is denied.
(b) Where the subject is not taken as distinct from every
attribute, what is denied of the subject is denied of its attri
butes, and where the subject is denied then, in that sense, the
attribute is denied.
(c) Where two subjects have the same or a different attri
bute, they are so far not different or not the same.
Examples: (a) "A triangle has not got two right angles;
this is a triangle, and has therefore not two right angles." " A
rectangular triangle is not equilateral ; this figure is equilateral,
and therefore can not be a rectangular triangle." (b) " Man
is not a quadruped, man is a mammal, therefore a mammal
may be (the human mammal is) not a quadruped; and a
quadruped is not a mammal in every sense of that adjective."
(c) " My horse is vertebrate, this animal is a worm, and there
fore is not the same as my horse."
II. The Synthesis of Identity must become a Synthesis of
Identity and Difference, "Where two terms have the same
point in common, and one of them by virtue of this point is
different from a third, there the other and the third differ in
this same point."
Example: "A piano (A) is in tune with B, which is not
in tune with C, and therefore A and C are not in tune with
each other."
In the Synthesis of Degree, of Space, and of Time, we have
no occasion to alter the formulae. We may give as examples,
III. A is as heavy as B, B is not lighter than C, therefore
A is not lighter than C.
IV. A is not before B in time, B is contemporary with C,
therefore A is not before C.
V. A is due east of B, C is not north of B, therefore C is
not north of A.
3. We seem to have performed our task successfully, but
must deal with a further complication. We may be taken to
have sinned against two prominent rules of the traditional
logic, since on the principles we have given you may get a
conclusion from two negative premises, and that conclusion
276 THE PRINCIPLES OF LOGIC BOOK II. Pi. I
may at least in part be affirmative. Yet I can not reject these
traditional rules as errors, and if they have committed over
sights is a question which turns on their interpretation. With
out doubt if you interpret negative premises strictly, that is,
take them in the shape of bare denials, then the rule which
forbids an inference is valid. And the second rule, which
confines the conclusion to a mere denial, is without doubt valid
unless you break through another syllogistic precept. If you
insist on eliding the middle term, then not only must the result
be partly negative, but it really is limited to a judgment which
denies. And thus, if in their statement the rules turn out to
have gone too far, they at all events have been based on a
solid foundation.
It is not hard to understand this; from two bare denials
there can come no conclusion, because there can not be any
construction. Why no construction? Because there is either
no common point, or, if there is a common point, because you
do not know the position of the other terms. Let us take the
last first; in negative reasoning we may represent the denials
by lines of exclusion ; but, if we interpret the premises strictly,
we find ourselves unable to give these lines any definite posi
tion. A is not C nor B, but the exclusion of C and the ex
clusion of B, though we represent them truly by lines of rejec
tion, fall we know not where. The excluded has got no
determinate position, and therefore no known relation to other
elements.
And this is not all, for if we wish to see the real state of
the case, we must go back to our doctrine of the negative
judgment (Bk. I. Chap. III.). A mere denial does not in any
way give existence or position to the thing it denies. 4 Thus
in " A is not B " we assert the simple rejection of B by an
unstated quality belonging to A, and in respect of B we know
nothing at all but its banishment from our universe. But it is
obvious that, when a term is so banished, we know about it
nothing definite save its rejection by A. No matter then how
many negative premises we may have, since by adding to the
number of our banished terms we do not get any nearer a
conclusion. The exiles do not move in any real world at all,
and to unite them by a line of connection is impossible.
Thus even if two denials have a common subject, we can
CHAP. V NEGATIVE REASONING 277
not go from those denials to a further relation.* And we
are stopped elsewhere by another obstacle, for we have not
got the common centre required for a construction. In " A is
not B and B is not C," we have in the one case the exclusion
of B, and in the other case the exclusion by B ; we have first
absence and then presence. And again, if we give our premises
another form and say " B is not A and B is not C," we can
not go to a relation between A and C, since (apart from
other reasons) the quality of B may be quite different in each
denial. Perhaps from " C is not A and B is not A " we might
be tempted to argue to a positive relation of partial identity
between C and B. But here again our centre would be
wanting, for we do not know if the quality which ensures the
rejection is not wholly different in each of these cases. And
thus our premises may furnish a ground for suspicion, but they
no more give us proof than would such positive premises as
" A is like B and C," or " A is like B, and B is like C." In
short given two denials there is either no common point, or
else the two relations which start from that centre terminate
in nothing which can be related.
The rule which forbids all the premises to deny is thus
shown to have a solid foundation; and we may say the same
of the rule which prohibits a positive conclusion. For since
the predicate denied is completely expelled from the world of
the subject, we are left with no relation beside the repulsion.
It is clear then that you can not have a positive connection
either between the predicate and that which exists in friend
ship with the subject, or between the subject and what shares
the fortunes of the predicate. In "A B B C," if one
relation is negative, we can not in any way draw a line A C
which falls outside B. For A and C will be separated in
two different worlds, and if one is in any way to come in
contact with the other, the line of connection must pass
through B. But on one side of B is a mere rejection, and it is
therefore evident that a positive line can not be drawn beyond
the centre, and that the new relation must add to the rejection
which already exists in B. It is indeed not true that this
* In "A is not B and not C, therefore B and C are so far alike "
the premises are positive. B and C are both discrepant in quality with
A, or have the psychical fact of rejection in common.
2321.1 x
278 THE PRINCIPLES OF LOGIC BOOK II. PT. I
extension is a mere denial, and again it is not true that the
conclusion must be wholly negative ; but for all that the second
traditional rule has, like the first, a rational foundation.
4. But though both the precepts stand on a solid basis,
the meaning of the first calls for some restriction, and the
second is not true without an exception. Two denials should
not give a conclusion at all, and yet you can not say that of
two premises which deny. In his Principles of Science, p. 63,
Prof. Jevons has called attention to the subject;
"Whatever is not metallic is not capable of powerful magnetic
influence, (i)
Carbon is not metallic, (2)
Therefore, carbon is not capable of powerful magnetic influ
ence (3)."
This argument no doubt has quaternio terminorum and is
vicious technically, but the fact remains that from two denials
you somehow have proved a further denial. " A is not B,
what is not B is not C, therefore A is not C." The premises
are surely negative to start with, and it appears pedantic either
to urge on one side that " A is not-B " is simply positive, or
on the other that B and not-B afford no junction. If from
negative premises I can get my conclusion, it seems idle to
object that I have first transformed one premise; for that
objection does not show that the premises are not negative,
and it does not show that I have failed to get my conclusion.
And if we leave the limits of the syllogistic logic examples
come to us from every side ; " A degree A can not be less
than B, B is not less than C, therefore C can not be greater
than A, or A must be equal to or greater than C ; " " Event
A is not before B, C is not after B, therefore A is not before
C, or C is simultaneous with A or before it ; " " C is not
north of B, B is not north of A, therefore A is not south of C,
or A is due east, or west, or on the north side of C." It is
bootless here to fall doggedly back on the technical rules of
mood and figure, since, if we keep to these, we can not even
prove the positive conclusions from the positive premises. If
" A to right of B " is a positive relation of A to B which can
not be reduced to predicate and copula, why should we not
have in " A not to right of B " a negative relation which is
CHAP. V NEGATIVE REASONING 27Q
also irreducible? The traditional logic may object to the
latter, but it has put itself out of court by first objecting to
the former; and, if it is quite wrong in one case, it may be
quite wrong in another.
5. In this case it is not wrong, for it happens to be right.
The restricted portion of the field it occupies happens here to
be the limit of the subject. For denial as such can not fall
outside the single category in which the syllogism is shut up.
A denial as such, we have seen long ago, is merely the
exclusion of an ideal suggestion, and hence no negative rela
tion between positive existences can ever be expressed by a
mere denial. But then on the other hand a bare denial can
never be found, for, when A excludes some relation to B
which is offered in idea, there must always be a ground for
that rejection. The base of the rejection must be a positive
quality, unspecified but necessary; and hence, wherever we
have negative judgment, we have in addition some positive
assertion, which may not be explicit but which must be there.
And this, as we saw, is such a fount of ambiguity that in
denials we seldom know all we are saying (p. 125).
We may verify this in the examples we have used. In the
first we assume that A has degree, and upon that basis of
positive assertion we proceed, by exclusion of the alternatives
denied, to a positive result. In the second the argument
really starts from " A is an event with a position in the series
after or simultaneous with B." In the third we assume that A
falls in space and in a relation to B marked out by exclusion.
In all these if we kept to mere denial we could not prove
anything, since we may deny " less than B," or " prior to B,"
or " north of B," of what has no degree and no time and no
position. Such a course might be unusual but is legitimate
and recognized, because the denial as such covers all pos
sibilities.
6. If we take as our rule that from negative premises you
can not argue, then, stated so, that rule is incorrect^; and it is
false even to say that denials give no inference, since every
denial has a positive side. That positive side is latent and
may escape us ; in " 7 is not less than 5 + i, 5 + i not less
than 4, and therefore 7 is not less than 4," we do not say that
7 is a number at all and must stand in some numerical
280 THE PRINCIPLES OF LOGIC BOOK II. Px. I
relation with 5 + i. And thus in assuming it we have passed
beyond the denial, though not beyond what the denial im
plies. It is necessary therefore in expressing our rule to
make a distinction. You can not argue, we must say, from
two denials, so long as you keep to bare denial. If you
treat the assertion which those denials imply, then you are
not keeping to the side of denial. And, if we formulate it
so, the rule will hold good.
Denial implies removal or exclusion, and from exclusions
or removals you can get a conclusion. " Removal of A is
removal of B, removal of B is removal of C," gives " Removal
of A is removal of C ; " and " Absence of A is absence of B,
absence of B is absence of C," proves that absence of A is
absence of C. But here our real premises are " What re
moves A removes B," and " That which is without A is also
without B." You can hardly say that these premises are
quite positive, but they contain much more than a bare denial.
Thus negation must always remain ambiguous (Book I.
Chap. III.), for "No A is B," may merely banish B, while
again it may assert " The absence of A is the presence of B."
" If A is there then B will not be there," and " Since A is not
there B must be there " are both expressed by this doubtful
formula. But if we confine negation to mere denial it is the
exclusion of an idea by an unspecified quality, and if we con
fine the denial to its negative side it is the mere exclusion of
a suggested idea. It is upon this last understanding that the
traditional rule is actually valid.
It would not be valid if negation were assertion. If in " A
is not B " the exclusion of B were a condition necessary to
the existence of A, then B must be banished if A is to be
there, and if B is not there B can not be banished. And from
negative premises, if so interpreted, it no doubt might be
possible to get some conclusion. But this interpretation we
long ago saw was erroneous. The denial excludes an ideal
suggestion, and the fact which lies at the base of the exclusion
need be no relation of A to B, but on the other hand a quality
of A or again of some more ultimate reality. But this quality
is latent and wholly unspecified.
7. We have seen that, upon a strict interpretation of
negative premises, the first of the rules we mentioned is valid.
CHAP. V NEGATIVE REASONING 28l
What then is to become of our principles of synthesis, since
they collide with the rule and can not be true ? But I think it
is better to leave them standing, for they are valid if the
sense of negative premises is not confined to what they deny.
Otherwise of course they must be corrected. It is im
possible to have any negative inference which will fall wholly
within the categories of identity, or time, or space, or again
degree. One premise at least must confine itself to the rela
tion of subject and attribute.
This is very obvious. One premise must deny, and no
denial as such can be referred to any category beyond the
relation of attribute to subject. The denial is the exclusion
of an ideal suggestion, and a relation of time, or space, or
degree falls within this suggestion which the subject repels.
It is clear then that the denial of a connection, say of space,
is not a connection in the category of space. The subject
excludes, it is true, by a quality, but you do not know what
that quality is. And since you do not know what quality
repels, the repulsion and the quality which forms its basis can
not pass beyond the sphere of simple attribution. Thus " A
is not north of B," if restricted to denial, means " A repels the
suggestion A to north of B ; " and we can not possibly take
this as anything more than an adjective of A.
If we refer to the examples we gave in illustration (2),
we must so interpret the negative premises. "B is not in
tune with C " means " B excludes the attribute of being in
tune with C," and " B is not lighter than C " means " B ex
cludes a certain relation of degree to C." But of course B
might repel these relations with C although it possessed no
note at all, and although it had no degree of any kind; and in
the same way the denial that B is in such a position may be
true though B has no place whatever. If one of the premises
be confined to denial that premise is shut up within the
category of subject and attribute. m f
But having so restricted the character of our premises it is
natural to expect a restricted result. Our rule will now be,
" In all negative inferences the conclusion is confined within
the relation of subject and attribute, unless that conclusio
can in any way be affirmative." m
8. But can the conclusion be anything but negative!
282 THE PRINCIPLES OF LOGIC BOOK II. Pi. I
This is the question we have next to discuss. The rule for
bade an arhrmative result, and we saw that this rule was
based upon truth. For since in A B B C one relation is
negative, A C can not be joined by a line of connection
which passes anywhere except through B. And, since part
of this line must consist of an exclusion, we saw that A C
must have a negative character (3).
The result is unshaken, but it omits a possibility. The
conclusion need not take the form of A C, since the result
which we get from the union of our premises, may be found in
the whole ideal construction. The syllogistic practice is to
elide the middle; but if we do not choose to perform this
elision, who on the one hand can order us to do so ? And on
the other hand who can deny that the result which we obtain
is a real inference? " A takes precedence of (is lighter than,
sits on the right of) B, B is not younger than C, therefore A
takes precedence of (is lighter than, sits on the right of) a
person (B) not younger than C." There is here no direct
conclusion A C, and there is again no inference within one
category, and at the same time one premise seems to be used
as mere denial. On the other hand I see no reasonable ground
on which we can deny that we have got a conclusion. Yet
this conclusion is neither a mere denial, nor does it fall within
the category of subject and attribute.
We may go beyond this. In the syllogism itself, if we
decline to elide the middle term B, we may have an inference
the conclusion of which is more than a denial. Take an
instance in Celarent, "A lung-breathing animal (B) is not a
fish (C). All Cetacea (A) breathe by means of lungs (B)."
From this the regular conclusion is " A is not C." But " All
Cetacea have a quality, viz., breathing through lungs, which
excludes the assertion that any are fish," will surely come with
out flaw from the premises. It certainly is more than a bare
denial, and it is no mere repetition of the premises. And to
say, If A does not exclude C after the middle has been elided,
there shall be no inference and there can be no conclusion,
seems purely arbitrary. Nor indeed do I see how this in
sistence on elision, if we pressed it to its consequences, would
prove compatible with the general validity of the third figure.
9. The result we are left with may thus be stated. From
CHAP. V NEGATIVE REASONING 283
two denials there is no conclusion. If one premise denies and
keeps to denial, then one premise at least is limited to the
genus of subject and attribute. If the middle term B falls out
of the conclusion, if A and C are connected through B, but
not by means of an intermediate B, then the conclusion denies
and falls also within the above-named genus. But if B is kept
standing, the conclusion may at least in part be positive, and
is not confined to a single category.
The general formula for negative reasoning, if we confine
ourselves to the side of bare denial, may be stated as follows : 5
If B repels a content C, and is in relation with a third term
A, then A and C will either be related directly by way of
denial or else will be elements in a whole A B C, of which
at least one member will be confined to the genus of subject
and attribute. And I think with this we may take leave of a
subject which has proved perhaps more troublesome than in
teresting.
ADDITIONAL NOTES
1 The statement that all reasoning, negative as well as positive,
depends on an ideal whole, and that this whole can be called a con
struction, is so far correct. But otherwise this section, and much of
what follows, is unsatisfactory. Every negation (see on Bk. I. Chap.
III.) implies a disjunction. And only because, and so far as, negative
reasoning is based on and further developes a disjunctive totality and
system does it possess a real value. For an admirable exposition
of this view the reader is referred to Bosanquet s Logic.
If we keep to mere denial, what is denied will certainly fall some
where else in the Universe, since no mere ideas are possible. But,
because the variety of special worlds within the Universe is indefinite,
and because the merely denied is not, so far, located, you can base
no special connection on the fact of mere simple denial. If negation
is to be fruitful, it must (to repeat this) stand upon and move within
a scheme of specialized alternatives, related to each other at once
as positive and negative.
Hence it is scarcely worth while for me to attempt to correct
chapter in detail. I will, however, touch on a certain number <
points.
2 The usual demand for the elision of the middle term seems n
defensible, and any rule that the conclusion must merely deny shou
therefore be modified. See 8. But the rule which condemns
284 THE PRINCIPLES OF LOGIC BOOK II. PT. I
two negative premisses, in the sense of two denials, must stand. For
what is denied may fall in worlds not so connected as to make a
construction possible. Hence, unless by going beyond mere denial one
premiss becomes positive, no conclusion can be reached. In 4 after
quaternio terminorum " we should add " or else one positive premiss."
3l lf you keep to mere denial, as distinct from exclusion, repulsion
or absence, all that is implied is an unspecified whole (x) containing
two diversities (A and B). These must be positive, but, so far as
you merely deny one of the other, you attend simply to their differ
ence. Further, by identifying one of them (A) with C, you can
deny the other (B) of C. But neither here nor elsewhere is there
any inference through mere denial beyond the category of subject
and attribute. As soon as you have assumed worlds containing
arrangements and relations other than those of identity and difference,
you have gone beyond mere negation in the sense of denial.
Hence the "general formula" (9) can not stand, and should
perhaps be read thus " If you deny of B a content C, C can also
be denied of that which is identical with B, and can further be
related indirectly by denial with that which is related positively to B."
But, though in the latter case the " conclusion " need not be " con
fined to a single category," the inference, and what actually is
concluded, never goes beyond the category of subject and attribute.
Statements to the contrary ( 2, 8, and 9) are erroneous.
4 In the way of minor corrections I may here note that we should
insert "definite" before "existence or position"; and (at the end of
the paragraph) should read "move in any one real world at all."
And, generally, I would remind the reader that such terms as "re
moval," " exclusion," " repulsion," and even " absence," all are affirma
tive in the sense of at least containing a positive aspect. And this
aspect goes beyond what is contained in negation, if and so far as we
take that as mere denial.
6 For " the general formula " see Note 3.
CHAPTER VI
TWO CONDITIONS OF INFERENCE
I. We may briefly recapitulate the result we have
reached. An inference is always an ideal construction result
ing in the perception of a new connection. So far as this
perception of the conclusion is concerned, there is no possibility
of laying down rules, and the syllogistic logic teaches a super
stition. That logic again has failed to include all the prin
ciples of synthesis which operate in construction, and it is
falsely confined to a single category. It is wrong again as
to the number of the premises ; and, in insisting on the neces
sity of a major premise, it is clinging blindly to exploded meta
physics in direct defiance of the most palpable facts. And it
makes a further mistake as to the necessity of elision.
It might seem that having thus rejected the syllogism we
must throw in our lot with its hereditary enemies. But yet,
if the friends of the syllogism will allow it, we would rather
take a place on their side. Our differences are trivial com
pared with our agreements, and as against the enemy our
cause is the same, for we have in common these two beliefs :
(i) It is impossible to reason except upon the basis of identity,
(ii) It is impossible to reason unless at least one premise is
universal. It will be time to say vlcerunt empirici when these
positions have both been forced.
2. (i) I will begin with the necessity of an identical
point. We know that an inference is an ideal construction,
and the reality of this construction depends on its unity; if
the construction is not individual it is merely fictitious. But
how can any construction have unity unless it is united by
a common point? And how can any point be common, unless
in both the premises it is one and the same?
It is obvious that suppose the problem before us is to find
the relation of S to P by means of their common relation to M,
and if, by the hypothesis, S-M and M-P must be given
separately, an advance is impossible, unless in both premises
285
286 THE PRINCIPLES OF LOGIC BOOK II. Px. I
M is the same. Given S M 1 & M 2 P you can make no
construction, for you have no bridge to carry you over from
M 1 to M 2 . The back of your inference now is broken and the
extremities no longer belong to any individual principle. Un
less M in both cases is absolutely the same you can not inter
relate S and P.
If we are willing to give up the superstition of the copula
and to admit a diversity of relations in judgment, we may say
that in inference every pair of premises has one term the same,
and that, if it is not the same, there can be no inference.
3. It is obvious, if we dismiss our hardened prejudices
and consider the question fairly by itself, that you can not
argue on the strength of mere likeness. 1 Whatever else may
be right this at all events must be wrong ; " A is similar to
B, and B to C, and therefore A is like C," is a vicious infer
ence, one that need not always be mistaken in fact, but that
always must be a logical error. In practice I think we should
all admit this. An inference based on nothing but likeness
is utterly invalid; it is certainly ambiguous and probably
false.
Likeness and sameness should never be confused, for the
former refers properly to a general impression. Similarity is
a perceived relation between two terms which implies and
rests upon a partial identity. If we say that A and B are
alike, we must be taken to assert that they have something the
same. But we do not specify this point of sameness, and the
moment we do that we have gone beyond mere similarity. If
A and B for instance both have lungs or gills they are so
far the same, and, on the strength of and because of this
partial identity, they may present themselves to us as
generally similar. But now add to these the further statement
" B and C are alike." If we reduce the likeness here to
partial identity we may find that the common point is here
once again the possession of lungs or gills, and on the strength
of this we may go on to argue that A and C (the extremes) are
alike. But what actually interrelates A and C is not general
similarity at all. If all you knew was that B was like C, the
point of identity would be quite unspecified, and the fact
might be, not that both had lungs or gills, but that each had
one eye or the freedom of the will. In this case though each
CHAP. VI TWO CONDITIONS OF INFERENCE 287
pair has its own internal likeness, you could not infer the
similarity of A to C.
And if in answer I am told that this is irrelevant, and that
it does not apply where the likeness is exact, I can only reply
that I am waiting, and have been waiting for years, to be told
what is meant by an " exact likeness." " A and B are not the
same, but they are exactly alike, and therefore whatever is
true of B must be true of A." But what can this mean? In
the case of some twins it might be right to punish one for the
other, and we should no longer care to identify criminals.
If a picture is " exactly like " a person, then if one is not dead
the other will be alive. If a cast is " exactly like " an original
I suppose the same thing will be in two places at once ; and it
is no mere metaphor if in certain cases the father is said to
survive in his children, though the children might then cease
to survive the father. But it is idle to pursue these frivolous
consequences; the meaning which "exactly like" carries to
my mind is nothing whatever but "partially the same" or
"identical in some point or points." Likeness is always a
perceived relation based upon a partial identity. In mere
general similarity the identity will be indefinite; where the
likeness is more special it must at least be partly defined,
and where the similarity is called "exact" I understand that
there is a definite point or points, in respect of which the same
ness is complete. And if likeness did not imply identity all
inference based upon it would be vicious. In practice every
one would allow it to be vicious, nor do I understand how in
theory it is possible to take it as having any other character.
I am most anxious to enter into (if I can), and to discuss
the meaning our "advanced thinkers" may have attached
" likeness " or " similarity." But I am forced to say again in
this place what I had to say elsewhere some years aga
While our "advanced thinkers" merely sing the old song
which they have learnt and which their fathers have taught
them, they can hardly expect to have its meaning discussed
nor can they complain if they are treated as having no
construction of given premises is not possible un-
less each pair of premises has a common point. And
* Ethical Studies, p. 151 ( Ed - IL P-
288 THE PRINCIPLES OF LOGIC BOOK II. ?T. I
common point must be an identical term. Thus in "A B
B C therefore A B C" the B in each premise must not
be merely alike, but must be absolutely the same. But here,
after having avoided one error, we are threatened by another
and opposite mistake. For if it is wrong to say that B is not
the same, it is equally wrong to deny that it is different.
This may look mysterious but is really quite simple. If
B in both premises were so far the same that no difference of
any kind belonged to it, then it is obvious at once that both
premises must be identical, or else that their differences do
not concern B. But in each of these cases the inference dis
appears. If the premises are the same their repetition is
meaningless, and if the differences they contain are indifferent
to B it is clear that no construction can be made, since, if B
is the centre, it carries no radii and has no circumference. An
identity which is not a synthesis of differences is plainly inert
and utterly useless.
B is the same amid difference, and though different is the
same, for it is an ideal content, the product of abstraction,
appearing in and differenced by two several contexts. So far
as it is the one content B, so far it is absolutely and entirely
the same ; so far as it is a member of diverse connections, so
far it carries with it a difference. And the process of inference
depends entirely on this double aspect; for it is because B is
different and yet the same, that its differences are able to be
interrelated. If it were not different it would have nothing
to connect, and if it were not the same there could be no
connection. Inference rests upon the assumption that, if the
ideal content is the same, then its differences will be the radii
of one centre. In other words if B is the same, what is true
of it in one context is true of it in another.
5. We have returned to what we called the Principle of
Identity (Book I. Chap. V.). We might call it again the
Axiom of the Identity of Indiscernibles, and we can put the
thing in more simple language if we say that inference rests
on the principle that what seems the same is the same, 2 and
can not be made different by any diversity, and that so long as
an ideal content is identical no change of context can destroy
its unity. The assumption in this principle may be decried as
monstrous, and I do not deny that perhaps it is false. In a
CHAP. VI TWO CONDITIONS OF INFERENCE 2Q
metaphysical work this question would press on us, but in
logic we are not obliged to discuss it (Book III. Part II.
Chap. IV.). The axiom may be monstrous or again it may
be true, but at least one thing is beyond all doubt, that it is
the indispensable basis of reasoning. It may be false meta
physically, but there is no single inference you possibly can
make but assumes its validity at every step.
6. It is easy to misunderstand it, and it is sure to be
misunderstood. I shall be told that spaces and times are
indiscernible and yet are not identical. But this objection
rests on a complete mistake. As spaces or times of a certain
character A and B surely are identical ; as different elements
within the same series A and B are surely not indiscernible.
