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1895
Library of Philosophy.
EDITED BY J. H. MUIRHEAD, M.A.
THE LIBRARY OF PHILOSOPHY.
THE LIBRARY OF PHILOSOPHY is in the first in-
stance a contribution to the History of Thought. While
much has been done in England in tracing the course of evolu-
tion in nature, history, religion, and morality, comparatively
little has been done in tracing the development of Thought
upon these and kindred subjects, and yet “the evolution of
opinion is part of the whole evolution."
This Library will deal mainly with Modern Philosophy,
partly because Ancient Philosophy has already had a fair
share of attention in this country through the labours of Grote,
Ferrier, and others, and more recently through translations
from Zeller ; partly because the Library does not profess to
give a complete history of thought.
... By the co-operation of different writers in carrying out this
plan, it is hoped that a completeness and thoroughness of treat-
ment otherwise unattainable will be secured. It is believed,
also, that from writers mainly English and American fuller
consideration of English Philosophy than it has hitherto re-
ceived from the great German Histories of Philosophy may
be looked for. In the departments of Ethics, Economics, and
Politics, for instance, the contributions of English writers to
the common stock of theoretic discussion have been especially
valuable, and these subjects will accordingly have special pro-
minence in this undertaking.
Another feature in the plan of the Library is its arrange-
ment according to subjects rather than authors and dates,
enabling the writers to follow out and exhibit in a way
hitherto unattempted the results of the logical development of
particular lines of thought.
The historical portion of the Library is divided into two
sections, of which the first contains works upon the develop-
ment of particular schools of Philosophy, while the second ex-
hibits the history of theory in particular departments. The
third series contains original contributions to Philosophy, and
the fourth translations of valuable foreign works.
To these has been added, by way of Introduction to the
whole Library, an English translation of Erdmann's “ History
of Philosophy," long since recognised in Germany as the
best.
J. H. MUIRHEAD,
General Editor.
ALREADY PUBLISHED.
THE HISTORY OF PHILOSOPHY. By Dr. JOHANN EDUARD ERDMANN.'
English Translation. Edited by WILLISTON S. HOUGH, M.Ph., Professor of
Mental and Moral Philosophy and Logic in the University of Minnesota.
In 3 vols., medium 8vo, cloth.
Vol. I. Ancient and Mediæval Philosophy, 155. . . . Third Edition.
Vol. II. Modern Philosophy, 155. .
. Third Edition.
Vol. III. Modern Philosophy since Hegel, 125. . . . Third Edition.
THE HISTORY OF ÆSTHETIC. By BERNARD BOSANQUET, M.A., LL.D., late Fellow of
University College, Oxford.
[SECOND SERIES.
The DeveloPMENT OF RATIONAL THEOLOGY since Kant. By Professor OTTO
PFLEIDERER, of Berlin.
[SECOND SERIES. Second Edition.
PHILOSOPHY AND POLITICAL ECONOMY IN SOME OF THEIR HISTORICAL RELATIONS.
By JAMES BONAR, M.A., LL.D.
[SECOND SERIES.
APPEARANCE AND REALITY. By F. H. BRADLEY, M.A., Fellow of Merton College,
[THIRD SERIES.
NATURAL Rights. By David G. RITCHIE, Professor of Logic and Metaphysics in the
University of St. Andrews.
(THIRD SERIES.
Sigwart's Logic. Translated by HELEN DENDY. 2 vols. [FOURTH SERIES.
Oxford.
LIST OF WORKS IN PREPARATION.
FIRST SERIES.
EARLY IDEALISM : Descartes to Leibnitz. By W. L. COURTNEY, M.A., LL.D. (St.
Andrews), Fellow of New College, Oxford.
GERMAN IDEALISTS : Kant to Hegel. By Wm. WALLACE, M.A., Whyte Professor of
Moral Philosophy, University of Oxford.
MODERN REALISTS : Leibnitz, Herbart, Lotze. By ANDREW SETH, M.A., Professor of
Logic and English Literature, University of Edinburgh.
SENSATIONALISTS : Locke to Mill. By W. S. HOUGH, M.Ph., Professor of Mental and
Moral Philosophy, University of Minnesota, U.S.A.
THE UTILITARIANS : Hume to Contemporary Writers. By W. R. SORLEY, M.A., Fellow
of Trinity College, Cambridge, and Professor of Philosophy in University College, Cardiff.
PRINCIPLE OF EVOLUTION IN ITS SCIENTIFIC AND PHILOSOPHICAL ASPECTS. By JOHN
WATSON, LL.D., Professor of Moral Philosophy, University of Queen's College,
Kingston, Canada.
SECOND SERIES.
THE HISTORY OF PSYCHOLOGY : Empirical and Rational. By ROBERT ADAMSON, M.A.,
LL.D., Professor of Logic, University of Aberdeen.
THE HISTORY OF POLITICAL PHILOSOPHY. By D. G. RITCHIE, M.A., Professor of
Logic and Metaphysics in the University of St. Andrews, and J. H. MUIRHEAD,
M. A., Lecturer in Philosophy, Royal Holloway College, Egham, and Bedford College;
London.
THE HISTORY OF THE PHILOSOPHICAL TENDENCIES OF THE NINETEENTH CENTURY.
By JOSIAH ROYCE, Professor of Philosophy, Harvard University.
THIRD SERIES.
First PRINCIPLES OF PHILOSOPHY. By JOHN STUART MACKENZIE, M.A., Fellow of
Trinity College, Cambridge.
THE THEORY OF Ethics. By EDWARD CAIRD, LL.D., Master of Balliol College,
Oxford.
EPISTEMOLOGY ; OR, THE Theory of KNOWLEDGE. By JAMES WARD, D.Sc., LL.D.,
Fellow and Lecturer of Trinity College, Cambridge.
PRINCIPLES OF PSYCHOLOGY. By G. F. STOUT, M.A., Fellow of St. John's College,
Cambridge.
[Shortly.
PRINCIPLES OF INSTRUMENTAL LOGIC. By John Dewey, Ph.D., Professor of Philo-
sophy, University of Michigan.
A
V
SWAN SONNENSCHEIN & Co., LONDON.
MACMILLAN & CO., NEW YORK.
iii
LOGIC
67878
BY
.
DR. CHRISTOPH SIGWART
Professor of Philosophy at the University of Tübingen
VOL. I
THE JUDGMENT, CONCEPT, AND INFERENCE
SECOND EDITION, REVISED AND ENLARGED
TRANSLATED BY HELEN DENDY

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London
SWAN SONNENSCHEIN & CO.
NEW YORK: MACMILLAN & CO.
1895
BUTLER & TANNER,
The Selwood PRINTING WORKS,
FROME, AND LONDON.
AUTHOR'S PREFACE TO THE ENGLISH
TRANSLATION
WHEN I was requested to give my consent to an English translation of my
Logic, I complied willingly, because in preparing and achieving this work
an essential part of my studies had been devoted to English logicians from
Francis Bacon down to Jevons, Bradley, and Venn; thus I may hope that
to English readers my book will not appear entirely as a foreigner..
Whoever has himself attempted to translate a philosophical treatise is
acquainted with the difficulties of the task; it is sometimes impossible to
find in one's own language simple and current expressions which might
exactly correspond to the terms of the original, and the translator is beset
by the danger of either missing the precise meaning of the text, or of
straining his own language and impairing easy understanding.
I think that Miss Dendy has done her best to overcome these diffi-
culties and avoid this double danger. I have carefully revised her
manuscript from beginning to end, and co-operated in correcting the
proofs, so that I may safely assure the reader that the translation is
completely free from misunderstandings, and that it represents everywhere
as exactly as possible the original text. I feel obliged to express my
hearty thanks to Miss Dendy for the trouble she has taken to give a
really faithful and reliable translation.
C. SIGWART.
TÜBINGEN, November, 1894.
vii
AUTHOR'S PREFACE TO FIRST GERMAN
EDITION
The following attempt to reconstruct logic from the point of view of
methodology, thus bringing it into active relations with the scientific prob-
lems of the present day, must be justified by the success with which it is
parts of the doctrine, and in them I have adhered as closely as possible to
the traditional form of the science. I would only ask that the small extent
to which I have referred to previous and contemporary treatments of the
subject as a whole, or to particular views on special points, may not be
taken amiss. In a science which has been so much discussed it seemed to
me that to commend or dispute even the most important previous doctrines
would be an undue extension of the work; and I further feared lest the
course of investigation and exposition prescribed by my view of the
subject would be confused if I made a rule of discussing at every point
opinions which are to a large extent based upon presuppositions quite
different from my own. I have therefore thought it right to confine myself
to what was indispensable for the correct representation and justification
of my own doctrine. I need hardly say that I have made extensive use of
both ancient and modern authors. Three of the men whose works have
been most frequently before me, and to whom I hoped here to express my
was being planned and carried out; I must also make special mention of
the assistance I have received from Prantl's great work.
July, 1873.
AUTHOR'S PREFACE TO SECOND GERMAN
EDITION
In the fifteen years which have passed since this book first appeared the
literature of logic has been enriched by a remarkable series of valuable
books. Important works have appeared by Lotze, Schuppe, Wundt and
Bradley—to name only the most eminent; and all start from the concep-
tion which has guided this attempt. That is, logic is grounded by them,
not upon an effete tradition, but upon a new investigation of thought as it
actually is in its psychological foundations, in its significance for knowledge
and its actual operation in scientific methods. Particular points of logic,
again, have received welcome elucidations from more special investigations,
and amongst these Windelband's studies on the negative judgment,
Meinong's treatment of relational-concepts, and Volkelt's acute and
original treatise are most nearly akin to my views.
It has thus become incumbent upon me to test anew my own views by
the conclusions arrived at by my fellow-workers, to find more accurate
expression where misunderstanding might arise, and elsewhere to amplify
and extend, or to fortify against adverse opinions. But for the reasons
already stated in my first preface, I have been obliged to refrain from in-
corporating more extensively in the work the considerations which deter-
mined me to adhere to my conclusions, or from mentioning in detail all
the critical observations which have been so abundantly bestowed. Where
these criticisms were really applicable to what I had said, I have gratefully
made use of them ; where they were due merely to misunderstandings, I
was loth to weary the reader with unfruitful discussions. In the same
way I have been forced to abstain from enriching the work by intro-
ducing more freely investigations not included in its original design, even
though I might agree with them; the subject is so inexhaustible that com-
pleteness is not attainable, and I would rather sacrifice the appearance of
completeness in treatment than obscure the clearness of the design.
TÜBINGEN, October, 1888.
CONTENTS.
.
·
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...
PAGE
INTRODUCTION .
§ 1. The Problem of Logic . . . . . . . . . I
§ 2. Limits to the Problem . . .
§ 3. The Postulate of Logic. .
§ 4. The Divisions of Logic. .
Part I. Analytical. The Nature of Judgment and its Presuppositions . .
§ 5. The Proposition as the Expression of the Judgment. Subject and
Predicate . . . . . . . . . . .
CHAPTER I. Ideas as Elements of Judgments and their Relation to Words'. . 29
§ 6. The Highest Categories of the Objects of Thought . . . . 29
§ 7. The General Idea and the Word
§ 8. Necessity of the Word as Predicate. .
CHAPTER II. Simple Judgments . . . . . . . . . 53
I. Narrative Judgments . . . . . . . . . 53
§ 9. Denominative Judgments. . . . . . . . . 53
§ 10. Judgments of Attributes and Activities, .
§ II. Impersonal Judgments and Allied Forms. .
§ 12. Relational Judgments. Existential Propositions . . . . 65
§ 13. Judgments about Abstract Nouns . . .
§ 14. The Objective Validity of the Judgment, and the Principle of
Identity . . . . . . . . . . . 79
§ 15. The Reference to Time in Narrative Judgments . .
II. § 16. Explicative Judgments . . . . . .
III. § 17. The Act of Judgment as expressed in Language . . . . 93
CHAPTER III. How Judgments arise, and the Distinction between Analytical and
Synthetical Judgments . . . . . . . . 102
§ 18. Immediate and Mediated, Analytical and Synthetical Judgments .
§ 19. The Process of the Synthetical Judgment. ..
CHAPTER IV. The Negation . . . . . . .
119
§ 20. The Negation as Denial of the Judgment. .
119
§ 21. The Different kinds of Negative Judgments. .
123
§ 22. Privation and Opposition as Ground of the Negation
127
§ 23. The Principle of Contradiction . . . .
§ 24. The Principle of Twofold Negation. . . . . · 148
§ 25. The Principle of the Excluded Middle . . . . . . 150
102
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xii
CONTENTS
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196
214
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239
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245
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CHAPTER V. Plural Judgments . . . . . . . .
· 157
I. Positive Plural Judgments . . . . . .
157
§ 26. Positive Copulative and Plural Judgments . .
157
§ 27. The Universal Affirmative Judgment
§ 28. The Particular Affirmative Judgment
166
II. § 29. Negative Plural Judgments . .
170
III. $ 30. The Negation of Plural Judgments .
172
CHAPTER VI. Possibility and Necessity . .
. . 176
I. $ 31. The so-called Modal Distinctions.
. . 176.
§ 32. The Law of Sufficient Reason.
II. Possible and Necessary as Predicates of Actual Judgments
§ 33. The Necessity of Reality . . . . . . .
$ 34. Possibility . .
203
CHAPTER VII. Hypothetical and Disjunctive Judgments.
I. $ 35. The Different Ways in which Propositions may be Combined, and
their Logical Significance . . . .
. 214
II. $ 36. The Hypothetical Judgment . .
220
III. $ 37. The Disjunctive Judgment . ..
228
RESULTS § 38. · · · ·
· · · · ·
PART II. Regulative . .
237
§ 39. The Conditions of Perfect Judgments
CHAPTER I. The Concept . . . . .
$ 40.• Nature of the Logical Concept .
§ 41. Analysis of the Concept into Simple Elements.
42. Super- and Subordination, Content and Extension of Concepts
§ 43. Division of Concepts . . . . .
277
§ 44. Definition . . . . . . . . . . .
CHAPTER II. The Truth of Immediate Judgments . .
§ 45. The Truth of Judgments about Concepts.
§ 46. The Truth of Statements about Ourselves
§ 47. The Truth of Judgments of Perception . .
306
§ 48. Axioms and Postulates . . . . . .
CHAPTER III. The Rules of Inference as the Ground for Mediated Judgments
§ 49. The Hypothetical Syllogism . . .
$ 50. The Introduction of a Subject in the Hypothetical Syllogism . . 330
§ 51. The Different Sources of Hypothetical Major Premises . . . 336
52. Inferences according to Formal Logical Laws . . . . 338
§ 53. Inferences from Relations between Concepts.
343
§ 54. The meaning of the Aristotelian Figures and Moods. . . . 349
$ 55. The Value of the Syllogism . . . . . . . . 357
§ 56. The Inference of Subsumption . . . . . . . 367
§ 57. The Inference from Divisive Judgments . .
- 368
§ 58. The Disjunctive Syllogism . . . . . . . . 371
§ 59. The Relation between the Truth of the Conclusion and the Truth of
the Premises
. . . . . . . . . 373
APPENDIX A . . . . . . . . . . . . . 377
APPENDIX B . . . . . . . . . . . . .
APPENDIX C . . . . . . . . . . . . .
·
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··
GENERAL INTRODUCTION
$ 1.
IF we consider the nature of our Thought, we find that an important
part of it is engaged in the attempt to arrive at propositions which
are certain and universally valid, but that it frequently fails to do this
when left to its natural development. Hence arises the problem
of ascertaining the conditions under which this object can be
attained, and of determining in accordance with those conditions
the rules to be followed in its attainment. The solution of this
problem would place us in possession of a technical science of
Thought, directing us how to arrive at certain and universally
valid propositions. Such a science we call Logic.
1. To determine what Thinking in general is, how it differs from
other psychical activities, in what relations it stands to these, and
what are its different varieties, is primarily the business of Psycho-
logy. It is true there is no generally accepted Psychology to
which we can refer, but for our present investigation it will be
enough to refer to our ordinary use of language. By Thinking in
its widest sense we always mean an Ideational Activity ; i.e. an
activity which in itself does not include that inner subjective ex-
citement which we call Feeling, nor yet give rise to an immediate
effect upon ourselves or others as in willing and acting. All that
1
object. It must however be further distinguished from Perception
and Intuition ; these express immediate reference to an object
which is given to the subjective activity independently of itself,
S. L,
GENERAL INTRODUCTION
while Thinking denotes a purely inner activity of ideation, thus
seeming to be a spontaneous action proceeding from the energy
of the subject alone. Its products—thoughts—are therefore dis-
tinguished, as merely subjective, ideal images, from the objects
which are looked upon as real in Perception and Intuition. In
bethinking oneself of something, and to Imagination, picturing
something in Thought, as well as to reflection and consideration.
But when Perception and Thought refer to the same object, as in
knowledge of the external world, we distinguish between the
spontaneous selection, combination and elaboration of the elements
given to Perception, and the immediate presentation of those
elements. It is the former which we regard as the factor belonging
to Thought.
2. If for the present we take Thinking to mean all that we mean
by it in our ordinary use of language, then it is certain that with
the development of conscious life Thought arises involuntarily and
of necessity. As soon as the individual begins to reflect upon his
inner activity he finds that he is already engaged in various kinds
of Thought; he can have no immediate knowledge of its be-
ginning nor of its development out of simpler and more primitive
activities. Only by means of a difficult psychological analysis of
Thought, as we find it at work, can we discover its particular
factors and the faculties which give rise to it, and thus form some
idea of the laws of its unconscious growth.
Moreover the involuntary production of thoughts continues
throughout our whole life. It is absolutely impossible, when
conscious and awake, to check the inner activity which is in-
cessantly excited by the most varied motives to form a constant
succession of ideas which it combines in different ways, and thus,
without any intention on our part, maintains an inner world of
thoughts present before us.
3. But besides this involuntary Thought, there is a voluntary
N
GENERAL INTRODUCTION
action, a will to think, which is led by definite interests and aims
to endeavour to rule the formerly involuntary course of the
thoughts and to direct them towards a given end. From amongst
the thoughts which arise involuntarily this activity makes its
selection, losing sight of some altogether and retaining and
developing others by means of attention, thus seeking for thoughts
and pursuing them. We need not enter here upon the question
as to whether the production of thoughts is ever really voluntary
in a direct way, or whether we can only indirectly bring about the
conditions necessary to the involuntary production of what is
desired. The result is practically the same in both cases ; that is,
thoughts which satisfy a definite interest are produced by the
influence of the will.?
