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," b 