It is one superstition to think you have relations whose
terminal points are nothing beyond the relation.* It is
another superstition to fancy relations as an arbitrary network
stuck on from the outside by destiny or chance, and making
no reasonable difference to anything. And the root of both
superstitions is the same. It is the refusal to recognize that
* I am prepared to go a good deal beyond this. 3 If occasion offered
I should be ready to argue that you can not have a relation between
points that are not different in quality. Not only, for instance, must
spaces related be more than a mere relation in space, but they must
also have a difference in quality. It is not possible to contemplate
points in relation unless you distinguish them by a qualitative reference
to the right or left or upper or lower sides of your body, and the
different sensations which are at the root of these divisions, or again
unless, by a qualitative mark such as A or B, you choose to make one
different from the other. It may be objected that in certain cases the
difference of quality is only one aspect of the whole relation. This
view at least recognizes the existence of the difference, and I will not
here discuss it. The ultimate connection of quality and relation is a
most difficult problem. But it is clear that taken in their phenomenal
appearance the one can not be reduced to the other. Is this double
aspect true of the reality? Has that, as we are forced in the end to
apprehend it, a single nature which combines two sides, and is so the
root of the double appearance? Can we suppose that qualities are
generated by the strife of some counterpart of what appears to us
as relations? Or is it true that supersensible qualities are the reality
which we perceive as phenomenal relations? Or is the question un
answerable? If it is, we at least must not do violence to the given on
the strength of a theory which we can not defend (cf. Book I. Chap.
II. 65 foil.).
2QO THE PRINCIPLES OF LOGIC BOOK II. PT. I
the content of the given has always two sides, 4 sensible quali
ties and relations, and that one side can never, except by an
artifice, be separate from or merged in the other. I do not
say that these two elements are metaphysically irreducible;
I do say that, taking them each as it stands, you must treat
them each as a character of the given. It is a dire illusion
to take the content of the given as either qualities without
relation or relations without qualities, or to treat the one
side as external to the other. Both are given together and
given within the content. It was shown above (Bk. I. Chap.
II. 21) that space and time-relations are no principium in-
dividuationis ; for they fall within the what, and do not make
the this.
And another result was brought out in that Chapter. Un
less judgments of sense make a false assertion they affirm
or deny connections of content, and they do not affirm any
thing else whatever. It is absurd to object that if Caesar is
the same, he is in Gaul and in Italy, two places at once, or
that if he is thirty he is also twenty-nine. The " at once "
and the "also " conceal the old error. Of course it is not true
that the identical Caesar under the same conditions 5 can be
differently related to Italy in space or to his own birth in
time; but then surely the conditions vary indefinitely. The
mere lumping together unspecified conditions under the head
" is now " does not show that the conditions are indiscernible,
and that striking the differences out of the account we are
forced to predicate contradictions of Caesar. What is true of
Caesar in a certain context is true of the same Caesar in any
other context. But this does not mean that one context is
the other or is to be confused with the other. It means that
Caesar has two different contexts, and that the truth of one
can be no reason whatever for the falsehood of the other. If
we fancy this is so we have given to one or to both assertions
a meaning which is false, and we must be sent back once
more to study the discussions of Book I. Chapter II.
7. And there is another misunderstanding against which
we must guard. That what is true of B here is true of B
everywhere, means that, wherever B happens to be, you can
say of it always what you have said of it once. This B you
assert of is the self-same B that appears in the differences, but
CHAP. VI TWO CONDITIONS OF INFERENCE 2QI
it is not the B just as it appears in those differences. In
A B, B C, the B is identical, and A and C are connected
by that identity. But A and C are not themselves identical,
and you can not predicate B C of A B. The B, of which
what has once been said holds good for ever, is not the B
which is one thing with A or one thing with C. It is the ab
straction, 6 the idealized content B, which is different from its
contexts and yet connected with them, and on the strength of
its oneness connects them together. The identity is always a
synthesis of differences which themselves are not identical the
one with the other, and apart from these differences the
identity disappears into blank indiscriminateness.
I will try to illustrate the whole question briefly. We
have a shed in the corner of a field, and, that shed being burnt,
another is set up not distinguishable in itself from the first.
Let the first be B A and the second B C ; in what sense
is it true that what holds of B once will hold of it always?
The objection is obvious, In the shed B A an event D hap
pened, but can we say that the event took place in B C?
And if we can not say that, and if B is not distinguishable, how
are we going to defend our axiom?
We are in no kind of perplexity. The content B is ob
viously not the individual shed. The two sheds are made
individual by their places in the series, and those places fall
outside the abstraction B. What is true of B is universal
propositions and is nothing besides. The event D can not
be asserted truly until it becomes a hypothetical statement
(Book I. Chap. II.).
But the objection will be pressed, " The sheds and their
environment are a certain content, and that content is the
same. If, on the strength of this content, we said of the shed
B A D happened here yesterday/ why can we not also
upon this ground now say of the shed B C D happened here
last year ? The content is what we go from, and we have
that in both cases." I reply, By all means: the content is
the same. Let us try to carry out the process you recom
mend. We can not of course connect D with B C unless
we establish a chain of relations through the identity of their
end-points (ibid.). You can not go direct from the content .
to the temporal event D, for that, as we have seen, is not
THE PRINCIPLES OF LOGIC BOOK II. PT. I
predicated categorically (ibid.). 7 You must start from the
content as given in one time. Well, starting from B A you
got a chain of events which took you back to D. But, if
you start from B C, you have a chain of events which takes
you back first to the origin of B C, when B did not exist,
and then again through the destruction of B A, to the time
when B once more existed and was connected with D. Your
process informs you that D the event will not fall within the
identity of the ideal content B C. That content has been
qualified by a limitation in time, and qualified again by a
definition of its component elements, which excludes their
identity with the elements of B A. If you deny that these
qualifications are objects of knowledge, then I admit D is true
of B C, and why in the world should we not think it true?
But if you admit that these qualifications are distinctions, then
the content of the sheds is not indiscernible, and therefore by
your admission is not identical. 8
This, I think, is a sufficient answer to the objection, but
it omits to take notice of several difficulties. There are ques
tions which no doubt might occasion us trouble, but they
do not seem to concern us here. We have been forced to
notice a metaphysical problem which, at least in this work,
we can not deal with, and hence objections which we can not
here attempt to answer may be directed against us. But at
least on one side I think we are safe ; we need fear no col
lision with the Philosophy of Experience, for that philosophy
does not know the ground it stands on. Since Hume s bold
speculations on the subject of identity were suppressed by
himself, the English school has repeated a lesson by rote and
flaunted a blind ancestral prejudice.
8. The importance of the subject may excuse a repe
tition. That what is the same ideally is really the same is
without any doubt an enormous assumption, and I do not say
that this assumption is true. What I do say is (a) that all
inference presupposes it, and (b) that the objection to it rests
on nothing but metaphysics.
(a) If we only will look at the palpable facts, we must
admit that logic stands or falls with this axiom. Wherever
we join one premise with another we must do so by means of
an identical point, which, given as it is in diverse presenta-
CHAP. VI TWO CONDITIONS OF INFERENCE 2Q3
tions, is held to be the same because it has the same content,
and which, so far as it is not ideally discernible, is taken as one.
Failing this identity the construction falls apart. I confess I
do not know how to make this any clearer. I can only say
to any one who doubts it, Show me an inference where this
does not hold good, and I will show you a vicious inference,
and you yourself shall admit that it is vicious.
(b) It sounds terrible to say that Identity is an ideal syn
thesis of differences, and that this identity is real fact. The
words are strange to the common mind, but it has always
tacitly accepted their meaning. We believe that a body has
changed its place, but at the end of the movement the change
that is past is no fact of sense. We abstract the body from
its present position and, treating this abstraction as a con
tinuous identity, we predicate of it the changing differences.
But do we doubt that motion is a real fact? And if we are
told, It is the material atoms which are the same throughout;
then why I would ask do we take them for the same, despite
their differences of time and space, except because their ideal
content is the same? The identity of indiscernibles may be
true or false, but not only is it impossible to reason without it,
but it is the abstract formula for our common-sense belief.
The authority of common sense is no authority for me,
but the result we have reached may bring out one fact.^ The
objection, raised by the Philosophy of Experience against a
real identity, does not rest on any difficulty felt by common
sense, and it is not an objection it would ever think of raising.
It is a metaphysical objection, and it rests entirely on a
metaphysical doctrine. It is because the Philosophy of Ex
perience is sure that there is no reality except exclusive par
ticulars, that it is horror-struck at the thought of a real
universal. And because its belief is not proved nor thought
to need proof, nor in any way discussed, because it is a mere
inherited preconception which has got to think itself a real
fact, it is scarcely so much to be called a doctrine as an
orthodox dogma and traditional superstition.
And, as it must happen with all orthodox dogmas, its
votaries do not take their professions in earnest. If an uni
versal content may ever be real, on what ground can they
deny the identity of thoughts because one is yesterday and
2321. I U
294 THE PRINCIPLES OF LOGIC BOOK II. Px. I
the other to-day? But if such ideal sameness is not real,
then how can any process or change or continuity be any
thing but illusion? If a thing is not now the same that it
was, if it is only alike, then it can not have changed. And if
it is the same, on what ground do we make that assertion
except on the ground of identity of content? It is frivolous 9
to say that identity may be real, where existence is continuous
and is not broken in the series of time, but is not real any
where else. For if you allow that any lapse or change is a
fact, you have admitted the reality of an element not confined
to this or that particular, and you have admitted it on the
ground of the identity of indiscernibles. You have already
thrown your principle overboard, and if it is false in one
place it may be false in another. Or to put the same thing
in another form, if you are afraid to break with common sense
in one point, what makes you so very bold in another? If I
am to answer the question for you, I am forced to say that
you have partly no head and partly no heart. You do not
see the consequences deducible from your doctrine, and when
a consequence begins to look like a reductio ad absurdum, you
refuse to follow it. And this is what we call or used to call
" advanced thinking." 10
9. It is against such opponents that the syllogism is right.
The doctrine of copula and terms which it cherishes is in
defensible, but it is right in demanding an identity in reason
ing. The middle is an identity which connects the differences,
and, being such an identity, the middle is an universal. In
this point again the syllogism is right. For though the major
premise is a superstition, one premise at least must be uni
versal or else there can be no inference at all. We have here
again a condition necessary to reasoning.
10. (ii) We saw in the second chapter of Book I., and
later on again in Chapter VI. 39, that in the end no judg
ment is really particular. 11 They are all universal. And we
might content ourselves here with recalling the result we there
have reached, but, perhaps at the risk of superfluity, we may
add some further remarks on the subject. If one of the
premises were not universal, how could they both have a com
mon identity? The term B must be shared by both the
premises. It is a single content in two different contexts. But,
CHAP. VI TWO CONDITIONS OF INFERENCE 295
since thus it is universal, at least one premise must have the
same character.
This simple consideration is, I think, sufficient for any
one who has put himself at the right point of view. But not
withstanding all our previous discussions, there no doubt will
be readers still unwilling or unable to follow us in this argu
ment. " In A precedes B and B precedes C can B," we shall
hear, "be really universal? Nay even in the syllogism, if we
take the third figure, is the middle term really an universal?
It is so technically because it is distributed, or understood in
its full extension, but these technical distinctions have long
ago been thrown overboard, and with them has gone the uni
versality of singulars." I will briefly reply to the above objec
tion.
II. An universal judgment is one that holds of any
subject which is a synthesis of differences. It is a proposition
the truth of which is not confined to any single this. The
subject extends beyond the judgment, and, where the subject
goes, the judgment is true. In this sense we have seen that
all judgments are universal. But we are limited here to a
simpler issue, for we have to show, given a valid inference,
that at least one premise is universal. It is quite enough, as
we have just remarked, to consider the identity of the middle
term: but a more detailed exposition may perhaps be wel
come.
There are certain cases which call for no discussion.
Where the middle term is an abstract attribute, and this forms
the subject of one of the premises, there one premise must
be allowed to be universal.*
The difficulty which is felt arises from those cases where
the middle term is a singular, or where it is not the ostensible
subject of either premise. Take for instance " A is to right of
B, and B of C, and therefore A of C," or " A and C have
the note B in common, and therefore C is in tune with A,
and both related by the identity of B." How in such infer
ences as these can we show that one premise must be universal?
* In order to bring arguments into this form we may freely convert
any negative judgments. Thus in the second figure we may convert
as required, negative premises or conclusions. The case
presents no difficulty. 12
296 THE PRINCIPLES OF LOGIC BOOK II. Pi. I
12. Unless our previous discussions have led us quite
wrong, such a question as this can be readily answered. " B
is to right of C " is an universal judgment because B is an
identity which has the differences of its spatial relations to A
and C. ia It transcends the context B C and is therefore
universal. Or, from another point of view, the relation B C
is true of a subject which extends itself beyond those limits,
and is the identical subject of which the relation A B is
also true. If you take the relations as qualifying B, then B is
the universal which exhibits these differences. Or again if you
go somewhat further back, then the unity of the common
space is the genuine subject of which these relations are
diverse attributes. We can always find an identical subject
although that subject need not be apparent. In " Caesar is
angry and Caesar is silent, and therefore silence may accom
pany anger," it is the grammatical subject which supplies the
universal within whose identity the synthesis holds good. But
where from " A has a certain note B and C has also the self
same note," we infer a relation between A and C, it is doubt
ful where the actual subject lies. If we are willing to accept
the grammatical subject, then in " C has the note B," C is our
universal. For C is disturbed from its original context and
expanded ideally so as to form a whole with A. And, if it
were not universal, it could not be treated as a subject waiting
to receive a predicate beyond its original given existence.*
This would be the right interpretation if A and C are to be
considered as subjects. But it is better here, I think, to take
the middle as the actual subject of both the premises. B is
the universal of which we predicate the difference B A and
the difference B C, and it is the bond of identity which
interrelates the whole.
13. We shall see hereafter that every inference may be
taken as holding within the identity of one subject (Book III.
Part I. Chap. VI. 34), and if we take this view it is obvious
that the subject of both premises is universal. For the present
it may prove sufficient to remember that, inference being an
ideal construction and involving therefore an ideal centre, one
premise must be taken as true beyond the limits of a par-
* Of course if you suppose the relation A C to be a perception
got simply from the given, then there is no inference and cadit qu&stio.
CHAP. VI TWO CONDITIONS OF INFERENCE
ticular subject. If we keep hold of this reflection we shall
not be shaken by any puzzles which are laid before us. In
the previous Book I have endeavoured to anticipate and
to cut the root of those difficulties which are the most likely
to be raised, and it is to the discussion of that Book that I
must refer back the reader who is still inclined to hesitate.
In the ensuing Part of the present Book we shall criticize
some inadequate views of inference, and shall begin with that
belief which is most opposed to the doctrines set forth in the
present Chapter.
ADDITIONAL NOTES
1 On Similarity, Likeness, and Identity, see the Indexes, to this
volume and to Appearance and Essays.
2 " What seems the same is the same." It should be " is so far
the same." Error as to the exact point of sameness remains possible.
And after " diversity " should perhaps have come " further " or
"added". What must be rejected everywhere is the idea of a simi
larity which does not imply sameness. The " Axiom " so far as it is
an axiom holds obviously also in Metaphysics. On the ultimate dif
ficulty as to Identity, see Essays, Index.
3 These points have been taken up by me in later works. There
is here a partial failure to realize the true conclusion that, just as
terms and relations are neither present at the beginning of knowledge,
so both alike are subordinated and transformed in the ultimate end.
Terms and relations are (as is seen in this volume) alike abstractions,
and (we must add) are, each alike, unreal as such.
* " The content of the given has always two sides." We must re
member here that, if so, Immediate Experience or Feeling must not
be called "given." See Bk. III. I. Chap. VII, and Appearance and
Essays.
With regard (three lines below) to "metaphysically irreducible,"
we can not possibly (I should say) "reduce" these "elements."
But we can know that in the ultimate whole they lose their characters,
as such, and so far as irreducible.
5 "Under the same conditions." What is true of B once is true
of B always under the same conditions. And, if you object that the
different conditions must both be true of B, that must be admitted.
It points to the conclusion that, while mere B A and mere B (
are in the end abstractions and neither in the end true, both are. still
true relatively. We have to assume a concrete whole containing still
further conditions such as to modify these terms and to unite them
in something higher. But in this whole, we ^ must remember, con
ditions and terms cease in the end, as such, to exist.
298 THE PRINCIPLES OF LOGIC BOOK II. Px. I
6 " It is the abstraction." It would be better to say " the universal,"
because the identity may perhaps be that of an organic individual
whole, and, so far, not "abstract."
7 " Is not predicated categorically." " Unconditionally " would be
better.
8 " Is not identical." And even in the case of a single shed, where
it remains throughout one and the same, it still is qualified by its
temporal diversity, so as to be also so far different, and, so far again,
not indiscernible.
9 " It is frivolous to say, etc." " Frivolous " may perhaps in some
cases go too far, but " irrational " would, I think, hold everywhere.
If you keep to change as perceived, then within that perception you
have identity in diversity, and you have ideality, though so far you
do not abstract it. Either that, or your perception is not the percep
tion of change.
On the relation of Continuity to Identity, see further Appearance,
the Index and the Note on p. 616.
10 " Advanced thinking." The above tirade, if unnecessary, was
in 1883, I still think, wholly justifiable.
11 " No judgment is really particular." We may put it thus, that
all judgments are of content, and that no content sticks in the mere
"this." See Appearance, Index. And further, on Designation, see
Essays, Index. The lesser conclusion as to one premiss is, however,
sufficient here. Cf. Bosanquet, Logic, II, pp. 203-4.
12 This footnote might without loss have been omitted.
13 " Because B is an identity, etc." " Because, in making the infer
ence, B is used as an identity, etc.," would have been better. And
so below, in " For C is disturbed, etc.," we should perhaps insert
after C the words "in the inference."
BOOK II. PART II
CHAPTER I
THE THEORY OF ASSOCIATION OF IDEAS x
I. The end we had before us in the first part of this Book
was to give a general account of inference. The account was
m a certain sense provisional, since the examples it dealt with
did not pretend to illustrate every kind of inference. But
within those limits the result we arrived at seemed irref ragably
The end we have before us in this Second Part, is the
criticism and refutation of certain theories which are out of
harmony with the conclusion we have reached.
The title of this chapter calls for explanation. "The
Association of Ideas," it may be objected, "is not so much a
theory as a fact; a fact which on the one hand is quite
indisputable, and which on the other hand can be discrepant
with no theory except a theory which runs counter to fact."
But the objection would rest on an entire misunderstanding.
The psychological fact of "Association" is of course un
questionable. The account of that fact which is given by the
orthodox English philosophy, is in my judgment not only
questionable but false. And, beside being false, it is incom
patible with any tolerably accurate theory of reasoning. For
the universality and identity, which we saw were necessary for
every inference, do not exist in the theory of " Experience."
We are offered in their stead a fictitious substitute, which does
not exist and therefore can not work, and which would not
work even if it existed.
2. "Inseparable Association," and the "Chemistry of
Ideas," are phrases which are only too familiar to most of us.
They recall a controversy which has served in some measure
to obscure the questions it professed to elucidate. But the
more refined developements of the Association doctrine do
299
3OO THE PRINCIPLES OF LOGIC BOOK II. PT. II
not immediately concern us here.* For they have no direct
bearing on the theory of inference; and it is solely as it
touches the subject of reasoning that we have here to do with
Association. We may confine our attention to the common
doctrine, as exemplified in the ordinary working of the Laws
of Resemblance and Contiguity.
3. The " association of ideas " is a phrase which may be
taken to express a well-known psychological fact. And if
taken so, it is nothing but a title. The fact, which it stands
for, is a familiar experience, and the meaning of the title is
not proposed as an accurate theory of that fact. It is a name
which must not be pressed into a doctrine.
But, as understood by the Philosophy of Experience, the
" association of ideas " has long ceased to be a way of marking
a thing which we all admit has real existence. It has become
the battle-cry of a school, and a metaphysical doctrine and
theory of things. It contains a belief as to the nature of the
mind, or at least as to the mode in which the mind works,
which is irreconcileable with the views we have already
adopted. Hence if " association " is to stand for a mere
psychological fact, then of course, like every one else, I believe
in it ; and I propose to give here the explanation of that fact.
But, if " association " means that view of the fact which has
been embraced by a certain school, then I do not believe in it ;
and I propose to show that in this latter sense " association "
has no real existence. It has not only been extended to take
in phenomena which can not properly come within its limits,
but within any limits, however narrow, it is a false view of
things.
4. The word Association, I suppose, implies properly
some kind of voluntary union. That signification of course
disappears, but it leaves a shade of meaning behind. For
things are not associated by their own necessity, and by virtue
of some internal connection. Such a group as the family, and
even the state, can hardly be called associations in any strict
sense. Association implies chance, that is, it depends on
circumstances external to that which is conjoined. And so,
when we use the term, we must be taken to suggest that, if
A and B had not been associated, they would nevertheless
* We shall append some remarks at the end of this chapter,
CHAP. I THE THEORY OF ASSOCIATION OF IDEAS 30!
have been A and B. For the conditions, which happened to
bring them together, do not follow in fact, nor are deducible
in idea, from the existence or character of mere A and B.
We may perhaps explain by a reference to the hypothetical
judgment. In such a judgment, if the condition is known, 2
you assert not a conjunction but always a connection. But
in a categorical judgment of perception, and that means in a
hypothetical judgment where the condition is unknown, you
assert a conjunction and not a connection. The former word
corresponds to Association. The conjunction with B is pre
dicated of A on the strength of a condition, that does not
come into the subject, but is imported by the force of such
circumstances as, in their relation to A, are chance.
Association thus comes to mean chance-conjunction, and
in our mental history we find of course very often that ideas
are conjoined by the merest accident. If you take these
ideas and consider them by themselves, you can find no con
nection and no reason for their union. Mere circumstances,
which, so far as the ideas are concerned, might never have
existed, did bring them together. And a union caused by
such chance-conjunction is the common meaning of Mental
Association. In this sense of the term it answers to that
which, I suppose, we all admit to be fact; but it conveys no
theory of any kind whatever. It makes no assertion as to the
nature of ideas, and it makes no assertion as to the laws of
their reproduction. It calls attention to one fact among others.
It does not profess to reduce well-nigh everything in the mind
but sensations, impressions, or feelings, to this single fact.
5. The school of Experience, in its more consistent de
velopment, has turned the metaphorical expression of one
fact into a theory which may be said to cover all. It has a
doctrine as to the ultimate constituents of mind. They are
particular feelings and particular ideas, in either case repellent
units. And they have absolutely no internal bond of con
nection. There is no ground common to the different units,
which could serve as a real basis for their union. Univer
sality and identity are derided as fictions. In the procession
of these units we may separate two trains, the train of sen
sations and the train of ideas; but these all are separate
individual realities. " All our distinct perceptions are distinct
3O2 THE PRINCIPLES OF LOGIC BOOK II. PT. II
existences, and the mind never perceives any real connection
among distinct existences" (Hume). The philosophy of
Experience is psychological Atomism.
There is nothing which the atoms possess in common, and
there could be no " real connection " between them. They
are conjoined by the agency of chance or fate. That im
pressions should come to us in a certain arrangement, and
should in some cases precede feebler counterparts of them
selves this springs from the unknown necessity of a nature,
which we can not say is the nature of the units. And the
secondary conjunction of impressions with ideas and of ideas
with one another, what is this but the accident of Association,
whose laws are nothing but general expressions for certain
recurring kinds of irrational combination ? Destiny and chance
are two names of one lord that sways the procession of fleet
ing units. In their short-lived occupation of that void which
is the soul, they are combined by the accident of presentation
or by the fate of association. And the " final inexplicability "
of J. S. Mill may recall an echo of the " free will " of
Epikurus.
6. Having thus anticipated by a sweeping theory the
nature of everything that is to be experienced, the school for
the future, so long as it keeps true to the metaphysical doc
trine on which it stands, may call itself the Philosophy of
Experience. And it is also analytical 3 ; for does it not assume
that every complex phenomenon of the mind is resolvable into
the units which its theory has established? Its first principles
no doubt are never analyzed; but analysis, it is obvious, must
be broken off somewhere. If the " analytical school " is con
tent to stop, then the limit of human thinking has been reached.
If the Philosophy of Experience is content with the result,
then surely the product of analysis must be fact. Analysis
in the future will consist in the attempt to reconstruct syn
thetically the phenomena of the mind from elements gained
in accordance with first principles, and according to the Laws
which first principles have established (cf. Book III. Part I.
Chap. VI. 10). It is hardly necessary that in every case
the existence of each element should be verified a posteriori.
If, for the explanation of visual extension, it were first neces
sary to verify in actual observation the fact of colour-sensa-
CHAP. I THE THEORY OF ASSOCIATION OF IDEAS 303
tions devoid of all extension, it is possible that the analysis
could not be performed. And, since that analysis has been
firmly established, it is clear that its basis can not be unreal.
If we confine ourselves to the limits and the method of the
school of Experience, we may be sure of one thing; if we
are true to Experience we must be true to fact.
7. We can appreciate now the nature of the claim which
is laid to the titles of " experience " and " analysis." But we
must hasten to examine the character of those Laws which
rule the void and which move ideas. They answer, in the
psychical empty space, to what is called " cohesion " or " at
traction " in the external void (Hume, Treatise, I. I. 4). The
two main principles are the law of Contiguity, and the law
of Similarity or Agreement.
I. " Actions, Sensations, and States of Feeling, occurring
together or in close succession, tend to grow together, or
cohere, in such a way that, when any one of them is after
wards presented to the mind, the others are apt to be brought
up in idea." Bain, Senses, p. 327.
II. "Present Actions, Sensations, Thoughts, or Emotions
tend to revive their LIKE among previous Impressions, or
States." Ibid.p.4$7-
Or, to put the same thing in the opposite order,
laws the first is, that similar ideas tend to excite one another.
The second is, that when two impressions have been frequently
experienced (or even thought of) either simultaneously or in
immediate succession, then whenever one of these impressions,
or the idea of it, recurs, it tends to excite the idea of the
other." J. S. Mill, Logic, II. p. 44, Ed. IX.
A briefer, and on the whole more accurate expression,
would perhaps be this; Mental units which have co-existed
cohere, and mental units which are like recall one ano
least in image.
88 In saying that I entirely and utterly reject each one
of these statements, I may be taken to deny the existence of
fact. But (to repeat once more a distinction I have drawn)
what I find it impossible to make myself believe is not
fact which these formula may be taken as loosely Beating-
It is on the contrary their theory of that fact which I can n
swallow And I have no insurmountable objection to the use
304 THE PRINCIPLES OF LOGIC BOOK II. PT. II
of such statements ; but I can not for one moment allow that
they are true.
I shall give hereafter in greater detail those reasons which
lead me to believe that these laws are nothing but fictions.
But the main ground of objection may be stated at once.
The ideas which are recalled according to these laws are
particular existences. Individual atoms are the units of asso
ciation. And I should maintain, on the contrary, that in
all reproduction what operates everywhere is a common
identity. No particular ideas are ever associated or ever
could be. What is associated is and must be always
universal.