But this interest is of two kinds. From one point of view the
voluntary activity which we direct towards our Thought falls
under the general law that the pleasant is sought after, the un-
pleasant avoided. Now we may regard Thought as pleasant in
a double sense. Firstly, in so far as every natural activity gives
a feeling of satisfaction within certain limits of intensity ; secondly,
in so far as the manifold content of our Thought affects us plea-
santly or unpleasantly.
Taking this question of pleasure alone, we find within us both
a general tendency to excite Thought, or let it be excited, as an
entertainment and escape from tedium; and also a tendency to
direct it in such a way that what we think may be pleasing to us.
When we linger over pleasant recollections and seek to intensify
them, when we make projects and build castles in the air, when we
strive to chase away disagreeable recollections or to dispel fear
and anxiety, then it is this motive which determines the influence
of the will upon our Thought.
1 Cf. Windelband, über Denken und Nachdenken (Präludien, p. 176 sq.). His
treatment contains much that is true and valuable on certain points, although he does
not seem to me to have rightly determined the relation between "unconscious" and
.conscious willing.
GENERAL INTRODUCTION
The satisfaction which arises in such cases is of a completely
individual character ; the particular subject refers only to itself,
to its own peculiar nature and circumstances. As a rule, therefore,
Thought of this kind varies with each individual, nor could we
wish it otherwise.
4. But this desire of obtaining immediate pleasure from Thought
is the subordinate interest of the two. By far the most important
part of our mental activity, both in extent and in value, follows
more serious aims.
In the first place, our wants and the necessities of life take
Thought into their service and set before it aims which are
consciously grasped and pursued. Our existence and our well-
being depend upon conscious action and upon our influencing
things around us to serve our purposes. This action does not
accomplish its purpose with the ease and certainty of instinct; it
calls for attentive and careful observation of the nature of things
and of their relations to us, as well as for manifold calculations
and considerations as to the way in which they may serve for a
means to the satisfaction of our wants.. Human Thought attains
its end--the preservation of our well-being--only when its know-
ledge of things enables it to predict the future ; when, therefore,
anticipation coincides with the actual course of events as partly
conditioned by our interference.
But the desire for knowledge which makes itself felt everywhere
seeks a right understanding of things and their relations even
beyond the sphere of our practical needs, Solely for the sake of
knowing it urges Thought to penetrate into the nature of things,
and thus to reproduce in the totality of our subjective knowledge
a faithful and complete picture of the objective world. Satisfac-
tion of the desire for knowledge must then include this aim of
practical Thought also. The immediate purpose which excites
Thought and determines its direction is knowledge of that which
is.
GENERAL INTRODUCTION
5. But the purposes towards which Thought is directed are far
from being exhausted by this one interest—the desire for know-
ledge. It is found to be just as active in a direction which cannot
be included in the idea of knowledge of that which is. We find
ourselves as a matter of fact under the dominion of certain laws
according to which we estimate the worth of human deeds, and to
which we are willing to submit our wills and actions. It matters
not for our present investigation whence these laws have their
origin, nor by what motive we are led to recognise them as valid
for us. Enough that we are constantly endeavouring to observe
the rules of propriety, of morality, of justice and of duty, and
are incessantly called upon to decide what we ought to do and
how we ought to act if we are to avoid conflict with the
principles, which we acknowledge, and maintain honour and
conscience unsullied. No material result informs us whether or
not our Thought has attained its end, by proving that our cal-
culations accorded with the nature of things. Even the re-
sult at which we aim consists solely in thoughts, and the
actual results also are the thoughts which accuse or absolve
us, the recognition or non-recognition by others and by our-
selves of the conformity of the particular action with the general
rule.
6. Let us consider more closely this, the most important part of
our practical Thought, as well as of our estimation of practical
relations. Before the Court of Conscience the only evidence we
have as to whether the Thought which guides our action has at-
tained its purpose or not, is the inner consciousness of the neces-
sity of our Thought; the certainty thať the given mode of action
follows inevitably from the general rule ; the self-evidence which
satisfies us that it was right and good to act so under the circum-
stances because the general principles of justice and morality
demanded it. Nor have we any external confirmation that we
have attained our end except the assent of others, who, starting
GENERAL INTRODUCTION
from the same presuppositions, affirm the same consequences to be
necessary.
In speaking of the necessity of our Thought we must guard
against a confusion of meaning. From a psychological point of
view everything which the individual thinks may be looked upon
as necessary, i.e. as an activity which results in accordance with
general laws from whatever conditions may be present. That just
this, and not something else, is thought, is the necessary consequence
of the particular individual's range of ideas, disposition and char-
acter, and the stimulus of the moment. But besides this necessity
of psychological causality there is another which springs entirely
from the contents and object of Thought itself; which is, therefore,
grounded, not upon the variable subjective states of the individual,
but upon the nature of the object thought of, and which may so far
be called objective.
It is in this consciousness then of its objective necessity and
universal validity that our Thought finds satisfaction, and we shall
find upon examination that the same characteristics express the
aim of our Thought in its search for knowledge of that which is.
Here, again, we can only define the end towards which our inten-
tional Thought strives by saying that it aims at satisfaction in the
consciousness of its necessity and universal validity.
It is true that any one unbiassed by critical reflexion is impelled
by a psychological necessity to objectify his sensations and the
thoughts relating to them, and to picture to himself a world to
which he ascribes an existence independent of his subjective
activity. When his desire for knowledge bestirs itself he does not
hesitate to attempt to know this objective world, and to frame his
thoughts in such a way that they may conform to that which is.
Nevertheless it is a question of dispute whether this purpose can
be achieved. We cannot refute the critical assertion that im-
mediately, and in the first instance, all our knowledge is only
something for us, consisting in a system of ideas. That there is
VY
GENERAL INTRODUCTION
an Existent corresponding to this thought of ours and in accord-
ance with it, is either a blind belief, or the certainty must be
grounded upon a refutation of the doubt it dispels upon the
proof that doubt is impossible. That is, it depends, on the one
hand, upon our finding that the assumption of an Existent in-
volves us in no unthinkable contradiction ; on the other hand,
upon the nature of our ideas being such as to force us to assume
this Existent. In both cases the proof rests upon a necessity in
Thought. It may be counted amongst the surest results of the
analysis of our knowledge that every assumption of an external
world is mediated by Thought, and in some way or another derived
by unconscious mental processes from the subjective facts of
sensation. Thus, except by Thought, we have no means of as-
certaining whether we have really achieved our purpose of knowing
the Existent; the possibility of comparing our knowledge with
things as they exist apart from our knowledge is for ever closed
to us. At the best we must be satisfied to find agreement and
absence of contradiction amongst the thoughts which presuppose
an Existent; just as we are fully satisfied in the region of outward
action when our ideas and movements, together with their con-
sequences, are in harmony amongst themselves and with the ideas
of others.
Granted that there is a knowable Existent, then a knowledge
of it is impossible unless there is some relation between the
Existent and our subjective action which is governed by laws,
and by virtue of which the thoughts necessitated by what is given
in consciousness correspond to the Existent. Further, if we grant
a knowable, external Existence, then it is the same for all know-
ing and thinking subjects, and all who know the Existent must
think alike in reference to the same object. Thus Thought which
knows the Existent is of necessity a universally valid Thought.
If, on the contrary, we deny the possibility of knowing anything
as it is in itself—if the Existent is only a thought of our production
GENERAL INTRODUCTION
-it still remains true that the ideas to which we attribute object-
ivity are those which we produce with a consciousness of necessity.
The fact that we regard anything as existing implies that all other
thinking creatures of like nature with ourselves (even when only
hypothetically assumed) would also be forced with the same neces-
sity to regard it as existing.
We may then unhesitatingly say that if all we can attain to is
but necessary and universally valid Thought, then knowledge of
the Existent is included therein, and when we think with the object
of knowing our immediate aim is nothing more than this necessary
and universally valid Thought. It is in this conception also that
the essence of “Truth” consists. When we speak of mathematical,
actual, or moral truths, the common characteristic of all which we
call true is that it is thought necessarily and with universal
validity.
7. This view of the task undertaken by the Thought of which
Logic treats avoids the difficulties which beset every system of
Logic calling itself a theory of knowledge. The difficulty of such
a system is that it must begin by showing whether and how far
knowledge is possible at all; and in doing this, it not only passes
into the disputed regions of metaphysics, but it presupposes in its
proofs and refutations that necessity and universal validity of
Thought from which the conviction of its objectivity is to proceed.
In the same way we avoid the one-sidedness into which the Logic
which professes to be a theory of knowledge is apt to fall—that of
treating only of the thought which aids us in our knowledge of the
purely theoretical, and forgetting the Thought which serves to
guide our action. Nevertheless the psychical activities are the
same in both cases, and the two aims must be classed together.
8. By thus including all Thought which pursues the common aim
of certainty of its own necessity and universal validity we can also
complete its psychological limitations. All such Thought results
finally in judgments, which are expressed inwardly and outwardly
GENERAL INTRODUCTION
9
:
as propositions. Every practical consideration of ends and means
terminates in judgments; all knowledge consists in judgments;
every conviction ends in judgments. All other functions come
into consideration only as being the condition of, and preparing
the way for the judgment. Again, the judgment can be an object
of scientific investigation only in so far as it is expressed in a pro-
position ; only through the proposition can it become an object of
general consideration, and only as a proposition can it aspire to
universal validity.
9. Now we know from the fact that error and dispute exist that
our Thought frequently misses its aim in the judgments which it
actually forms. Sometimes these judgments are relinquished by
the individual thinker himself under the conviction that they are
invalid, i.e. that it is necessary to think otherwise. Sometimes,
again, other thinkers refuse to accept them : they dispute their
necessity, affirm them to be mere conjecture, or even deny their
possibility inasmuch as they find it necessary to judge differently
concerning the same matter.
Since then actual Thought can and does miss its aim, we have
need of a discipline which shall teach us to avoid error and dispute,
and to conduct Thought in such a manner that the judgments
may be true—that is, necessary and certain that is, accompanied
by a consciousness of their necessity, and therefore universally
valid.
Reference to this aim distinguishes the logical from the psycho-
logical treatment of Thought. The latter is concerned with the
knowledge of Thought as it actually is, hence it seeks the laws
according to which, under certain conditions, a certain thought ap-
pears in just one way and no other. Its task is to explain all
actual Thought according to the general laws of psychical activity,
and as arising from the particular conditions of the individual
instance, thus dealing with all Thought alike, whether erroneous
and disputable, or true and generally accepted. The antithesis
IO
GENERAL INTRODUCTION
of true and false is no more a psychological one than is the anti-
thesis of good and bad in human action.
The logical treatment, on the contrary, presupposes the desire
to think the truth; it has no meaning except for those who are
conscious of this desire and in that region of Thought which is
governed by it. Starting with this aim before it, and investigating
the conditions of its attainment, Logic proposes, on the one hand,
to set forth those Criteria of true Thought which are due to the
demand for necessity and universal validity; on the other hand, to
direct us how to conduct the mental operations in such a way that
the end may be attained. In one aspect then Logic is a critical
discipline having reference to Thought which has already taken
place; in the other, it is a technical discipline. But as criticism is
of value only as a means to the end, the principal task of Logic
and that in which it properly consists, is to be a technical discipline
or Art.
§ 2.
Logic as the Art of Thought cannot undertake to instruct us
how, beginning at any given time, we may attain to Thought which
is entirely and absolutely true. It must restrict itself to showing
what are the general Conditions which, from the nature of our
Thought, every proposition must satisfy in order to be necessary
and universally valid, and under what conditions and according to
what rules we can pass from given premises in a manner which
shall be necessary and universally valid. It declines to give any
judgment as to the necessity and universal validity of the premises
from which we start at any time. Thus observance of logical
rules ensures merely the formal correctness of the procedure and
not the material truth of the results. In this sense our doctrine
is of necessity formal Logic.
I. Instruction in an art which claims to ensure success for the
activity to which it gives rules presupposes that this activity is
GENERAL INTRODUCTION
IK
T1
completely free and voluntary. This implies, first, that I am able
to bring about the conditions necessary to the activity whenever I
choose ; secondly, that I only need to be conscious of the aim and
of the rules of its attainment in order to fulfil every particular
operation in accordance with those rules, and so as to attain the
end in view. If there is to be an Art ensuring the production of
necessary and universally valid Thought, by means of which we
may know the Truth, we must assume that all the conditions lie
within our grasp, and that at any given time we are completely
free to control our Thought in accordance with its rules.
This it was which Descartes had in view when he designed his
“Methodus recte utendi ratione et veritatem in scientiis investigandi.”
It was to put an end, once and for all, to all possibility of error,
to exclude all doubt, and to produce a series of thoughts which
-starting from one necessarily true and certain proposition and
proceeding by infallible steps-should contain none but absolutely
true propositions. His assumption was that, though we may not
be free to choose what ideas shall be present to us, still judgment
is a completely free and voluntary act, inasmuch as we can with-
draw our assent to every proposition which we do not recognise
with full conviction to be true and certain. Hence it is possible,
by means of a thorough-going scepticism, to free oneself from every
presupposition involving danger of error, and to make an entirely
fresh start in the activity of Thought. In the same way he as-
sumed that the chief conditions of this activity-concepts and
principles are innate in us, and that they are thus dependent
upon our self-consciousness alone.
Now even if this latter assumption were as true as it is disputed,
the method would at best find complete application only in the
region of a priori knowledge, and only for those capable of making
and carrying out the resolution to free themselves from all presup-
positions. But it is absolutely impossible voluntarily to break the
continuity between past and present Thought, and to begin com-
1 2
GENERAL INTRODUCTION
pletely ab ovo. Voluntary Thought grows out of an involuntary
production of thoughts by which it is continually fed, and we could
make no progress unless there were a supply of these thoughts
forthcoming and a language representing them. We need only
turn to Descartes himself to see how, in spite of the best inten-
tions, elements of past Thought will force their way into the
newly started series. Nor is it true that we can voluntarily refrain
from any judgment while we have no choice as to whether the
ideas to which it relates shall be present or not. One reason for
this is that a part of the presuppositions we bring with us are
judgments which inevitably involve others; another, that our judg-
ments concerning the relations of ideas are predetermined by the
nature of those ideas, and we are not at liberty to choose whether
we will affirm or deny.
There can then be no method whatever by which we may begin
Thought entirely anew. All that we can look for is a method of
carrying it on from already existing data, which must always form
the starting point for future Thought, even when acknowledged to
be uncertain.
2. The necessity of confining Logic to the regulation of the
procedure of Thought makes itself felt more especially with refer-
ence to the Thought which aims at empirical knowledge of the
world. Such knowledge presupposes correct perceptions; and in
dent not only upon the Thought which accompanies them, but also
upon the conditions of sensation and the relation between our
senses and the object. The art of correct observation is only
partially included in the art of right thinking ; it depends also
upon the acuteness and training of the organs of sense, upon me-
chanical adroitness, and upon the art of bringing the object into
the most favourable relations with our organs of sense and of
eliminating errors of observation. It must be guided in its differ-
ent expedients by the varying nature of the objects with which
GENERAL INTRODUCTION
13
it deals, each class of these requiring its particular technology.
If we were to suspend Thought and Judgment in the region of
empirical knowledge until we could start from absolutely certain
and necessary premises, empirical science would be altogether impos-
sible. We should be forced to leave in suspense, together with the
validity and exactness of our perceptions, not merely the whole
question as to the reality of the material world, but also the pos-
sibility of universally valid laws of phenomena.
Moreover, the history of the development of our knowledge
shows that the discovery of truth has often been indirectly attained
by starting from erroneous and uncertain premises. In the course
of scientific research dispute is frequently settled by pursuing false
propositions to their conclusions. Every apagogical proof is an
example of this procedure.
Finally, a large part of the Thought which aims at universal
validity is connected with premises which derive their validity
from a Will, and which are so far purely arbitrary. To insist
that Logic should establish the material truth of all propositions
would be to exclude from logical consideration all practical juris-
prudence.
3. Thus all that an Art of correct Thought can achieve, and all
that it can propose to do, is to instruct us how we may proceed in
Thought from given data in such a way that each step shall be
accompanied by the consciousness of necessity and universal
validity. It does not teach us what we must think-to do
that would be to comprehend all science. It teaches only that
if we think this we must also think that, no matter how our
data-the supply of involuntary ideas and of particular obser-
vations and general propositions—may be constituted in other
respects.
It must be understood that by “proceeding” we mean a progress
in any direction--from grounds to consequences, as well as from
consequences to grounds, from general to particular, as well as the
14
GENERAL INTRODUCTION
reverse. Thus the art must be applicable to all problems whatever
which present themselves to our Thought.
4. This then is the sense in which we take Logic to be a formal
science ; for the sake of the generality and practical fulfilment of
our task we cannot undertake to construct Thought without in-
volving any presuppositions, nor do we extend our logical investi-
gations to the validity of the data from which Thought actually
starts at any time, but only to the correctness of its procedure from
those data. But by calling Logic formal, we do not mean that it
should make the vain attempt to regard Thought in general as a
merely formal activity, which may be considered apart from all
matter of Thought, and which is unaffected by differences of matter.
Nor do we mean that logical investigation should entirely abstract
from and ignore the general nature of the matter and presupposi-
tions of actual Thought. Of Thought developing entirely from
itself in the particular individual we have no knowledge; we know
it only under the general relations and conditions, and with the
general purposes of human Thought. Hence we can abstract
neither from the particular manner in which our Thought receives
material and contents from sensations and forms them into ideas
of things; nor yet from the way in which its history has been
determined by the community of mankind. We abstract only
from the particular nature of the occasions which at any given time
give rise to a series of mental processes.
1
$ 3.
The possibility of determining the criteria and rules of necessary
and universally valid procedure in Logic depends upon our ability
to distinguish objectively necessary Thought from that which is not
necessary, and this we find in the immediate consciousness of evident
truth which accompanies necessary Thought. Experience of this
consciousness and belief in its trustworthiness form a Postulate,
beyond which we cannot go.
GENERAL INTRODUCTION
15
I. When we ask whether and how it is possible to solve the
problem as we have stated it, the question resolves itself into the
difficulty of finding an infallible sign by which we may distinguish
objectively necessary and universally valid Thought from that
which differs according to the person thinking, and thus, as we
saw, misses its aim. And here there is, in the last instance, no
answer but an appeal to our subjective experience of necessity, to
the inward feeling of certainty by which some of our Thought is
accompanied, to the consciousness that, starting from the given
premises, we cannot think otherwise than we do think. Belief in
the truth of this feeling and in its trustworthiness is the last an-
chorage of all certainty; for the man who does not acknowledge
it there is no knowledge--nothing but accidental opinion.
2. Certainty of the universal validity of our Thought rests
ultimately upon the consciousness of necessity, not the conscious-
ness of necessity upon certainty of universal validity. When we
assume a reason common to all men we are convinced that what
we think with a consciousness of inevitable necessity others will
also think in the same way. Our assumption that other people
are bound by the same laws as ourselves, may indeed be
strengthened by empirical confirmation when all agree; but this
cannot supply the place of the immediate feeling of necessity,
much less give rise to it. Habit, also, to which the empiricists
appeal, and coincidence between experience and our calculations,
affect only the validity of the data from which we start; they can
necessity. Here, then, we have the fundamental fact upon which
every logical system must rest. Logic can do nothing but bring
i to our knowledge the conditions under which this subjective feel-
ing of necessity arises, and express them in a general form. It
may be said that if this be so, then Logic is an empirical science,
and this is true in the same sense in which it is true that mathe-
matics is an empirical science. Mathematics also starts from facts
16
GENERAL INTRODUCTION
of consciousness and the necessity by which they are accompanied,
but both are distinguished from merely empirical science in that
they find in their facts the necessity which is wanting to accidental
experience, and make this the basis of the certainty of their pro-
positions.
§ 4.
By stating the problem in this way we find the course of our
investigation determined for us. First we must consider the
nature of the function for which rules are to be found then we
must lay down the conditions and laws of its normal action ;
finally, we must try to find rules for the process by which natural
Thought working with given presuppositions and expedients may
pass from an imperfect into a perfect state. Thus our investiga-
tion falls into three parts; analytical, normative and technical.
1. Since it has been shown-$ 1. 8—that the activity in which all
intentional Thought fulfils its purpose is Judgment, we must begin
by a right understanding of the nature of this function with the
correctness of which we are concerned, and by recognising what
elements and presuppositions are involved in it. This is all the
more necessary because the judgment takes the same form whether
the Thought expressed by it be successful and universally valid or
fail to attain its purpose. Only in so far as Thought takes shape
in judgments and finds, or seeks to find, in them its final expression
can we have truth and error, certainty and doubt, agreement and
dispute. It is the same function which is in the one case correctly
carried out, in the other incorrectly; and not until we know in
what it consists can we give the rules for its correct operation.
This knowledge can only be gained by an analysis of actual
judgment, by considering what it is that we do when we judge,
and what other functions, if any, are presupposed in Judgment.
We must also consider the process by which Judgment is formed
from these other functions, and the general principles by which
GENERAL INTRODUCTION
17
TY
this process is naturally governed. Meanwhile we must assume
for the present that we know what mental acts are included under
the name of Judgment; language will serve us here for a guide, and
the immediate object of our investigation may be defined as all
propositions which claim to be true and to be believed or acknow-
ledged as valid.
Of the propositions enumerated by Grammar, we will for the
present put aside all which, like Imperatives or Optatives,
1 No doubt the Imperative also includes the statement that the speaker wills the act
which he commands; while the Optative states that he wishes what he says. But the
statement is here contained in the fact of speech, not in what is said ; it is just as true
that in every utterance of the form A is B the mere fact of speech involves the statement
that the speaker thinks and believes what he says. All speech alike is accompanied by
such statements concerning the subjective state of the speaker, which are implied in the
fact of his speech and are valid on condition of his veracity; we cannot therefore found
any distinction amongst propositions on these. The Imperative “Silence!" is of course a
way of varying the expression of the statement “it is my will that you should be silent," but
its purpose is not direct communication of this fact, but the determination of the will of the
person spoken to, it does not call for belief but obedience. I have spoken of it as con-
taining an intransferable element because the person addressed does not repeat the act of
will of the person giving the command in the way in which he appropriates the thought
of the speaker when he believes a statement.
No essential difference occurs in this primary and usual meaning of the Imperative as
the expression of a particular individual will when it takes the form of a general law.
When the legislator addresses an Imperative to the citizens of the State or members of
the religious community his relation to them is that of one individual to another. His
purpose in speaking is not to communicate a truth which they are to believe, but to
announce a command which they are to obey. It makes no difference whether the
source of the command be an actual individual or a collective body, whether the assumed
motive of obedience be submission to personal authority or an impersonal constitution-
the import of what is said is not the communication of a truth but the summons to do
this, to leave that undone.
The form “Thou shalt" again, which appears in laws such as those of the Decalogue,
has originally no other significance. Shall is the correlative of will. In delivering the
command of master to servant we say “thou shalt do so and so ” ; it contained originally
no more than the simple Imperative, the revelation of a law to one whom I hold to be
subordinate to the will of another, either of a third person or myself.
But this form does now contain a twofold meaning not to be found in the simple
Imperative. “Shall ” (sollen=shall tought) may also have the force of a proper Predi-
cate in a statement meant to be true; it signifies duty, obligation, and is thus a modal
Predicate (see below $ 6. 3 d) expressing the relation between the subjective individual
will and an authoritative power, or an objective law. The original Imperative here
passes over into the significance of a Predicate expressing the obligatory relation of a
command to the will to which it applies; and if we assume a legal or moral constitution,
the statement that I am under an obligation may be true or false. In “may” again we
also find two meanings. “You may” is originally the expression of momentary per-
S. L.
GENERAL INTRODUCTION.
or
contain an element peculiar to the individual and intransferable
to others. All those again which while they refer to an assertion,
do not present it as true, may for the time be disregarded ; such
are questions, or propositions which express merely an opinion or
a subjective view. How far the latter come into consideration as
preliminary to the judgment, further investigation alone can show.
But all propositions of actual statement or declaration, no
matter to what they refer, must be investigated by us. In this we
follow Aristotle, and reject the distinction of the so-called logical
judgment from other statements, according to which Logic would
deal only with the subsumption of the particular under the general,
and exclude the mere communication of facts. But such com-
munications also aim at truth, and make claim to be believed ;
error and dispute arise in reference to them and hence they, as
well as judgments of subsumption, must have the conditions of
their validity investigated. The desire to limit Logic to judg-
mission by which I liberate the will of another, disclaiming the determination of his
subjective fact that I have no wish to prohibit. The real import of the proposition
is practical, and to this extent “ you may” is akin to an Imperative. On the other
hand “may” may also be the Predicate of an actual statement expressing the fact that
no authoritative prohibition is opposed to an action, that the existing order of things
permits it.
Finally the same ambiguity extends to propositions which bear the grammatical form of
a simple statement. That portion of the penal code which says that whoever acts in a
certain way will incur a certain penalty, is not meant, like the formulæ of a natural law,
as a communication of what actually happens, it conveys a command. But when the
law is depicted as taking effect the same proposition contains an actual statement ; it
states what regularly happens within a given state. Cf. here Zitelmann, Irrthum und
Rechtsgeschäft, p. 222, sq. Bierling, zur Kritik der juristischen Grundbegriffe, ii.,
259, sq.
Thus the mere grammatical form is no infallible indication that we have to do with a
statement. A statement is nothing more than a proposition which is meant to be true,
and of which we can ask whether it be true or false.
1 Aristotle constantly mentions as the characteristic which distinguishes the judgment,
the Topavors, from other forms of speech, the fact that we can attribute truth or false-
hood to it. De interpr. 4 (16yos) åropartikÒS oủ tâs, állèv To åndevel) yeúdeo dal
ůtrápxel. Again, De anima, iii. 6.
2 Cf. on the other hand Ulrici, Comp. der Logik, ed. 2, § 72, p. 266, 267. Hegel,
who calls the judgment the determination of the concept by itself, says first (Logik,
Werke, iv. 69) : “ A proposition has indeed Subject and Predicate in the grammatical
sense, but is not therefore a judgment. For this it is necessary that the Predicate should
GENERAL INTRODUCTION.
19
ments of subsumption could have arisen only under the scholastic
view of the nature of science, the view that Definition alone has
any scientific value. Where it is recognised that particular facts
are the basis and test of a great part of our knowledge, Logic
must also deal with those judgments which express particular
facts.
It also forms a part of our plan of investigation to take up the
analysis of the judgment at the point where it takes shape in the
natural course of Thought without skill or reflection on the part of
the thinker.
2. Our investigation of what takes place in Judgment completed,
we may then proceed to enquire as to the conditions which a
judgment must fulfil in order to be perfect and answer fully to its
purpose. In this way we may set before us an ideal, agreement
with which will be the end and object of our Thought. That is,
we begin by asking that Thought shall be necessary and universal,
and apply this test to the function of judgment after discovering
all its conditions and factors; there then result certain laws to
which judgment must be submitted, and hence certain criteria by
which we may distinguish between perfect and imperfect judg-
ment. These laws, so far as they fall within the scope of a logical
treatment in our view, may be summed up in two principal points.
First, the elements of the judgment must be completely determined,
i.e. fixed in concepts ; secondly, the act of judgment itself must
proceed from its data in such a way as to be necessary. Thus
1
stand to the Subject in the relation of conceptual determinations, that is, as general to
special or particular. Aristotle died in the 73rd year of his age, in the 4th year of the
115th Olympiad,' is a mere proposition, not a judgment.” But he adds decisively,
“It would have something of the nature of the judgment only if one of the circumstances,
the time of death or the age of the philosopher had been called in question and there
had been some ground for affirming the given number. ... Thus the communication,
'my friend N has died’ is a proposition, and would be a judgment only supposing it to
be questioned whether he were really or merely apparently dead.” So that Hegel also
agrees in calling every proposition a judgment, in so far as we can ask whether it is true
and what are its grounds. Cf. also Franz Kern (die deutsche Satzlehre, 1883, p. 189),
who errs only in directing his remarks against Logic instead of against a one-sided logical
theory.
20
GENERAL INTRODUCTION.
20
this part of our treatment will contain the doctrine of concepts
and inferences as subject matter of the normal laws for the forma-
tion of perfect judgments.
3. But knowledge of the nature of ideally perfect Thought does
not necessarily enable us to attain to this ideal state, nor even
show us the way which leads to the goal. Hence we have also to
consider how, starting from a given state, with the means placed
at our disposal by Nature, and subject to the conditions imposed
upon human thought, we may reach logical perfection. We are
concerned here, therefore, with the methods of obtaining right
conceptions and hypotheses which will serve towards the formation
of judgments and inferences. This is the domain of the Art in
the two preceding parts form a necessary preliminary. The most
important place in this technical instruction is taken by the Theory
of Induction as the doctrine of the method by which concepts
and general propositions may be obtained from particular percep-
tions.
4. We believe that by thus apprehending our task and arranging
our investigation, the different views which have made their
appearance as Logic has been elaborated, are combined and justice
done to each One view has assigned to Logic the task of ex-
pounding the natural forms of Thought and the natural laws which
it necessarily follows, and we also recognise the necessity of stating
the natural laws to which all Judgment is subject, and of discover-
ing the principles applicable to it as a conscious function of a
particular kind. But we deny that this completes the task of
Logic, which aims at being not the Physics but the Ethics of
Thought. Others, again, have defined Logic as the doctrine of
the normal laws of human Thought or Knowing, and here again
we recognise this regulative character as an essential feature. But
we deny that any knowledge of these laws can be attained that is
not founded upon the study of the natural forces and functions to
GENERAL INTRODUCTION.
21
be regulated by them, and we deny also that a mere code of
normal laws can by itself be productive or fulfil the purpose for
the sake of which alone it is worth while to construct a logic.
Much rather do we hold it necessary that Methodology, which is
generally made to take a subordinate place, should be regarded as
the special, final and chief aim of our science. And since this
Methodology must have for its principal object the growth of
science from the natural data of knowledge, we hope to satisfy
also to some extent those who endeavour to avoid the barrenness
and abstract character of the formal scholastic Logic by making
it include a Theory of Knowledge; nevertheless we exclude all
questions relating to the metaphysical significance of the processes
of Thought, and keep strictly to the prescribed limits within which
we regard Thought as a subjective function. We do not extend
our claims upon it so far as to demand a knowledge of Being, but
limit them to the sphere of that necessity and universal validity
which, even in ordinary language, are always and everywhere
regarded as the distinguishing and essential characteristics of what
is logical.
PART I
THE NATURE OF JUDGMENT AND ITS
PRESUPPOSITIONS
LOGIC
PART I
INTRODUCTION
§ 5.
THE Proposition, in which something is stated about something, is the
verbal expression of the Judgment. This originates as an active move-
ment of Thought, and always presupposes that there are present to the
person forming and uttering the judgment, two ideas—the Subject and
Predicate ideas, which can at first be only superficially distinguished by
saying that the Subject is that of which something is stated, the Predicate
that which is stated.
1. The judgment which we find in the form of a spoken assertion
appears in the first instance as a completed whole, a finished product of men-
tal activity. As such it is reproducible in memory, capable of entering into
new combinations, transferable by communication with others, and such
that it can be perpetuated in writing to all time. But this objectivity and
independent existence, which leads us to speak of it as stating, connecting
or disconnecting, is apparent only, and the expressions merely figurative;
rightly speaking, the judgment as such has real existence only in active
judging, in that mental act of a thinking individual which takes place at a
given moment, and the only possible way in which we can perpetuate the
judgment as an active process in thought is by consciously repeating it.
The judgment itself never attains to objective existence, but only its
material sign, the spoken or written proposition, which, by being externally
present for others and recognisable, announces that a certain mental act has
taken place in active Thought.
Now the proposition, as this outward sign, presents two aspects for our
consideration, which must be carefully distinguished from the beginning.
26
INTRODUCTION
On the one hand it refers to its source, the mental processes of the person
who gives utterance to it, and in so doing reveals his thoughts. On the
other hand it addresses itself to the hearer by whom it is to be understood;
he is called upon to interpret the outward signs, and out of them to re-
construct the thought expressed by the speaker. But the functions of the
person understanding the spoken words are not the same as those of the
speaker; although if we assume complete understanding, the final result in
the mind of the hearer must coincide with that from which the speaker
started. When I express a perception in the words “the castle is on fire,”
my starting point is the image of the burning castle. In this image I
recognise the familiar form of the building, and the flames rising from it,
and I describe what I saw by first separating these two elements, and then
uniting them in the proposition. The person who hears my proposition
must begin by uniting the ideas which are excited in him by the two words,
and which are at first separate; only when this is done does he obtain the
idea from which the speaker set out.
Grammar and Hermeneutics, which start from the spoken or written
word, naturally tend mainly to the standpoint of the hearer ; they direct
their attention to those functions which are active in understanding, and
treat of them in the order in which they occur in the hearer. But in
psychological analysis, where our aim is to investigate the nature of thought
in judging, the other side—the action of the speaker-is of primary im-
portance; and this the more so because communication to others is not
necessarily the object of all Thought which clothes itself in words.
For us, then, the investigation of the nature of the judgment consists in
a consideration of the mental act which takes place when we are actively
engaged in judging, and to which we proceed to give expression in words.
And since every repetition of a judgment (whether mental or spoken) pre-
supposes its original production, the cases with which we must deal are
those in which our Thought produces a new judgment and provides it with
its verbal expression (as, e.g., whenever we give utterance to a new
observation).
2. The process which goes on when I form and utter a judgment may
be described for the present by saying that I state something about some-
thing.1 There are always two elements present, the one is that which is
stated, tò katnyopoúuevov, the Predicate; the other one is that about which
1 lóyos katapatikÒS åtopatikÒS tivòs katà tivós. Aristotle's Anal., pr. 1. 1. We
shall consider later on (§ 12) the view that judgments do not all have two elements.
INTRODUCTION
27
the statement is made, or to which it refers, tò ÜTokelpevov, the Subject.
But this description is merely superficial, and derived from language.
Statement is an activity of the organs of speech, and the question arises :
what is the mental process of Thought when we "state something about
something?"
3. If we start from the spoken proposition we must begin by making
a distinction. There are some propositions in which we mean only the
words as such to be Subject or Predicate, the words as these particular
combinations of sounds. Possibly remarks are made about them which
are purely grammatical and have no reference to their meaning (Samiel
is a Hebrew word, Contra is a preposition); or it may be that the pro-
position refers to the meaning of a word or name, (Oxide is a compound of
oxygen ; Alexandros is another name for Paris; Jagsthausen is a village
and castle on the Jagst). We may for the present put aside these merely
etymological and hermeneutic statements, and there then remain for our
investigation only those propositions in which the words appear as signs of
ideas, and are assumed to be understood by both speaker and hearer, i.e.,
to be connected with the same definite ideas, so that the statement is not
concerned with the words themselves, but with the ideas connected with
the words.
4. Here then, if the statement is to have any meaning, each element,
Subject as well as Predicate, must be some idea immediately present to my
consciousness. At first sight, and speaking generally, the Subject-idea
appears to be that one which is first present to me. Any object whatever
which I can retain independently in consciousness is qualified to become
by itself the subject of a judgment; it may be the immediate intuition of a
particular thing, or an abstract idea, an object or an event. To it is added
as second in consciousness, the Predicate-idea. It is essential that this
should be taken from those of our ideas which are already known to us and
.named by words which are understood. It must be an idea which has been
already received into consciousness, which is connected with a word
enabling us to retain and reproduce it, and which is distinguished from all
other ideas. I cannot say “this is blue, this is red,” unless I am already
familiar with the ideas blue and red, and can reproduce them with the
1 It has been objected that the real meaning of this phrase is : That which is called
Jagsthausen is a village, etc., hence that the proposition does not refer to a mere name.
But for anyone as yet ignorant of the significance of the word, the only possible import of
the proposition is to give him the meaning of a hitherto unknown word; he cannot con-
nect any idea with the subject.
28
INTRODUCTION
word. Judgment is possible only where a number of such distinct ideas are
retained and easily called into consciousness. Hence conscious judgment
presupposes that these ideas are already formed.
Now, it is true that some Thought is already involved in the process by
which these ideas are formed. Whatever we may think of the functions by
which we arrive at ideas of definite objects, or at any ideas which can serve
for Predicates, it cannot be denied that it is necessary to distinguish between
different sensations, to comprehend a plurality as a whole, to refer this
whole as a unity to its manifold content, and to retain in memory the pro-
duct so gained; and these are all of them acts which we can only think of
as analogous to conscious mental acts of the nature of judgment. But this
activity which results in distinct and independent ideas, precedes our con-
scious and intentional Thought, and is governed by laws of which we are
unconscious. If we begin to reflect upon it we are conscious only of the
results of these processes in the form of ideas already possessed of names.