It will be found, I think, the most convenient course, if
I first give some account of the way in which I conceive
association is effected, and then attempt to show that the
method, commonly accepted as fact, is wholly fictitious.
9. In the previous Book (p. 34, foil.) I have to some ex
tent anticipated this discussion, and, trusting that the result
to which we there came may be recalled by the reader, I may
perhaps be here allowed to be brief. I have no hope of
persuading the orthodox believer, and others may be willing
to help in working out the sketch of a doctrine.
The main Law of Reproduction may be laid down thus;
Any part of a single state of mind tends, if reproduced, to
re-instate the remainder; or Any element tends to reproduce
those elements with which it has formed one state of mind.
This may be called the law of Redintegration. For we may
take this name from Sir W. Hamilton (Reid, p. 897), having
found nothing else that we could well take.
There are several points in the formula which call for
explanation. We might ask, in the first place, What is a single
state of mind? Does it exclude succession? It certainly does
not do so. It may be further defined as any psychical com
plex which is present together, presence signifying presenta
tion, a certain direct relation to the mind which does not imply
succession in time. As I have endeavoured (p. 53) to throw
some light on the meaning of this term, I must be excused
from a further discussion of it here.
In the second place the " parts " of this present state need
not be either perceptions or ideas. For the formula includes
CHAP. I THE THEORY OF ASSOCIATION OF IDEAS 305
every possible kind of mental element; and this is the reason
why we can not accept the principle as we find it laid down
by Wolff and others. I will not here ask, if in the end it
is not possible that association is confined to intellectual or
perceptive elements (vid. Book III. I. Chap. III. 20-22).
It is better for ordinary purposes to suppose that it also ap
plies to desires and feelings. But subject to this correction
we may adopt, if we please, Wolff s statement of the law.
" Si quse simul percepimus et unius perceptio denuo pro-
ducatur, sive sensuum sive imaginationis vi ; imaginatio pro-
ducit et perceptionem alterius seu quod perinde est per
ceptio praeterita integra recurrit, cujus prsesens continet
partem" (Psych. Emp. 104).
Maas, following Wolff, has thus formulated the principle.
" Given an idea or perception, then all those ideas, which be
long with it to one total perceptive state, may immediately
associate themselves with it, and no other ideas can do so."
Or " Every idea, or perception, recalls to the mind its total
perceptive context" (Versuch, Verb. Ausg. 1797, 13).
This law of Redintegration, we must bear in mind, does
not exclude any succession of events which comes as a whole
before the mind; and it is not to be confined to perceptions
and ideas.
10. The law of redintegration is a very different thing
from the law of contiguity, as that is understood by the school
of Experience. Superficially alike, they are separated by the
chasm that divides irreconcilable views of the world. For
contiguity is cohesion between psychical units, and its elements
are particular existing phenomena. What it couples is the
actual individual impression or image, as such. It is not asso
ciation between universals. But Redintegration is not any
thing else. For it never re-instates the particular fact,
can not deal with anything that could be a phenomenon, or
could ever exist. It does not couple psychical units, but is
entirely confined to what is universal.
We should find it hard to overstate the enormous diver
gence of these two interpretations of the fact of association.
Contiguity asserts a conjunction between existences,
integration asserts a connection between universals, which as
such do not exist. What operates in the first is an external
306 THE PRINCIPLES OF LOGIC BOOK II. Px. II
relation between individuals. What works in the second is an
ideal identity within the individuals. The first deals with the
that, and the second with the what. The first unites facts, and
the second mere content.
According to the view which to me seems the truth, to
talk of an association between psychical particulars is to utter
mere nonsense. These particulars in the first place have got
no permanence ; their life endures for a fleeting moment. In
the second place they can never have more than one life;
when they are dead they are done with. 4 There is no Hades
where they wait in disconsolate exile, till Association an
nounces resurrection and recall. When the fact is bodily
buried in the past, no miracle opens the mouth of the grave
and calls up to the light a perished reality, unchanged by the
processes that rule in nature. These touching beliefs of a
pious legend may babble in the tradition of a senile psychology,
or contort themselves in the metaphysics of some frantic
dogma, but philosophy must register them and sigh and
pass on.
There is nothing we know which can warrant the belief
that a particular fact can survive its moment, or that, when it
is past, it can ever live again. We know it is true in our actual
experience that reproduction presents us with particular
images; but to assert that these are the perished originals is
to demand a miracle to support our false beliefs. We have
absolutely no kind of warrant in experience for our assurance,
that what comes into the mind by Association is the particular
as we had it. For the particular fact is made particular by
an elaborate context and a detailed content. And this is not
the context or content which comes back. What is recalled
has not only got different relations ; itself is different. It has
lost some features, and some clothing of its qualities, and it
has acquired some new ones. If then there is a resurrection
assuredly what rises must be the ghost and not the individual.
And if the ghost is not content with its spiritual body, it must
come with some members which are not its own. In the hurry
of the moment, we have reason to suspect, that the bodies of
the dead may be used as common stock.
But if we are willing to throw over our orthodox creed, we
may escape with less demand on our faith. The doctrine of
CHAP. I THE THEORY OF ASSOCIATION OF IDEAS 307
Redintegration does not ask us to subscribe to the belief that
what is past exists over again. It offers a simpler explanation
of the facts. Given any presentation X, which has a content
such as . . .abode. . ., it asserts that the oneness
of this presentation is in a certain sense a connection of its
content. The fact of the presentation absolutely disappears.
What is left behind is a mental result, 5 into the ultimate meta
physical nature of which we do not here enquire. But this
result is not a phenomenon, not a particular image or relation
of such images. It is an alteration of the mind, which shows
itself to us as a tendency to pass from content to content.
It is a connection, not between this a and this &, or this c
and this d, but between the universals a and &, or c and d.
It is a quality of the mind which manifests itself in the fact
that, if we have one part of the content which appeared in X,
then although everything which particularized that content in
X, and gave it existence, has disappeared this bare universal
a b, c, or d, when given with a different set of particulars, may
re-instate by its ideal identity any other of the universals, a, b,
c, or d. It will recall it certainly in a particular clothing, but
this clothing will be determined by present mental circum
stances, and will not be the clothing of its past existence. And
this particular clothing, again and in the second place, is not
the bond which works in the reproduction. What works is the
connection between the universals, and the basis of that work
ing is the ideal identity of some element in what is present am
in what is past.
ii I have illustrated my meaning already by anticipa
tion (p. 35), and shall illustrate it hereafter. At present
must hasten to meet an objection. I maintain that all asso
ciation is between universals, and that no other associate
exists Every kind of reproduction, in my judgment, takes
place by virtue of identity plus the connection of universals.
"And do you really," there may here come a protest,
you really believe this holds good with emotions? If castor-
oil has made me sick once, so that I can not see it or even
think of it without uneasiness, is this too a ^J^J5
universals?" I reply without hesitation that beheve t
so; and that I must believe this or else accept a ^miracle a
miracle moreover which is not in harmony with the facts it
308 THE PRINCIPLES OF LOGIC BOOK II. Pi. II
is invoked to explain. You believe then, I feel inclined to
reply, that the actual feelings, which accompanied your vomit
ing, have risen from the dead in a paler form once more to
trouble you. I could not credit that even if it answered to
the facts. And it does not answer, since the new feeling is
clearly different from the old one. The old feeling was the
event it was, by its presence in a certain series of events. It
had a number of accompaniments, conditions, and circum
stances, which belonged to it as this feeling. The psycho
logical environment was in great part different. Nay, if we
could observe it, we should probably find that its actual in
ternal content has varied. We should see degrees or shades
of quality, which in the two cases would probably not be the
same. Your miraculous supposition is therefore not even a
fiction which will work.
And if you say that, by the sameness of the feeling, you
mean a feeling which is the same in kind, and for all practical
purposes one with the other, this is exactly the thesis which
I wish to establish, and which you have objected to. The
feelings of sickness are the same in the main, that is, they
have an identical content, which is the same although the
contexts are different. But, if so, is it not, I would ask,
admitted that what is reproduced is not the particular but is
the universal? The first conjunction of castor-oil and sick
ness has no longer the smallest existence as fact. But it gave
rise to a connection of elements in the mind, which elements
are an idealized part of the content of this perished fact.
The new presentation of castor-oil is a fact which is certainly
not the old fact ; yet it has a content which is partly the same.
The presence of this identical universal supplies the antecedent
to the hypothetical connection of elements in the mind, and
this then passes from hypothesis into actual fact. In other
words the ideal identity of this castor-oil with that castor-oil
recovers ideally, and in an universal form, another element of
the original context, And, so far as mere reproduction goes,
nothing but the universal could ever be called up. It is the
fresh presentation which adds detail to the reproduced ele
ment. This new perception re-particularizes the universal, and
does so in a way which will not be the old way, and in many
cases will be strikingly different. But such re-particularization
CHAP. I THE THEORY OF ASSOCIATION OF IDEAS 309
(if the term may be allowed) is not association, and is not
reproduction. For though the new particular feeling of sick
ness is no doubt the result of reproduction, yet it never was
associated, and it can not have been reproduced, since it exists
now for the first time. You may say that by a miracle the
old feeling of sickness without detriment to its sameness has
been changed en route; but this very change and this very
difference is the denial of your doctrine, unless your doctrine
too is from time to time changed by a parallel miracle.
I do not say that we should be right to reduce all repro
duction to logical redintegration. 6 That is a point on which I
shall touch hereafter (Book III. I. Chap. III. 20). It does
not concern us here. For it is not necessary to believe that
the " idea " of a feeling is a logical idea, and that it is a con
scious or even an unconscious symbol. What must however
be believed is that it is an universal. And this need give
rise to not the smallest psychological difficulty. Whatever
differences may separate the various kinds of psychical phe
nomena, they are all alike in one point. They all have con
tent 7 as well as existence. They are not confined to the
"that," but each has a "what," since there is a complex
quality and relations of quality.* And, this being so, we
have all that is required for the formation of universals. For
an identity of content in different contexts is and must be an
universal, whether we are dealing with perceptions or feelings
or volitions.
12. To suppose the presence and the operation of uni
versals in all reproduction, introduces a unity into our view
of the soul. It enables us to interpret all stages of mind
as the growth of one principle. We can thus accept without
abridgment the very highest phenomena, and we can show
their root in the lowest and rudest beginnings of the soul.
We may say that experience will begin when a present per
ception has one part of its content identical with a past,
and when this common universal re-instates another part of
the original context. But that past element most certainly
does not reappear in its particular form. It too is universal,
and it is the connection of these universals which operates in
the mind. Hence the content of the perception, which is now
* Quality at this stage covers quantity.
2321.1 X
3IO THE PRINCIPLES OF LOGIC BOOK II. PT. II
present, is extended by means of this ideal synthesis, and,
itself individual, individualizes the result. This true account
is in harmony with fact. But, on the other hand, to suppose
that one or more particular feelings or images are magically
recalled and adhere to the perception, is directly contrary to
the plain facts of observation. For these separate particulars
are palpably absent; and in order to explain their obvious
absence it is necessary to invoke a Law of Obliviscence, by
which their details may again be shorn off. But this Law of
Obliviscence has no title to exist in the shape which is given
to it, except that it is demanded by an erroneous theory (vid.
inf. 25). A miracle is first invoked to explain the facts,
and then a fiction introduced to square the facts to the miracle.
But the unviolated facts support redintegration by identity.
In a rudimentary soul a present sensation has its content in
creased by internal extension. There are not several facts
before the mind, but there is a single fact whose content,
after enlargement, consists in part of an unconscious inference.
The sensation is extended by an ideal supplement, and this
supplement, through union with the individual sensation, be
comes for the mind individual fact. On this view there is
no psychical phenomenon which intervenes between the sensa
tion and the resulting perception. We have not to postulate
the irrelevant and conflicting detail of particular images, and
have no need to rid ourselves of this palpable fiction by any
arbitrary Law. Or again, if the result of the new sensation
be desire or action, our theory still maintains its superiority.
Let us however try to exhibit this in detail.
What is the fact to be explained ? It is, I think, this.
A sensation Ab has once led to an action Cd; and now a
sensation E& (the same with A in respect of &) is presented.
E& is then followed by an action ~Fd, which in respect of d is
identical with Cd. Such is the fact, and we have two com
peting explanations. On the first and incorrect interpretation
E& calls up a particular image of Ab. The latter is associated
with the particular idea of an action Cd, and Cd produces Fd.
The transition is thus, E& Ab Cd d; and this transition
is discrete from atom to atom. This is the first interpretation.
On the other, Eb directly redintegrates d f and Ebd directly
produces EbdF. The transition may be stated as Eb d F ;
CHAP. I THE THEORY OF ASSOCIATION OF IDEAS 3! I
but, since b and d are universals and are not psychical phe
nomena, the actual transition is unbroken from E to F. Now
which of these explanations accords best with fact ? The fact
is that the supposed intermediate units, A& and Cd, can not be
verified in observation. Their presence is deduced a priori,
and is not pointed out a posteriori. We are then asked to
believe that their presence exists though we can not see it;
for it is hidden by the Laws of Obliviscence. But this mys
terious agency has itself been manufactured a priori. It again
can not be verified in actual experience. Hence we have first
a principle which produces something other than our fact,
and then an arbitrary invention to patch up this mistake.
Such is the first interpretation ; and let us look at the second.
On that, I will not say that nothing is asserted either more
or less than what can be observed, but I will say this. Not
only is one principle used throughout, and that one sufficient
to explain the facts, but there is no result, and not the fraction
of a phenomenon, postulated by this principle, but what can be
shown a posteriori. And, even apart from all question of truth
and falsehood, a theory which demands two compensating
hypotheses, must surely be rejected in favour of a theory,
which works as well with one single hypothesis.
13. But I shall be told, " This statement of the case is
absurd. In the first place, and apart from truth and falsehood,
the theory you advocate does not cover the facts. It fails
to explain the suggestion of similars. Again and in the second
place, the hypothesis you adopt is demonstrably false. And a
single hypothesis is not admissible if it is insufficient, if it is
not true, and if a true explanation is within our reach,
answer, In the first place, as I shall soon point out, the
reduction of suggestion to redintegration is an accomplished
fact. And in the second place the falsity of redintegration
can not be shown; but on the other hand what can be demon
strated is, that your hypothesis is false. For (i) there is no
such thing as Association by Contiguity; (ii) there is no such
thing as Association by Similarity. I will try to make both o
these last points quite plain, and will then return to de
the true explanation.
14 (i) Let us begin with Contiguity. What is the true
view? The true doctrine is that, when elements have co-
312 THE PRINCIPLES OF LOGIC BOOK II. PT. II
existed, they tend to be connected. What does this mean?
It means that if (say) in a perception A the elements p and
y are conjoined, the mind gets a tendency to join one to the
other whenever either reappears. But what are P and y ?
They are universals. They have been detached from their
original environment, and to some extent stripped of their
particular qualities. They are not individual images. Thus
if I have seen a black man stabbed with a sword in a certain
street at a certain time and under certain conditions, what is
left in the mind is not a connection between these special
sensations, or between special images which are their feebler
counterparts. I might shudder when I saw a white cow
threatened with a butcher s knife at another time and place
and under different conditions. For what is associated is not
the images, it is always universals or types, which as such
have no real existence, even in the mind. This is the true
view. We will pass to the consideration of the erroneous
doctrine.
There is not much doubt, I think, as to what that doc
trine really is. But its adherents allow themselves a looseness
of statement which is sometimes excessive; and we hardly
know the point at which their mythology becomes conscious.
We are at times led to think that past perceptions continue
to exist, and on occasion rise to be seen of men. For observe
the definition.
" Actions, Sensations, and States of Feeling, occurring to
gether or in close succession, tend to grow together, or co
here, in such a way that, when any one of them is afterwards
presented to the mind, the others are apt to be brought up in
idea." " When two impressions have been frequently experi
enced (or even thought of) either simultaneously or in im
mediate succession, then whenever one of these impressions, or
the idea of it, recurs, it tends to excite the idea of the other."
A definition is not the place where one looks for fancy, but
for actual belief. But consider these phrases, " when any one
of them is afterwards presented" " whenever one of these im
pressions recurs." Are they feasible unless the writer believes
in the coarsest form of subterranean existence and of the
Resurrection of the Body? But neither of the writers pro
fesses to hold that belief. They both repudiate it. And yet
CHAP. I THE THEORY OF ASSOCIATION OF IDEAS 313
that does not prevent both of them from speaking as if they
accepted it in full, and at least one of them from reasoning on
the assumption of its truth.*
15. This point perhaps may be dismissed as a mere ques
tion of statement ; for there is no doubt that our authors would
stoutly deny that the past impression is recalled to life.
" Whenever one of these impressions, or the idea of it, re
curs " are words that must be used in a popular sense. Then
what is the exact sense? Are we to amend the formula by
writing simply, " whenever the idea of one of these impres
sions recurs " ?
Even so we are still in the land of mythology. The
" ideas " that are meant are particular existences. The fleet
ing impressions in their passage through the void throw off
feebler counterparts, shed pale doubles of themselves. And
the idea, like the impression, is a particular unit ; it is no uni
versal but an actual phenomenon. It certainly is called " the
idea of the impression," but this phrase does not mean that
the two have any substantial identity. It means that one fol
lows the other in time, and in fainter traces shows a similar
detail. But if this is what is meant, it is not what is said.
" Whenever," we are told, " the idea of it recurs." But the
idea, like the impression, exists only for a moment. Then
how can it " recur " unless it is the same ; and how can it be
the same unless it has remained? We may figure to ourselves
the faithful ghost, haunting the place where the body is not,
and called up to the light by the spell of Association. But
we surely must know that these pious legends are not literally
true. For the image, like the sensation, endures but for a
moment. And if the impression does not "recur/; then the
idea does not "recur"; since in this respect there i
ference between them.
It is mere mythology to talk of the copy, which the im
pression has sloughed off, persisting in the world and preser
ing its identity through the flux of change. The word recurs
*I refer to J. S. Mill. See his Hamilton, Chap. XI. and
314 THE PRINCIPLES OF LOGIC BOOK II. PT. II
We must call them " different ideas of the impression." And
here, I think, we are approaching danger. For we naturally
consider that, in a case of association, there is some one con
nection throughout all the instances. We can hardly help be
lieving, and talking as if we believed, that when (as we should
like to say) something " recurs," then something else " recurs "
also. But we must strip off this illusion, or wear it only
when we come before the public. There is nothing that recurs.
The original impression is one mental unit, the first idea is
another, the second idea is a third passing atom, and so on for
ever. There is no real bond which unites them together.
There is no common internal identity, which is the same in all
and recurs amid change. If we call them " the ideas of one
impression," even this is mere fable. We have a likeness no
doubt, in all these cases. A hundred images, or more it may
be, with all their differences and all their particularity, are yet
each of them particular in such a way that they are all like
each other, and all like the impression. This is startling, I
admit, but even this does not warrant us in considering any
one to be the same as the other, and united by holding the one
substance of their prototype. If we desire a legend which
perhaps may be harmless, we may call them all " ideas of the
impression " in the sense that, like Abraham, the impression
while it lived had them all in its loins. For no vehicle conveys
the eternal verities half so well as does the labyrinth of a
fantastic genealogy, with its one-sided begettings and ab
normal parturition.
16. " Whenever one of these impressions, or the idea of
it, recurs, it tends to excite the idea of the other." This is
what we started from. What are we left with ? " Impres
sions " is gone : " recurs " is gone : " idea of it " is gone. It
seems that we must thus amend our formula, " Whenever an
idea like one of these impressions occurs, it tends to excite
the idea of the other." This surely will stand: this at last
must be true. Unfortunately not so; for it still says too
much and must be further cut down; and yet already it has
begun to say too little, and will now no longer cover the facts.
But I will at present keep to the too much. The phrase " to
excite the idea of the other " must at once be corrected. It
should run "to excite an idea like the other." And we must
CHAP. I THE THEORY OF ASSOCIATION OF IDEAS 315
further amend the beginning of our formula. For " when
two impressions have been frequently experienced" is quite
mythological. // two impressions were " frequently experi
enced," they would be two no longer. The phrase is nonsen
sical, unless several experiences are one experience: and that
we know is not true. We must alter this also, and in our final
correction the law must be stated.
" When we have experienced (or even thought of) several
pairs of impressions (simultaneous or successive), which pairs
of impressions are like one another; then whenever an idea
occurs which is like all the impressions on one side of these
pairs, it tends to excite an idea which is like all the impressions
on the other side."
This I believe to be the meaning of Association by Con
tiguity. And at this point perhaps it may occur to us to ask,
what is it that is contiguous, and what is it that is associated?
The impressions are not associated; I presume that is ob
vious. They are conjoined in presentation, just like anything
else we perceive together is conjoined. It is the ideas which
are associated, since one, as we see, can bring up another.
But then in what sense are the ideas contiguous? They are
now successive, or simultaneous, because of the contiguity.
Contiguity conjoins them, and it would be nonsense to ^say
that they become conjoined because already they are contigu
ous. For if they are contiguous, then both must be there, and
how can one call in the other? And if they are not contigu
ous, then it is not their contiguity which brings them together.
This consideration seems to me quite palpable; but the result
is fatal to the Law of Contiguity.
The law operates by means of and through contiguity, and
therefore presupposes it. But there is no contiguity save that
of the impressions. It must be then the contiguity of
impressions which works. Because they were together once,
the ideas come together now. But, if so, what becomes of
association? For the impressions are not associated, and
association is, if anywhere, between a present and an absent
idea What is associated was therefore not contiguous, and
what was contiguous is now not associated. Association and
contiguitv fall hopelessly asunder; and hence let our law b
never so real, it can not be the Law of Association by Con-
3l6 THE PRINCIPLES OF LOGIC BOOK II. PT. II
tiguity. In short, the whole thing comes to this. If impres
sions have been contiguous, then ideas which are like them
now tend to excite one another. And for myself, I can not
see how in any intelligible sense this is the association of ideas.
17. And now (to come to the other side of the failure) if
we state the law in this corrected form, it will not cover the
facts of the case. For commonly an impression is what is first
given, and then this impression calls up an idea. Thus if one
fire has already been felt to be hot, then, if another fire is seen,
the idea heat comes. Thus an idea is excited by what is not
an idea, and by what never has been contiguous to anything.
We must once more and finally thus amend our formula,
"If any mental units have been contiguous, then any others
which resemble them may excite one another." There is not
left here a vestige of association. And the union of the ele
ments somehow takes place by virtue of the past contiguity of
something else.
1 8. Association by contiguity may be taken as exploded.
But the philosophy of Experience is, to some extent at least,
prepared for this result. It will admit so much, that mere
contiguity will not work by itself. And it proposes to sup
port it by another agent. There is no such thing, it is ready
to allow, as association by bare contiguity. All reproduction
in a certain sense depends on similarity.
" There never could have been association by contiguity
without a previous association by resemblance. Why does a
sensation received this instant remind me of sensations which
I formerly had (as we commonly say), along with it? I
never had them along with this very sensation. I never had
this sensation until now, and can never have it again. I had
the former sensations in conjunction not with it, but with a
sensation exactly like it. And my present sensation could
not remind me of those former sensations unlike itself, unless
by first reminding me of the sensation like itself, which really
did co-exist with them. There is thus a law of association
anterior to, and presupposed by, the law of contiguity : namely,
that a sensation tends to recall what is called the idea of
itself, that is, the remembrance of a sensation like itself, if
such has previously been experienced." " There is, therefore,
a suggestion by resemblance a calling up of the idea of a
CHAP. I THE THEORY OF ASSOCIATION OF IDEAS 317
past sensation by a present sensation like it which not only
does not depend on association by contiguity, but is itself the
foundation which association by contiguity requires for its
support." J. S. Mill, on James Mill, I. 112, 113.
"There can be no contiguity without similarity, and no
similarity without contiguity. When, looking at a river, we
pronounce its name, we are properly said to exemplify con
tiguity; the river and the name by frequent association are so
united that each recalls the other. But mark the steps of the
recall. What is strictly present to our view is the impression
made by the river while we gaze on it. It is necessary that
this impression should, by virtue of similarity or identity,
re-instate the previous impression of the river, to which the
previous impression of the name was contiguous. If one could
suppose failure in the re-instatement of the former idea of the
river, under the new presentation, there would be no oppor
tunity given to the contiguous bond to come into operation."
Bain, ibid. p. 121.
Let us try to understand this amended doctrine. In the
first place we must remember that, when identity is spoken of,
it is not really mecmt. What is meant is more or less of
similarity. And this point must not be lost sight of.
In the second place I must be allowed to complain of a
serious inaccuracy in the extract I have quoted from Professor
Bain. It surely is nonsense to talk of " re-instating the
previous impression," and I must add that in this context the
nonsense seems inexcusable. And again in the first of the ex
tracts there is ambiguity. The " remembrance of a sensation,"
we must clearly understand, does not revive the sensation itself,
and does not establish any actual relation with that mental
unit which no longer exists. If this is not so, and if a psy
chical phenomenon can maintain or recover its existence and
identity through the flux of events, then the whole theory
from which the school of Association starts has been tacitly
thrown over.
But, if an impression when past is done with, if it is really
non-existent, then not only can it not be re-instated bodily,
but itself can not even be re-instated in idea. The fact which
is covered by the delusive phrase " idea of it," is merely the
fact that a sensation came first, and then subsequently there
318 THE PRINCIPLES OF LOGIC BOOK II. PT. II
came a paler counterpart. And, when we once discern this
fact through the mist of ambiguous and misleading formulae,
there is an end to the theory which hides or obscures it.
What was contiguous is now non-existent, and what is
" re-instated " has never been contiguous. Let us look at the
facts. A sensation A excites by similarity an image b, and,
on this, contiguity has to do all the rest. But has b ever been
contiguous to anything? In the case before us there are two
possibilities. The fact from which we start is this we have
had an impression B along with an impression C, and we have
an impression A. Now what are the two possibilities ? In the
first place it is possible that we never have had a feeble image
resembling B. And this is more than possible, for in an early
mind it is also probable. But in this case, when A excites an
image b, there is absolutely no contiguity of anything with
anything. Not one of the supposed elements in our reproduc
tion has ever been contiguous with any other; and, this being
so, reproduction will not take place. This first possibility ap
pears to me to have been overlooked. Let us now pass to the
second. We here have had the contiguous impressions B C.
These we suppose to have been followed by one or more pale
pairs of images & 1 c 1 , b 2 c 2 , & 3 c z . These are all like
each other, but they all are realities each of which is not the
same as any other. We now experience a sensation A. This
also is like the previous sensation we have called B, and is
like the images & 1 , b 2 , b\ But every one of these, I must beg
the reader to remember, is by this time absolutely non-existent.
What then is to happen when A is presented? It calls up by
similarity an image b 4 . But this is not what we want. For
we want an image b* c 4 ; and contiguity is invoked to pre
sent us with c 4 . But is invoked in vain. For as yet c* has
never existed, and ex hypothesi it is to be made to exist by
means of contiguity. On the other hand b* has never been
contiguous to anything at all. We have reached once again
the old result. There is no association by contiguity. What
is called up by association has never been contiguous; and
what has been contiguous can not be called up. The contiguity
which now operates is a past contiguity, which is not recalled
and can not be recalled, but which, according to the pious
legend, is somehow passed on like original sin.
CHAP. I THE THEORY OF ASSOCIATION OF IDEAS 319
But if this is so, then Association by Contiguity is exploded
finally. No exciting of similars will save it from annihilation.
For the similars excited have not been contiguous, and what
was really contiguous can not be excited. If present sensations
are qualified by images in the way described, still on that
(false) hypothesis there is no reproduction by association.
There can be no association where the elements are not co
existing associates. But if they do already co-exist and thus
are associated, then how in the name of all that is miraculous
can one bring about the co-existence of the other, and by
means of their co-existence?
19. If the school of Experience is in earnest with its
principles there can be no such thing as Association. But is
it in earnest? Notwithstanding all its public protestations
may it not secretly look for the Resurrection of the Body?
Does not the charm of Similarity shake the realm of Hades,
and conjure from its grave the reluctant past? Is anything too
hard for Association? Its spell has prevailed over the mind
of its votaries, and, though their lips may deny, yet Associa
tion itself has helped their unbelief by its own divine power.
They do believe in the miracle of resurrection. But they be
lieve blindly and unconsciously, compelled by the strength of
a tacit conjunction of meaning with phrase.
We saw that, by the admission of its advanced disciples,
association depends upon similarity. If there is no reproduc
tion by Similarity, it is admitted that there is no Association at
all. I shall now press this consequence. If you do not believe
in this kind of Association, you believe in none. But if you
do believe in it you believe in a miracle which upsets all law.
And furthermore there is no evidence a posteriori to confirm
this miracle. In plain words Association by Similarity is a
downright fiction. It is not called for by the facts; and it
involves besides metaphysical assumptions which I confess
stagger me, and which I think may somewhat surprise others.
I shall show the reader how the school of Experience has
swallowed the most outrageous metaphysical doctrines, and
that he must follow their example or leave their company.
20. (ii) Association by similarity, if it is anything at all,
is a means of exciting ideas that are not present. If it will
not give us what at present, and apart from its agency, we are
32O THE PRINCIPLES OF LOGIC BOOK II. PT. II
without, then it surely is a self -condemned fiasco, that is not
worth discussing. We may perhaps agree that an agency
which recalls and yet recalls not anything but what is already
on the spot, is something like a piece of nonsense. And I
propose to show that Association by Similarity is this piece
of nonsense.
Similarity is a relation. But it is a relation which, strictly
speaking, does not exist unless both terms are before the
mind. Things may perhaps be the same in certain points
although no one sees them ; but they can not properly resemble
one another, unless they convey the impression of resemblance ;
and they can not convey it unless they are both before the
mind. This is not merely an assertion I have chosen to make. 8
Let us see what is told us by J. S. Mill.
" Any objects, whether physical or mental, are related, or
are in a relation, to one another, in virtue of any complex
state of consciousness into which they both enter" (on James
Mill, II. 10).
" Likeness and unlikeness are themselves only a matter of
feeling: and that when we have two feelings, the feeling of
their likeness or unlikeness is inextricably interwoven with
the fact of having the feelings. One of the conditions, under
which we have feelings, is that they are like and unlike: and
in the case of simple feelings, we can not separate the like
ness or unlikeness from the feelings themselves. It is by no
means certain, however, that when we have two feelings in
immediate succession, the feeling .of their likeness is not a
third feeling which follows instead of being involved in the
two" (ibid. p. 18).
" I have two sensations ; we will suppose them to be simple
ones; two sensations of white, or one sensation of white
and another of black. I call the first two sensations like;
the last two unlike. What is the fact or phenomenon con
stituting the fundamentum of this relation? The two sensa
tions 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" (Logic, I. 75).
Is not this quite plain? Does it leave any doubt? Is it
not clear that two mental elements are not like, unless I have
CHAP. I THE THEORY Of ASSOCIATION OF IDEAS 32 1
them before me at once or in immediate succession? But, if
so, what meaning can we attach to the calling up of an idea
by similarity? If the relation does not exist until the idea is
called up, how can the idea be called up by the relation? Is
it not, the moment we look below the surface, mere verbiage
and nonsense?
21. In the first place what is called up is absolutely
non-existent. We are told, not once but again and again,
that a feeling gone is gone for ever. And the same thing
holds of particular images. If these exist, then the past
exists, and the procession in the mind is not real but illusory.
Are we to believe this, and believe it in the teeth of our as
severations? But if we can not believe it, and if the past
does not exist, then we must believe in a relation between the
existent and the non-existent; and believe that the whole
(relation and relateds) is one state of our minds. If, on
the other hand, the past can exist, this miracle will not save
us from annihilation. In the relation of similarity both terms
must be present, and the fact that one calls up the other by
this relation, postulates that one of the terms must be absent.
It is therefore both present and absent at once. On either
hypothesis we are landed in contradictions; and I have re
deemed the promise I gave to the reader. An idea is absent
and at the same time present. It is not there and so is
brought in by a relation, which relation is nothing if the idea
is not there. And a union, which is impossible out of the
mind, persists between the existent and what is wholly non
existent. Could anything be more insane than this wild meta-
physic ?
22. But I shall be told " You are deceiving us ; it is
incredible, it is impossible that our sober countrymen can
have been so imposed upon." I answer, That question is
easily settled. It is admitted that by " association " they must
mean something, and what else do they mean?
The Experience Philosophy has to meet two objections.
It has to explain how the non-existent can be related to the
existent. And when it has done that, it must explain how
the absent can be recalled by the present, when similarity
implies common presence and reproduction excludes it. Sup
pose that the former difficulty has been slurred over by some
322 THE PRINCIPLES OF LOGIC BOOK II. PT. II
metaphysical formula of " the potential and the actual," or
some distinction between my mind and other minds, yet the
second remains. Suppose that your past series somehow
exists, yet how, I ask, are you going to get at it? Mere
partial identity of the present and the past would not be what
you want, since this would not be an actual relation in your
mind.
This is what Maas meant by the following objection.
" The mere similarity of two ideas (or sensations) can not
possibly be a cause of their association. For similarity is an
objective relation of the ideas themselves; while association
is a subjective connection in the imagination. But the latter
does not follow from the former, nor tend to follow from it "
(Versuch, p. 55). By " similarity " Maas of course here meant
"partial identity," and his argument is quite simple. The
question is, Why does my mind go from one element to
another? If you say, it goes because the elements seem like
to it that supposes both to be there. But if you say, it goes
because they are like apart from it then it goes by a miracle,
for it is influenced by something which to it is nothing. Sir
W. Hamilton (Reid, p. 914) has replied to this argument
by a criticism which shows that he did not understand it.
The Experience Philosophy may have a reply to these
objections, but I confess I can not anticipate its answer. Per
haps it may fall back on a simpler view. It may say, after
Wundt (Phys. Psych. 788), "every perception or idea tends
to call into consciousness another like itself." As to the truth
of this expression I shall have something to say afterwards.
But at present I say this. Whatever else it is, it is giving
up Association and throwing it overboard. For it is the mere
statement of a phenomenon; and it is not an explanation.
The entirest belief in the truth of this formula is compatible
with the entirest disbelief in the doctrine of Association. We
might explain the alleged fact that, given any one element,
another like it may come up, by a theory of the spontaneous
fission or gemmation of ideas ; and this in my opinion would
be a theory which, by the side of Association, is sober and
rational. We might explain it again by a physiological dis
position to a certain cerebral function, which (given the
stimulus of a new perception or idea) passes into fact. And
CHAP. I THE THEORY OF ASSOCIATION OF IDEAS 323
against this explanation I will not say one word. I will in
sist only on this, that it is not a psychological explanation at
all, and that in the hands of those who know their own busi
ness it is not offered as such. If this is the only possible ex
planation, then a psychological explanation is relinquished as
impossible, and the Laws of Association as commonly given
will not explain anything. Thus the Philosophy of Experi
ence must take its choice. It must either rehabilitate its bar
barous mythology, or admit that, though the fact of reproduc
tion is known, it has no psychological explanation to offer, and
is confessedly bankrupt. It has rested its all on reproduction
by similarity, and we have shown that this is an impossibility.
23. But our proof no doubt will not cause much disquiet.
I shall be told " You can not demonstrate away the facts."
And I will therefore proceed to my second contention. The
explanation offered is not only impossible, but it is also un
called for. There is no evidence for it a posteriori. The facts
of reproduction are much better explained on another theory.
We have seen this already in our first Book, but I will exhibit
it once more.
Let us take a fairly simple instance of reproduction. A
young child, or one of the lower animals, is given on Monday
a round piece of sugar, eats it and finds it sweet. On Tuesday
it sees a square piece of sugar, and proceeds to eat it. In
this we have of course volitional phenomena as well as intel
lectual, but perhaps we may simplify the case so as to make it
serve.
Now on the Association theory how is the fact inter
preted? I suppose in some way like this. The presentation
to the eye of Tuesday s piece calls up by similarity the
idea of Monday s piece. That is a feeble counterpart of the
original sensation, and it calls up by contiguity feeble
counterparts of Monday s felt movements and Monday s
following sweet taste. The fact which ensues is hence the
mental presence of Tuesday s perceived square piece, felt to
be like another paler imagined round piece, with which latter
a whole set of other images come in. Now the conclusion, at
which we have to arrive, is the qualification of Tuesday s
piece by these images which are attendant on the idea of
Monday s piece; and at first sight there seems no way to this
324 THE PRINCIPLES OF LOGIC BOOK II. Pi. II
result. For the conclusion is not merely a vicious inference,
but it does not even look like a probable mistake. Tuesday s
sensation and Monday s image are not only separate facts
which, because alike, are therefore not the same; but they
differ perceptibly both in quality and environment. What is
to lead the mind to take one for the other ?
Sudden at this crisis, and in pity at distress, there leaves
the heaven with rapid wing a goddess Primitive Credulity. 9
Breathing in the ear of the bewildered infant she whispers,
The thing which has happened once will happen once more.
Sugar was sweet, and sugar will be sweet. And Primitive
Credulity is accepted forthwith as the mistress of our life.
She leads our steps on the path of experience, until her fal
lacies, which can not always be pleasant, at length become
suspect. We wake up indignant at the kindly fraud by which
the goddess so long has deceived us. So she shakes her
wings, and flying to the stars, where there are no philoso
phers, leaves us here to the guidance of I can not think
what.
The school has not yet accepted this legend, and I narrate
it partly because I am not sure that it is not relevant, but
mainly because it has always seemed to me perhaps the most
striking of all those creations which we owe to the imagina
tion of Professor Bain (Emots. p. 511 and foil.).
24. The less poetical but not less fabulous view would
appear to be this. Given a perception A together with an
image b, which resembles it and has a train of attendant
images c, d, and e the problem is how to transfer to A the
content of e. And what accomplishes the feat is the Law of
Obliviscence. This powerful agent obscures everything in the
train between A and e; and it also obscures any part of e
which is not suitable to A. The residue of e then adheres to
A; that is, I think, the two run into one. And so we get
the conclusion "This piece of sugar is sweet," by a process
which logically may seem rather vicious, but which appears
none the less to be the essence of reasoning.*
* In the lowest stages of mind this theoretical conclusion of course
would not appear. There would be action or attempt without anything
like a judgment. The principle however would be exactly the same;
and when the theoretical conclusion comes, it must come in this way.
CHAP. I THE THEORY OF ASSOCIATION OF IDEAS 325
I can not say if this statement of the Association doctrine
is fair, but I hope it may be so. Let us see what objection
we can find to its process.
The main objection is that there is a great deal too much
of it. It is much too elaborate for simple phenomena. It
first introduces a complication which does not exist; and
then, having invented this complication, it removes it by a
process which is not real.
It is obviously no fact which we can discover by observa
tion, that when Tuesday s sugar is presented to sense, a similar
piece or similar pieces come up, in their particularity and with
all their differences, before the mind. No one gets such a
fact from observation. It is in short a theoretical fiction. I
do admit that afterwards, when memory is developing, there
is something which can give ground for a mistake of this
kind. But then of course reproduction must come before
memory, and in the present case we are not concerned with
the latter (cf. p. 36). The fact before the mind is that this
sugar suggests both sweetness and eating without any images
of any other pieces of sugar at all. In the first Book I
enlarged on this point by anticipation, and, I confess, it seems
to me quite plain.
25. But I shall be told, that although we can not be aware
of them, these images exist, and they are removed or adapted
by the Laws of Obliviscence. But this process strikes me as
another fiction, piled up to support the first fiction against the
pressure of experience. I will quote a passage from J. S.
Mill.
" The reader ... is now . . . familiar with the . . .
fact, . . . that when, through the frequent repetition of a
series of sensations, the corresponding train of ideas rushes
through the mind with extreme rapidity, some of the links are
apt to disappear from consciousness as completely as if they
had never formed part of the series. It has been a subject of
dispute among philosophers which of three things takes place
in this case. Do the lost ideas pass through the mind without
consciousness? Do they pass consciously through the mind
and are they then instantly forgotten ? Or do they never come
into the mind at all, being, as it were, overleaped and pressed
2321. I Y
326 THE PRINCIPLES OF LOGIC BOOK II. PT. II
out by the rush of the subsequent ideas?" (on James Mill,
I. 106).
The question opened in the above quotation may be stated
thus : Given an indirect connection of ideas in the mind, to
find the way in which it becomes direct. I do not wish here
to enter into this general question. But I must point out that
Mr. Mill has raised it in a form which precludes any satis
factory solution. For the ideas connected are not really a
mere series of particular images, and the fact has thus been
perverted beforehand. And if we suppose that, in some ex
ceptional case, we have got a mere train of individual images,
then not one of the " three things " could possibly be opera
tive. For so long as the ideas remained these mere images,
no connection at all would be established between them. We
may be sure that, whatever in the end may be the detail of
the psychological process, one side of it would consist in turn
ing these images into universals. And for this reason the
Laws of Obliviscence, as we have them stated by Mr. Mill,
are fictitious processes. Even if you start with a complica
tion and a train of ideas, yet they can not deal with it.
But the point on which I desire to insist, is that in an
elementary case of reproduction, such as we are now con
sidering, the complication presupposed by these Laws has no
existence at all. The data from which they start are pure
inventions, and it is hence an impossibility that any one of the
suggested " three things " should happen. The fact which
Obliviscence postulates is this: A is the sugar calling up by
similarity an image of sugar b; and b calls up by contiguity
an image of movement c; and c calls up an image d of a
particular sweet taste. But this fact does not exist, and the
alleged process stands therefore on unreality.
There is in the first place no reason to suppose that this
train of ideas, which is presumed to rush through the mind, is
a counterpart of the original perception and action. What
ground can we have for an assumption that the particular
images, b, c, and d f are like in all their detail to any train of
impressions we ever have had? Admit the train, what reason
have you to affirm that there is anything more than a general
likeness? What ground have you for the assertion that, if
you could look into the past, you would see a train of impres-
CHAP. I THE THEORY OF ASSOCIATION OF IDEAS 327
sions B, C, and D, of which these present images are copies?
Why must d be an " exact likeness " of the particular pleasant
eating D? These dogmas seem to me to be nothing but
postulates. The fact, so far as I observe it, shows me that,
without respect for the past, such images vary freely within
a certain limit, and that this limit is fixed by the universal
connection which appears in all of them. But, if so, then
what is associated is not particular images. The universal
which has been deposited is the active principle, and the par
ticular images as such are quite inert.
And in the second place the alleged process imports an
other gross fiction into the data. It tells us that similarity calls
up an image b, which is a copy of Monday s piece of sugar.
We have just seen that, if present, the image need be no copy:
and now we go further. For in our elementary case the
image b has no existence. I repeat once more that it is a
pure invention, necessary for the theory but absent from the
fact. When Tuesday s piece of sugar is present, the attributes
of whiteness and crystalline appearance reproduce the ideas of
movement and sweet taste, without any such link as another
and different piece of sugar. It is not merely that we can
not find such an image now. We never could have found it.
It never has been there. And we need not ask at length if
the Laws of Obliviscence could serve to obscure it, unless
some evidence is produced to show that it is more than a mere
chimaera.
And, as we have seen, it is a chimsera that will not work.
For when you have got your image of Monday s sugar, you
are left precisely where you were before. You have got an
element which has just been born, and which therefore can
never have been contiguous to anything in its life. And if
you say " But it resembles what was contiguous ; " then this
is not only to desert your principles, but it also tends to
expose you to ridicule. If you want what is the former piece
of sugar, you can not get it. But if you want what is like the
former piece, then you have it already in the present per
ception.
Your fictions do not help you, and why should you cherish
them? Why invent the existence of similar images which
lure the unwary to vicious inferences? Why suppose that
328 THE PRINCIPLES OF LOGIC BOOK II. PT. II
" trains of ideas," of which the mind knows nothing, float
across it in procession, and then go on to manufacture a Law
of Obliviscence which ties a bandage over its eyes? Because,
if you do not, you are forced to admit that the mind does not
go always from particulars to particulars, that indeed it never
can go from particulars direct to particulars, that in short the
Experience psychology is exploded.
26. Let us give once more the natural interpretation of
the simple fact. The natural view is that Monday s experience
remains in the mind, not in the shape of particular images,
but as a connection between elements of content. This is a
result which in its metaphysical nature we can not here char
acterize, 10 but, in its appearance to us, it is easy to describe.
It is a tendency to pass from one universal to another, when
ever the first of these is presented in an actual perception or
image. In the instance we are examining, the shape, the size,
the person giving, the where, the when, and the how have all
gone. Nothing is left but a tendency to pass from element to
element, from whiteness and crystalline appearance and hard
ness to eating and sweetness.
Monday s experience, let us say, has established the con
nection " white-eaten-sweet." On Tuesday " white " is given,
and so we have " this-white." We advance by means of an
elementary synthesis to " this-white-eaten-sweet," and, ignor
ing that part which does not interest us, we get " this-eaten-
sweet," or, elliptically, " this-sweet." I grant you the " sweet "
is now fully particular, but its particularity has had nothing
to do with its recall. On the contrary its detail depends upon
the context which has recalled it. And there is no particular
image of " white " at all ; for the universal " white " is what
has worked, and that of course was given in the present
perception.
Where is Similarity here? It does not exist. Similarity
implies the feeling of diversity, and here the difference of
particulars never comes before the mind; it is in no sense
present.
Let us give up Similarity - Contiguity -(- Obliviscence or
Primitive Credulity. Let us postulate Identity + Contiguity,
and then all is easy. But there are two things we must re
member. The contiguity is a connection of universals, and is
CHAP. I THE THEORY OF ASSOCIATION OF IDEAS 329
therefore not the contiguity of the Association school. And
the identity is not present to the mind. The mind, if you
keep to simple cases, knows nothing of any difference. It
goes straight from what is given to an additional fact.
27. Let us state our view as a working hypothesis,
something that need not be true or even possible. Let it be
granted there is a mind X with certain functions; let it be
granted that X may be stimulated to perform again any
function which it ever has performed ; let it be granted that in
every function there is a connection of elements, as a-b; let it
be granted that presence of a tends to excite X to per
form again the function which contains a-b; then let a be
given in a fresh context, as Ca. On this X is stimulated to go
on to b thus, Car-b; and the product Cab now comes before
the mind which is the fact to be explained. If this ex
planation is false, admit at least that it is simple.
We are asked to believe it is more in accordance with
" experience " to say, Similarity is a tertium quid ensuing only
on the presence of a pair of elements, and, when but one is
present, Similarity brings the other. It is " science " when we
asseverate that mental phenomena are realities which can exist
only while they are perceived, and then speak of " recalling "
them, as if they were ambassadors on foreign employment, or
" calling them up " as though they were servants in the kitchen,
and as if " relations " were wires that rang the bell, or were
fishing-lines baited with similarity to draw up from non-
existence the ghosts of the past. It is " positive knowledge "
to make that come before the mind which does not come be
fore the mind, and then to remove it by a fictitious expedient.
Yes, sooner than run the risk of believing in metaphysics, there
is no superstition so gross, no mythology so preposterous that
we ought not to believe in it, and believe anything sooner than
cease to believe in it.
28. But what is it that forces us to these desperate
shifts? Not the facts themselves, for we violate them. It is
simply the shrinking, as we think, from metaphysics. And
this, after all, is nothing but metaphysics. It is our unreason-
ing fidelity to a metaphysical dogma which has driven us to
adopt these embarrassing results. For why is it we are so
sure that identity is impossible, and that a synthesis of urn-
33O THE PRINCIPLES OF LOGIC BOOK II. PT. II
versals is a " survival " of superstitions, which in the nine
teenth century are out of date? It is because we are sure
that there can be no reality but particular existences, and no
mental connection but a relation of these units; and that
hence identity is not possible. But this is of course a meta
physical view, and, what is more, it is nothing but a dogma.
The Philosophers of Experience have, so far as I know, never
offered any proof of it ; they have heard it from their fathers,
and their fathers had heard it. It is held true because of
the continuity of tradition in a Church, which must have truth,
since it has never failed to preserve its continuity. Has the
school ever tried to support it by any mere rational con
siderations ?
So far as I know, it has been assumed that, if you are not
able to swallow down this dogma, you are forced to accept
an intolerable alternative. You are given a choice between
naked universals, existing as such, and bare particulars. You
can not stomach the first, and so you take the last. But why
should you take either? Why not adopt the view that the
real is the concrete individual, and that the bare particular
and abstract universal are distinctions within it, which, apart
from it, are only two forms of one fiction? You say, This is
unintelligible. But perhaps you never heard of it, or heard
of it too late, when you were already compromised, and had
no inclination to begin life again. Let it then be unintel
ligible ; but permit me to add that the view you have adopted
calls for something stronger, to back it against facts, than an
a priori deduction from a metaphysical alternative.
29. We have shown so far that, in the extension of our
experience, there is a synthetic construction by virtue of
identity, and that association by similarity has no part in it.
We have shown that the test which we bring to inferences, in
order to examine their validity, is also the principle which
operates in all extension of experience. On our view the
origin of the fact is explained, and its existence is at the
same time justified. But, on the fashionable theory of Asso
ciation, early inferences are made by what afterwards we find
to be the essence of bad reasoning. And, to explain the origin
of this unjustifiable fact, open fictions have had to be invented.
But not only is Association by Similarity a fictitious ac-
CHAP. I THE THEORY OF ASSOCIATION OF IDEAS 33!
count of the reasoning process. It is a fiction altogether;
there is no evidence for it at all. And it is to the final proof
of this point that we must now address ourselves.
Our previous objections have raised at least a presumption
against the alleged phenomenon. Let us now ask, Is there
any evidence of any kind which tends to confirm it ? I know
of none whatever.
We are told (J. S. Mill, Hamilton, p. 315, note) that the
elementary case of the suggestion of similars will not come
under the head of redintegration. But the answer to this is
very simple. Reproduction by mere similarity is a fact which,
if real, would certainly stand by itself. Who doubts it? But
then the existence of this fact is just what we deny. The
general fact that ideas and perceptions give rise to others
which are like them, is of course admitted. But this not only
can be reduced to redintegration, but long ago it has been so
reduced. I will exhibit this in a concrete instance.
30. I am walking on the shore in England and see a
promontory A, and then suddenly I have the idea of another
promontory B which is in Wales, and I say How like is A to
B. This is the fact which is to be explained. The false theory
tells us to explain the fact by postulating a direct connection
between A and the idea of B, for it says The suggestion is
perfectly simple. But in the first place the postulate de
mands an absurdity, and in the second place the suggestion
is certainly not simple. If instead of asserting we are
willing to analyze, we soon find the true explanation c
fact
The content of A, like the content of every other percep
tion, is complex, and has several elements. Let us say that
it has an element of form which is p. Now let us look at B,
the idea which is to come up. That also possesses a complex
content, and we find in it the same element p, in connection
with others, q, r, s, t. These are the conditions, and let us ;
what follows. , . ,
In the first place A is presented, and so presents p, which
by redintegration stimulates the mind X to produce qr. Wl
happens then? 1 i-rr.^u
Several things may happen, and it is exceedingly difficult
to work out the minute psychological conditions which settle
332 THE PRINCIPLES OF LOGIC BOOK II. PT. II
the result. But this is a question with which we are not here
concerned. One result would be the identification of qr with
Ap. A would then be qualified as Apqr, and this would be
an unconscious inference. In the present case we are to sup
pose that this can not happen; for we suppose that q, r (say a
certain colour and a certain size) are discrepant with A.
What then may we expect? We might expect that qr would
be simply dropped. It might not catch the attention, and the
mind might be arrested by a new sensation. We might expect
again that, if qr is not dropped, it might be used as a means
for a wandering course through a train of ideas, foreign to
both A and B, and which might take us anywhere. But we
are to assume that none of these possibilities become real;
and that instead the idea B rises in the mind. How do we
explain this?
Very simply. B (we remember) had a content pqrst, and
now we have A which has brought in p, and so introduced
qr. But qr will not coalesce with A. Let them then instead
go on to complete the synthesis pqrst, a synthesis which by its
discrepancy with A is freed from union with it. But an inde
pendent pqrst is B, and may be recognized as B. And now,
B being there along with A, the perception of its resemblance
calls for no special explanation. This account of the matter
appears to me simple and natural and true.
31. It may be objected, in the first place, that, if the
sensation is simple, this theory will not work. I admit it, and
I should be sorry if in such a case it did work. I would
rather that any theory, which I adopt, did not explain im
possibilities. And that any actual presentation should be
simple is quite impossible. Even if it had no internal charac
ters, yet it must be qualified by the relations of its environment.
And this complexity would be quite enough for the purpose.
For the identity of the simple internal character, over against
the difference of two sets of external relations, would give
rise to redintegration and to the perception of the resemblance.