The processes themselves must have been originally guided by a psycho-
logical necessity, since their course has been essentially the same in all
human beings; or else they have become so much a matter of habit, and
attained to such mechanical facility, that they take place with unconscious
certainty even within the conscious life. We must further presuppose the
first beginnings and appropriation of language, since conscious and volun-
tary Thought takes place almost entirely through its aid. Properly
speaking, then, that Thought by which ideas are first produced does not
come within the scope of our enquiry, nor yet the investigation of the origin
of language, and the appropriation of it by the individual, although we may
be obliged to touch upon these questions as our analysis proceeds. Still it
is necessary to take a survey of those ideas which are capable of entering
determine the relation between the mental fact and its verbal expression.
CHAPTER I
IDEAS AS ELEMENTS OF THE JUDGMENT, AND THEIR RELATION
TO WORDS
$ 6.
1
If we examine the contents of our Thought, that which can enter into our
judgments as Subject or Predicate, or as part of Subject or Predicate, we
find that it consists of:-
I.--THINGS, their Attributes and Activities, and Modifications of these.
II.-- RELATIONS OF THings and of their Attributes and Activities.
These may be Spatial and Temporal, Logical, Causal or Modal.
1. Language itself in its classification of words seems to give us the
clue to the different kinds of objects of Thought; a clue which was certainly
made use of by Aristotle in his enumeration of the Categories as the highest
classes of that which is thought and that which is. But the clue is not
an infallible one. It is the peculiarity of the structure of language that as
it develops its different forms vary in their functions. A special form is
not coined for every new kind of idea; but as in the organic kingdom
morphologically equivalent organs can discharge functions which are
essentially different physiologically, so it is also with classes of words, such
as Substantives, Verbs, Adjectives. Different kinds of words do not neces-
sarily correspond to differences of meaning in such a way that we can be
guided entirely by these external characteristics, While still keeping sight
of the indications given by language, we must take a general survey of the
nature of the objects of Thought, which alone will show us how far
differences in forms of speech correspond to differences of mental content.
2. The most universal possession of humanity consists in that series of
ideas which constitutes the world of the Existent, and though as a matter
of fact this series is generally accompanied by language, we are forced to
think of it as possible to every individual, even without the co-operation of
language. To this series belongs, besides the idea of self, the idea of our
30
IDEAS AS ELEMENTS OF THE JUDGMENT
A
whole empirically known surroundings, as well as the idea of everything
which we think of as existing in the same way as ourselves and the objects
of immediate perception.
Ideas of particular Things form the material from which this world is
built up, and the words by which they are denoted are concrete Substan-
tives. These Things we think of as supporting Attributes which find their
expression in Adjectives, and as developing with the course of time
Activities and falling into conditions which are expressed by Verbs.1
This distinction between the ideas of Things and the ideas of Attributes
which inhere in them, and Activities in which they are engaged, must be
regarded as a fundamental fact of Thought. That part of our judgment
which is conscious and can be guided by reflection-and here alone can
there be any logic~presupposes both this distinction and the necessity
which obliges us to refer the different kinds of ideas to each other, and to
regard every thinkable and independent object as the unity of a Thing with
its Attributes and Activities. No doubt the impressions from which we
1 The generality of the process by which the affections of sense are referred to Things,
is in no way prejudiced by the fact that such reference may be uncertain in particular
cases, and that a thing perceived in a certain phenomenon may be apprehended in various
ways. Night, shallow, rainbow, wind, etc., are originally things in the fullest sense of
the word-concrete and particular. It is scientific reflexion which first deprives them of
this solidity, and causes us to look upon them as merely the results of certain relations
amongst things. Hence, also, we avoid using the expression “substance” in this con-
nection ; for it is an expression which implies that a scientific reflexion, and a criticism of
those ideas which arise immediately and naturally, have already taken place. Not every-
thing which the ordinary consciousness—led by the analogy of its own mental processes
apprehends as a thing, is for that reason substance in the strict sense, or will permit of
the conscious application of this category.
We need not enter here upon the difficult question as to whether the present verbal
form, in all its applications, is founded upon one definite common conception, nor what
that conception may be. To me it appears certain that according to the original dis-
tinction between noun and verb, the expressing of temporal action (in its widest sense) be-
longs to the latter ; and the thought of movement and change which proceeds from, and
arises in, the Thing, and which can, moreover, extend its influence to other things, forms
the nucleus of that group of ideas which the verb serves to denote. In proportion as our
imagination looks upon things as alive, even persisting states, such as lying, standing,
remaining, etc., seem to be reflective actions—the result of a resistance to change which
is active and almost volitional. Or at least it is looked upon, as is evident in the Greek
FOTnka, kádnual, as the result of an activity. It seems to me, then, more correct to regard
the concept of action as original, and to subordinate to it the concept of state, than to
reverse the relation, as Wundt does. That according to our present treatment many
verbs seem to have the value of Adjectival Predicates, in no way alters the original dis-
tinction. The same state of a Thing may be regarded either as its inactive Attribute, or
as its continuous Activity-as, for example, at rest and resting, ruber and rubeo, silent and
holding one's peace, etc.
IDEAS AS ELEMENTS OF THE JUDGMENT
31
EWT
gain the idea of light and that of the light-giving object, or the ideas of
hardness and coldness, and those of hard and cold Things, are the same in
each case: but we cannot in conscious Thought force ourselves back to a
point prior to the distinction, any more than we can talk in the roots from
which the forms of Verb and Noun have developed. What the linguistic
forms of Substantive, Verb and Adjective imply is just this unity in differ-
ence. Every Verb implies a Subject, every Adjective a Substantive, and
only when they are thus supplemented can Thought come to rest in a
pendently and by itself. In this process the part of the Substantive is to
denote more especially the unity, a unity, however, which tends constantly
to develop itself into its elements; the Adjective and Verb exhibit these
elements as abstracted from, but always striving back to unity. Thus wher-
ever we find our ideas denoted by various forms of speech such as Substan-
tives,. Adjectives and Verbs, there Thought has been busy, distinguishing
and unifying according to the categories of Thing, Attribute and Activity ;
our way of speaking is governed by our habit of bringing everything under
these categories. Only in a few onomatopoëtic words at the most-such as
pop, splash—can we reproduce an impression which has not yet been seized
upon by categorizing Thought.
The antithesis between Verb and Substantive claims priority, both
actually and etymologically. Even if it were true that roots in their
original signification are of the nature of verbs, and that names were first
given to events, changes and movements, this would prove no more than
that quick movement and activity exercise the strongest stimulus, and
excite the accompanying sound more easily, not that the idea of activity in
general preceded the idea of the agent. Movement, the fundamental in-
tuition upon which all ideas of external activity are grounded, cannot be
perceived without a localization of the moving object and its background,
and a comparison which presupposes that stationary images have been
seen and retained by memory." It is just in movement that the identity of
the agent in its activity, as the distinction of the permanent Thing from the
temporary event, is most easily grasped; it is more difficult in beginning
and ceasing—in change of attributes. For the attribute expressed by the
adjective when it has a purely sensuous signification-e.g. colour—is not
distinct from the idea of the Subject, it is permanent like it, and what we
1 This agrees with what Steinthal says, Abriss der Sprachwiss., 1,396 sq.
32
IDEAS AS ELEMENTS OF THE JUDGMENT
perceive of the thing is just its Attribute. It is the plurality of Attributes,
their different combinations in different Things, and their changeableness
in one continuously intuited object, which first impels us to disengage them
from one another, and makes us able to think of each independently; and
it is the repetition of action which first impels us to express its permanent
ground by an Adjective. Thus there arise the two classes of Adjectives;
those which partake more of the nature of Nouns, and those which
approach more nearly to Verbs.
While the ideas of Thing and Activity are so bound together that an
action or attribute must always be the action or attribute of some Thing,
and a Thing must always be thought of as having a definite Attribute and
Activity, we are nevertheless enabled by the distinction to think of an
Attribute or Activity by itself, and disengage it from reference to any par-
ticular Thing. In this way they are thought of as abstract, i.e., withheld in
artificial isolation from the unity towards which they naturally tend. In
this abstraction not only are they cut off from unity with definite Things,
they are also raised to universality ; i.e., it becomes possible to refer them
to and find them in any number of particular instances. These two pro-
cesses—that of resolving a given complex idea into the different elements
of Attributes and Activities, and that of forming from these elements ab-
stract and general ideas—are mutually dependent, or rather we should say
that they are one and the same process, and that their result presents
different aspects. In my intuition of a stone as a round, white Thing, the
ideas of round shape and white colour disengage themselves from this par-
ticular combination, and thus it becomes possible for them to enter into or
be recognised in any other combination.
By the distinction of Attributes and Activities from Things we are
enabled to think of the same Attributes and the same Activity as belong-
ing to different Things; and a basis is also given for the comparison of
similar Activities and Attributes in different Things, and the recognition of
differences between them, which we think of as variations in degree or in
mode. And just as Things are distinguished by their Activities and
Attributes, so the similar Activities and Attributes of particular Things are
distinguished by degrees and modes which we may comprehend under the
name of Modifications. Here we have a new distinction and a new unity
which finds expression in language in the relation in which Adverbs stand
to Adjectives and Verbs. The etymological form of the Adverb also
announces it to be a dependent element which must be united to the idea
IDEAS AS ELEMENTS OF THE JUDGMENT
33
of an Attribute or Activity; it is incomprehensible except in connection
with such an idea as its more accurate determination.
So far as Abstract ideas can be retained independently, and form a
centre to which other ideas may attach, language gives them a substantival
form ; they are Abstract Substantives, and their meaning consists in ideas
of Attributes and Activities. This form implies that they are comparable
with Things, in so far as their relations to Adjectives and Verbs are similar
to those of Concrete Substantives. But they are not therefore really Things,
and the unity between them and their determinations, as expressed in
Adjectives or Verbs, is not that unity of inherence or action through which
they themselves, as abstract, indicate a something which supports them.
Except where Relations are involved, only the differentiation of a common
element, the modification of the Attribute or Activity, can be thought of in
connection with that Attribute and referred to it in a manner analogous to
that in which it is itself referred to a Thing. The chief point which the
two relations have in common is that in both there is contained a unification
in the sense that where we have a substantival idea, its determinations and
the distinguishing characteristics which it offers for comparison both occupy
an independent position in consciousness, and at the same time maintain
their unity with it. (The ball is round-the ball moves—the movement is
rapid—the rapidity increases).
The one characteristic common to the ideas of Things and their
Attributes and Activities which we have been considering is, that in all
there is an immediately intuitable element, which is determined by the
function of one or more of our senses, or by inner perception. This
intuitable content never constitutes by itself the whole of the idea ; it is
seized upon by Thought which gives it form, and it is then retained as the
idea of the Attribute or Activity of a Thing to which it is referred as to a
permanent unity. This unity is as much a part of our idea as the element
of sense intuition ; but while the categories of Thing, Attribute and Activity
are always the same, the product of sense-intuition, or of imitative imagin-
ation, constitutes the real essence of the idea, and gives to it its distin-
guishing content.
3. It is this element which distinguishes the ideas of Things and
their Attributes and Activities from the second main class—IDEAS OF
RELATION. In these the ideas of Things are always presupposed ; while on
the other hand their content is the result of a relating Activity, and indues
them from the first with a generality which makes it impossible to excite
the idea of the particular by means of the corresponding words..
S. L.
LOGIC
(a) The relations which are first and most easily comprehended,
because already implicitly contained in our intuition of Things and their
Activities, are those of Time and SPACE. Right and left, above and below,
before and after, are ideas which, as consciously distinguished elements of
our ideal world, are due entirely to a subjective Activity, passing to and fro
between Things which are already intuited in spatial and temporal exten-
sion; their content consists in the consciousness of the determination of
this Activity as it passes through Space and Time, and is therefore inde-
pendent of any particular reference. It is true that these relations are all
implicitly contained in our ideas of Things as spatially extended and
enduring in time~in the manifold which extends before us in spatial and
temporal order, but they do not as yet come into consciousness independ-
ently. We have an idea of a spatial object in which there is right and left,
above and below, and our intuition moves through space in these various
directions in order to grasp the spatial image as a unity; but this does not
necessarily imply that we are conscious of the movement and of its different
directions. At first we are conscious of the result only, of the definite
figure and its situation with reference to others. Relational words have no
meaning for us until this Activity of movement to and fro itself comes into
consciousness, until we distinguish one direction from another, the further
reaching movement of sight or hand from the shorter : they presuppose
a spontaneous movement of Thought supervening upon the immediately
given material, and being thus disengaged from any particular sensuous
affection they possess a generality peculiar to themselves. “Movement”
must always be thought of in the last instance as movement of something,
however faint the sensuous image of that something may be : but“ direction"
presupposes only that we ourselves describe a line in space and are con-
scious of its determinations. These relations are expressed by Adverbs of
Space and Time, and these, when used to denote relations thought of as
connected with the objects to which they refer, become prepositions or
case-suffixes, or blend as prefixes with Adjectives and Verbs; in other
words, again, such as “follow," "fall,” a spatial or temporal relation is
blended with the meaning of the word, and finds no separate expression.
The relation of Whole and Part is also derived from spatial relations.
Intuition begins by a process of limitation and distinction which disengages
what we perceive as a single Thing from the surroundings by which it is
accompanied in immediate sensation. It is in this way that we obtain
images of men and animals, their power of movement compelling us to
IDEAS AS ELEMENTS OF THE JUDGMENT
35
distinguish them from their background, and for this reason also, because
their shape facilitates complete limitation and distinction, we regard trees
and stones as unities. But within this original unity there appear new
differences, and we can describe new boundaries, and thus there arise
subordinate spatial unities within the circumference of the first. Their
relatively independent power of movement causes the limbs of the human
or animal body to appear as such unities, and when we break a stone the
separate pieces are perceived as distinct by the same intuition to which it
is still present in its original shape. Now, when we thus break up a whole,
what we have at first is merely a plurality of new unities, new things to fix
limitations to. The fact that we have an idea of the head as well as of the
whole body, of the finger as well as of the hand, does not necessarily make
us think of the head as part of the body, or of the finger as part of the
hand. Immediate intuition or reproduction may even proceed to com-
plete the idea of the head by that of the body, the idea of the finger by
that of the hand; but not until we are conscious of the relation between
the subordinate unity and the higher, not until we reunite what we have
separated, and refer the two processes to each other, does the head appear
as part of the body, the finger as part of the hand. No doubt the idea of the
idea of such things as the limbs of the body, which we always perceive as
parts, and never as isolated wholes (hand, arm, limb, etc.) than it is with
objects which may be indifferently presented as parts or as independent
wholes (e.g. flower as a whole, blossom as a part).
This relational idea is thus presupposed in every idea of magnitude. A
is large in comparison with B if B is a part of A, or can be regarded (by
means of contact, superposition, etc.) as a part of A. All comparison of
magnitudes and all true measurement is grounded upon the observation or
establishment of the relation of parts to a whole, and the first principle,
" the whole is greater than the part,” is really an interpretation of the idea
“ great.” (Such words as great and high first appear as absolute predicates
or Attributes after we are familiar with a definite standard of measurement.)
Again, the idea of the whole as a Thing with Attributes and Activities
is not without influence upon the idea of the parts. The parts do not
merely stand side by side in external juxtaposition, the whole does not
merely surround them as a frame; a causal relation is implied, the whole
embraces the parts, holds them together and has them. More of this here-
after.
36
LOGIC
The same differentiation takes place in the region of Time. The word
breaks up into syllables, the melody into single phrases; and here also
the ideas of temporal magnitudes, of longer and shorter, are developed
in proportion as the temporal relations obtain an independent position in
consciousness.
(6) These ideas have their origin in the relating Activity which moves
in Space and Time, and their content consists in the intuitive consciousness
of the movement through Space and Time. But their completion requires
also the co-operation of functions of relating Thought, which gives rise to
other ideas of relation resulting from distinction and comparison. The
idea of Difference is not something which is given. In our consciousness
of several distinct objects it is certainly presupposed that we distinguish
them; but at first it is the result only of the function which comes into
consciousness, that is the co-existence of several objects, each of which is
independently perceived. The idea of Difference, of likeness or unlikeness,
does not develop until distinction takes place consciously, and is accom-
panied by reflection. The idea of Identity does not presuppose merely
that the same object was present for some time, or repeatedly; it arises
first through negation of difference in the contents of two or more ideas
which succeed each other in time, and it is this Activity which forms its
content. Only in so far as it presents conditions and ground for this
Activity can identity be ascribed to an object. Difference, Identity and
Similarity are never to be regarded as mere abstractions from the intuited
content, which can give nothing beyond itself; they are mental processes
of which we have become conscious, and it is this that gives them their
content. Number also has its origin in such mental processes, and arises
when similar contents are spatially or temporally differentiated, and the dis-
tinguishable repetition of the same intuition comes into consciousness as
such, while each step of the repetition is retained in memory and compre-
hended in a new unity with the preceding series. The fact that I see three
things, and that the impression made by them differs from the impression
made by two and one, is not sufficient to give me the idea three. The
difference is not perceived by me as one of number until I count: i.e. con-
sciously perform the act of proceeding from one unity to another.
(c) The third main class consists of the CAUSAL RELATIONS. These all
contain, in infinitely varied modifications, the idea of Efficient Action, that
is, of action which is directed upon some other thing (transitive verbs).
Any explanation of the origin of the causal conception, and even the
IDEAS AS ELEMENTS OF THE JUDGMENT - 37
question of its exact meaning, is reserved for later enquiry ; nevertheless
we must indicate the position occupied by it in the totality of our ideas.
This is not easy inasmuch as the close connection between efficiency and
action impels us to regard the latter as a relation because the former is one,
and in so doing we are in danger of representing the position of the agent
towards his action as mere relation, and the action of the Subject as other
than himself, an independent something of his creation. We are all the
more liable to regard the position of a Thing towards its varying actions as
a relation, inasmuch as the identity of a Thing throughout its changes
cannot be thought except by a unifying synthesis, so that as a matter of
fact we are forced to distinguish between the changes and the Thing. The
impossibility of drawing any fixed line of distinction seems to find confirm-
ation in two ways. When a man walks he moves his legs; that which from
one point of view is mere action, appears from another as an effect upon
his limbs, which are relatively independent things; and it is the same in
all cases where there is room for doubt as to what is a single thing, and
what must be regarded as a complex of different things. Even the inactive
relation of the whole to its parts appears as an influence exerted by the
whole upon the parts, or by the parts upon the whole. The whole has—i..
holds—the parts, binds them into unity by its influence, the parts “form”
the whole. Again, in view of the fact that what we ordinarily look upon as
Attribute, such as colour, smell, etc., has been resolved by the progress of
knowledge into an effect upon our sense-organs, much can be said for the
proposition that efficacy and Attribute pass over into each other, and that
Substance is causal in its Attributes. Thus Inherence and Causality
become merely different ways of regarding one and the same relation.