I think a sober antagonist will hardly deny this. And if it
should be denied, then I am inclined to reply with a reductlo
ad absurdum. If the suggestion is quite simple, perhaps there
is no difference between the similars, or perhaps they are
quite different. But on either alternative they can not be
CHAP. I THE THEORY OF ASSOCIATION OF IDEAS 333
similar; and again, if neither alternative is true, then the sug
gestion is now admitted not to be simple, because the elements
have a complex content.
I can think of another case where mistake is possible, and
where suggestion might seem to dispense with redintegration.
If an idea before the mind is unsteady and wavering, it tends
to pass into something different. This difference may be
recognized, and may appear as an idea, which is not the first
idea, and yet is seen to resemble it. But the unsteadiness
will in no case be reproduction by similarity. If the new
idea, which is similar to the other, is produced by a change
in the actual impressions, then this of course is not reproduc
tion at all. But if the alteration takes place apart from the
stimulus of a fresh sensation, it will still be a case of redinte
gration. For that will be the principle which determines the
direction of the idea s unsteadiness.
We must pass next to an objection which I feel bound to
notice, though I confess I am not able to understand it. We
are told that the form, say of a triangle, is not one single
feature among others, which therefore could call up the other
features ; and that yet a triangle may call up another which
is similar in nothing but form (J. S. Mill, on James Mill, I.
113). But why the form of a figure is not to be a " feature "
of it we are not told, and I at least can not imagine. I was
glad to find when, after forgetting this passage, I came on it
again, that accidentally (30) I had chosen to work out an
instance where the form is the base of the redintegration.
And I will say no more.
And there is another misunderstanding which we may
remove in conclusion. After pointing out that " in the very
heart of Similarity is an indispensable bond of Contiguity;
showing that it is not possible for either process to be ac
complished in separation from the other," Professor Bam, i:
L understand him rightly, goes on to argue that, notwithstand
ing this, at least a partial reproduction by pure Similarity
does actually take place.
" It might, therefore, be supposed that Similarity is, after
all, but a mode of Contiguity, namely, the contiguity or asso
ciation of the different features or parts of a complex whole^
The inference is too hasty. Because contiguity is a part
334 THE PRINCIPLES OF LOGIC BOOK II. PT. II
the fact of the restoration of similars, it is not the entire fact.
There is a distinct and characteristic step preceding the play
of this mutual coherence of the parts of the thing to be
recovered. The striking into the former track of the agreeing
part of the new and the old, is a mental movement by itself,
which the other follows, but does not do away with. The
effect above described, as the consciousness of agreement or
identity, the flash of a felt similarity, is real and distinct. We
are conscious of it by itself ; there are occasions where we
have it without the other, that is to say, without the full
re-instatement of the former object in its entireness. We are
often aware of an identity without being able to say what is
the thing identified ; as when a portrait gives us the impression
that we have seen the original, without enabling us to say who
the original is. We have been affected by the stroke of
identity or similarity ; but the restoration fails from the feeble
ness of the contiguous adherence of the parts of the object
identified. There is thus a genuine effect of the nature of
pure similarity, or resemblance, and a mode of consciousness
accompanying that effect; but there is not the full energy of
reproduction without a concurring bond of pure contiguity.
A portrait may fail to give us the consciousness of having
ever seen the original. On the supposition that we have seen
the original, this would be a failure of pure similarity " (Bain
on James Mill, I. 122-3).
Before I criticize this passage, let me show how easily the
fact which it mentions comes under our theory. When the
promontory A by means of p calls up q, r, these are not
referred to A. And, unless the synthesis p, q, r, s, t is com
pleted, they can not re-instate B. The uneasiness of partial
but incomplete recognition is caused by the presence of con
nected elements, such as p, q, r, s, which, by actual incom
pleteness and by vague suggestion of completeness, give us
the feeling that at every moment another object is coming.
But, although the whole pqrs keeps calling in other elements
such as u, x, y, w, yet none of these makes up a totality we
are able to subsume under any head which we know. Should,
however, t be called in, then B comes at once. In this case
we have the feeling of discovery, while in the former case we
have the feeling of search. And all is consistent.
CHAP. I THE THEORY OF ASSOCIATION OF IDEAS 335
In Professor Bain s account we have no consistency. 11
His view, as I understand it, is that though, for the full
reproduction of B, contiguity is required, yet partial repro
duction takes place without it. In other words, the stroke of
similarity affects us enough for us to strike into a former
track, but the adhesion of the contiguous bond is too feeble to
drag on the mutual play of the parts. The hammer of simi
larity comes down, but the flash of agreement is a flash in the
pan, which fails to explode the barrel of contiguity. But in
this place again, I think truth has been sacrificed to imagina
tion.
If anything is brought up which suggests agreement, then
this must involve what is called contiguity. For apart from
such contiguity there would be nothing to recognize. This is
readily shown. In the first place let the similarity " amount
to identity": let the differences, which went along with and
qualified B, be none of them called up. Then what is there?
Why nothing but one part of the content of A, say p. And
p agrees with nothing; for what can it agree with? There is
nothing save itself. But in the second place, if the differences
which qualified B and made it B, are called up, then obviously
we have contiguity at once ; for p by contiguity has re-instated
pqrst. " Oh but," I may hear, " we do not go on to t, and
so we never do get so far as B. We go only as far as fqrs,
so that we are not able to recognize the result. It would be
contiguity if we went from p to t : but if we stop at s, it is not
contiguity at all.
But this would surely be no less feeble than arbitrary. ^
the whole of the differences between a portrait and the idea
of the original can not be given by contiguity, why then should
any of them? Why not all be given by similarity? And if
any are given by contiguity, why should not all be given, fo
all of them are demonstrably " contiguous "? In oth
words, if similarity will not bring up all the differences why
should it bring up any? Why should not all be
contiguity ?
Because as before we do not start from the fact, but start
from a vicious theory of that fact. In the perception A/> the
* is not really a particular image; and if you said q,r,s, t
were associated with this mere adjective p, you would have
THE PRINCIPLES OF LOGIC BOOK II. PT. II
deserted your vicious theory. You try to save it by inventing
a fictitious substantival image p, which then can be brought
in by similarity. But the result is a system of compromise
and oscillation. You will not boldly say that A brings up all
of B by similarity, and your theory forbids you to say it does
so by contiguity. To satisfy both the fact and your theory
you say, One arbitrary part is done by one agency, and the
rest by the other. And you satisfy neither your theory nor
the fact. For what is actually contiguous is not like, and what
is supposed like could never have been contiguous. The par
ticular image, which on your theory is called up, has never
been contiguous to anything whatever. And the actual ele
ment, which does re-instate qrst by contiguity, is not anything
we can call like A at all. It is an universal which is part of
A s content. Into this confusion we are led by forcing on the
facts our bad metaphysics; and the confusion at once gives
place to order when we recognize that Association by Simi
larity has no existence.
32. We have seen that reproduction of a similar idea
comes under the general head of Redintegration. And if the
English votary of Association, instead of declaiming against
the blindness of Germans, had been willing to learn from them,
he might long ago have amended his theory.
" Si quod nunc percipitur specie vel genere idem est cum eo,
quod alias una cum aliis perceptum fuerat, imaginatio etiam
horum perceptionem producere debet. Quae enim specie vel
genere eadem sunt, ea sibi mutuo similia sunt, quatenus ad
eandem speciem, vel ad idem genus referuntur (233, 234,
OntoL), consequenter qusedam in iisdem eadem sunt ( 195,
Onto!.). Quare si nunc percipimus A specie vel genere idem
cum B, quod alias cum C perceperamus ; qusedam omnino
percipimus, quae antea simul cum aliis in B percepimus.
Quamobrem cum perceptio ceterorum, quae ipsi B inerant et
in A minime deprehenduntur, vi imaginationis una produci
debeant ( 104) ; imaginatio quoque producit perceptionem
ipsius B. . . .
" Idem confirmatur a posteriori. Ponamus enim nos in
convivio simul vidisse hospites et vitra vino plena. Quodsi
domi die sequente oculos in vitra convertis, quibus vinum
infundi solet; extemplo tibi occurrit phantasma hospitum ac
CHAP. I THE THEORY OF ASSOCIATION OF IDEAS 337
vitrorum vino plenorum rerumque ceterarum in convivio
prsesentium. Vitra, quae domi conspicis, specie saltern eadem
sunt cum vitris, quae videras in convivio." *
Let us hear now what Maas has to say. I translate from
the second edition of his Versuch iiber die Einbildungskraft,
1797-
" The first of these rules we have mentioned is the so-
called Law of Similarity: All ideas which are like are asso-
ciated.f I am aware that many psychologists give this law a
place co-ordinate with the law of partial perception " [redinte
gration] " and consider it independent. But on this view the
former stands too high, and the latter too low. Similar ideas
can not be associated unless, and so far as, either they or their
marks form part of one total perceptive state. But this holds
good without exception. Two ideas, a and b, are like one
another in so far as they have a common mark /3. Suppose
now that it is a fact that b has associated itself with a." [The
explanation of this fact is that] " b contains the marks ft tf,
f,and a the marks /?, or, y." [On the presentation of b] " the
marks , y associate themselves with the 0," [which appears
in &, and Pay is then recognized as a.] : The association
which takes place is thus between connected ideas, which are
parts of one perceptive state." s. 55.$
I admit that the passage is so brief and cramped that ]
have been obliged to interpolate a commentary. But there
* These quotations are from 105 of Wolff s Psych. Emp. Ed. Nova,
1738. First published in 1732.
t" Ideas" here includes perceptions.
$"Die erste von den eben erwahnten Regeln ist das sogenannte
Gesetz der Aenlichkeit : alle ahnlichen Vorstellungen associiren sich.
Es ist mir nicht unbekannt, dass diese Regel von vielen Psychology
dem Gesetze der Partialvorstellungen koordinirt, und fur em, von
diesem unabhangiges Gesetz gehalten wird. Allein das heisst dem
erstern einen zu hohen, dem andern einen zu niedrigen Rang anweisen.
Aehnliche Vorstellungen konnen sich nur in sofern associiren als sie,
Oder ihre Merkmale, zu einer Totalvorstellung gehoren, welches aber
bei ihnen ohne Ausnahme der Fall ist. Zwei Vorstellungen a und
sind einander ahnlich, sofern beide das gemeinschaftliche Merkmal
haben. Wenn also b, der die Merkmale fi,*, zukommen, sich mit
worin die Merkmale ft a, y angetroffen werden vergesellscha tel : so
associiren sich a, 7 mit ft sind also zusammengehonge Partialvorste
lungen."
338 THE PRINCIPLES OF LOGIC BOOK II. PT. II
are other passages, which I need not quote, which would settle
the meaning even if it were doubtful.
From these extracts it will be plain that the school oi
Association have had something to learn which they never
have learnt.*
33. There is a possible objection we may here anticipate.
" Admitted," it may be said, " that your theory explains the
suggestion of similars, yet it does so indirectly. We explain
it directly and by a simple law. And the simpler explanation
is surely the better one." Anything more unscientific than
such an objection I can hardly conceive. It proposes to give
a simple explanation of a complex case; in other words, to
decline analysis, and to reassert the fact as a principle. And
it proposes in consequence (as we have shown at length) to
treat the simple as a complication of the complex. But the
price you pay for turning a derivative law into an ultimate
principle is somewhat ruinous. You have to import into the
simplest processes a mass of detail which is demonstrably not
there. And this is surely a procedure which science will not
justify.
And if I am told, " At all events the process of suggestion,
as you describe it, is much too complex for a primitive mind,"
that objection once more only serves to strengthen me. For
the process does not exist in a primitive mind. Similarity is a
somewhat late perception, and hence can not appear at an
early stage. For a rude understanding, if things are not the
same, they are simply different. To see, or to feel, that two
things are not the same and yet are alike, are diverse and yet
in part identical, is a feat impossible for a low intelligence.
It demands an advance in reflection and distinction which no
sane psychology can place at the beginning of mental evolu
tion. No doubt you may say that from the very first mental
* Sir W. Hamilton not only refers to the true account of Associa
tion by Similarity, but even criticizes it. Unfortunately he had not
the least idea of its meaning. He tells us first that we are to discount
" Wolff who cannot properly be adduced." I have no notion what
"properly" stands for here, and perhaps Sir W. Hamilton did not
really know what Wolff says. He then proposes an emendation in
the passage from Maas, which reduces it to nonsense, and his criticism
shows that he had no idea of the real meaning of either Wolff or his
followers (vid. Reid, 913-14).
CHAP. I THE THEORY OF ASSOCIATION OF IDEAS 339
elements are alike, although the mind does not perceive it.
But in saying this you open a question not welcome I should
judge to the disciples of Experience. For if states of mind
can be alike, and yet not like to the mind, what is such simi
larity but the identity of elements within these states? The
distinction on the one hand between what is or was in the
mind, and, on the other hand, that which is felt by the mind
or is now before it, is, if admitted, quite fatal to the orthodox
English creed. We should have an attempt to purchase con
sistency by suicide.
If the school of Association desired to be consistent, it
might find perhaps in the " mechanism of ideas," apart from
consciousness, a way of propping its tottering beliefs. But
that mechanism implies metaphysical doctrines as to the unity
of the soul and the permanence of ideas, which in themselves
would be somewhat difficult to maintain, and which would
give the lie to our most cherished prejudices.
But if consistency can be reached by no way but suicide,
something after all may be said for the admission of the
doctrine we have adopted that all association is between uni-
versals, and that all consists in redintegration by identity.
34. The answer no doubt will be the old " Non possumus.
No two states of mind can have anything in common ; for, if
so, they would be the same, and that is impossible." On this
rock of obstinate metaphysical prejudice our explanations are
broken. It would be useless to point out, as we have already
pointed out, to the disciple of Experience that his own theory
has been wrecked on this same iron dogma. He would say,
I suppose, "Let the facts go unexplained, let miracles be
invoked and fictions multiplied, let analysis be neglected and
experience contemned only do not ask me to be false to my
principles, do not ask me to defile the grave of my fathers.
An advanced thinker once, an advanced thinker always." And
I could not answer or reproach. I respect a fidelity which I
can not imitate.
But to those whose honour is not yet pledged I may per
haps in conclusion be permitted to address myself. Do you
wish I should like to ask in the first place, to speculate on
first principles, or are you content to engage yourself on
special subject matter? In the first case I would beg you
34O THE PRINCIPLES OF LOGIC BOOK II. PT. II
seriously to examine the question for yourself, and not to
take any assertion on trust. I can not venture to anticipate
the result you will then reach (if indeed you reach any), but I
feel sure that any conclusion you do come to, will not be quite
the same with the orthodox doctrine as handed down in
England. And to those who are not prepared for metaphysical
enquiry, who feel no call towards thankless hours of fruitless
labour, who do not care to risk a waste of their lives on what
the world for the most part regards as lunacy, and they them
selves but half believe in to all such I would offer a humble
suggestion. Is it not possible to study the facts of psychology,
without encumbering oneself with beliefs or disbeliefs as to
the ultimate nature of the mind and its contents ? You can not
have metaphysical disbeliefs without corresponding beliefs;
and, if you shrink from becoming a professional metaphysi
cian, these beliefs must be dogmas. Would it not be better
to study the facts, and to let metaphysics altogether alone ?
If this can be done in the other sciences, it surely can be
done in psychology too. In the other sciences we know how
it is done. The so-called principles which explain the facts are
working hypotheses, which are true because they work, and
so far as they work, but which need not be considered as a
categorical account of the nature of things. The physicist,
for example, is not obliged to believe that atoms or ether do
really exist in a shape which exactly corresponds to his ideas.
If these ideas give a rational unity to the knowledge which
exists, and lead to fresh discoveries, the most exacting demand
upon the most exact of sciences is fully satisfied. The ideas
are verified, and the ideas are true, for they hold good of the
facts to which they are applied. And to suppose that the
metaphysician should come in, and offer to interfere with the
proceedings of the physicist or to criticize his conclusions, is
in my judgment to take a most wrong view of metaphysics.
It is the same with psychology. There is no reason why in
this science we should not use doctrines which, if you take
them as actual statements of fact, are quite preposterous. For
the psychologist, as such, is not interested in knowing if his
principles are true when taken categorically. If they are
useful ways of explaining phenomena, if they bring unity into
the subject and enable us to deal with the fresh facts which
CHAP. I THE THEORY OF ASSOCIATION OF IDEAS 34!
arise, that is really all that, as psychologists, we can be con
cerned with. Our principles are nothing but working hy
potheses : we do not know and we do not care if they turn out
to be fictions, when examined critically.
That is the way in which psychology surely might be
studied. And if we studied it in this way we should escape
some controversies. I, for instance, should lose all right and
all desire to criticize the " Laws of Association " on the ground
of their untruth, if they only ceased to proclaim themselves
as statements as to the real movement of the mind. Within
the same field of empirical psychology I should offer what I
think is a more convenient hypothesis, and any objection to
that which rested on metaphysics would be at once ruled out
of court. We might perhaps thus advance the study of the
subject in a way which now seems quite impossible. And if
we did not make much advance in knowledge, we should save
ourselves at least a good deal of bitterness.
35. The suggestion is offered in great humility, since the
obstacles it must meet with are overpowering. The first
obstacle is the prejudice of a bad tradition. It is supposed
that the psychologist must be a philosopher. He is used to
think himself so, and he is not likely to accept a lower place.
And this objection is in fact, I fear, unanswerable. I would
give him the name of philosopher for his asking, but I could
not admit him as a student of first principles. And the second
obstacle is like the first. We get into what, I suppose, deserves
the name of an antinomy. The psychologist is to confine him
self within certain limits; he is not to cross over into meta
physics. But unfortunately if he is not a metaphysician he
will not know what those limits are. And it is the same to
some extent with all the sciences. The physicist, for instance,
is constantly tempted to think that his ruling ideas are ultimate
facts. And this temptation is fatal to the mere specialist.
It is only, on the one hand, a general culture and largeness of
mind, or else some education in metaphysics, which saves him
from this error. And it is much worse in psychology. 12 The
subject brings with it a special temptation; and, if all the truth
must be told, the same great minds that devote themselves to
physics, to chemistry, or to biology, do not take up psychology.
And then again the psychologist is probably a dabbler in meta-
2321.1 Z
342 THE PRINCIPLES OF LOGIC BOOK II. PT. II
physics. A little metaphysics is not enough to show that his
so-called principles are fictions. And our leading English
psychologists perhaps only know a very little metaphysics.
And, having a limited acquaintance with the subject, they
persuade themselves, and (what is worse) one persuades the
other, that they have completely mastered it. It is to be feared
that this evil must to some extent continue.
And there is a final obstacle. The student of metaphysics
may form an opinion as to the real nature of psychical phe
nomena. And knowing, as he thinks, the truth about these
facts, he will be led to insist on a psychological interpretation
which is strictly true. He will interfere with the empirical
psychologist, and will himself contribute, by what he thinks
good metaphysics, to the begetting of bad metaphysics in
opposition. This is certainly an error, but it is an error, I
fear, which will never quite vanish. When a man has once
seen that every single science except metaphysics makes use
of fictions, he is apt to conclude that the next step is for him
to remove these fictions and to substitute the truth. But, if he
looked closer, he would see that human beings can not get on
without mythology. 13 In science, in politics, in art, and re
ligion it will always be found, and can never be driven out.
And, if we confine our attention to science, we must say that
there is only one science which can have no hypotheses, and
which is forbidden to employ any fiction or mythology, and
that this science with some reason is suspected of non-
existence.
36. We have approached a large subject which we can
not deal with, and which might well occasion misgiving and
doubt. We need give way to neither in our rejection of the
principles of the school of Association. We reject them in
the name alike of metaphysics, of psychology, and of logic.
In behalf of metaphysics we protest against the basis of dog
matic Atomism, and we protest against the superstructure of
a barbarous mythology. It is not true that mental phenomena
are mere particulars. It is not true that ghosts of impressions
leave their graves. It is ridiculous to couple the existent and
non-existent, or the present and the absent, by a relation which
implies the presence of both. In defence of psychology we
protest against an hypothesis which has to postulate phe-
CHAP. I THE THEORY OF ASSOCIATION OF IDEAS 343
nomena which are clearly absent, and then to postulate their
removal by a process which is not present. When a single
hypothesis explains the facts, it is surely unscientific to employ
a complication which works no better. And, in behalf of logic,
we must protest once more. The essence of inference can
hardly be a principle which later we recognize as a principle
of error; and which, if the theory of Association were true,
we should hardly get to perceive was false. It is an ill omen
for Logic if it fails to show that what in the highest stage is
accepted as a canon, was active from the first development of
the soul as the guide of its conduct and ruler of its life.
NOTE TO CHAPTER I
I. Though I have no space, and perhaps no strict right, to deal
with the subject here, I must yield to the temptation of making some
very brief remarks on the doctrines noticed in 2 of this chapter.
These go by the names of Indissoluble Association and the Chemistry
of Ideas.
The first of these doctrines is supposed to have a very great
metaphysical importance. Mere chance conjunction, if often repeated,
will beget, we are told, an union of ideas which is irresistible. This
shows that what seems to be a necessary connection may be no more
than an accidental adherence. From this we conclude that a necessary
connection is no canon of truth. And this proves that our trust must
be placed elsewhere. The Logic of Experience tells us, of course, what
it is we are to trust to.
For myself, in the first place, I never could get any information
from that Logic which seemed intelligible, and so I will confine myself
to the former part of the preceding statement.
2. The first fault I have to find is that it does not go far enough.
We need not have a repeated conjunction. One single instance is
enough to give rise to a necessary connection. For, as we should say,
what is once true is true always.
3. I have to complain, in the second place, that all kinds oi
combination are called association. But association surely implies that
the elements which are joined might not have been joined. And
should be proved, or at all events made probable, before co-existei
is assumed to be mere association.
84 It may be replied, "Even if the things are connected, yet, as
we perceive them, their union for us must be chance conjunction, and
therefore association." But this again should in no case be asserted
without some ground. It is not always self-evident that the mind co^
have had one element without the other. And where you fail
show that this is the case, you cannot talk of association.
344 THE PRINCIPLES OF LOGIC BOOK II. Px. II
5. I shall be answered, " What we prove is that in certain cases
mere chance association has produced necessary connection; and we
argue from this that it may be fairly suspected of doing so in all.
The possibility is proved and the possibility is enough." I can not
enter here into the merits of this argument which I shall hereafter
show is logically vicious (vid. Bk. III. II. Chap. III. 22) 14 ; but sup
pose that for the present we admit it. What conclusion follows?
That we are fallible men? We knew that before. That we are to
trust to anything else? Then what else? Admit for argument s sake
the possibility that all our beliefs are baseless, what then? Why
nothing. If we mean to go on living and thinking, we dismiss this
possibility as idle. Suppose we all are victimized by chance con
junction, are we not right to be so victimized?
6. Association implies other conditions. It implies contingent
circumstances. When a chance conjunction is taken by an error
for a necessary connection, the mistake really consists in defective
analysis. The remedy is found in the progress of analysis, assisted
probably by fresh fact. Where this remedy is impracticable, no remedy
can be applied. For no other is possible.
7. Apart from mental chemistry, which we shall consider pre
sently, a connection of ideas could not continue to be necessary when
it demonstrably has arisen from association. And this is quite ob
vious. For the connection of ideas supposes a content which is
ideally inseparable, and the knowledge of the association involves
this ideal separation. The experience which shows the fact of the
association, is at the same time the analysis which loosens its bond.
8. This however is a minor point. To the objection that
possibly all truth may be nothing but chance association, we reply (as
above) that, supposing this for argument s sake to be true, we can
not trouble ourselves with idle possibilities. But if you wish to go
beyond this idle possibility, you must show cases where unreasoning
chance conjunction has produced false belief -without confusion. You
must show, that is, that the belief in the connection was wholly false;
that it was not a true belief in a real fact made false simply by a
confusion between the relevant and irrelevant elements in the connec
tion. But this, I think, has never been shown.
9. If association rests on conjunction in perception, then that
is a valid ground for belief. It is deceptive merely so far as it is
unanalyzed, and confuses the irrelevant with the relevant. Otherwise
it is a proof of necessary connection. But then this latter is not mere
association. For it is not every conjunction in presentation which
can be called an association, but only those conjunctions which
result from chance. And chance disappears before analysis.
10. I will now turn to the doctrine of mental chemistry. Ele
ments by virtue of repeated chance conjunction are said to cohere
in such a way that they form a third product which has the qualities
of neither. But this in the first place would not be association, since
that term implies that the individuals continue. In a chemical union l5
CHAP. I THE THEORY OF ASSOCIATION OF IDEAS 345
the molecules of the substances cease to be molecules of either sub
stance. It is therefore nonsense to say that they are associated.
11. This of course may be said to be a question of words.
But the fact of such union in the case of ideas has, at least in my
knowledge, never yet been shown. It can not be called impossible,
nor should I at least have said that it was even improbable, but I
have never seen any certain instance of it.
12. In the case of emotions this " chemical union " does seem to
take place. But even here there might be doubt if the emotion
should properly be considered as an " union." It might rather be a
new reaction on a fresh compound material. 16 But, however that be,
it is true that the emotional product often can not be analyzed. 17 It
can only be reconstructed perhaps in part hypothetically. And again
if we take intellectual functions, there is no doubt that in the process
of mental development " faculties " are produced which are different
in kind from what went before. 18 But then again these functions are
hardly unions of ideas. When you strictly keep to mental objects, I
think you must say that no instance of what looks like chemical
combination has yet been found.
13. It is of course mere waste of time to bring forward as evi
dence cases where the fact of the association is not admitted. It is
for example a mere circle to instance the idea of visual extension,
since visual sensations without extension are the merest hypothesis.
Not only can this alleged fact not be observed, but there are very
strong reasons for rejecting it wholly.* It is not less idle to bring
forward a product, such as the sensation of white, and then roundly
assert that it is the fusion of different sensations. Perhaps it is, but
you would have to show the existence of these sensations in the
particular case, and give some reason for your belief that they were
transformed. It is finally ridiculous to adduce, as a chemical product,
an idea which can be separated at once and with ease into its
component parts. J. S. Mill when hard pressed seems to play as his
trump card the idea of infinity (Hamilton, Note to Chapter XV.).
But infinity, as he understands it, hardly calls for analysis. <
it falls apart into its elements, for it is a mere mechanical union.