But these considerations merely show the difficulty of deciding where
the determinations of Attribute, Action and Efficiency can be applied with
objective validity; they do not obliterate the distinction between the
concepts of Attribute, Action and Efficiency as distinct elements in our
ideas. We may come to think that what we used to regard as an Attribute
inhering in a Thing, such as colour, does not really inhere in the Thing,
but is its effect upon our sensibility ; nevertheless it takes effect because
of some attribute, which we must conclude to be there, even though it is
not directly cognizable through the senses—the effect, that is, is due to
the structure of its surface and its power of reflecting and absorbing light.
And before it can take effect it must, before all, be active, it must enter
upon a change of state, or some sort of movement. The fact still remains
LOGIC
that if we think of a definite Thing we must think of it as possessing
Attributes which inhere in it, and constitute its particular nature, and can
be predicated of it without reference to anything else. It is the same with
Action. Our world would be a chaos, presenting no clear distinctions for
our recognition, unless we think of it as a plurality of particular individual
Things, each having its definite nature, and active in so far as it asserts
this nature in Time, or changes and alters it, moves or grows. Of course
in this action it is both determined by other Things which affect it, and
affects other Things and determines their action, but that is not the
question here. Efficiency cannot even be expressed without distinguishing
it from Action. The antithesis is that between causa immanens and causa
transiens. That which proceeds from the former is inseparable from the
idea of the Subject, a mode of its being ; that which proceeds from the
latter cannot be thought except in relation to something else. We cannot
therefore obliterate the distinction that the idea of Efficiency belongs to
the ideas of Relations between different Things, while that of Action
constitutes an inherent portion of the idea of the particular Thing by
itself, and involves only the Relations of space and time without which no
particular Thing can ever be thought. It is for this reason also that the
idea of efficiency is never intuitable, since the passing over of Causality
from one thing to another is an addition of the Thought which connects;
only the Action itself, the change in the Things which are entering into
Relation with each other, can be intuited.
The many forms in which this Relation finds expression can only be
briefly indicated. It is most accurately and appropriately denoted by
transitive verbs ; but when these are regarded as proceeding from a perma-
nent ground, adjectives are developed which indicate that a Thing is
capable of producing an effect, is constantly doing so, and always prepared
to do so. And when the idea of efficiency is joined in Thought to the
Thing itself, and the Thing takes its name from the effect which it pro-
duces, then there arise the numerous substantives which denote Things
according to their Causal Relation alone. From this there naturally
results an incongruity between the substantival form, which indicates
permanence and independent existence, and the fortuitousness and change
of the Relation, and the possibility arises of confusing between what is true
only of the Relation, and what is true of the thing. This applies to the
expression “cause” itself. A Thing is a Cause only in so far as it takes
effect, and at the moment in which it takes effect; but on the other hand
IDEAS AS ELEMENTS OF THE JUDGMENT
39
we give the name of Cause to a Thing having a permanent existence.
Now with reference to the Relation it is quite correct to say that where
there is no effect there is no Cause ; but it is incorrect to extend the
proposition to Things which might become causes under certain circum-
stances, or are causes from some other point of view. This is true again
in reference to the Relation of subject and object in the famous proposition
“no object without a subject.” If I mean by the word Object merely the
Relation by virtue of which the name of object is conferred upon a Thing
only when it is actually presented, then the proposition becomes merely
a truism. But I may mean by Object everything existing externally to
myself, or, indeed, everything which is other than my Thought, because
under certain circumstances it may be presented to me; and then it is
not true that all the things ever presented to me vanish so soon as the
subject withdraws and the Relation ceases. If it were so I must needs
vanish myself when I fall asleep. We do not hesitate to say “I have been
asleep,” but “I” denotes a subject which is conscious of itself, conscious-
ness disappears in sleep, hence “ 1” cannot sleep if by “I” is meant the
subject in so far as it is conscious of itself. According to the theory “no
object without a subject " I must cease to be during sleep. “Cavalry on
foot” is an absurd contradiction, if cavalry means only men on horseback;
but if I mean men who serve in a cavalry regiment, then it is a matter of
course that they sometimes walk. The proposition “no object without a
subject ” is true in the same sense that the proposition “a rider cannot
walk" is true.
(d) The relation between ourselves as the subjects of psychical activity,
and the objects of our subjective action-of our intuition and thought as
well as of our desire and will— cannot be compared with any other. An
object or definite content of Thought or Will, contains in itself as such all
the categories we have been considering ; it is Thing, Attribute, Activity
or Efficacy. But under which category shall we class seeing, hearing,
intuiting, thinking, willing, etc., when we consider these functions in
reference to their objects, and not merely as manifestations of activity on
the part of the subject ? Do seeing, hearing, and thinking, belong to the
Causal Relations ? They are not mere action, for they refer to something
other than the subject ; but neither are they efficient, for they neither
produce nor alter a Thing. Only that which never exists but in Thought
(such as imaginations and fancies) comes under the Causal Relation of
production and creation, and this only in so far as we may be justified
40
LOGIC
=
in regarding a thought or a dream as a “ Thing." But what we can
think of as in any way existing is not produced by our Thought; it makes
no difference to the real Thing when we think about it; nevertheless
we regard it as an object of Thought, and as standing in relation to
it. By an extension of the Kantian phraseology we may call this class
of Relations MODAL ; it will contain all the relations which exist between
objects and ourselves when we think of them, and desire, wish for, and
estimate them according to their value for us. Thus it will include not
only all the verbs which express an ideational activity with reference to an
object, but also adjectives and adverbs, such as “true" and "false,” which
express the relation between my idea and the Thing to which it refers, or
“ beautiful” and “good,” which express the reference of a thing to a
standard of value, and therefore express an attribute belonging to the
Thing as such only indirectly and when this standard is absolutely fixed.
Finally it includes such substantives as “sign,” or “purpose.”
$ 7.
Every object of which we form an idea is thought of in one of two ways.
We may think of it as having particular existence (i.e., existing as a
particular Thing, or as an Attribute, activity or relation of particular things)
or as subject to the conditions of particular existence (as with the images
produced by imagination). Or we may think of it without attending to
its particular existence, and as general in the sense that as mentally repre-
sented it may enter into the thought of any number of things or instances.
This mental representation finds its expression in the Word as such.
But when words are appropriated from existing language and employed
to express the natural thought of the individual, their meanings differ with
the individual and are liable to great transformations.
I. The ideas which have preceded the act of judgment in a judging
subject are generally indicated by means of the words that denote them.
Now there is no doubt that what language aims at is that a word should
have the same meaning for every one; but in actual life this is far from
being the case. It is more true to say that words have different meanings
for different people, and for the same person at different times.1 Hence
in the analysis of actual judgment we must never start by assuming that
a word has a generally accepted meaning without further investigation;
1 Cf. Paul, Principien der Sprachgeschichte, ed. 2, p. 83.
IDEAS AS ELEMENTS OF THE JUDGMENT
41
we must always regard the word as being merely the sign of the idea
present to the individual who is making the judgment.
2. The relation between the verbal expression and the idea which it
denotes is not always the same. Some words (such as nouns and verbs)
are connected with a definite ideal content, which constitutes their mean-
ing as understood by the individual. Others—such as pronouns and
demonstratives-denote nothing definite by themselves or by the mere
sound of the word; all they serve for is to express a reference to the
thinking and speaking Subject (or to that of which he speaks), and they do
not therefore become the sign of a definite idea until this reference is
understood by means of actual intuition. I and you, this and that, here
and there, do not express by their sound the idea of a definite person,
thing or place, although they are used to denote definite things or places.
As the circumstances in which, and the people by whom they are used
differ, they denote different objects, and these objects must be supplied
from some other source.
3. But words which are significant in themselves are all of them, so far
as understood, and in their primary and immediate meaning, no more than
signs of ideas which are present to the mind, and can be reproduced by
inemory. Whether a word be a proper name or quite general in meaning
it can never be of use until it has become capable of calling into con-
sciousness a definite ideal-content, by the mere sound alone, and without
help from present intuition. On the other hand we cannot have certain
and firm possession of an idea, or use it in thought, unless we have a word
by which to denote it ; when the word is wanting to an idea we always feel
it as a want, and have a difficulty in grasping the idea in its individuality
and difference from others, in reproducing it with any certainty, and in
guarding it from confusion. As a matter of fact the process of psychical
development always is aided by language and greatly influenced by it, and
every ideal-content, as it becomes a new mental possession, seeks a word to
denote it. This is why we are always so anxious to know names, and are
content to be answered by a name we have never heard before, in answer
delusion of thinking that the learning of names adds to our knowledge of
things, though we really gain nothing directly from knowing that this plant
is called Aristolochia and that one Clematis. Still we have gained a
means of recurring more easily to these things, of fixing them in our
memory, and of afterwards extending our knowledge. Hence all progress
42
LOGIC
in knowledge is accompanied by a change and extension of scientific
terminology.
4. Let us now consider the nature of the ideas which accompany our
words. It is most important here to remember that the thought we are
dealing with is that which takes place in the particular individual in the
natural course of his mental development; and the idea as it is connected
by the individual with one and the same word passes through stages of
development which cannot be explained either by philology, which aims
merely at determining the generally accepted meaning of the word, or by
the ordinary logical treatment of the word.
5. Words are generally held to be the signs of CONCEPTS. But a
Concept in the logical sense is a work of art, produced by a conscious
elaboration of our ideas in which its characteristics are analysed and its
definition fixed, and it is the work of logic to help us to attain to the ideal
state in which words represent such Concepts. As a matter of fact most
of our words only approximate to this state, and when we are treating of
the beginning of judgment in the first appropriation of the simplest
elements of language, it can only lead to confusion if we call every mental
counterpart to a word a Concept, without further discrimination. If we
did this we should have to follow Herbart's example, and give a much
wider meaning than the ordinary one to the expression “ Concept.”
6. We seem able here to distinguish a twofold relation between the idea
and the word. Some of our ideas—those, that is, which rest upon
immediate intuition-form themselves up to a certain point without the
help of language; and these ideas, developing independently in every
individual, are the conditions under which speech first becomes possible.
Here speech is added to an image which is already formed. But others
amongst our ideas, e.g., all those belonging to the region of the non-
sensuous, are aroused in us by tradition, and the formation of these is
occasioned and determined by the range of the Thought of the Com-
munity as expressed in the language we hear. The word comes first, and
becomes only gradually richer and more definite in meaning in proportion
as the individual enters into the Thought of the Community. The con-
trast between the two cases is, however, merely apparent. We never
understand a word except by connecting it with our own ideas, and its
contents consist in just those elements which the individual has really
consciously grasped and retained. Even the immediate sense-intuition of
the child is guided at an early stage by language ; and on the other hand,
IDEAS AS ELEMENTS OF THE JUDGMENT
43
the most abstract terms are no more than empty sounds until their Con-
tent is independently reproduced in Thought. It is always a discovery
when a thought of our own is found to agree with the meaning of a word
as accepted in common language, and all our explanation of words aims
at bringing about the conditions under which the ideas corresponding to
them must be produced according to psychological laws. The real
difference is merely that in the natural development the sensuous ideas
come first and are all formed in more or less the same way, while the
number of elements involved in the higher and more abstract ideas
increases the variety of ways in which they are formed, and the individual
differences of the products become more difficult to expound. But the
general process by which idea and word become wedded together for the
individual is essentially the same throughout. We connect the word with
an ideal-content which must at one time or another have been self-
produced, and it then passes through a series of developments in the
process of which this content becomes enriched and modified.
7. Look how the child obtains the almost exclusively sensuous ideas,
which belong to its first words, and enable it to make its first judgments.
It always starts from the particular intuition of a thing or an event which is
named to it; words are first understood in reference to particular cases.
But in proportion as it is little practised in apprehension and scantily pre-
pared by a previous store of ideas, the intuitive image which enters into
memory, and is afterwards reproduced with the word, falls short of being
a faithful and exhaustive copy of the thing presented to sense, and of con-
taining all which might have been perceived in the object. Even what
the man-unless a practised observer-actually sees in the presented
object, what he receives in intuition and stores in his memory, is generally
quite inadequate to the object itself. Hence when we first begin to speak
the traces which remain of the particular object seen can be no more than a
rough and faded copy of the thing, in which, as in a hasty sketch, only
the more prominent features appear. Generally speaking then, we can
have no idea of what image the child really connects at any time with the
words which it hears. When an intuition occurs similar to those already
retained in memory none of the conditions are present which would enable
it to perceive a difference between the present and former objects; the
fusion takes place immediately and is expressed by the fact that the new
object is called by the name already learned. Children will give the same
name to things only remotely similar so long as they agree in all or some
CD
44
LOGIC
of those characteristics which have been securely apprehended, and this
makes it possible for them to get on with few words. Here we may find
the explanation, both of the wit which so often surprises us in child.
language, and of the numerous confusions into which, as we think, they
fall. Progress, for them, does not consist in subsuming something new
under familiar ideas, but in learning to apprehend more completely and
distinguish more exactly.
8. We may say, then, that in the earlier stages of the Thought of the
individual the meaning of every word is connected with a particular in-
tuition, and there is here no difference whatever between particular and
general ideas. The memory image which remains from our first imperfect
apprehension of an object is not retained by the mind as a fixed im-
pression. Its reproduction is always the result of a new activity, and
instead of speaking of images and ideas as of solid things lying in the
memory as in a store-house, we ought really to speak of having gained
habits and capabilities of reproducing ideas, such as do not exclude
changes of more or less importance in every act of reproduction, and
hence in the product itself. How often when seeing a familiar object-
a house, or landscape-after an absence of some time, we find that its
actual appearance is quite different from our recollection of it. This
uncertainty of the memory-image, and the general law appropriately
expressed by Beneke as the “attraction of the similar,” are all that is
needed to unify it with a series of new images, and so to give it the
function of a general idea. The process of continually naming new things-
to confine ourselves for the present to substantives-serves on the one
hand to fix the prominent features common to all, and on the other to
keep the image fluid and shifting, so that now one, now another, feature
can come to the fore and determine new associations. It is for this reason
that in the natural course of Thought all words have a tendency to widen
their sphere ; their boundaries are indefinite, and always ready to open
and admit new ideas of the same kind. This extension is continually
favoured by the fact that in new objects we always notice and apprehend
most easily those characteristics which coincide with an outline already
familiar to us; we cover things, as it were, with our ready made images,
and so conceal any new and distinctive features they may possess.
But side by side with this process there runs another. As we gain
1 Cf. the very appropriate remarks of Steinthal, Abriss der Sprachwissenschaft, i.,
p. 148 sq., 401 sq., and Paul, Princ. d. Sprachgeschichte, ed. 2, p. 75 sq.
IDEAS AS ELEMENTS OF THE JUDGMENT
45
practice in apprehension we observe not only the more striking features,
but also those which are less prominent. In this way our images become
more defined and richer in content, and in proportion as their application
to new objects diminishes, their number and our power of distinguishing
between them increases. But in distinction of this kind wholes are
compared with wholes : we do not begin by taking account of the differ-
ences in detail, and consciously sorting out the characteristics which agree
and differ. We constantly and unhesitatingly distinguish between persons
whom we know and do not know, without being conscious exactly how
they differ. It is an unanalysed total impression, as immediate in its
judge that the unfamiliar is not known.
It is not so much frequency of observation as interest, which determines
the individual's attention and the accuracy of his apprehension. The
images of objects which rejoice or terrify him, or which are connected
with his needs and inclinations, impress themselves upon his memory in
all their details ; but where objects are indifferent to him, he does not
trouble himself with accurate apprehension, and hence they leave only
faded impressions which contain only the more striking characteristics
and can fuse with similar impressions over a wide range.
In this way we may explain how it happens that of the images stored
in his mind and connected with his words, some are well defined and
rich in content, others less defined and more liable to change in meaning.
He may give special names to the hen which lays eggs for him, the sparrow
which is troublesome in his garden, the stork which builds upon his roof;
all other varieties are “birds,” and he cares nothing about the different
kinds. Nor is he conscious that the idea “bird” includes in its inde-
finiteness all the specific kinds; we may hear others than children say
" that is not a bird, it is a hen.” Where there is no interest in distinguish-
ing things the less defined and poorer image, which is derived only from
the two principal characteristics of form and flight, is sufficient, and this
extends to flying beetles and butterflies.
The history of language shows a similar development. Its roots are
very general in meaning, not because the most general features were fixed
upon from the first by a comprehensive process of abstraction, but because
few distinctions were made, and only those phenomena retained and
named which were easily apprehended and especially prominent. Particu-
lar things are generally named after some one of these phenomena; the
LOGIC
river from its movement, the cock from its crowing, and so on. Then as
different aspects are apprehended in the things they receive new names,
and there arise the numerous synonyms which cause them to be classified
in different series of similar phenomena. Further specialization does not
take place until, as language develops, derivates arise, and words originally
synonymous are applied to different specific classes of things and events;
the more general meaning continuing side by side with the special. Contrary
to the common doctrine of the formation of general ideas, general precedes
special in the individual as in language, as certainly as the incomplete and
indefinite idea precedes the complete idea in which careful distinction is
presupposed.
A similar process takes place with regard to ideas of qualities and
activities. Here, again, apprehension is at first of the most general kind,
and deals only with considerable and easily distinguished characteristics.
With the child—as with language—the first ideas of colours are few and
uncertain in their differentiation, it is only gradually that sight is practised
to distinguish differences which were formerly indiscriminately classed
together ; in movement it is the most familiar forms which are appre-
hended and unconditionally extended to all similar forms, only at a later
stage are the manifold differences observed and denoted. How many kinds
of movement are denoted by such a word as “going” or “running."
9. Assuming that the idea connected with a word arises originally in
this way from the intuition of a particular object, the incomplete and
shifting image of which constitutes the first meaning of the word, we can
now see in what sense Generality attaches to such an idea.
That any idea may be general, i.e., applicable to any number of particu-
lar ideas, is involved in its nature as reproducible, and in no way depends
upon its having been formed from a number of such particular ideas. As
soon as it has disengaged itself from the original intuition with its spatial
and temporal connections, and is a mental image which can be freely
reproduced, it is capable also of fusing with a number of fresh intuitions
or ideas, and of appearing as their Predicate in a judgment. If we con-
fine our attention to the contents of the idea this kind of generality belongs
not only to images such as those of the sun or the moon, but also to the
images of particular persons. As often as the sun rises in the sky, or the
moon becomes visible we have a new particular intuition, which is unified
with the idea left by a previous intuition. The recognition of the material
identity of all these suns and moons follows later, and, where continuity
IDEAS AS ELEMENTS OF THE JUDGMENT
47
of intuition is absent, by no means of necessity. In a similar way the
reflection of a person in a mirror, or his portrait, is immediately identified
with the memory-image, and here again our knowledge that these are
merely images, and that the name belongs properly to one individual,
comes later, and checks our attempt to treat the idea as general, in the
widest sense ; so far, indeed, as concerns the idea itself, it is a matter of
chance that it is not really general.
Thus it is not the special content of the idea, nor yet its origin, which
determines whether or not it is general in the ordinary sense, but the fact
that the idea is actually applied to a plurality of particular intuitions
assumed to be copies of a real plurality of things, we being conscious of
this plurality as such—the Singular must extend to a Plural.
10. This plurality is at first merely numerical. When a number of like
or indistinguishably similar things present themselves contemporaneously
or successively in intuition, not only is each one identified with the
memory-image, but the fact that the content of the idea is the same each
time makes it necessary to count in order to reconcile the external spatial
or temporal difference with the sameness of the image. It is here that the
antithesis between singularity and plurality first appears.
11. As a rule, however, it is not this numerical generality to which we
refer when we say that words are general in their signification. What we
mean is that their generality is such that they include different objects,
which are distinguishable and are actually distinguished by their contents.
In this sense the idea tree is said to be general with respect to oak, beech,
fir, etc., the idea colour with respect to red, blue, and green.
Here we must be careful to distinguish between the generality of the
idea and the generality of the word. So far as the actual meaning of words
for the individual is derived from particular images, the very indefiniteness
of an idea renders it applicable to things which differ, not merely spatially
and temporally, but also in their content. A visible thing may be repre-
sented by copies of every degree of resemblance, from the few lines with
which schoolboys draw horses and men in their books, to the perfect
photograph, and in the same way we may have a series of ideas, represent-
ing the same object with a gradually increasing definiteness, all continuing
to exist side by side. The more indefinite the idea, the easier it is of
application. But until we become conscious of the difference between
the various objects to which an idea once formed is constantly being applied,
that 'idea is of the same kind as the idea of the sun, or an idea having
LOGIC
merely numerical generality. When the word grass brings to mind only
a group of green, narrow, pointed leaves, and we disregard the differences
between particular kinds of grass, then we merely see grass and all is grass
alike; but as each apprehension becomes more definite and we notice
distinctions between things which at first sight all coincided with a given
idea, then, while the common name still remains, new ones are formed
for the more fully determined ideas. In course of time these crowd out
the more indefinite idea, which becomes too vague to be made vivid. The
botanist has no ideal image corresponding to the word grass or tree; for
him there arises a rivalry between differently determined forms which
would be set down as alike by a less practised apprehension—a rivalry
like that in the field of vision when different images are presented to the
two eyes. To such ideas there is nothing in common but the word. The
word is general in its signification in so far as it comprehends different
things, and denotes a number of distinguishable images by elements which
are alike in all. It is here that we are first called upon to realize the
common element in difference; i.e. to form by abstraction the concept in
the ordinary sense of the word.
The same process goes on with the more fully determined ideas. Here
also, as apprehension becomes more acute and memory for small differences
more faithful, the originally single image resolves itself into many. But
language cannot keep pace in its derivatives, combinations and qualitative
determinations with this process of specialization ; memory also fails to
be equally retentive of all particulars and imagination to lend an equal
vividness to all images. So that for every word there finally remains a
group of distinguishable ideas, all of which it serves to denote. They do
not, however, all bear the same relation to the word; one image, more
definite than the others, is specially connected with it, as the centre of the
group round which the others gather. In a neighbourhood where fir
trees grow the image of the fir is that which a man primarily connects
with the word tree; any other varieties he may know are less distinct
and fall into the background. The word “red” is most immediately
connected with an especially striking impression, easily distinguished from
all others; as it becomes extended in application to further modifications
of the colour it ceases to denote anything definite, and calls to mind now
this shade, now that, amongst a number which occur to us as equally
possible. The word has become general by losing its definite meaning
and reproducing a series of shades which is not at first distinctly limited.
IDEAS AS ELEMENTS OF THE JUDGMENT
49
1
Each of these shades is a general idea, in so far as it is itself applicable
to a plurality of particular intuitions, but their names (blood-red, rose-red,
etc.) serve to remind us of the original process by which words derive
their meanings from particular intuitions.
12. Essentially different from this natural development of the relations
between word and idea is another process which is conditioned by the fact
that in naming we are always under the influence of a language which is
already there. The language in use hinders combinations which would
naturally take place, and forces upon us others which would not. To
declare the common element in all the things which language denotes by
one word is a very different matter from declaring what things any given
individual subsumes under the idea which he considers they resemble.
Many words are for the individual mere homonyms, the essential similarity
of the ideas which first caused them to be named alike escapes his notice ;
and in the same way it is language which first makes us conscious of many
similarities which would never have been discovered by one man carrying
on his comparisons independently. On the other hand the language in
use prohibits and destroys many similarities, and forces upon us distinc-
tions which might never have occurred to the individual thinker. In the
latter case the idea is forced into fuller determination, but in the former
it is impossible to say how many really disconnected ideas may correspond
to one and the same word. In Etymology we aim rightly at tracing the
most remote connections, but our task then is quite different from what it
is when we endeavour to realise the actual process of thought in the indi-
vidual..
For the individual the meaning of a word is determined, not by its
etymology, but by the thought of those objects to which it is applied in
ordinary language. We never think, until we have been taught, that there
may be something common to the cock on the barrel, the cocking of the
trigger, and the cock in the poultry yard, which led to their all being
called by the same name; for us the three meanings are completely dis-
connected, the words have become mere homonyms. In the same way
the original meaning of the words by which we denote most of the
psychical activities is completely lost to us; no one feels now the figura-
tive, metaphorical force of words such as concept, judgment, conclusion.
13. If the words which we use are only signs of a definite ideal con-
tent, which in its detachment from present intuition has gained an in-
dependent existence in that it is capable of mental reproduction at will,
S. L.
50
LOGIC
11
then it follows that by themselves, by their mere .sound, they can never
denote the particular as such, and as it is presented to intuition. In order
that a word may be understood to apply to a definite particular object we
have to make use of special expedients, such as possessive or demonstra-
tive adjectives or gestures; or else we must be able to assume that though
the reference to a definite particular thing is unspoken, it will be correctly
carried out by the hearer. But when a particular thing is denoted by
means of a word it is always because it is recognised as agreeing with the
general idea expressed by the word; I can denote the thing lying before
me as this book, or my book, only because the general meaning of the
word book is applicable to it.1
It is true that one class of words denotes particular things as such.
This is either because the thing corresponding to the idea is actually to be
found only once in the world, as in the case of sun and moon, sky and
earth, or because a name has been given by express agreement to the
particular thing as such, on purpose to distinguish it from other similar
objects, as with the proper names of people, towns, mountains, etc. Where
the meaning of these is still recognisable it may be traced back to general
words, as in Mont Blanc, Neustadt, Erlenbach ; but this meaning,
which explains the giving of the name, is in most cases forgotten, and the
idea aroused by the now meaningless name is only that of a definite
particular object. Nor can they fulfil the function of comprehensible
words even in this way unless the object has been intuited and remem-
bered. The import of the name is related to the momentary intuition of
the person or mountain, as the general word to the particular thing; it
cannot be applied to anything present to sense unless the identity of the
present intuition with the mental image is recognised. The proper name
is distinguished from the general word only by the consciousness which
accompanies it that the corresponding reality is a particular thing and
always the same in fact.
Finally, there are also certain relational words of general content, which
apply only to a single thing; reference to a single object forms part of
their meaning, as with all true superlatives, or ordinal numbers. In so far
as only their context can tell us what is compared or counted they are
like demonstrative adjectives, which also can express their particular
1 In reference to this Mill's analysis is superficial (Logic, bk. I., ch. 2), when he classi-
fies the adjectives, white, heavy, and even the demonstrative adjective “this," as names
of things. Cf. also Paul, Princ. d. Sprachg., ed. 2, p. 66 sq.
IDEAS AS ELEMENTS OF THE JUDGMENT
51
object only by means of a Relation. The first of January 1871 is a single
day, but it is definite only if we assume a definite system of enumeration ;
it differs for the Russian calendar and for ours, and the meaning of the
expression depends further upon the idea of a series of days and years
which is nothing more than an object of Thought.
$
8.
The peculiar function of words makes it indispensable to the completion
of the judgment that the predicate should be expressed in them; the
subject, if not general, can dispense with the verbal expression.
1. It follows from what has been said of the nature of words that we must
be careful to distinguish whether a word signifies merely the ideal content
immediately denoted, or whether it is being used to denote a definite par-
ticular thing which is not indicated as such by the meaning, but which
represents that meaning and can therefore be named by the word.
Upon this distinction depends the essential difference of the way in
which words are related to the subject and predicate of a judgment. When,
that is, a statement does not refer to the content of the subject term as
such—as in definition-but to a definite particular thing, it is quite unneces-
sary that we should denote, or even be able to denote, the subject idea by
a significant word. We may merely use a demonstrative—“this is ice,"
“this is red,” “that is falling ”; and we may substitute for this demonstra-
tive a mere gesture, or even give utterance to the predicate without anything
further,—the mental process will still be a judgment in which a statement
is made about something.
We see this most clearly in the judgments in which all human judgment
begins, those in which definite objects of sense-intuition are recognised
and named. The child makes a judgment when it names the animals in
its picture-book by pointing to them and pronouncing their names, and
the exclamations elicited by a startling sight (father! fire! the cranes of
Ibycus !) are proper judgments; it is only the verbal expression which is
incomplete, not the mental process.
1 Herbart, Psychologie (sämmtliche Werke), iv. Tóg. The first step is the sight of the
thing ; the idea immediately given by this arouses the previous idea, which fuses with it.
The immediate perception gives the subject, it is the fusion which would be denoted
by the copula ; the place of the predicate is taken by the previous idea, which is aroused
and fuses with the perception.
Paul (1.c., p. 104) takes sentences in which what is said is the subject for both speaker
and hearer, the situation being the predicate : “ Some one sees, for example, that a child
52'
LOGIC
2. On the other hand it is essential to the completion of the judgment
that the predicate should be spoken. It is true there may be cases where
(e.g.) an object is recognised for which the approximate word is wanting,
and where, therefore, the mental process can find no expression ; but for
this very reason we regard the process as incomplete—as an immature
production, and consider that judgment alone to be complete in which
the predicate appears, denoted by a word. It is indeed essential to the
predicate that the idea belonging to it should be none other than the
meaning of the word, the ideal content which is connected with the word
as such and has thus become ours. It is no matter whether this idea is
general in the ordinary sense, or whether it is the idea of a particular thing.
“This is Socrates” is as much a judgment as “Socrates is a man”;
“to-day is the first of January” as much as "to-day is cold”; although
neither Socrates nor the first of January are general ideas in content.1 It
is enough that they are ideas at all-ideas which can be reproduced by
and with the spoken word.
is in danger ; then he merely calls to the person in charge of it—the child.' This only
indicates the object to which attention is to be directed, that is the logical subject ; that
which the person addressed sees when she obeys this direction of her attention gives her
the predicate.” But here, I think, we must distinguish between two things. The ex-
clamation is, in intention, an imperative, not a statement; and it can only be understood
as an imperative. For the judgment really passed by the person speaking—"the child is
in danger ”-finds no place in the words of the exclamation ; at the most it makes
itself felt in the anxious tone of voice. The object is to direct attention to the thing
named. With this view it is simply namel; thus the full expression of the thought
would run thus, “take care of the child.” It is a distinction similar to that between the
cry of alarm, “Fire !” and the word of command, “ Fire.” The former is a judgment,
of which fire is the predicate; the latter is an imperative. “Fire” is the object, not the
subject, of the incomplete imperative ; and the case is the same with “child” in the
preceding example. By merely exclaiming “the child ” all that I can communicate to
any one as the object of his and my belief and assent, is that what I see or think of is
the child. But then the word is predicate. In like manner the exclamation, “the
rascal,” or “a Daniel, a second Daniel,” contains the judgment that the person thought
of is a rascal, or a second Daniel ; and on this is based the indignation or joy which is
manifest in the tone of the exclamation.
1 Volkelt holds (Erfahrung und Denken, 319) that in propositions such as “ This is
my father, this is the moon,” the predicate indicates the common characteristics of that
which I denote as my father, etc., hence not the individual as such. It is certainly true
that the relation between a proper name which is used as a predicate and its subject
(according to p. 42) is similar to the relation between a general idea and an idea compre-
hended under it. It is similar, that is, in so far as the proper name (particularly in the
case of changeable things) does not indicate a momentary state, but that which is identical
through all states, or that which might with less accuracy be called the common element.
It does not, however, follow from this that it is not the individual as such which is
meant.
CHAPTER II
SIMPLE JUDGMENTS
By a SIMPLE JUDGMENT we mean one in which the subject may be regarded
as a single idea ; it does not include a plurality of independent objects,
and may therefore be represented as singular; the statement made con-
cerning this subject takes place in one act of judgment. Two classes
must be distinguished of these simple judgments : those in which the
NARRATIVE JUDGMENTS; and those of which the subject idea is the general
meaning of a word, nothing being stated about any definite particular
thing—these are EXPLICATIVE JUDGMENTS.
1. NARRATIVE JUDGMENTS.
§ 9.
The simplest and most elementary form of judgment is that in which
we name particular objects of intuition. The subject-idea is given im-
mediately to intuition as a unity, the predicate-idea is mentally reproduced
with its appropriate word, and the act of judging consists in the thought
by which the two ideas are consciously unified (σύνθεσις νοημάτων ώσπερ
èv ÖvtWV, Aristot., de anima, III. 6. 430a, 27).
1. It is easy to explain the inward process which corresponds to such
a sentence as “this is Socrates,” “this is snow," " this is blood”; or to
the abbreviated exclamations “fire,” “the stork,” when these appear as
the expression of immediate recognition. The object before us awakens
an idea left by some former impression, and connected with the word,
and the two are unified. That which I am looking at is, according to
its content, one with that which I have in my idea; I am conscious of
this unity, and it is this consciousness to which I give utterance in the
proposition. By this the judgment is distinguished from the kindred
processes. In the first place it is distinguished from what has been called
53
54
LOGIC
unconscious fusion—we will not here discuss whether the expression is
appropriate and descriptive of an actual process. Here the new image is
supposed to unite at once with previous ideas in such a way that the
product of the union is merely a repetition of the previous idea—at the
most more vivid ; there is no distinguishing nor holding apart of new and
old, of that which is present and that which is remembered. With re-
ference to this Herbart is right in pointing out that a judgment as a
conscious act is possible only when such fusion is delayed and the two
ideas are held in suspense, and that it therefore has its most characteristic
form when a question or a doubt has intervened. As a rule, however, it
is true that attention is chiefly claimed by the present, and only its utter-
ance reveals that the idea already in our possession has become active,
particularly in the case of the mere exclamation which accompanies re-
cognition.1
In the second place, the judgment is distinct from the merely involun-
tary reproduction of a previous image which might co-exist with the first
without being unified with it. It might happen, for instance, that on
seeing a fire I should remember other occasions of fire, but that each
image being accompanied by its distinguishing circumstances, they should
be prevented from combining into one, and being thus retained in their
1 From the Denominative Judgments described above, in which the object presented is
(according to his view) compared with others previously known and called by their name,
Stumpf (Tonpsychologie, vol. i., p. 5) distinguishes yet another kind of judgment—the
Judgment of Habit. It often happens entirely as a matter of habit that a phenomenon
when seen or heard reproduces in consciousness both the appropriate name and the
judgment " x is red, x is the note A”; “in which case the previously perceived object
does not enter into consciousness at all, much less is compared with the present object.”
I cannot however find sufficient reason for this distinction. On the one hand it is not,
generally speaking, the case that in denominative judgments as I understand them-a
present object is compared with previous objects in the sense that the latter are present
to thought as differentiated particulars and their name transferred to the new object.
That which is reproduced by the present object is only the general idea connected with
the word, and there is no need of any express comparison in order to be aware of its
coincidence with what is present. On the other hand it is clearly too much to say that
what was previously perceived “does not enter into consciousness at all”-how else
should a recognition take place ? Only so much is true : that it is not necessarily as
differentiated that it comes into consciousness. The process goes on so rapidly that I am
not aware of each particular step; when I meet an acquaintance the memory-image
which is necessary before I can recognise him pales in contrast with my present percep-
tion, but it must have taken effect in consciousness. Thus it becomes impossible to
draw a line between judgments of habit and those which are not of habit; all that we
can allow is that when we are dealing with familiar ideas which are well known and
often applied, the process, which is always essentially the same, takes place more rapidly.
SIMPLE JUDGMENTS
55
individuality present merely a number of similar images. The union can
only take place when no such hindrance occurs either because all the
accompanying circumstances are the same, or because the content of the
idea is already isolated and raised into generality.
2. When this simplest and most immediate form of judgment-know-
ing in its original sense of recognising-takes place, it is presupposed that
both ideas are undivided wholes, not consciously resolved into their
particular elements. Immediate unification is thus distinguished from the
other case in which a series of intermediate acts of thought is necessary
in order that subject and predicate may be unified. When “snow" or
“ blood ” denotes a scientific concept, the distinguishing characteristics of
which are present in memory, we do not form a judgment at first sight,
but investigate the object in order to ascertain whether all the charac-
teristics of the concept are appropriate to it. It is only upon the ground
of a process of inference that we place the object under the concept; i.l.,
that we attribute to it the whole complex of qualities universally accepted
as contained in the term snow or blood. This judgment, then, is mani-
foldly mediated ; in it is repeated several times the process which takes
place at once in the coincidence of two images through the unanalysable
act by which they are brought together. Between these two extremes
there lies a whole series of ideas which may be connected with the predi-
cate terms, and corresponding to it a graduated series of mediation of the
judgment. But what the judgment always states is, that the idea of the
predicate agrees with that of the subject in such a way that the predicate,
as a whole, is one with the subject.
It might also be held that there is a process of inference in the numerous
cases where the predicate contains more than can be offered by the first in-
tuition which gives rise to the judgment. When a child sees an apple and
names it, then the predicate-idea includes also its taste and its quality as
edible; and in the judgment “this is an apple” we might suspect an in-
ference from the visible image to the presence of the other attributes. But
previous experiences have made the association of the other attributes with
the visible image so firm that there is no conscious distinction between
them; the visible image at once awakens recollection of the other attributes,
and it is with this enriched intuition that the predicate-idea is connected.