The conclusion must be that the chemistry of ideas is no more
than a hypothesis. I do not think in any case it would be the right
way to state the fact. But the fact itself has not been clearly shown
to exist. 19 In the second place, were we convinced that mere chance
conjunction was able to lead to it, then nothing would follow except
what we know, viz. that there is some general antecedent probability
that any conviction is false. This result makes no difference either
to theory or to practice.
*Vid. Stumpf, Raumvorstellung.
346 THE PRINCIPLES OF LOGIC BOOK II. PT. II
ADDITIONAL NOTES
1 The length of this Chapter was, I think, justified by the general
state of psychology in England in 1883. The reader is asked to bear
in mind that perhaps the greater part of it was written at a particular
time, and for a special purpose, and hence should now be superfluous.
This remark does not, however, apply to the doctrine that Association
holds only between universals. This doctrine, as I have long ago
mentioned (in Mind N. S., No. 20, p. 472, and, I think, elsewhere)
I owe to Hegel (Encyk. 452 foil.). For my indebtedness to him
in psychology otherwise see on Bk. III. I. VII. I may add here that, so
far as I remember, in 1883 I had not yet made the acquaintance of
Herbart, with Drobisch and Volkmann, or even of Waitz or of
Lotze s Medicinische Psychologic. I had, however, read most of
Steinthal s Sprachwissenschaft, I.
2 "If the condition is known." It would be better to say "is taken
to fall within the subject," and for "where the condition is unknown"
to write " where you can not specify the condition."
3 " Analytical." Cf . Bk. III. I. VI. 10.
4 " When they are dead, etc." I should certainly have used other
language here with reference to "survival," if I had been better ac
quainted with the excellent work done in psychology by Herbartian
writers. The doctrine that every mental state still survives and is
active below the conscious level, was, and is, as a working hypothesis,
not to be treated with contempt.
5 "What is left behind is a mental result." Cf. 26. We have
here the problem of Dispositions. This, I should say, is in the end
insoluble, if you ask for anything beyond an empirical Law or Laws.
Cf. Mind (O. S.), No. 47, p. 363, No. 13 (N. S.), p. 25, and No. 33, p. 9.
6 " Logical." Cf. Bk. III. I. III. 20 and 23. Association becomes
logical by its use for, and subordination to, a logical end ; where, that
is, it is controlled, for the purpose of truth, by the identity and indi
viduality of an object. Cf. Mind (O. S.), No. 47, pp. 381-2, and
Essays, pp. 362 foil.
7 " They all have content." Cf. 30 and 31. The point here is
that you do not anywhere have a psychical fact which is purely simple
and in this sense unique. Everything given, we must remember, is
always in some sense itself qualified by its context. See T. E. V.
8 "This is not merely an assertion I have chosen to make." Prof
Sully on the other hand, in The Human Mind, I, 331 (1892), says (I
understand) that it is so. While directing the reader to this criticism
I may add that I neither saw nor see any need to reply to it. The
reader who can not deal with it for himself will, I think, have read
this Chapter in vain.
9 " Primitive Credulity." Cf . Bk. III. I. VI. 32, and Essays, p. 377.
10 " This is a result." See Note 5.
CHAP. I THE THEORY OF ASSOCIATION OF IDEAS 347
11 " In Professor Bain s account, etc." Though the temptation
was irresistible, I am sorry that I treated Bain, here and elsewhere,
with so little respect. Let me say now that, so far as I know, he was
the only writer of his time and school who made an original con
tribution to psychology. Though one may find him at times to be
absurd, one seldom finds that he has not at least made an instructive
effort to see the facts for himself.
12 " And it is much worse in psychology." The reader here must
not forget that I was pointing to psychology as it was in England,
still at least in the main, in 1883. To use such language now would be
absurd and even monstrous.
13 " Mythology." Cf. my Appearance and Essays, and, in particular
on psychology, see Mind, Vol. IX, N. S., No. 33. It is hardly neces
sary, I hope, for me to inform the reader that this view of truth, as
being more or less mythological everywhere outside metaphysics, came
to me from Plato and again still more from Hegel.
14 Cf. here Appearance, p. 620.
15 " Chemical union." I am of course here not endorsing but
merely adopting the view offered me as to the real nature of chemical
union.
This, I presume, might be the place to discuss the doctrine of
Fusion whether of one sensation with another or with ideas and
Dispositions or again of these two last, each with themselves or
with one another. But I can not venture upon such a difficult subject
here.
is "It might rather . . . material." This seems certainly 1
better view. No psychical state, as a unity, can be wholly resolved
into the mere compounding of units even " chemically."
" " Often can not be analyzed." The meaning here is that there
are some emotions, to ."analyze" which, except quite inadequately,
you must have recourse to what you believe is their origin.
is " Functions " and " faculties." This statement of course will apply
to much of what are called "instincts."
19 "But the fact itself . . . exist." By "the fact itself I mean
the appearance of a complex psychical state, in which the elements,
as such, have become indistinguishable, and which can nevertheless
be taken as the mere product of their union. There are but few
psychologists, I should think, who would now accept such a fact
However that may be, we can and must, I should say, maintain that
new products have been developed, but certainly not by chemical
union of ideas. Every new mental product is rather a fresh reaction
from the individual totality; and, to explain, we .must seek .to find the
Laws by which Dispositions are formed, and by which the result
former experience meets and more or less transforms the incoming
stimulus.
CHAPTER II
THE ARGUMENT FROM PARTICULARS TO PARTICULARS 1
i. At the point which we have reached a discussion of
this subject may seem inexcusable. If we have shown that
no association is possible except between universals, and that
in the very lowest stages of mind universals are used, we may
fairly be reproached by the reader who is anxious to learn
something new, if we linger over errors the root of which has
long since been torn up. For supposing that the results we
have attained to are sound, the question is settled. To
reason directly from particulars to particulars is wholly im
possible. It must be at most a desire of the mind which
this world can not gratify, a postulate a priori given by an
intuition, that disappears before analysis and is rejected by
experience.
2. But since it is possible that the reader of this Chapter
has not accepted the conclusions we obtained, since it is not
unlikely that he has passed them over, let us try once again
if we can not do something to turn the light into this refuge
of darkness. We must not expect to persuade the disciple of
the Experience Philosophy. It is not for anything we are
likely to offer, that he will desert the fashionable and easy
creed in which he has been reared. But at least we shall
have tried not to leave him an excuse. He must not say
that we have been afraid to look his idol in the face.
There is however one thing we will not do for his sake.
We decline to supply a direct examination of the well-known
chapter in J. S. Mill s Logic. It would require much more
space to set out the ambiguities inherent in that chapter, 2 than
we can give to the discussion of the question itself; a dis
cussion to which, I may remind the reader, I consider that at
this stage he has no right.
3. Why should we not reason from mere particulars?
Do our reasonings never rest upon fact ? And what are facts
if they are not particulars? Either then we never, starting
348
CHAP. II THE ARGUMENT FROM PARTICULARS 349
from fact, conclude to fact, or else we infer particulars from
particulars. This result may so be deduced from first prin
ciples. And common experience supports the result. From
cases we have known we go to fresh cases without an appeal
to any general principle. We have seen something happen
and, given a new instance, we argue at once that it will hap
pen again. But we have no reason other than this fact to
give for our conclusion. We thus in the second place have
proved our thesis a posteriori, as before we proved it a priori.
And now we add an indirect proof. If for reasoning were
wanted major premises, then the lower animals could not
reason. But they do reason, and therefore the thesis is proved.
4. How shall we escape from this array of proofs ? Are
they not unanswerable? To me they seem unanswerable, and
I have not the smallest wish to escape them. I admit them
and embrace them ; but I ask a question, What is it that they
prove ?
They prove first that, when we go from experience of
facts, this experience is the foundation of our inference. They
prove again that we do not always go from an explicit major
premise, and that therefore another way of reasoning is pos
sible. And in defence of these results I am as zealous as
any of my readers can be. If he likes to say beside that a
syllogism in extension is a petitio principii and no argument at
all, he will urge what long ago I have endorsed. But let us
come to the conclusion. If you mean to argue to no more
than this, that experience of particulars is a basis of inference,
and that no explicit major is required, I am ready to support
you. But if you mean to conclude, Therefore we reason from
particulars as such direct to particulars, I object at once. The
conclusion does not follow from the premises, and it also is
wholly contrary to experience.
5. We have in fact to do here with a common-place
logical blunder. The thesis to be proved is that an inference
is made direct from particulars, as such, to other particulars.
The conclusion which is proved is that from experience of
particulars we somehow get a particular conclusion. Not to
see the enormous difference of these assertions is to fall into
a gross ignoratio elenchi. To prove the thesis in dispute it is
necessary to assume that either we go direct from particulars
35O THE PRINCIPLES OF LOGIC BOOK II. PT. II
to particulars, or else advance through an explicit syllogism
(perhaps even an explicit syllogism in extension). No sort of
evidence is offered to show that this alternative exhausts the
possibilities ; and it disappears the moment we confront it with
facts.
6. In reply to the assertion that we are able to argue
from particulars to particulars, I would ask in the first place
what particulars are meant. Am I to understand that the
past experiences in their particularity are the premises used
in this supposed inference? If I am told this is so, of course
I reply that we have here a mere psychological fiction. Par
ticular images of past occurrences, which retain the special
marks of the originals, are not available. The doctrine that
each perished perception leaves an unblurred unabridged
counterpart of itself, is a preposterous invention (cf . pp. 35-7,
and Book II. II. Chap. I.).
7. It is again a mere error which sees in the lowest form
of inference the presence of one or more images of the past,
together with a fact which they are used to qualify. When a
present perception is modified by the suggestions of past ex
perience, these suggestions do not come from particular images
of perished events. This theory is a second pure invention
(cf. ibid.).
8. In the third place when, at a higher stage of develop
ment, the past event is as such called to mind, and when we
do argue from a particular image, yet even then we do not
argue from its particularity, from its psychological environ
ment and temporary colouring. We argue from the content,
the idea which can exist in different times and under diverse
psychological conditions. And once more, and in the fourth
place, this idea itself need not be used as a whole, but we
may argue from one part of it.
9. A child has come to know that, when the dog is
pleased, he wags his tail. On this he argues that, when the
cat wags its tail, it must be pleased. What is it he proceeds
from? The error we are considering actually supposes that
one or more images of foregone occasions, presenting the dog
pleased and with his tail in motion, come before the mind, and
that, on this, the perception of the cat now moving its tail
directly gives rise to the conclusion, The cat is pleased. But the
CHAP. II THE ARGUMENT FROM PARTICULARS 351
question arises, How is it that one attribute is taken from the
dog-images and given to the cat, without the rest going with
it? Does not this use of one part of the dog-images, and the
neglect of the rest, show that something happens to the images
in question, and that, however it has come about, the inference
is not drawn from the whole of any one of them? Suppose
again that they differ among themselves, do we argue direct
from the whole of all of them? But if not, from what else?
10. The facts, I should have thought, would have left
little doubt that the result of experience is a connection of
attributes, where the differences of their particular subjects are
blurred a confused universal, which may appear to the mind
in a particular imagery, but is used without any regard to
that. I confess I should have thought that it was very clear
that, in the special cases where we argue from recollection, we
use the past event as a type or instance. And since both this
past event and the present perception come to us as instances,
we neglect some of the differences that exist between them.
We do not know the principle, but we feel " it is the same
thing " in both cases. But, if so, the premise from which the
conclusion directly comes, is not the particular. It is an
universal extract, what we call a " general impression."
ii. Reasoning from a particular to a particular is obvi
ously an argument from analogy. In this we all know that
we do not use the whole of that particular from which we
argue. It was an inference by analogy which deceived the
child (9). He took from the dog a relation of qualities and
transferred it to the cat. What he argued from was this
general relation, and it was a false analogy, just because it was
a bad generalization. Again, why do we object to false
analogies? Is it not because in them we treat some fact as
another instance of a rule, when there is no common rule and
the facts are not instances? And is not this a hint that in
true analogy we use a principle though we can not state it ?
12. This leads us to put another question. Suppose that
per impossible we did have before our minds a number of
particular images, and did argue from them directly; would
not this inference be a very bad one? If I say " A, B, and C
are a, and there is no difference between D and A, B, and^C,
therefore D is a" is not this a circle a frivolous prtitiof
352 THE PRINCIPLES OF LOGIC BOOK II. PT. II
Again if I say " A, B, and C are a, and D is different from
A, B, and C, therefore D is a" is not this a bad argument,
so glaringly bad that no child and no beast could be got to
use it?
But if we amend this semblance of reasoning, and bring it
to the form of a real inference if we say " A, B, and C are a,,
and therefore D, which resembles them, is a" we are no longer
arguing from mere particulars. We are arguing from the
resemblance, from a point or points which D has in common
with A, B, and C. It is not because A, B, and C are a, but it is
because in them some element $ is a, and because again we
find /? in D, that we argue " therefore D is a." For whenever
we reason from resemblance we reason from identity, from
that which is the same in several particulars and is itself not a
particular. And is it not obvious that, in arguing from par
ticular cases, we leave out some of the differences, and that
we could not argue if we did not leave them out? Is it not
then palpable that, when the differences are disregarded, the
residue is an universal? Is it not once more clear that, in
vicious inferences by analogy, the fault can be found in a
wrong generalization?
13. I will conclude with an appeal to common experience.
We all know very well that in our daily life we reason habitu
ally from the results of past experience, although we may
be wholly unable to give one single particular fact in support
of our conclusion. We know again that there are persons,
whose memory is so good that they recall past details in a
way which to us is quite impossible, and who yet can not
draw the conclusions which we draw, since they have never
gone beyond the reproduction of these details. It is not the
collection of particular facts, it is the general impression one
gets from these facts which is really the sine qua non of
reasoning ; and it is that from which we really go to our result.
If you begin the discussion of a question, such as this, with
a vicious disjunction, you can not go right. As a preliminary
to discussion you have excluded the truth. From the alterna
tive either an explicit syllogism or an inference from particu
lars to particulars you can hardly fail to get a false result.
You may infer The syllogism in extension is no argument,
and therefore we go from particulars to particulars. You may
CHAP. II THE ARGUMENT FROM PARTICULARS 353
infer It is not possible to argue from particulars, and there
fore we reason always in syllogisms, explicit and (if you like)
also extensional. But to me it is nothing which conclusion
you adopt. For both are errors, and both at bottom are one
and the same error. They are twin branches from one root
of inveterate prejudice and false assumption.
14. The present chapter has been so short that I take this
opportunity to deliver my mind from a weight that oppresses
it. I intend to be guilty of what some readers may think an
unpardonable omission. It is true that I do not undertake to
criticize every theory from which I dissent; but there is one
of those theories which I propose to pass over, that may seem
to call for recognition and enquiry. Mr. Spencer, in his
Psychology, has developed a view of the nature of inference,
which, despite its ingenuity, despite its perception of some of
those truths which the syllogism has forgotten, I am obliged to
consider fundamentally mistaken. It has always seemed to
me so arbitrary and so forced, so far away in the end from the
real facts, that I can not believe a discussion of it here would
tend to throw any light on the problems of logic. 3
More than once, I admit, Mr. Spencer s position in English
philosophy induced me to think that I had no right to omit
all notice of his peculiar views. The sacrifice of space, the
chance that I had failed to follow the process which had
brought him his results, did not weigh against the danger that
I might have seemed to avoid confronting my own doctrines
with those of an established master in the subject. But there
came to my mind another consideration, which decided the
result and fixed my purpose to omit the examination,
late Mr Mill and Professor Bain have both written systematic
treatises on logic. They have entertained a view of Mr. Spen
cer s powers and philosophical performances which is not
mine. Mr. Mill especially has expressed his conviction in
such terms, that beside it those praises, I should otherwise have
felt were due to Mr. Spencer, would sound like detrac too*
Both must have been aware that Mr. Spencer has ^more than
once published what appears to be a novel theory of reasomng
And yet neither (so far as I know) has examined the 1
peculiar and salient assertions of that theory.
354 THE PRINCIPLES OF LOGIC BOOK II. PT. II
And I thought that I might venture on a humble imitation
of their common silence. Did they fail to follow Mr. Spencer s
demonstrations, did they even think them an unprofitable sub
ject, in either case I claim the protection of their authority.
But, if neither is the truth and they considered Mr. Spencer
to be of one mind with themselves, and to say the same thing
in a different form, then once again they unite in excusing me.
I surely am not wrong if I too omit all criticism, or at least
delay it till I have seen some cause to think that it is wanted.
ADDITIONAL NOTES
1 On the argument from particulars, beside the references given,
cf . also Bk. III. I. VII. 8 and III. II. I. 5.
2 " The ambiguities inherent in that chapter." These are such that
apparently (given sufficient good will) the chapter can mean that we
never do or can argue directly from particulars (see Appearance,
p. 596, note). With regard to J. S. Mill the questions to be answered,
if any one thinks them worth answering, are these, (i) Had J. S.
Mill any new view to offer? (ii) If so, what was it? (iii) What is
the view logically required by his general position? But I must be
forgiven if I go on to add " Let the dead bury their dead."
3 With regard to Mr. Spencer s view I would suggest, as a possi
bility, that it never was taken from the facts, but was a development
of or from something about Comparison which he found in Hamilton.
Reading so few books, Mr. Spencer was naturally more at the mercy
of those that he did read.
CHAPTER III
THE INDUCTIVE METHODS OF PROOF
I. We have seen that in reality there is no such thing
as an inference from the particular to a fresh particular In
this chapter we approach a cognate superstition. In England
at least if we go with the fashion, 1 we all have to believe in
an Inductive Logic, which, starting from particular given facts
goes on to prove universal truths. Its processes, exact as the
strictest syllogism, surrender themselves to the direction of
Canons, reputed no less severe than Barbara and believed with
reason to be far more fertile. I am afraid I may lose the
reader s sympathy when I advise him to doubt the union of
these qualities.
2. To question the existence or deny the efficacy of those
methods of reasoning (whatever they may be), by which
modern science has made its conquests, would of course be
absurd. To succeed on a great scale is to prove one s title.
And it is not within the scope of this work to investigate either
the nature of the processes which science employs, or the
amount of evidence which it accepts as proof. What I wish to
assert is that, starting from particular perceptions of sense,
there is no way of going to universal truths by a process of
demonstration perfectly exact, and in all its steps theoretically
accurate. The induction of logicians, so far as it professes
to make that attempt, I shall try to show will not stand
criticism.
3. We need not discuss at any great length the Method
which is called Complete Induction. 2 To examine a number
of individuals and to say of all what you say of each, is in the
first place no inference to an universal truth. A collective
term, if taken collectively, is no more universal than if taken
distributively (p. 82) ; and the inference, if admitted, does not
reach the conclusion which we have in view. But in the
second place, the inference itself is inadmissible. In other
words, if you start from each and end with each, there is no
355
356 THE PRINCIPLES OF LOGIC BOOK II. Px. II
process ; but if you predicate of the collection what is true of
each member, there is palpable error. The Induction by way
of Complete Enumeration must be rejected as either tautolo-
gous or false (cf. Book II. I. Chap. II. 5).
Or again if we take the Induction in another sense, it
changes its character. If first by counting you arrive at all,
and then from all pass on to any, that is not a process which
need be false or need merely repeat the fact it began with;
but then it is not based simply upon the particular data. If
a flock of sheep have all had medicine, I know that, within the
given enclosure, any sheep has been dosed, and I connect the
attributes without thinking of the individuals. The conclusion
is valid and is really universal ; but it implies a process which
goes beyond counting. " This sheep and that sheep and the
others are dosed ; " that is the first premise ; but a second is
wanted. We may write it " This sheep and that sheep and
the others are every sheep that is within this fold," or again
" The fold does not contain any sheep but these which we
have counted." It is on the strength of this premise that we
go on to conclude, "If any sheep is now within the fold he
must have been dosed." We seem to argue from " all " to
" any," but the " all " has ceased to be the mere collection.
We have first the assurance that the whole field has been
surveyed, and that we have not neglected any relevant matter.
Counting is the way in which we attempt to obtain this assur
ance. But the enumeration, if it is to be complete, must be
qualified by the privative judgment, Nothing in this fold can
have been uncounted. The collection is thus identified with
every possible sheep that comes under the condition of being
in the fold. This is one side of our process. The other side
consists in an act of abstraction, and in the selective perception
of one connection of attributes throughout our whole subject
matter. Then, given an individual possessing the condition of
belonging to our fold, we pass at once to the other connected
attribute.
Now the procedure by which we get this general connection
is in a sense " inductive " ; and assuredly once more it has
employed counting. But then the counting by itself is not the
induction, and is not by itself a generalization. The discrimi
native analysis, that goes with the counting, is the real agent
CHAP. Ill THE INDUCTIVE METHODS OF PROOF 357
which procures the universal, and which contains the " induc
tion " (cf. Book III.). It is this which generalizes from the
facts. But it does not go beyond one single case, 3 since its
validity depends on the privative judgment by which any folded
sheep must be one case with the sheep observed.
To repeat, if you confine yourself to mere counting, you
get no general result. If you attempt to advance from the
basis of mere counting your ground is unsafe. If you proceed
from a complete Enumeration, then the warrant of complete
ness falls outside the counting. What generalizes is the selec
tive perception which isolates and secures the connection of
adjectives. But the conclusion depen ds on the guarantee of
completeness. It is valid because the connection is found in
a whole, which is warranted to anticipate every possible case
of a certain kind.
4. But induction by way of Enumeration is not the
method we are asked to believe in.* In the treatise which,
partly from merits of its own and partly also from other
causes, has threatened to fasten itself on us as a text book,
we find the so-called Canons of Induction, collected and de
veloped from other writers, and formulated with a show of
rigorous accuracy. It is the illusory nature of these self-
styled proofs that I wish to point out in the present chapter.
We must not be afraid of the shadow of authority. The
balance of authority among modern logicians is, I think, against
the claim of the inductive proofs, and is not on their side.
And perhaps already, from experience we have had, we may
be prepared to find that Mr. Mill may at times be mistaken.
5. We must remember above all things throughout this
discussion that the question is not, Can discoveries be made by
the use of the Methods ? They may be as efficacious in actual
practice as is asserted by some, or as practically inadequate
and unsuited for work as is affirmed by others. That is not
the issue which we have before us. The question we have to
answer here is, Are they valid ways of proof, by which we can
go from facts to universals?
For that is the claim which the Canons set up. " The
* The reader of Mill s Logic will remember, on the other hand, that
with him the whole inductive process is taken to stand or fall with a
proof by way of incomplete Enumeration.
2321.1 A a
THE PRINCIPLES OF LOGIC BOOK II. PT. II
business of Inductive Logic is to provide rules and models
(such as the Syllogism and its rules are for ratiocination) to
which if inductive arguments conform, those arguments are
conclusive, and not otherwise. This is what the Four Methods
profess to be " (J. S. Mill, Logic, Bk. III. ix. 6). " In saying
that no discoveries were ever made by the Four Methods, he
affirms that none were ever made by observation and experi
ment; for assuredly if any were, it was by processes reducible
to one or other of those methods" (ibid.). "But induction
is not a mere mode of investigation." " Induction is proof ;
it is inferring something unobserved from something observed ;
it requires, therefore, an appropriate test of proof; and to
provide that test is the special purpose of inductive logic "
(Logic, III. ii. 5). We can have now no doubt about the
nature of this claim; and this claim it is that we are going
to discuss.
6. I shall endeavour to show three things : first that the
Four Inductive Methods can not be used if we start with mere
facts, that the Canons presuppose universal truths as the
material upon which the work is to be done ; and that therefore,
if valid, the Methods are not inductive at all, in the sense of
generalizing from particulars. In the next place I shall briefly
exhibit the real nature of the reasoning used in the above Four
Methods, and shall point out that its essence is not thus in
ductive. And finally I shall show that not one of the Canons is
a test of proof, and that by every one you can bring out what
is false. None of these three positions depends on the others.
If the Canons are invalid, if their essence is not inductive, or
if they can not be applied to individual facts if, in short, any
one of these contentions is established, the inductive logic is
certainly refuted. And I hope to establish firmly all three.
7. (I.) In the first place there is no doubt at all that
the basis, from which we are to start in induction, consists
primarily of particular given facts. I need cite no passages to
establish this point. We naturally expect then to see on the
one side the material as yet untouched by the Methods, and on
the other the operation of these agents on the crude subject
matter with which they must begin. This natural expectation
is doomed to disappointment.
(a) A suspicion of the shock which we are destined to
CHAP. Ill THE INDUCTIVE METHODS OF PROOF 359
receive may have come from the effrontery of the Method
called " Residues." This estimable exemplar of " our great
mental operation " comes up to us placarded as one of " the
means which mankind possess for exploring the laws of nature
by specific observation and experience," and then openly avows
that it depends entirely on " previous inductions." Unless
supplied beforehand, that is, with one or more ready-made
universal propositions, it candidly declines to work at all. We
enquire of " Residues " where we are then to begin, and it
says, " I do not know ; you had better ask Difference/ " We
anxiously turn to consider " Difference," and are staggered
at once by the distressing extent of the family likeness. A
chilling idea now steals into the mind; but we have gone too
far to retreat at once, so, resolutely turning our back upon
" Residues," we begin our examination.
(b) We look at the samples of the work produced, and
we find the same thing turning up everywhere. The material
supplied to be dealt with by the Methods is never facts but
is always universals. Sometimes an open and professed
generalization is used as a starting point. But, where this is
not done, the material is never a particular fact. It has always
been subjected to such previous operation that it is able at
once to be taken and used as a " case " or " instance." But
this means that already it is an abstract statement, ideal and
not real, capable of repetition with other environment, and
without doubt universal. Take the very first instance : " Let
the antecedent A be the contact of an alkaline substance and
an oil. This combination being tried under several varieties
of circumstances, resembling each other in nothing else, the
results agree in the production of a greasy and detersive or
saponaceous substance " (Logic, III. viii. i). And this is the
raw material which is supplied. Before I begin my induction
I am to know already that, under certain sets of definite con
ditions exactly known, certain results have followed. But, i1
I know this, I also know that these results will always follow
given the conditions. Every one of the instances is already
an universal proposition; and it is not a particular fad
phenomenon at all.* . .
8. It seems at first a strange obliquity of instinct
* Cf . Whewell, Philosophy of Discovery, p. 263.
360 THE PRINCIPLES OF LOGIC BOOK II. PT. II
choose illustrations which can not illustrate.* But on turning
to examine the Canons themselves, our surprise gives place to
another feeling. The illustrations have been selected, not
according to choice, but from hard necessity. For the Canons
are such that ex hypothesi they can not possibly work upon
any material but universal propositions.