The child does not make the inference “this looks like an apple, there.
fore we can eat it”; but the sight of it gives rise to desire, and both together
reproduce the idea “apple” and lead to its being named. In such cases
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LOGIC
also, then, we still have the simple coincidence between the present intui-
tion and the remembered idea, and they are to be distinguished from
cases in which further attributes only occur to us in consequence of the
name,
3. Complete coincidence between a present and a reproduced image
does not take place only when we recognise one and the same object as
such; when, that is, we may add to the judgment which identifies the ideas,
a consciousness of the material identity of the things which is not itself in-
cluded in the judgment. It occurs also whenever there is no conscious-
ness of difference between subject- and predicate-ideas, so that what is ap-
prehended and consciously noticed in the object exactly coincides with the
predicate-idea. This will always be the case where particular phenomena
of the same sort are only distinguishable by special attention (this is
snow—this is a sheep-this is a poplar); or, again, when the apprehension
of an object is determined by a preconceived idea, and that part of it which
comes into consciousness is exhausted by the predicate-idea; here the
predicate-idea itself is not absolutely fixed, but is often 'unconsciously
affected by the subject which happens to be present.
4. To these must be added other cases, in which we are conscious of
difference, but are not led by it to an express judgment. Such are the
judgments which merely make a comparison or note a similarity, and which
frequently as in fanciful or humorous comparisons-take exactly the same
external form as denominative judgments : most of the metaphors of lan-
guage also depend upon this process. Such, again, are the judgments in
which the subject-idea is richer and more fully determined than the predi-
cate-idea, but only that part of it is noticeable which coincides with the
predicate-idea ; judgments, that is, in which the predicate is a less definite
and more general idea than the subject, which we know is not exhausted
by it. This is particularly evident when I do not know the special name
of the idea coinciding with my object, and am therefore obliged to be
content with its more general name (this is a bird, a tree, a fluid); or when
the special name is not so familiar to me as the more frequently used
general name; for in the natural course of thought the predicate-idea
which most easily connects itself with every image is that which is most like
to it and most fully determined. Not until scientific thought begins is
there any interest in subsuming under the most general ideas; ordinary
thought, which is concerned with the particular, clings to the most concrete
ideas at its command. (For logical purposes ideas which are expressed in
SIMPLE JUDGMENTS
language by the more exact attributival determinations of a substantive,
such as “ black horse,” “round leaf” —are just as much one as those which
can be expressed by one word. Their comprehension into one whole has
already taken place when they appear as predicate.)
5. In naming we naturally think first of the ideal content as a unity,
but in the process of thought the predicate-idea becomes connected with
the idea of plurality wherever we have the numerical generality of many
vaguely remembered individuals, or wherever the meaning of a word con-
sists in a number of slightly different ideas. When a word denotes a sharply
defined individual image, this is accompanied by a number of individual
images amongst which the new object ranks itself as another (this finds
expression in the form “this is a tree”); when the meaning of the word has
not this individual determination the generality of the predicate appears in
our consciousness of other ideas which are nearly akin to the one which
happens to be before us (“this is paper,” “this is wine”; here the words
paper and wine stand for a number of slightly different ideas). So far
Herbart is right in saying (Introduction to Philosophy, l. 92) that the con-
cept which serves as predicate always loses part of its meaning in that cap-
acity, only so much of it enters into thought as can be connected with the
subject which it determines. Of all the many ideas comprehended by the
word, that one is pre-eminent which coincides with the subject.
6. These denominative judgments? have always preceded, when the
definite object concerning which the judgment is being made is denoted,
not merely by a demonstrative, but by a significant word. “This flower
is a rose” includes a twofold denominative judgment; first, there is the
naming by the less definite word flower, which has taken place previously,
and of which only the result appears in the verbal expression of the subject;
then the more exact naming in which the judgment itself consists.
1 I choose this expression in order that I may have one denotation to cover statements
which elsewhere are sometimes treated as judgments of subsumption (when the predicate is
a more general idea), sometimes as judgments of identity (when the predicate completely
coincides with the subject). In the simplest cases there is no clear line between the two ;
in both the process is essentially the same, i.e. we are conscious that what is presented
is in its totality one with a previously known idea. Schuppe (Erk. Logik, p. 375 sq.),
in his thorough and appropriate treatment of the subject, calls this process pure identifica.
tion; but since it is seldom a question of absolute identity between the ideas of subject
and predicate, I should prefer to avoid the expression. In the same way I avoid using
the expression subsumption ; for this, when applied in its strict sense, does not represent
the general idea which is connected with the term in its popular use, but a logically deter-
mined generic concept under which we place a particular thing or a specific concept.
LOGIC
7. The habit of referring attributes and processes to things is so strong,
that there are comparatively few instances in which denominative judg.
ments about them do not also include a judgment of attribute or activity.
Still our power of abstraction enables us by means of “that” and “this"
to denote even the mere attribute or activity as such. “This is not
walking, but running”—“this is dark-blue, not black,"—it is not things
which are spoken of here, but colours and activities apart from things.
There is however always the tendency to pass from the attribute or activity
to the thing. Cf. § 11.
§ 1o.
When the predicate of a judgment concerning a specified particular thing
is a verb or an adjective, then the judgment contains a twofold synthesis.
1. The synthesis which unifies the thing and its activity, the thing and its
attributes, in the subject-idea itself ; 2. the synthesis which unifies the acti-
vity or attribute contained in the thought of the subject with the activity
or attribute denoted by the predicate-word, that is, names it by the predi-
cate word.
1. In uttering a judgment, such as : “ this cloud is red ”—“the stove is
hot”—“the iron glows "_" the horse runs,” we first express the unity of
a subject with its activity or attribute, this being indicated by the form
of the words; we then name the attribute or activity which we have per-
ceived by unifying it with the general idea “red,”—“hot”-“glow" or
“run.” That which is given to perception is the red cloud, the hot stove,
the glowing iron, the running horse ; but we analyse the originally undivided
whole of perception by distinguishing and separating the attribute and
activity from the idea of the subject. We have recognised by its shape and
position that what we see is a cloud, and this recognition is expressed in
calling it by the definite subject-word cloud; we are struck by its colour,
and hence this is easily disengaged from the whole. It is this colour which
we call red, and ascribe to the cloud as its attribute. We recognise the
thing which is running to be a horse ; as presented to us it is in move-
ment, it is running, but we distinguish this incident from the subject which
under other circumstances is known to us as standing still. It is this par-
ticular kind of movement which we express as running. We have thus
distinguished two constituent parts in the total-image, the thing and its
activity ; in each of them we find again an idea already familiar to us, and
by uniting these two elements in our statement we express just what we
SIMPLE JUDGMENTS
59
have seen as a unity of a thing with its attribute or activity. Thus the
judgment presupposes an analysis, whilst its own work is to synthesize the
different elements.
By this twofold synthesis the judgments which state attributes and acti-
vities are distinguished from the simple denominative judgments; in the
latter it is the subject of an undivided whole which is unified with the
predicate.
We have spoken of the generality of substantives when treating of the
ideas of things; and what we then said applies also to the relation between
the generality of the predicate-idea and that element in the subject-idea
which corresponds to it. Such a relation may vary from the case in which
we are conscious of a complete coincidence (as, e.g., with sharply defined
colours, “this lichen is sulphur-yellow"), down to cases in which the predi-
cate-word is too indefinite to denote the fully determined attribute or
activity of the subject, and can only be made to agree with the idea by
means of further determination with adverbs and other distinguishing words.
2. The view we here take is opposed to that which would force even
such judgments as these into the conception of a simple subsumption of
the subject under the more general predicate. But the predicate which
expresses an attribute is general only with reference to the attribute of the
subject, never to the subject itself. The predicate which expresses an
activity is general only with reference to its activity. We must distinguish
attributes and activities in the subject before we can apply adjectival or
verbal predicates to them. Simple naming is the answer to the question,
“What is this?” But if we are to answer with an adjective or verb, the
question must be, “What is the quality of this ? What does it do?” Such
a judgment presupposes, therefore, that we have distinguished between the
action or attribute and the thing.
§ II.
In judgments which express the attribute or action of a thing, the move-
ment of thought is not always the same; that which first comes into con-
sciousness is sometimes the thing (the grammatical subject), sometimes the
attribute or activity (the grammatical predicate). In the former case the
attribute or activity is first distinguished as a part of the total idea, and
then named; in the latter it is perceived first by itself and named, and then
referred to a thing.
1 Cf. Wundt, Logik, 1. 136 sq. Also my treatment of the question in the Vierteljahrs-
schr. für wiss. Philos., 1880, iv. 458 sq.
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LOGIC
This last act-reference to a thing—is, under certain conditions, omitted,
and in this omission we find the explanation of the so-called impersonals.
Strictly speaking, impersonal propositions are those only from which all
thought of a subject-thing is excluded, not those in which a subject-thing is
implied, but only vaguely indicated and expressed. 1
1. When the statement which ascribes an attribute or activity to a thing
starts from immediate perception, two things may happen. I may perceive
from the first the thing with its action, state and attribute, so that I analyse
this total idea, and form my judgment out of it :-the leaf is faded, the
iron glows, the balloon rises ; or I may perceive at first only that element
which is expressed by the adjective or verb, a colour, a flash of light, a
movement; and then it is not until afterwards, by a second act, that I
recognise the definite subject of the attribute or activity, and can name it :
“there runs—a hare"; "there flies—a dead leaf”; “there sparkles—the
Rhine," etc
In the latter case the synthesis which first takes place is that which
names the given phenomenon of shining, sparkling, movement; the refer-
ence of the attribute or action to its thing is not added until afterwards.
In such cases language will also naturally begin with that which is first
present in consciousness, with the adjective or verb. The Hebrew custom
of putting the predicate first is the immediate expression of a mode of
thought which moves pre-eminently in sense-perception; and in proportion
as particular languages continue to be the immediate and unartificial ex-
pression of the active movement of ideas, they have retained their freedom
of beginning either with the predicate or with the subject. French, which
determines the position of the word entirely according to its grammatical
character, is furthest removed from this original flexibility.?
1 Cf. with this $ F. Miklosich, Subject lose Sätze, 2nd ed., Vienna, 1883; W. Schuppe
in the Zeitschrift fiir Völkerpsychologie und Sprachwissensch., vol. xvi. 3, 1886; my essay,
die Impersonalien, Freiburg, 1888, and Steinthal's review, Zeitsch. für Völkerps., xviii.
170.
? It might be maintained that we must always regard that which first enters into con-
sciousness as the logical subject, because it is the given point with which a further ele.
ment is connected. But it would be a doubtful proceeding to ground the distinction
between subject and predicate only upon the chance priority of the elements of the
judgment as they might happen to succeed each other in the individual, instead of upon
the contents of the ideas themselves. The relation between the ideas which we denote
by verbs and adjectives on the one hand, and by substantives on the other, necessarily
involves the thought that the objective foundation and presupposition of that which is
expressed in the verbal form is that which the substantive denotes. When we apprehend
motion, etc., we are led by its similarity to other cases to think of it as something depen-
SIMPLE JUDGMENTS
61
2. These two acts, the naming of a perceived attribute or activity, and
the reference of it to its thing, are sometimes still more widely and ob-
viously distinct. All that is immediately perceived is an impression, which
is denoted from its resemblance to previous cases, by an adjective or verb;
the thing belonging to it being added in thought only through association and
on the ground of former experience. This takes place especially with sen-
sations of hearing and smelling. That I can predicate a sound or a smell
of a visible and tangible object is due to an act of combination by means of
which the sensation of the ear or the nose is referred to the object which
makes itself known at the same time to the eye and the hand. We cannot
here investigate how this combination comes about; but in all ordinary
cases it is so much a matter of habit, the visible signs of the origin of the
sound are so familiar (as with crying and talking, the knocking of a ham-
mer and the stamping of the foot) that we think the sound is immediately
perceived by us as the activity of a definite visible thing. But when a
noise strikes the ear without our being able to see the thing which pro-
duces it, this thing must be added in thought; our judgment does not
appear as the result of the analysis of a given complex, as when I say, “the
leaf is yellow,” but as the result of a synthesis by which the thought of a
thing belonging to it is added to the sound which was given alone. In
very many cases this association is perfectly easy and certain, and we are
scarcely conscious of it. When I hear my dog barking at the door, the
familiar idea of the dog is there as soon as the sound is heard; my idea of
it represents it in the act of barking, and my judgment, “the dog is bark-
ing,” may be regarded as the analysis of the idea of the barking dog which
has thus been put together by association. But it is different if the associa-
tion is not certain, if I hear unusual or imperfectly defined noises, such
as the cry of an unknown animal in the wood. Now there intervenes the
question, “What is that crying ?” and I am unable to put together any
definite image. I am certain, from the analogy of my former experience,
that the sound proceeds from a thing, but I cannot get any definite idea ;
the synthesis referring the sound to a thing remains uncompleted, and the
dent, something which presupposes and demands a reference to a thing. By our choice
of the adjective or verbal form, we indicate that there is a subject, of which the verb and
adjective are to be regarded as determinations. Grammar is right, therefore, in retaining
the substantive as subject, even when the concept of the verb is the first in the psycho-
logical series of which we are clearly conscious; it contradicts the fundamental presup.
positions of our thought, to predicate a thing of an attribute or activity. How far this rule
is subject to apparent exceptions will be discussed hereafter.
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LOGIC
thing can only be denoted by a “something” which is quite indefi-
nite.
It accords with this that we are apt to look upon the sounds which we
hear as independent objects, and to abstract from the things producing
them. Having a longer or shorter duration in time, and definite limits,
they are apprehended as distinct phenomena; and substantives like thun-
der, shot, whistle, call, etc., waver between being abstract nouns, which
point to a thing, and concrete subjects which denote independent objects,
and of which, in their turn, verbs may be predicated :—a call resounds,
1.g., where there is no reference to the person who calls. The same thing
occurs in the region of the other senses. Coldness and warmth are on the
one hand names of the attributes of a thing ; on the other they appear as
independent existences, the question of the subject to which they belong
remaining in the background. Here, again, the synthesis by which thought
adds a thing to every sensation (which can at first be expressed only by an
adjective or a verb) is not complete—or, at least does not find complete
expression.
3. By recognising the twofold synthesis in all propositions which ascribe
actions or attributes to a subject-thing, we obtain the key to the solution of
the difficult and much-discussed question as to the logical nature of the
so-called Impersonals; more correctly speaking, of impersonal proposi-
tions.
Amongst the statements which contain a predicate-whether a simple
verb or the verb “to be” combined with an adjective or substantive,
without any expressed or definitely denoted subject, it is important to
distinguish two classes; those which are really impersonals, and those
thought of the thing to which the predicate would apply is entirely
wanting, in which we cannot even ask what the thing is. The others are
propositions in which a subject, though not named, is nevertheless implied,
although the idea may be indefinite and denoted only by the neuter
pronoun or the terminal inflection. When we say in German “mich
hungert,” “mich dürstet” there is no room for the question what
“hungert mich"; any more than a substantive can be added as subject to
“pudet,” or “pænitet.” But when I say “it is beginning,” “there it
goes,” “it is over,” “it is finished," I always mean something definite, a
series of events either expected or going on: a play, a piece of music, or a
battle; and I assume that the person who hears me has his attention
SIMPLE JUDGMENTS
directed toward the same thing, so that any more accurate denotation is un-
necessary. Here "it" is a real pronoun, which is only chosen for the sake of
brevity, because the express denotation of what I mean is superfluous, or
perhaps owing to the nature of the thing meant, too circumstantial. In
the same way when I say, “it is slippery, dusty, wet,” I mean the roads ;
it would be difficult to name a definite subject in words, because of the
indefinite extension of that which is slippery or wet; on the other hand,
the subject is already indicated definitely enough by the nature of the
predicates belonging to them. When we say “it is shady, it is full,” we
can only mean a certain space; when we say “it thaws "-snow and ice.
It is true that an imperceptible transition from one class to the other
often takes place; and we cannot tell from the mere grammatical form
whether or not the pronoun “it” or the personal ending of old languages
still indicates a subject-thing to which the predicate applies. This explains
why the two classes of so-called impersonals are often confused, although
in extreme cases they are definitely distinguished. It explains also why it
has been thought that for all impersonal forms we must be able to find a
subject in the sense of a thing to which the predicate belongs as its
attribute or activity, though all that could be finally found to serve as such
a subject was an indefinite idea of the totality of being, an idea which no
one really thinks of in speaking of a particular perception.
When real impersonal propositions serve to express something which is
accessible to immediate outer perception,-it thunders, it lightens,—then
we start from a simple sense-impression to which neither perception itself
nor memory supplies a subject. When, for instance, I see a rocket rise or
hear a carriage rattle over the pavement, the action immediately added to
the sound or sight which was given alone is naming, the unification of the
present impression with a familiar idea. This naming may take place by
means of uninflected, onomatopoëtic words, which merely reiterate the
special characteristics of the impression; or by substantives (that is
thunder, that is lightning) which, wavering between concrete and abstract,
leave it undetermined in what direction thought will proceed to follow out
the event. But language, guided by experience of similar cases, offers
verbs for the temporal event, and the present perception is expressed by
means of the customary inflections, the justification of this being that
the personal ending of the third person was without doubt originally a
demonstrative adjective. If a substantive were added, it would interpret
what was thus indicated, and would determine it more exactly as the
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thundering thing. But if this reference which the verb implies cannot be
actually carried out, then only the impression itself remains as the subject
of the statement, and the termination can indicate nothing but the present
impression. The reference to a subject-thing which is contained in the
pronoun of modern languages is then an empty customary form; we
cannot ask “what lightens ? ” and answer “it” in the sense of a thing,
however indefinite. All that the impersonal proposition can do is to name
the phenomenon present at the moment; the subject is nothing more than
the particular flash of light itself.
This limitation becomes very clear in cases where we know quite well
what the thing is which flashes or makes a noise, but omit any expression
of it in language as a matter of course, because we are interested merely
in what is seen or heard. “Es läutet," " es pfeift," " es klopft,” we say in
German, when we are quite certain as to the nature of the cause of the
sound. What we are interested in is the signal we have heard and its
meaning; there is no object in saying who makes the signal. In the same
way "es brennt” lays stress upon the fact that a fire has broken out; of
11
something burning, it is merely the fire itself as perceived by us.