FIRST CANON.
// two or more instances of the phenomenon under investi
gation have only one circumstance in common, the circum
stance in which alone all the instances agree, is the cause (or
effect) of the given phenomenon.
SECOND CANON.
// an instance in which the phenomenon under investiga
tion occurs, and an instance in which it does not occur, have
every circumstance in common save one, that one occurring
only in the former; the circumstance in which alone the two
instances differ, is the effect, or the cause, or an indispensable
part of the cause, of the phenomenon.
THIRD CANON.
// two or more instances in which the phenomenon occurs
have only one circumstance in common, while two or more
instances in which it does not occur have nothing in common
save the absence of that circumstance; the circumstance in
which alone the two sets of instances differ, is the effect, or
the cause, or an indispensable part of the cause, of the phe
nomenon.
FOURTH CANON.
Subduct from any phenomenon such part as is known by
previous inductions to be the effect of certain antecedents, and
the residue of the phenomenon is the effect of the remaining
antecedents.
FIFTH CANON.
Whatever phenomenon varies in any manner whenever
another phenomenon varies in some particular manner, is
either a cause or an effect of that phenomenon, or is connected
* There is an exception which I will deal with in 9
CHAP. Ill THE INDUCTIVE METHODS OF PROOF 361
with it through some fact of causation. (Mill, Logic III
viii.)
Consider the phrases "only one circumstance in common"
every circumstance in common but one," "nothing in com
mon save the absence of that circumstance." Only think for a
moment and realize what they mean, and then take on the
other hand a given fact of perception. The fact is made a
particular fact by the presence of that, the absence of which is
postulated beforehand by these formulas. A universal judg
ment is made universal by just those attributes which are
pronounced indispensable in the material for these Methods.
The moment you have reduced your particular fact to a per
fectly definite set of elements, existing in relations which are
accurately known, there you have left the fact behind you.
You have already a judgment universal in the same sense in
which the result of your " induction " is universal. Let us
take once again the very first instance. The universal which
you come to is " that the combination of an oil and an alkali
causes the production of soap." The universals which you
start with are that an oil and an alkali, if combined under con
ditions be and de, in each case produce soap. But how can you
deny that these latter are universals? No doubt they are
impure ; but the result of the " induction " is surely not quite
pure. And is an impure universal no universal at all? If
you assert this, you deny the efficacy of your " induction."
If you will not assert it, then you admit that your "induc
tions " are not inductive, since the base they start from is
not individual facts. If we regard the formulas for a little
steadily, we must surely see that an " instance " which is
capable of being so formulated, has had already done upon it
that work which we heard the Methods, and the Methods
alone, were capable of performing. And, if so, these Methods
must retire from the field or withdraw their claims. Some
thing like a farce has been played before us, whether we
consider the airs and pretences of the Canons, or remember
the promises and the boasts of their patron.
9. But I may be reminded of and in fairness I must quote
an instance, selected by the author himself, to show that his
Methods can deal with common material. And the instance
362 THE PRINCIPLES OF LOGIC BOOK II. PT. II
has the greater relevancy here, since he devised it expressly to
meet the objection that the conditions of his formulas could
not be found in facts.
"If it had been my object to justify the processes them
selves as means of investigation, there would have been no
need to look far off, or make use of recondite or complicated
instances. As a specimen of a truth ascertained by the Method
of Agreement, I might have chosen the proposition Dogs
bark/ This dog, and that dog, and the other dog, answer to
ABC, ADE, AFG. The circumstance of being a dog, answers
to A. Barking answers to a. As a truth made known by
the Method of Difference, Fire burns might have sufficed.
Before I touch the fire I am not burnt ; this is BC ; I touch it,
and am burnt; this is ABC, aBC." (Logic, III. ix. 6.)
The Canons we think are not hard to content if this will
satisfy them. But surely their author had forgotten them for
the moment. By seeing three barking dogs I perceive that
they " have only one circumstance in common." By standing
in front of a burning fireplace, and then touching the fire and
being burnt, I am to know that the two facts " have every
circumstance in common but one" Is not this preposterous?
Surely it is clear in the first case that Mr. Mill s way of
arguing might prove just as well that all dogs have the mange,
and in the second that every fireplace blisters. And these con
clusions hardly seem to be sound.*
If we have succeeded so far in establishing this point,
then the Methods of induction are placed in this dilemma.
Because they presuppose universal truths, therefore they are
not the only way of proving them. But if they are the only
way of proving them, then every universal truth is unproved.
10. (II.) The second assertion I have now to make good,
is that the process of the Methods is not inductive. I do not
mean merely that, as we have seen, they can not be applied
except to universals. I mean in addition that it is not at all
* As a test of the writer s accuracy in small points, we may notice
that in the second example there is a mistake in the working of the
Method. The right conclusion is " Touching burns " ; for the fire is
not the differential condition. It was there before I touched it, and
if it was not there, then we have two differences and another kind
of mistake.
CHAP. Ill THE INDUCTIVE METHODS OF PROOF 363
of the essence of their process to bring out a conclusion more
general than the premises. The process is one of elimination
(cf. Book III. p. 412). By removing one part of an ideal con
struction you establish the remainder. And hence the result
will be more abstract than the whole original datum, but it
need not be more abstract than some of the premises ; on the
contrary it may be less so. 4 If five plums, two apples, and ten
nuts balance the scales against three pears, two peaches, and
six grapes, when I know that the nuts weigh the same as the
grapes, and the apples as the peaches, I infer that the plums
and the pears are equal by an ideal process of removing the
rest. But if this is " induction," then " x r -f- 5 3 = a + 4
2, and therefore x = a" and again " A is either b or c, A
is not c, and therefore it is b" will also be inductions. And
if everything is induction which is not syllogism, then cer
tainly these inferences are all inductive. But such an assump
tion would surely be quite erroneous. It finds its parallel in
the counterpart mistake, that, because the Inductive Methods
are not really " inductive," therefore they are syllogistic.
The Methods are all of them Methods of Residues or
Methods of Difference, and they all go to their conclusion in
the self-same way. They fix a relation between certain wholes,
and then, by the removal of parts of each, establish this
relation between the remaining elements. In the Methods of
Agreement and Concomitant Variations the principle is the
same as it is in the rest. In the former the data are ABC-
def, AGH dij, AKLdmn. It is then assumed that the d
in def, dij, and dmn, can not be produced by a different cause ;
and hence, since BC, GH, KL are different, they do not
produce d. A is the residue or difference, and therefore A is
the cause. The process we shall see is vicious, but, such as it
is, it is elimination. In Concomitant Variations we seem to
have A X BC d 1 ef; and then, when A 1 becomes A 2 , we have
A 2 BC d 2 ef. From this whole take away X BC - - *ef, 2 BC
*ef and the conclusion is A d. The principle involved is the
same throughout, and the apparent failure to see this, and the
setting down of two or three co-ordinate axioms for the
different Methods, is another sign that the writer had never got
really inside his subject. The different Methods are different
applications of one single process, and since the premises
364 THE PRINCIPLES OF LOGIC BOOK II. Px. II
eliminated may be just as abstract as the conclusion left be
hind, this process can hardly be called " inductive."
ii. Having seen first of all that the Canons will not
work unless applied to universals ; having seen, in the second
place, that within these limits their procedure is not essentially
one of generalization, we come now to the third of our objec
tions. The Methods are vicious and the Canons are false.
(III.) I do not mean to say that, for all the purposes of
discovery, the flaws in the Methods amount to serious mis
takes. Such a contention would lie beyond the scope of my
volume. It is certain, however, that independent logicians,
such as Dr. Whewell and Professor Jevons in our own coun
try, and Professors Lotze and Sigwart in Germany, have taken
a view of the process of scientific discovery which is not
favourable to the claims of the Four Methods. But whatever
may be the usefulness of these Methods, the point here at
issue is their validity as proofs.
What I wish to show is that they will not prove anything
beyond this or that individual case. They pass to their more
general conclusion by illegitimate assumptions.
12. I think the reader will agree that, if a method will
prove a false conclusion from premises which are true, then
that method must be logically vicious, and its Canon, which
serves as a test, must be false. Now it is stated by Mr. Mill
himself that the Method of Agreement will prove false con
clusions (Logic, Chap. X.). The Method is "uncertain"
and has an " imperfection." But it still continues to figure as
a proof, and the Canon is left standing in its naked falsity.
We also have " axioms " implied in this Method, which can
hardly be true if the Method is false, and which yet are left
exposed to the daylight. We are told (Chap. X. i) that in
chapters preceding false assumptions have been made, and
yet the chapters with all their contents are recommended to
us still as a sort of Gospel. And here I must frankly confess
myself at a loss. Can the writer really have known that all his
Canons were false statements? Whether he did or did not, I
will not here enquire, for the discussion would not be likely to
profit us. It will be perhaps convenient for the sake of argu
ment to assume that he did not know the full vice of all his
Methods.
CHAP. Ill THE INDUCTIVE METHODS OF PROOF 365
The Method of Agreement starts from the premises ABC
def* AGH dijt AKL dmn: and its conclusion is that
A is the cause of d. The principle it goes on is (as we saw
before) that whatever is different in the different cases can be
eliminated. And this principle is false, since a consequence,
such as d, need not always follow from the same antecedent. 5
The generalization is therefore vicious, and the Canon which
regulates it is false. The axioms also, given in 2 of the
same eighth chapter, are no less false. To make them true
you must qualify them by adding " in this one case." But
that means you must destroy their generalizing power.
13. The Method of Difference is no less vicious. f From
the premises ABC def, BC ef, it goes to the conclusion
that A is the cause or an indispensable part of the cause of d.
But this conclusion is fatally unsound. A may be here a single
factor in the production of d, the presence of which is quite
accidental. The rule may be for d to be produced entirely
without A, and for A to be present without producing d.
The foundation of the Method $ " that whatever can not be
eliminated, is connected with the phenomenon by a law " is
quite false, unless we add to it " in this one case" and thereby
make it ineffectual for the purpose of generalizing.
The Method of Joint Agreement and Difference is essen
tially the same, and presents the same flaw. Its premises con
sist of ABC def, AGtt dij, AKL dmn, BC ef, GH
ij, KL mn. It infers from these the conclusion A d.
The mistake is the same as that which vitiated Difference.
The right conclusion is that, in these three cases, A has gone to
produce d. .
In the Method of Residues the process is the same, and is
bad for the same reason. From ABC --def, B f, C e,
the Method goes on at once to A d. But it could do so
legitimately, only if it excluded the possibility of B or C, o
*I have of course altered Mill s lettering. If his letters mean any
thing, they involve a flagrant petitio; and if they do not, their sug
gestion must tend to confuse us.
t For further explanation see Bk. III. II. Chap. III. 11 foil.
^ t There is no material difference between this and what is wrongly
given, in the same 3, as different, and as the ground of the Method
of Agreement; for you have postulated a connection your premises.
I have given above the real ground of the Method of Agreement.
366 THE PRINCIPLES OF LOGIC BOOK II. Pi. II
both, having influenced, and been influenced by, A. Other
wise the conclusion like all the rest is vicious, and its Canon
is false, unless qualified by the words " in this one case"
We come in the end to Concomitant Variations, and the
principle of this has, I think, not been formulated with the
desirable exactness. In the first place the words whenever
in the Canon itself and invariably in the Axiom assigned to it
are both ambiguous. If they mean that the groups of elements
are causally connected, then this must rest upon a previous
Method, and not upon mere facts. And in the second place,
if we consider the process as a conclusion from these idealized
premises, still it is impossible even then to demonstrate a
result which will hold beyond this or that case (or cases).
The premises appear to be A^C fref, A 2 BC d 2 ef, A 3 BC
d z ef, and the conclusion arrived at seems to be A d. We
have apparently to eliminate everything but A d, which is
hence left as proved. But since once again the factors are not
isolated, we have the old mistake of Difference once more.
The real conclusion is "In this one case (or set of
cases) without A no d." Because the modification of A has
altered the result, therefore A is relevant to d in this alteration,
or series of alterations. I may add that no amount of instances
and of " approximation " will suffice to demonstrate logically.
Should however finally the premises not have been so
idealized as to be reducible to the formula we have given if
we really have nothing whatever to start with but a certain
number of observed concomitances then there literally is no
conclusion at all, for the co-existence always may be mere
chance coincidence. And, according as we understand the
Canon and the Axiom, we must pronounce them to be either
insufficient or false.
14. I have shown that, if used in order to generalize
beyond this or that individual instance as prepared for
treatment, the Methods are vicious, and their Canons false.
Their eliminative process will only show that the whole
antecedent has been concerned in producing the whole con
sequent (cf. Book III.). The attempt to go further and,
by isolating the factors, to transcend the limits of the premises
supplied, we have seen has broken down at all points. 6
In the premises ABC def, BC ef, you are supposed to
CHAP. Ill THE INDUCTIVE METHODS OF PROOF 367
know that def is connected with ABC, and ef with BC: what
you do not yet know is if, in ABC, A is really a factor. For it
might be irrelevant, and BC without it might produce def.
But now, having BC ef, and resting on the assumption
which we call the Principle of Identity (Book I. Chap. V.), you
are sure that, if BC ef is once true, it will be true for ever.
And you proceed from this to argue that BC def must be
false. For to produce def B must have been altered: and
since in ABC def the result is produced with no possible
alteration except mere A, A there must be relevant to the
presence of def. Hence A in this case (of ABC def) must
be, directly or indirectly, relevant to d. But you must not go
further, and try in any way to specify the connection. For
you can not do that without closing possibilities, and assum
ing something not given in your premises.*
And we must not forget that even this conclusion depends
on our having assumed in the premises that, in ABC def f d
is not irrelevant. Unless we are perfectly sure beforehand
that the whole def has been produced by ABC, we can not
advance one single step. This shows once more how absurd
it is to imagine that the Methods can be applied to particular
facts. They depend entirely on such an artificial preparation
of the material supplied, as has already reduced it to the
form of an universal. It would be waste of time to dwell
further on the detail of the Four (or Five) Methods, since the
process in all is the same at bottom.f
15. We have seen that the Methods are not " inductive,"
since they will not generalize beyond the given instance. They
fail again of being " inductive," since they can not be applied
to simple facts. They will not work unless they are supplied
with universals. They presuppose in short as their own con
dition the result they profess alone to produce. Once more,
the essence of their procedure is as much deductive as it is
" inductive." The conclusion in some cases has less generality
than some of the premises.
On any one of these grounds (and I hope on all of them)
*I should like here, and on the whole subject, to refer to Lotze s
Logik, II. VII.
f I must refer to the following Book for an account of inference by
way of Elimination.
368 THE PRINCIPLES OF LOGIC BOOK II. PT. II
we may set down the Inductive Logic as a fiasco. And, if I
am told that these flaws, or most of them, are already ad
mitted by Inductive Logicians, I will not retract the word
I have used. But to satisfy the objector I will give way so
far as to write for fiasco, confessed fiasco.
1 6. If it really is the case that the Methods are not
sound; if it really is the case that the Canons are not true;
if it really is the case that " induction " is not proof, and
that he has all along known this, and been well aware of
it in that case I would suggest to the Inductive Logician
that he has provoked a possible harsh remark. And however
mistaken that harsh judgment might be, yet I can not help
thinking that it would be better if he were to tell the public,
what they certainly do not know, and the opposite of which
his too large professions have led them to believe. But if, as
I suppose, the Inductive Logician himself makes the mistake
which his public has accepted if, that is, while admitting
that, like all things human, his Methods have " imperfections,"
he has no idea that, taken as proofs, they are radically vicious
in that case I will end by expressing the hope of a final
agreement. 7 By abridging claims that will not stand criticism,
and by reforming the root and principle of his fabric, he will
bring no ruin to the bulk of his edifice. Even if we confined
ourselves to Mr. Mill s Logic, we should find that, when his
so-called Four Inductive Methods were wholly removed, and
his inference from mere particulars banished as a misunder
standing, the more valuable and even the larger part of his
discussions on Science would remain untouched.
ADDITIONAL NOTES
1 " If we go with the fashion." I have to remind the reader once
more that this refers to the year 1883.
2 This account of Complete Enumeration and the Collective Judg
ment is very seriously wrong. Indeed what is said in this volume
about the Collective Judgment (see Index) needs correction perhaps
throughout. For a true account of the matter I must refer the reader
to Bosanquet, K & R, pp. 76 foil., and Logic, I, 152 foil. The
main point is this, that all counting presupposes and depends on a
qualitative Whole, and that the Collective Judgment asserts a generic
CHAP. Ill THE INDUCTIVE METHODS OF PROOF 369
connection within its group. Hence no mere particulars can be counted.
I regret the superficiality of my treatment in this work.
3 " One single case." If this means " One single sheep," it is ob
viously wrong; and it is still wrong even if it means "each single
sheep." What is true is that the group is taken as a region within
which a universal connection holds throughout. Hence, and hence
alone, we can use such expressions as " any " and " one case with."
A minor point is that for " any folded sheep " we should read
"any sheep folded here." This difference points to the weakness
of the Collective Judgment. But on the whole subject see Bosanquet,
Logic, I, 152 foil.
4 " On the contrary it may be less so." What I meant here is
this, that the residue may be less abstract than something which has
been removed, or which has at least been used in the removal. But
the point (however defensible) might have been omitted as superfluous.
5 " Need not always follow from the same antecedent." This state
ment would, of course, be false if the sequence were pure and so
" reciprocal." But here you can not assume that your premises are
pure, since you are not taken to know what your " one circumstance "
really is. On the Method of Difference cf. Bk. III. II. III. 13.
6 " At all points," i.e. if induction is taken as proof.
7 There is no positive doctrine as to " Induction " set out in this
work, nor had I any independent view on the subject. In the main
I should have accepted, and should still accept, the view advocated
by Jevons, with its two main features of Hypothesis and Verification.
CHAPTER IV
JEVONS EQUATION AL LOGIC *
i. It is pleasant, after leaving the delusions of one s
youth, to find oneself in contact with something like fact. The
Equational Logic has proved by its results that it has a hold
on the world of reality. What works must at least be partially
right. And this new theory of logic does work. One may
see that its method remains inapplicable to part of its subject.
One may question its convenience in certain cases, and even
doubt its formula in all. But one must believe so much as
this. At the lowest estimate the new system will prove what
ever the syllogism is able to prove. In some points it certainly
is a far more rigid test of true reasoning. It deals very easily
with many of the problems which accommodate themselves
to numerical reasoning. And it maintains, on the ground
both of reason and experience, that, in comparison with the
syllogism, it is both easier to learn and harder to forget.
In writing this chapter on equational logic, as it appears
in the theory of Professor Jevons, I wish I could do two
things I can not do. I wish I could give an account of the
doctrine intelligible to those who have no acquaintance with
it. And I wish I could form something like an estimate of
its educational value and practical powers. But both want of
space and want of experience compel me to a narrower and
less grateful task. The object of this chapter is to ask if that
account of the reasoning process which has been offered us is
strictly accurate, whether as a theory it is free from mistakes.
An answer in the negative will be given to this question.
2. We may divide the enquiry into three main parts. In
the first (A) we shall ask if propositions are identities: in the
second (B) if direct reasoning consists in substitution. In the
third (C) we shall discuss the Indirect Method, and with it
the claims of the Logical Machine. It may prove convenient
to state beforehand the main results which we expect to reach.
We shall show in the first place (A) that, though every propo-
370
CHAP. IV JEVONS EQUATIONAL LOGIC 371
sition does and must assert identity, yet that is not the
object of all propositions. Our second conclusion (B) will be
that substitution is not the real essence of reasoning, and that
certain inferences will not by fair means come under this head.
We shall show again that, although most arguments can be
exhibited in the form of equations, yet the formula of inference
which our author has given is not correct. In the third place
(C) we shall argue that the Indirect Method, though perfectly
valid, does not proceed by substitution: and finally we shall
give our reasons for contesting a part of the claims put forth
by the Machine. The reader is supposed to have made some
acquaintance with the early part of The Principles of Science.
3. (A) In asking if propositions are equations, we must
remember that the sign = does not mean equal (cf. p. 23).
It denotes sameness or identity. So that the word " equa
tion," which we have chosen to start with, may at once be
dismissed. The question is, Do judgments consist in the
assertion of identity ? This point has already come before us,
and great part of what follows is repetition.
1. If we dismiss all theories and look simply at the facts,
then to ask that question is to answer it in the negative. How
can it be said that in " Caesar is sick," or " This pond is
frozen," or " Mammals are warm-blooded," we really mean to
assert self-sameness? To say that, in making such statements
as these, our real object is the denial of difference that we
wish to say, Although Caesar is sick he still is Caesar is pal
pably absurd. We do not wish, premising the difference, to
insist on the identity. The difference itself is the information
which we wish to convey.
2. If all propositions asserted mere identity, then every
proposition would have to be false. If A = B and B BC,
and we go from this to the conclusion A C, then either B
makes a difference to A or it makes no difference. In the one
case the proposition becomes quite false, and in the other it
disappears, since B = o. How can it be true that ABC is
the same as A? Is BC nothing, then nothing is asserted.
Is BC a difference, then how are they the same?
Partial identities are thus all false; but simple identities
will fare no better. If " = " is taken to stand for " is the
same as," then " A = B " can not possibly be true. If there is
372 THE PRINCIPLES OF LOGIC BOOK II. Pi. II
no difference, then nothing is said; if anything is said, then
sameness is denied.
3. It is obvious, if we are to keep to identity, that sub
ject and predicate must be wholly the same. AB = AB,
ABC = ABC. But even here it is doubtful if we can stay.
For even when we reach a tautologous statement we have still
a difference in the position of the terms (cf. Book I. Chap. V.).
If we wish to be consistent even that must go. We must
take one side of our former reduplication; we must say, for
instance, AB or ABC. In that, having given up our search
for identity, we suddenly find the whole content of our asser
tion. Assume AB, then A is B. Assume ABC, then A is C.
In our seeking to get an equational truth, we got all the dif
ferences together on each side. But the synthesis of these
differents was just what we really wanted to assert. Strike
out one side, and strike out the " =," and we have the content
of the whole judgment.*
Assertion is not confined to the affirmation of sameness,
and identity and equality are but one kind of predicate. If
we use the language of the traditional logic, then in " S = P "
the " = " has nothing to do with the copula : it falls entirely
within the predicate, and " A = AB " is " A = AB." If
we wish to say that A is equal to or the same as B, the natural
mode is, I think, to say that A and B are the same or equal.
If we will not do that, and so openly admit the existence of
difference, we must come in the end to " A = B," on the left
hand side, is just the same as " A = B," on the right hand
side. And since the sides are different even that is not true.
4. The foregoing section merely asserts that a difference
is affirmed by every proposition. Judgment can not be reduced
to one-sided identification. In the attempt to reduce it we
found that we got the whole matter of the judgment on each
side of the copula. Thus in " sodium = sodium metal con
ducting electricity " the judgment falls on the right hand side.
The assertion consists in the synthesis with sodium of the
being a metal and conducting electricity; and, when we know
that, the " sodium " and the " =," of the subject and copula,
are false or meaningless. You say that it makes no difference
* We are not dealing here with " simple identities." For them
see 6.
CHAP. IV JEVONS EQUATIONAL LOGIC 373
to sodium that it is a metal and conducts electricity. That
surely is a rather odd method of saying that there is no
difference whatever to make, and a still more eccentric method
of implying that this makes all the difference to sodium.
5. No proposition asserts mere identity, but without the
statement or implication of identity no judgment can be made.
The solution of this puzzle, which the end of the foregoing
section hints at, is that sameness and difference imply one
another, and are different sides of the self-same fact. Mere
identity or difference is therefore unmeaning. And hence,
although it is false that in judging we always mean to identify
the subject and predicate, yet in every judgment an identity
can be found. For where sameness is asserted difference is
presupposed. Where difference is asserted there is a basis of
sameness which underlies it. And it follows as a consequence
that, if you do not mind your implications being put on a level
with your meanings, you can show every judgment in the form
of difference united by identity.
6. For in every judgment the differences joined may be
taken as the qualities of a single subject 2 (cf. p. 27, and p.
180). In " sodium = sodium metal" we assert that within
the subject called sodium the attributes sodium and metal
are conjoined; and if you please you may express this by
saying, that, under the differences sodium and metal, there is
yet no change from one subject to another. Again, in " Equi
lateral triangle = equiangular triangle " what I mean to say
is that, despite these differences, you still have one and the
same triangle, or again that, if one of these qualities exists, you
will have the other in the self -same subject. Take again " The
Pole Star = the slowest-moving star : " this means either that
one star possesses these two differences, or that, in spite of
these differences, the star is the same. In every case we have
identity and diversity, and, though we accentuate one or the
other, yet in every case both must co-exist.
I will illustrate the foregoing by other instances. Take
" These fifteen statements are every one perjuries." The
identical subject is here either each statement or the quality
of perjury which appears in each. There are hence four
meanings. In the first I assert that in every statement
perjury must be added to its other qualities. In the second
2321. I
374 THE PRINCIPLES OF LOGIC BOOK II. PT. II
I deny that, though the statements are false, 3 we have any
right to abolish the perjury by making thirty statements out
of fifteen. In the third I complain that a single crime has
occurred with fifteen different sets of details. In the fourth I
refuse to admit the diversity of the fifteen qualifications as any
proof that the crime is not the same.
Or take the instance of equality or sameness itself. When
I say that A and B are equal, I assert that in the differents A
and B their quantity x is for all that the same. If I say " A
and B are precisely the same," I must first take A and B as
differenced by place or time or some other particular, and then
against that assert their identity. The equality in one case
and the sameness in the other may be treated as the subject
in which A and B co-exist as attributes.
If the doctrine already put forward is true, there can be no
such things as " simple identities." " Equiangular triangle =
equilateral triangle " is false if it denies the difference of
quality, or is false if it ignores the distinction of subjects. The
identity it asserts must exist under differences. Thus among
triangles the subject of equilateral is one and the same with
the subject of equiangular. The natural way to state the fact
is to say, The different subjects are the same, or The diverse
qualities imply one another.
7. The result of our enquiry as to propositions is not of
good augury for the doctrine of Substitution. True we find
that all subjects assert an identity, but then they no less assert
a difference. Our sign " = " has turned out quite inapplicable.
If S and P are made quite identical, the judgment disappears
or falls only on one side. If again S and P are allowed to be
different, the sign of identity asserts a falsehood. This so far
is ominous. It is ominous again that every identity can be
shown as the connection of attributes within a subject. And
there is another omen we have not yet noticed. All judg
ments, we long ago have found, can be understood as assertions
of identity. But the class of relations in time and space, it
appears, are not amenable to the Method of Substitution, or
at least in public decline to appear so (cf. Book I. p. 22). I
can not but think that with such auspices against it any cause
must be lost.
8. (B) We come now to the second branch of our sub-
CHAP. IV JEVONS EQUATION AL LOGIC 375
ject. Does the process of reasoning consist in substitution?
The foregoing has shown that this is not possible.
(i) The terms which we substitute must be the same: but
if the same then you can not substitute. If your process does
not give you a difference, it is no process. If it gives you a
difference you have broken the identity. Thus if reasoning
consists in substitution, its essence lies in the substitution of
differ ents.
Let us take as an example, " A is equal to B, and B to C,
and therefore A to C." It is impossible here by substitution
of identicals to come to any conclusion whatever. For what
is there identical ? A is not the same as B, nor B as C, nor is
" equal to B " the same as A. The identity really lies in the
quantity of A, B, and C. The quantity of A and B is the
same, and so is that of C and B. The quantity therefore of
A and C is the same. But you can not show this by substi
tution. For in the quantity of each there is no difference.
The terms are x A, x B, x C. Now if you substitute x A for
x B, you substitute things which are not the same. But if you
substitute mere x, you do nothing at all, for already you have
the term x B. A is equal to B, but it is not the same. The
quantity is the same, but it is one and not two.
The real process of the reasoning consists in connecting
the differences A and C on the basis of their common identity
x. It may also be stated as a substitution. Take x with any
one of the differences, and substitute x with any other differ
ence. The differences then found co-existing in x will be the
conclusion which we require. But this substitution is a re
placement by differ -ents.
9. (2) Substitution, so far as it works at all, is an
indirect method of synthesizing differences. The rule is to
substitute the " expression " for the term. But the " expres
sion " is the judgment about the term. The rule then says
" Substitute the judgment for the term." In other words,
a term will not do ; you must have a premise, and that means
a judgment. You must leave your identity and get to dif
ferences.
In "sodium is metal and conducts electricity" (4),
sodium-metal takes the place of sodium, and metal gives way
to metal-conductor, and we say this makes no difference to
376 THE PRINCIPLES OF LOGIC BOOK II. PT. II
sodium, or sodium is the same with all this difference. But
the real subject, which remains the same, is something which
underlies these differences; and the real process is the addi
tion of difference which developes the connection of attributes
in this subject. It is entirely to mistake our object in view
if, while we try to get the synthesis of diverse attributes, we
talk as if all we wanted was to keep the identity of the subject.
It is simply to stand the process on its head, if we make every
step by uniting differences, and then speak as if throughout
we had done nothing but remove them.
" Substitute for the terms their expressions," that is in
other words combine the premises. It is an artificial way of
performing the old task. For reasons which I can not here
enter into, the artifice in some cases is very useful. But it is
simply the syllogism turned upside down, and it is confined
to the same insufficient limits.
10. (3) The method of Substitution has set itself free
from some of the superstitions of the traditional logic. For
certain purposes it is far more useful. Everything again that
can be proved by syllogism can also be proved by its modern
rival. But on the other hand Substitution will prove nothing
that can not be shown by syllogism. The limit of both is
precisely the same. They are confined to the relation of sub
ject and attribute and the connection of attributes within a
subject; and beyond that category neither will work (cf. Bk.
II. Parti. Chap. II. 6).
To prove syllogistically that, because A and C are both
equal to B, they are equal to one another, is quite impos
sible.* But it is just as impossible to prove the conclusion by
substitution. The premises you have got are A = A equal to
B, B = B equal to C; and the quaternio terminorum can only
be avoided by taking the premises in a sense which is false.
It is needless to repeat against the equational logic the
* " Quantity of A is the same as quantity of B, quantity of B is the
same as quantity of C, and therefore quantity of A is quantity of C "
will not do at all. If the quantity is taken in abstraction then it
certainly is the same, but you can not show from that that A, B, and C
are related as equals or related in any way. But if you take the
quantity in its relations to A and B and C, in that case you have
quaternio terminorum, or otherwise the premises become false. The
relation of equality never could be got out in the conclusion.
CHAP. IV JEVONS EQUATIONAL LOGIC 377
objections we have urged against the syllogism. If a logic
will not deal with the syntheses of degree, of space, and of
time; if even, as we shall see, its own Indirect Method falls
outside its boundaries, then that logic does not give the true
method of reasoning. It is not made too narrow because it
requires an identity underlying the terms of its premises. It
is made too narrow because in its conclusions it is confined to
the category of subject and attribute. In a remarkable pas
sage (Principles, Ed. II. p. 22) I understand Professor Jevons
to admit these limitations. His logic, so far as it exists at
present, appears to be confined to " simple relations." " A
simple logical relation is that which exists between properties
and circumstances of the same object or class." But, if that
is so, then the theory of reasoning will cover only one portion
of the facts.
ii. (4) We have seen that, within the syllogistic limits,
equational logic will work very well; and we also have seen
the nature of its process. However right it is to insist that in
reasoning identity is necessary, yet exactly the same must be
said of difference. And I can not think that, in laying down
his principle of inference and in reducing it to a formula,
Professor Jevons has avoided serious mistakes.
" So far as there exists sameness, identity or likeness, what
is true of one thing will be true of the other." " In whatever
relation a thing stands to a second thing, in the same relation
it stands to the like or equivalent of that second thing " (pp.
9> I?)-
Now if the " likeness " in these formulas means absence of
difference, we see at once that they are tautologous or false.
For so far as mere identity exists, what is true of any one
thing must for that very reason be false of another. If, in the
case of A, B, and C, the judgment A C is true of A so far as
A is simply the same as B, then it either is not true of A at
all, or else the differences have all disappeared, and the judg
ment becomes x = x. So again, if A is related to B, it is
related to that which is the same as B. But " the same as B "
will be simply B, and we have not advanced one single step.
12. But if the formulas have another meaning, then what
shall we say that their meaning is? They certainly can not
mean that mere likeness will do. A need not be like C because
THE PRINCIPLES OF LOGIC BOOK II. PT. II
both are like B. And it is obvious that if B and C are
" equivalent," A need not stand in one relation to both. Two
coins are equivalent and one is in my pocket, but neither logic
nor fact makes me master of the other. It is clear that this
can not be our author s meaning.
The equivalence or likeness, to be that which is meant,
must exist to a sufficient extent or degree. But what is the
degree which is sufficient ? " The general test of equality is
substitution" (Principles, p. 19). But here again our ques
tion is not answered. It would never do to say, you may sub
stitute when you have a sufficient degree of likeness, and that
degree again consists in your ability to make a substitution.
And this is not what is meant. What I think is meant is that
a certain amount of likeness will give conclusions, and that,
when you can substitute, you may know it is there. But I
do not think that Professor Jevons has anywhere told us in
what that degree itself consists.
13. Still I think he has given us the materials for an
answer. The question we have before us is this: Given a
term B in relation with C; or otherwise, Given C as what is
true of B, then what amount of sameness between A and B
will warrant us in writing A for B? The first answer to be
given is that no amount is wanted. There is not the very
smallest need for A and B to be like or equivalent. But the
second answer to be given is this: the sameness required is
the sameness of the one subject. If A and B are both qualities
of X, or again if B is a quality of A, then A and C will be
interrelated. The quality of the subject is the middle term,
whose predicates in some way qualify the subject. Or the
identity of the subject 4 is the middle term and, so far as this
identity extends, the attributes must all be related and con
joined.
We have finished our examination of the theory of propo
sitions, and also of reasoning by substitution. We come now
to a third and most important point, the question of the Indi
rect Method and the Logical Machine. I will anticipate briefly
the result we shall reach, (a) The essence of the Indirect
Method is a process which can not possibly be reduced to
substitution, (b) In part of that process substitution may
be used, but another form of reasoning is just as applicable,
CHAP. IV JEVONS EQUATIONAL LOGIC 379
(c) The Machine will not really give complete conclusions.
(d) It is improperly limited to one kind of reasoning.
14. (C) (a) The Indirect Method is a process of ex
clusion. In using it you must first find all the possibilities,
and then by removal of the rest you leave only one. In other
words, you have a disjunction, and remove all alternatives
except a single remainder. Because the subject, if taken as
real, must be taken as fully determined and particularized,
therefore the remaining possibility is real (cf. Book I. Chap.
IV. ) . A is b, c, or d, it is not b or c, it therefore is d. This
is the essence of the Indirect Method, and we already have
to some extent made its acquaintance.
15. We know that this process falls outside syllogism.
And from that we might argue at this stage of our enquiry
that it can not be reduced to substitution. But if it can not be
reduced to substitution, Professor Jevons best work contra
dicts his theory. Let us see how he tries to avoid this conse
quence.
" The general rule is that from the denial of any of the
alternatives the affirmation of the remainder can be inferred.
Now this result clearly follows from our process of substi
tution; for if we have the proposition
and we insert this expression for A on one side of the self-
evident identity
Ab = Kb,
we obtain Ab = AB& -|- AbC -|- A&D ;
and, as the first of the three alternatives is self-contradictory,
we strike it out according to the law of contradiction; there
remains
Ab=AbC-\-AbD.
Thus our system fully includes and explains that mood of
the Disjunctive Syllogism technically called the modus tollendo
ponens" (Principles, p. 77).*
But this, I think, will not stand a moment s examination.
*I may remind the reader that [ here means "or," and b means
" Not-B." I do not use these signs in the text.
380 THE PRINCIPLES OF LOGIC BOOK II. Pi. II
In the first place the operation of striking out one part and
asserting the rest is the essence of the method, and yet it is not
even in appearance reduced to substitution. In the second
place in this example the reasoning by substitution is perfectly
useless. It does not bring you one step on your way towards
the conclusion.
I will take a perfectly simple instance. " A is b or c" and
" A is not b" These are the premises, and from these I
should say that you go directly to the conclusion " A is c"
Professor Jevons, if I understand him rightly, contends that
you go through a process of substitution. A = b or c,
A = not-b. Insert the expression for A, "A is b or c" on one
side of A not-b = A not-b. Then A not-b, = A not-b and b
or A not-b and c. But A not-b and b = o, therefore A not-b
= o or not-b and c.
But surely, if words have any meaning, when I know that
A is b or c, and that A is not b f I do know at once that b
must be removed. And, on my removing b by an ideal
experiment, c by itself is what I have left. If I please I may
write this " c or o." But I really can not perceive what
advantage I get by turning in a circle to come back to my
starting-place. A is b or c, and it is not b. If possible how
ever let A be b. But, if it is b, it will be b and not-&. That
is impossible, and therefore follows what? Why simply that
A is not b. I have used the premise to prove itself. And,
if in answer I am told that this is not so, for I have enriched
what was given me by the alternative " or o," then it seems
to me that I may fairly reply, If you do not know, given
only b and c, that when b is gone, c is what is left behind;
then how on earth can you tell that, given " c or o," when o
is gone, c is all that is left? I confess to me one is no clearer
than the other.
1 6. What I think has occasioned this complete mistake
is an erroneous idea as to indirect reasoning. For that we
must have a disjunction to start with, and by removing one
member we prove the other. And we generally have to use
direct reasoning downwards. We assume as one of our
premises that alternative which we want in the end to get rid
of, and on this assumption we bring out a conclusion which
contradicts something contained in the premises. This is the
CHAP. IV JEVONS EQUATIONAL LOGIC 381
usual course, but it is not more than usual. Direct reasoning
downwards is not always wanted. For when the premises
themselves give the removal of one alternative, what more can
we prove by such direct reasoning? We have in our hands
not only the disjunction, but also the exclusion of one alter
native. Where direct reasoning is required it is simply pre
liminary to the final operation, and is wanted merely to prepare
the subject; and when the premises give the subject ready
prepared, what is there which we possibly can have to wait
for?
And I think this mistake is connected with another. I
suspect that an error as to the Laws of Contradiction and
Excluded Middle has helped to lead our author into this pitfall.
But when we know that the Law of Excluded Middle 5 is one
case of disjunction, and in no sense the basis of it (Book I.
p. 151), we see at once that no mystical force arises from the
proof of a self-contradiction. If we get to that by turning
in a circle, the end will hardly justify the means. It has no
power to absolve our consciences from the ordinary sin of
logical fallacy.^
I must not be considered as wanting in respect, if I
illustrate what I mean by another instance. Suppose that my
premise is " A is b." Will any one deny that to prove from
this that " A is b " is a frivolous circle ? But it is easily done.
For, if possible, suppose that A is not b; then A will be both
b and not-&: or insert, on one side of the self-evident identity
A not-fc = A not-&, the expression for A. Then A not-& = A
not-& and b. As one side of our equation is now self-contra
dictory, we strike it out according to the law of contradiction,
and then there remains A not-& = o, or A is b. I must be
allowed to state my conviction that this circle is the same as
what we had above. In both cases alike the premise has been
used to bring out nothing whatever but that which it gave.
The Indirect Method, we so far have seen, can not be
reduced to a process of substitution.
17. (b) If we consider that Method as employed by
Professor Jevons, it does make use of the equational form,
but there is no real necessity for its so doing. This process
consists of the following four steps.
"i. By the Law of Duality develope the utmost number of
382 THE PRINCIPLES OF LOGIC BOOK II. Px. II
alternatives which may exist in the description of the required
class or term as regards the terms involved in the premises.
2. For each term in these alternatives substitute its de
scription as given in the premises.
3. Strike out every alternative which is then found to
break the Law of Contradiction.
4. The remaining terms may be equated to the term in
question as the desired description " (Principles, pp. 89-90) .
The one part of this process which employs substitution,
we see, is the second. But it is performed just as well by the
ordinary method. All the possible combinations of the terms
are given us, and our object is merely by means of the premises
to remove those combinations which the premises contradict.
In what shape then ought we to have our premises? Surely
one would say in the shape of -combinations. It is just such
combinations that the ordinary process would give us directly,
and we get them by substitution in a roundabout way. For the
" description " of the term is, as we saw, the judgment we
make about the term. Hence this part of the method, as
employed by Professor Jevons, is valid just so far as it can
be stated syllogistically. For the premises are combinations
of attributes. They are related, as Professor Jevons says,
" just as the qualities of the same object " (ibid. p. 114) ; and
if they were anything else, his method could not deal with
them. We can combine them directly, if we please : and it is
simply our choice, and perhaps sometimes our convenience,
if we combine them from behind through their common
subject.
Thus we may use substitution to prepare for our conclu
sion. But we can not use it to draw that conclusion. Its
operation ends with the second step.
18. We see, from examining the method itself, that it
deals with syntheses or combinations, and does not deal at
all with equations. And the method, as practically worked
with the machine, confirms the truth of the view which we
have taken. Professor Jevons himself with the greatest can
dour has called attention to this consideration.
" It is no doubt a remarkable fact that a simple identity
can not be impressed upon the machine except in the form of
two partial identities, and this may be thought by some logi-
CHAP. IV JEVONS EQUATIONAL LOGIC 383
cians to militate against the equational mode of representing
propositions" (Principles, 112).
It would be to me even more than remarkable if the ma
chine could work with simple identities. But the fact, which
Professor Jevons rightly finds remarkable, has I think a still
more remarkable counterpart. The conclusions of the machine,
if I understand them properly, contradict one another when
read as equations in the sense of assertions of simple identity.
A B C is consistent with Not-A B C ; 6 but how
can we reconcile A = C with C = Not-A ?
19. (c) We come now to the subject of the Logical
Machine, and we have to enquire what work it performs. Of
the mechanism employed I have no knowledge. I am so
incompetent to say anything about it, that I can not have the
pleasure of congratulating Professor Jevons on what I must
believe is no small achievement. But what the machine does
perform is this. All the possible combinations of the terms
are worked out, and are lying ready drawn up in the machine.
The operator puts in at one end his premises, each in the
shape of a combination. The combinations of these premises
remove, each one, all the possibilitites with which it is irrecon-
cileable. And what comes out, so to speak, at the other end
of the machine is all the residue of possible combinations
which have not been so excluded by the premises. It is easy
to exaggerate the powers of the machine. But I think it is
impossible to deny that it executes such work, as must other
wise be done by a process of thinking. For myself I do
not hesitate to say that it performs mechanically an operation
which, if performed ideally, would be an inference. And in
this sense I think Professor Jevons is justified in his claim to
have made a reasoning machine. 7 Apart from the practical
utility of the instrument, which in certain cases may be con
siderable, we must admit that, from a merely theoretical point
of view, it is a most interesting and instructive phenomenon.
If Professor Jevons had made no other contributions to logic,
we might yet be sure that his name would go down with the
history of the science.
But to say on the other hand that the machine will execute
the whole process our minds perform in the inference that
the raw material goes in at one side, and the finished con
clusion comes out at the other, would be travelling far beyond
384 THE PRINCIPLES OF LOGIC BOOK II. Pi. II
the fact. Before the premises can be worked on the instru
ment, they have of course to be reduced and formulated, so as
to take the shape of combinations of letters. But this is not
the most important point. The result that comes out and is
presented by the machine, is not really the conclusion. The
process is not finished when the machinery stops; and the
rest is left to be done by the mind. What is called " reading "
the conclusion is to some extent making it.
20. I will explain what I mean. In the machine is drawn
up a complete disjunction of the possible arrangements of
those terms which we employ. Before we begin to work
the problem the machine thus supplies us with one of our
premises. It states all possibilities, and this is its strength.
But it states mere possibilities, and this is its weakness. We
begin our operation, and insert the combinations which are
given us by our data. These combinations are the rest of the
premises. The machine, as it receives each combination, re
moves from the list of all the possibilities those which are
inconsistent with this datum. Then the remainder of the
possible combinations are exposed. But they still remain bare
possibilities, and are never stated as actual facts.
The process may be taken as having five parts, i. The
complete disjunctive statement of possible combinations.
This is given ready-made by the machine. 2. The reduction
of the premises to the shape of combinations. This is done
entirely by the operator. 3. The discovery of those alterna
tives which are inconsistent with the combinations of the
premises. This step is performed entirely by the machine.
4. The removal of those alternatives. This step again is
performed by the machine, and it is the first part of that final
inference which gives the conclusion. 5. The assertion that
what is left is true, and that, if but one possibility remains,
that is fact. This is absolutely necessary to complete the
inference, and this is done entirely by the operator.
The final step may seem to some persons a final super
fluity. But on that view of the nature of reasoning by way
of the exclusion of alternatives which has seemed to me
true, it is integral and essential. Yet it can not be said to be
performed by the instrument.
21. I wish to stand on this statement of the case. But
CHAP. IV JEVONS EQUATIONAL LOGIC 385
it is possible to use also an argumcntum ad hominem. If the
too undiscriminating friends of the machine assert that its
result is a categorical statement, they can hardly fail to com
promise it deeply. They will make it an instrument for the
production of falsehoods. Let us take one result that is given
by the machine (Principles, 109).
A B C. NotA B C.
A not B C. Not A not B not C.
Now, there being here but one possibility, if A is assumed,
we are practically safe in contending that the machine cate
gorically asserts this one possibility. But, suppose we take
the same line throughout, we plunge at once into a sea of non
sense. Contradictory possibilities can co-exist as long as they
remain mere possibilities, but the moment you affirm them
as actual fact, they exclude one another. And, if so, either
the machine brings out false conclusions, or all must be read
as mere possibilities. You have no warrant from the machine
for the assertion A is C. A may be C ; and because it may
be, and because there is nothing else that it may be, and
because you know that it must be something to C one way or
the other, you therefore infer that A is C, a conclusion not
given to you by the machine.
22. (d) The machine performs more than we have a
right to ask, and it is a pity to credit it with fictitious powers.
We have seen that it does not bring out a conclusion. But it
is limited beside in another respect. Although it does not work
by substitution, yet its range is limited to that kind of inference
which is possible in equational logic or in syllogism. It can
not deal with any other combinations than those which repre
sent the co-existence of qualities within a subject. And this
is a very serious defect; for it means that the machine refuses
to touch more than a part of the subject.
This is not the fault of the Indirect Method itself. Apart
from restrictions artificially imposed on it, that is applicable
everywhere and to all kinds of matter. If my premises are
" A is to the right of B, and B of C," I may go directly from
these to my conclusion; but, if I choose, I may use the i
direct method. The possibilities of A with respect to C are
386 THE PRINCIPLES OF LOGIC BOOK II. PT. II
either absence of any spatial relation, or A to the right of C, or
to the left of C, or neither and above it, or below it, &c. But
the premise " A to the right of B," will exclude (as we should
see by an ideal construction) every alternative we can find
other than A to the right of C. For, if we assumed any one of
the others, we should bring out a result incompatible with our
premise. The remaining possibility is therefore fact. This is
perfectly familiar and common-place reasoning, and a system,
in which it can find no place, must assuredly be called at least
incomplete.
23. The result of our perhaps too brief examination may
be stated as follows:
1. The Indirect Method has absolutely no vital connection
with the Substitution of Similars.
2. That Method itself is flawless and complete, but as used
by Professor Jevons it is improperly limited.
3. The machine which works within these limits will not
actually give a categorical conclusion.
4. These unfortunate limits are also those of equational
reasoning.
5. They coincide exactly with the boundary of the syllo
gism, and a large part of reasoning falls entirely without them.
6. The method of Substitution is syllogism upside down,
and its principle has not been accurately formulated by Pro
fessor Jevons.
I must leave this subject with an expression of regret. I
am sorry to have had no more space available ; and I am
sorry to have dwelt almost wholly on those points in which I
am unable to follow the author. It would have been more
pleasant, if it had been possible, to have called attention to
the various merits of his logical work. But still, even if my
praises could do him any service, fortunately he does not
stand in need of them. I may end this chapter by expressing
my belief, that no living Englishman 8 has done one half the
service to logic that Professor Jevons has done. No living
writer, to the best of my knowledge, now Professor Lotze is
dead, has done more. Personally to myself, and so far as my
own studies are concerned, Professor Jevons book has been
of very great use ; and I could not truly say that of any other
English Logic. It is not inability to accept conclusions which
CHAP. IV JEVONS EQUATIONAL LOGIC 387
prevents one learning. And there can not be any one who has
left unread the Principles of Science, who has not something
to learn from it.*
* Since this chapter was written Professor Jevons lamented death
has taken place, and has deprived me of any opportunity I might other
wise have had of learning from him in what points I have failed to
understand his doctrines. I have thought it best to leave the chapter
as it stood.
But there is another point on which the reader may look for some
explanation. He may ask why I have failed to examine one of those
views of Equational Logic which treat the subject mathematically.
And I am compelled to throw the burden of the answer on those who
had charge of my education, and who failed to give me the requisite
instruction. It would have been otherwise a pleasure to have seen
how the defects of the Equational theory appeared in a mathematical
form. For, at the risk of seeming no less prejudiced than ignorant, I
am forced to state the matter so. If I knew perhaps what Mathe
matics were, I should see how there is nothing special or limited about
them, and how they are the soul of logic in general and (for all I
know) of metaphysics too. Meanwhile I may suggest to the mathe
matical logician that, so long as he fails to treat (for example) such
simple arguments as " A before B, and B with C, therefore A before
C," he has no strict right to demand a hearing. Logic is not logic
at all if its theory is based on a previous mutilation of the facts of the
subject. It may do something which perhaps is very much better, but
it does not give any account (adequate or inadequate) of reasoning in
general. And at the risk of exhibiting prejudice once more, I may
say that this consideration seems to me to be vital. 3
ADDITIONAL NOTES
1 On the subject of this Chapter see the Notes on Book I, Chap. VI,
and also T. E. III.
2 "Single subject," "self-same subject." Cf. Bk. I. VI. n and
T. E. III.
3 " Though the statements are false." These words would, I think,
have been better omitted. The " four meanings " are as follows,
(i) Every statement contains a diversity, but (ii) its diversity does
not make it two, so that by dividing it you can get rid of the connected
unity which makes its character here of wilful falsity. And the
essence of its character, while (iv) remaining throughout one and the
same, is yet (iii) affected by, and made more intense by the number
of its instances.
4 " The identity of the subject." See Note 2.
THE PRINCIPLES OF LOGIC BOOK II. PT. II
s Excluded Middle." See Bk. I. V, Note 12.
6 "A B C is consistent, etc." It would be better before "is"
to insert "(as commonly understood)"; for, if A is taken as pure,
i. e. as unconditional, the above statement would be incorrect. Cf . 21,
and see the Note on Bk. II. II. III. 12.
7 " A reasoning machine." Dr. Bosanquet (K & R, pp. 327 foil.,
and Logic, II, 150) has called attention to the point that all instruments
of measurement and observation have a right to be called " reasoning
machines."
8 " No living Englishman." This was of course published in 1883,
and I think that it was true. My eulogy may perhaps on the whole
be exaggerated, and that question I leave to others to decide. What
I wrote remains as the expression of the gratitude I felt towards one
whose book had helped me greatly in my logical struggles.
9 The second paragraph of this foot-note would have been better
omitted. When writing it I did not know of the existence of a
mathematical logic which was not equational. But even now I am
in effect perhaps in no better case.
Whether a student of logic, who is incapable of learning mathe
matics and has therefore to leave out of his theory a recognized part
of the facts, should never have written on logic at all, or should
later at least suppress all that he once wrote I will not offer to
discuss. And what should be his attitude towards a claim to base
the principles of logic on mathematics, I once more hardly know.
If a person like myself ventures to point out that something of
what is thus offered seems to himself to be untenable and irrational
he can be met with the reply that, if he understood mathematics,
he would forthwith think otherwise. And what his answer to this
should be, I confess I can not say.
I am of course unable to accept a claim made on behalf of mathe
matics to have rationally solved logical and metaphysical problems
in a way unintelligible except to the mathematician. And there is
one thing only which would incline me to accept such a claim. It
would have to be made by a man, who can meet on their own ground
the non-mathematical logicians and metaphysicians can show that he
understands and enters into their views and their puzzles and can
inspire the belief that he himself is somehow able better, even outside
mathematics, to deal rationally with ultimate problems. But my whole
acquaintance with this subject is unfortunately too limited even to
justify perhaps what now I have ventured to set down.
BC 71 .88 1922a v.l SMC
Bradley, F. H.
The principles of logic
47092899