Nor is there any doubt that this limitation of the statement to the state
which is perceived or felt, applies also to the numerous impersonals which
express subjective states of feeling—“Mich hungert, dürstet, mir ist heiss,
mir schwindelt, ekelt, graut,” etc. permit of absolutely no reference of
these verbs to a subject of which they are the activity. Nothing is given
but the present feeling itself, and this contains no reference to a thing
giving rise to it.
Again, we find also statements which express in the passive form, and
without any reference to an agent, an activity which has been perceived :
“es wird gespielt,” etc. Here again, all that we do is to name the event
perceived without proceeding further to the denotation of the subject in
which it takes place. For further examples I may refer to my above-
mentioned treatise.
The way is already prepared for this separation of the synthesis of naming
from the synthesis which refers the named phenomenon to a subject-thing,
by the distinction between the verbal forms of substantive, adjective and
verb. From verbs and adjectives we can abstract substantives which
enable that which generally appears as dependent upon a thing to be
thought of by itself; we can make use of infinitives (I hear talking, ringing,
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etc.), which are quite impersonal; and in the same way a statement is
possible of which the logical subject is nothing more than the event or state
perceived at the moment.
These propositions are “ without a subject" only in the narrower sense
that a subject-thing is wanting; they are no exception to the general nature
of the proposition which expresses a judgment. They contain the synthesis
of a known general idea with a present phenomenon; and it is this
phenomenon which is the subject, and which is indicated by the personal
ending with its originally demonstrative significance.
But just because they name something which is present, such proposi-
tions also contain an implicit statement of the actuality of the event named ;
for it is always immediately assumed that the particular object of perception
is something actual. This does not, however, make them existential
judgments in the ordinary sense; when we say “it lightens !” we do not
mean to predicate actuality of the lightning, but to predicate lightening of
something actual. The naming of the present impression is the funda-
mental act, without which the proposition, as the expression of present
perception, could never come about. When we say “it lightens, it
thunders,” we must have seen a flash in the sky and recognised it as light-
ning, we must have had a sensation of sound and called it thunder ; but
all that we directly say is that what we have seen is lightning, and what
we have heard, thunder. It is true that the hearer goes through the same
process as with an existential judgment. He first receives the general idea
of lightning from the word, and by its inflexion is called upon to think of
the flash of lightning as particular and present; to this general word he
must add in thought the corresponding particular phenomenon. So far
those who start with the completed proposition and explain it grammati-
cally are justified in emphasizing this view, according to which the judgment
declares the actuality of the lightning. In some cases of propositions
derived from the original form this declaration of existence comes to the
fore for the person speaking as well; when, for instance, his information is
based upon memory or hearsay, and also in the future tense and in general
propositions. “It often rains in the Alps” means — “raining often
occurs”; it is the two-sidedness of the original form which makes this
application of it possible.
- § 12.
Those judgments which predicate a relation of a definite particular thing
contain a manifold synthesis. The connection which is brought about by
S. L.
U
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the relational idea itself takes the place of the unity of the thing and its
attribute or activity upon which the judgments treated of in § 10 are
grounded. Every relational idea presupposes at least two points of
reference which are thought of as independent; these it connects by an act
of mental reference, though not coalescing with either. Thus a judgment
stating a definite relation between given things, names the given relation
by a general relational idea, and at the same time unifies the necessary
points of reference with definite objects.
Logically considered Existential Judgments come under the same point
of view as Relational Judgments; what they express in the first instance is
the relation in which an object of thought stands to me, the subject think-
ing and intuiting it, but the meaning of their predicate extends beyond
this mere relation.
I. Judgments which state relations (A is equal to B, different from B,
greater than B, to the right of B, to the left of B, earlier, later than B,
etc.) contain a synthesis of another kind from that contained by statements
which ascribe attributes and activities to a subject. These predicates
remain distinct from the subject-idea ; no inward unification can take place
between them. Their predicates never belong to the subject when thought
of alone as this particular definite thing; whether they are affirmed or
denied of the subject nothing is changed in the idea of the subject itself.
For my thought the sun is just the same sun whether it is to the right or
the left of me, whether it is visible or invisible; the different predicates
do not affect the idea of the sun itself, as when I say, “ the sun is pale,”
“ the sun is blood-red,” “the sun moves," "the sun stands still.” The pre-
dicates considered hitherto, whether predicates of denominative judgments,
or attributes and activities, form a part of the subject-idea. But in order to
state a relational predicate I must pass beyond the idea of the subject, and
must first place it in relation to something else, and then realize what kind
of relation that is.
The peculiarity of relational ideas consists just in this—that they pre-
suppose at least two objects, which are in the first place thought of as sepa-
rate and independent of each other ; our ideas of these must be already
there before a relation can be stated of them. Thus the unity which binds
together the elements of relational judgments is of quite another kind
from the unity of the constituent parts of a particular object which can be
thought of alone; it is contained only in the relational idea itself, and in
this therefore lies the ground of the peculiar synthesis now before us.
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67
It follows further from the nature of the connection between these
relational ideas and the points of reference presupposed by them, that
every relation between two objects A and B can be apprehended and
expressed in two ways, according as we pass from A to B, or from B to
A. The reference is always mutual, but the relations are of different
kinds; they may be the same, whatever the direction, or they may be the
opposite of each other—A beside B, B beside A, A equal to B, B equal
to A; or A upon B, B below A, A greater than B, B smaller than A.
relation how a given reference shall be apprehended or expressed. Thus,
every relational judgment implies in its nature a second equivalent one,
every relational concept has its correlative concept.
2. If we look for the psychological ground of the synthesis brought
about by relations, we shall find it most easily in spatial relations, as these
are immediately intuitable. It belongs to the nature of our idea of
spatial things that we can never perceive them apart from their surround-
ings, and from these we have to separate them as particular things. In
intuition itself, before any conscious reflection takes place, we combine the
particular parts of all that is perceptible around us into a spatial image ;
and thus every particular thing appears to us as comprehended in a larger
spatial whole. We are able to isolate a particular object--this tree, this
house-and attend to it alone, and the fact that a great number of parti-
cular things are movable favours this isolation by enabling us to think of
them as disengaged from any given surroundings. But wherever we may
perceive them they always stand amongst others in one continuous space.
As soon as we pass beyond the intuition of the particular thing, we find
others already there occupying a definite position. We distinguish and
become conscious of the directions in which we thus pass beyond one
Thing to combine it with others—directions which originally all have
reference to our own standpoint, such as right and left, before and behind,
above and below; and in so doing we analyse the complex picture pre-
sented to us, and express it by means of general relational concepts which
represent the particular kind of unity in which the spatial whole contains
its parts.
When I say " the house is on the road,” the starting point of my judg-
ment is a complex image of the house with its surroundings. I notice
bourhood, and call what I see here a road.
The position in which the
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two parts of my image stand to each other is immediate contiguity, and I
denote it by the preposition “on,” which is used to name this kind of
spatial co-existence. In the same way the propositions, “ The stork is in
its nest,” “ The dog is under the table," presuppose the same analysis of
a given complex image into its parts, and their particular kind of spatial
co-existence. It is the preposition, containing as it does the relational
idea and applying it to what is given, which expresses unification into a
whole, and which is needed by the hearer to enable him to unify in a
definite way the parts presented to him. In order then that the judgment
may be expressed, we must have a threefold naming of the particular parts,
besides the unity contained in the thought expressed by the relational
word. One of these namings preceded the judgment and appears in the
word by which we denote the subject; the other syntheses are expressed
by the judgment itself.
3. Now these various syntheses may be combined in various ways, and
take place in different orders. This is mainly because we are accustomed
to connect with every object the thought of relations in which it may
possibly stand. When two objects, A and B, are presented to me side by
side, I may look at A first; but since every object stands in spatial
proximity to others, the idea of something next to it presents itself, and I*
proceed to make this second point of reference clear. On the other hand,
I may start from B, connect the relation first with it, and then attribute
this relation to the second point A as subject. Finally, I may look at
both together and determine their relation to each other. These different
ways of proceeding are expressed as A next to B; next to B, A; A and
B next to each other. This is most obvious in those spatial relations
which start from myself as point of reference. A judgment such as
“Socrates is here” proceeds from an intuition which comprehends
Socrates and myself in one and the same space. Now in every intuitable
idea of a space, the place which I occupy and a space surrounding it is
posited, and this idea, which always accompanies me and which is ex-
pressed by “here,” is added to the intuition now given and unified with
it. But the space surrounding me must have something in it; it is the
general possibility of something else, and in the present instance this some-
thing else is Socrates. Socrates occupies the vacant position of the “here."
Thus our natural way of describing such relations as these, in which I am
first conscious of my own position as point of reference, is to place the local
predicate first. (To the right is A, to the left B, before C, behind D.)
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On the other hand, it may happen that what we first observe is one of
the objects-it is recognised as Socrates. But with this idea, as with that
of every other spatial thing, we can at once connect the idea of a sur-
rounding, of the proximity of other things. Socrates is somewhere; and
this indefinite reference is now unified with the definite one; the space
surrounding him is unified with my space, with “ here.” In this case also,
then, a judgment such as “Socrates is here” may take place in two ways :
on the one hand, in answer to the question, “Who is here?” on the other,
in answer to the question, “Where is Socrates ?”
There are many predicates, primarily expressive of states and move-
ments, with which relational ideas may be connected to determine them
more exactly. The dog stands, sits, lies, denotes, in the first place, differ-
ent positions of its body, which have reference to it alone. But the verbs
themselves contain a further reference to that upon which it stands or sits,
or its definite place, and the relational idea connects itself with the
predicate as its more exact determination. In other verbs, such as
“ follow" and "fall,” a relation to something else is part of their meaning;
hence in such statements the synthesis of the thing with its state of
activity is also combined with the relation.
What is true of space-relations applies equally to time-relations. Here
again, from the nature of our apprehension, every particular object appears
to us in temporal connection with others, and as a member of a temporal
series running parallel to other temporal series.
4. The relational ideas denoted by like, different, similar, etc., are less
intuitable. Here the reference to something else is not given with the
intuition itself, but is added by our thought, which can, at will, bring to-
gether the most remote objects for its purposes of comparison. Two
things which are alike or different do not, apart from my reflection, form a
single whole, which can be resolved into its constituent parts; the unity
in which they are placed by the relational judgment arises from my con-
sciousness of mental activities having reference to the content of the objects
of thought. The immediate and evident certainty with which we appre-
hend and recognise likeness, difference and similarity in the simplest cases,
is apt to make us look upon these determinations as if they were some-
thing sense-given, and to overlook the particular functions through which
we become conscious of them-functions which always presuppose that
several objects are presented and compared as to their nature. Here also
the relational ideas, when taken alone, are quite without significance; it
would be meaningless to say A is like, A is different. Like and differ-
ent are really predicates only when combined with a definite point of
reference.
It is for this reason also that mathematical equations, of the form “ A and
B are equal,” cannot be looked upon as judgments which state the same
predicate of two subjects, such as “A and B are ten feet long”; for they
cannot be resolved into the two judgments, “ A is equal,” and “B is
equal.” If we start from both subjects then the full expression is, “ A and
B are equal to each other,” and here we have the two judgments, “A is equal
to B,” “B is equal to A”; thus the real predicates are “equal to B,”
“equal to A.”
A mathematical object again naturally calls forth the question, “What is
equal to it ? ” and has a reference beyond itself to something else. In the
same way comparisons between larger and smaller things are always forcing
themselves upon us ; then A> B or B < A according as one or the other
magnitude is first noted.
5. The causal relations, which are expressed by propositions containing
transitive verbs and their objects, are difficult to analyse because of the
with a definite intuition, which is to be narrated by the judgment, e.g. the
is immediately given together with the idea of the subject is its action,
which we can think of by itself as a definite form of movement. Butting,
striking, hurling, grasping, etc., all contain the idea of definite forms of
movement, which can be thought of without any reference to a particular
object, and can therefore be referred to the subject simply as its action.
But the judgment, “the bull butts," does not completely exhaust the
image, in which the bull is accompanied by the tree; that which happens
must somehow be expressed as a relation between the two. This may be
done by merely determining the general form of the movement by its
direction, as, for instance, by adverbs of direction (the bull “butts against
the tree”-local significance of the case and the preposition). So far the
only relation contained in the judgment is that necessitated by the spatial
nature of the movement in which the action consists, if it is to be expressed
as determined in the particular case. By specifying a definite object we
merely determine the predicate-idea more exactly; the idea itself is not a
purely relational predicate, it only includes an action which is made more
complete by a relational idea.
CD
SIMPLE JUDGMENTS
But if we look to the result upon the object of the activity of the subject,
the shaking and bruising of the tree, then to this extent the causal relation
appears. This result is no longer confined to the action of the subject in
itself, it extends to that which takes place in the object ; the effect, as
such, lies outside of the efficient agent. The general idea denoted by
“ butting” no longer contains merely a form of movement which needs a
subject, but a movement which has the effect of shaking or crushing some-
thing else. When we look upon what takes place as conforming to the
idea of butting in this sense, we must determine the idea more exactly by
reference to a definite object, and this gives us the first two syntheses; the
reference to the subject is the third.
In the case of verbs, whose nature it is to signify an effect, production,
annihilation, destruction, etc., the causal relation is to be found in the
meaning of the word itself; it is the generalization of definite effects
upon various particular objects, and it necessitates a something which is
produced or destroyed. “To cause,” and “to cause something,” are
equivalent expressions; the idea of an object, which is affected by the
activity expressed in the verb, and with which the given object is partially
unified, is more or less definitely connected with the verb itself. The
meaning of the word includes also the idea of the second point of reference,
the source of the effect, and with this the subject is identified. The
meaning is just the same whether I say, I eat, I eat something, or I eat
food ; whether named or not, the two points of reference are given with the
verb. The point to notice is that now the process is reversed—the idea of
action is included in that of causation, and the syntheses brought about
by the relation are accompanied by the syntheses in the category of action.
We may see how these syntheses may succeed each other from the ques-
tions, “Who causes B? What does A cause? What is A doing?”
6. The nature of this relation shows itself in the interchangeableness
of the active and passive forms by which the same event can be expressed.
When I say, “The stone is thrown,” the event is not expressed as it first
appears to us, i.e. as action of the stone (the stone flies). Instead of this
first immediate statement there is substituted the more distant relation,
which denotes this action as the effect of something else, and with the
idea of which is connected definitely or indefinitely the thought of the
whence of this effect. Thus predicate-ideas which are denoted by passive
verbs cannot be subsumed under that form of unification which has for
its ground the category of action ; they are neither more nor less than
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LOGIC
relational predicates, although they include an action having reference to
the subject alone.
It is true that these simple and different fundamental relations are fre-
quently concealed by infinitely varied forms and disguises of verbal
expression. The forms of language as ordinarily understood, are far from
coinciding exactly with the distinctions of the idea. “To suffer” is itself
an active verb, and we generally forget that as such it represents the subject
in the activity of endurance or of feeling pain; as a rule we think of it
only in opposition to efficacy, as the relation to some efficient agent.
7. The predicate“ to be,” in the so-called Existential Propositions, must
also be regarded as a relation—that is a modal relation—though it occupies
a unique position.
In the first place, there can be no doubt that in their external form
these propositions exhibit exactly the same structure as any other proposi-
tions, whatever their verb. “Being” is stated of that which is denoted by
the subject-term, and thought of under the subject-term, and a definite
unity is brought about between the subject and the general concept of
Being. In these judgments, therefore, as much as in any others, a synthesis
of distinguishable thoughts takes place. Nor can the question, “does A
exist ? " be understood except as expressing the doubt whether actual ex-
istence can be declared of the A we are thinking of, whether it is in
accordance with truth to connect the thought of existence with it.1
1 Brentano (Psychologie vom empirischen Standpunkte, vol. 1, 1874, p. 266 sq.) disputes
the ordinary doctrine that a connection or separation of two elements takes place in every
judgment. According to him, the essential characteristic of judgment is acknowledgment
or rejection, which refers to the object of an idea ; in acknowledgment and rejection con-
sciousness is related to an object quite otherwise than when framing an idea of it. But
in acknowledging and rejecting we are concerned sometimes with connections between
ideas, sometimes with isolated objects. In the proposition “A is,” the object of our
acknowledgment is not the connection between a characteristic “ existence" and A but
A itself.
It is undoubtedly true that judgment does not consist merely in a subjective connecting
of ideas, and we shall deal more fully with this below (§ 14). But that there is a kind of
judgment which contains no connection of ideas at all, that in addition to judgments
having two terms there are to be found judgments having one only, and that these judg-
ments of one term are none other than existential propositions—this I cannot allow.
When I form the idea of an "object" A, I am first conscious of it as an idea, as something
thought; its primary relation to me is that of being the object of which I form an idea.
In so far as I actually have an idea of it, I cannot reject it; and should I wish to
acknowledge it, then all I could acknowledge would be that I actually have an idea of
it. This “ acknowledgment,” however, would not be the statement of its existence.
The very point in question is whether, in addition to my having an idea of it, it is further
implied that the object forms a part of the actual world surrounding me, can be perceived
SIMPLE JUDGMENTS
About the meaning of the predicate also there can be no doubt, if we
start from its popular meaning as it appears before critical and philo-
sophical reflection; though indeed we cannot define the concept of Being,
nor derive it from other concepts, but can only contrast it with its opposite.
“Being ” is opposed to that which is merely an idea, a thought, an imagina-
tion. That which "is” is not merely produced by my mental activity
but is independent of it, and remains the same whether I am thinking of it
or not. Being belongs to it in the same sense as to myself; it is opposed
to me, as I think of it, as something independent of my thought, something
which is not made by me, but only recognised in its independent exist-
ence. But although the chief meaning is this independence of the existent,
the judgment also includes an open or concealed reference to myself, as
the subject which is thinking the existent and which can be actually
affected by it.
The attempt to derive the thought of being from anything else is as
vain as the attempt to find an explanation of self-consciousness in the
unconscious. It is included in self-consciousness from the beginning; as
often as we say “I” it is present in thought, although not expressly empha-
sized. In the same way it is from the first inseparable from the objects of
our intuition and thought, for we never find ourselves conscious without
being surrounded by a world of objects which are, in just the same way
is, and as opposed to other things which are not ourselves.
from this original connection with the consciousness of ourselves and of
the objects before us, or for expressly declaring Being of ourselves and of
the external world. This is because the thought never arises that it is
by me, and can take effect upon myself and other things. If I wish to maintain the
existence of the object, I must connect this last thought with the mere idea. When I
begin a proposition “the tower of Babel—" these words are in the first place a sign that
I have the idea of the tower of Babel as it is aroused by the story in Genesis, and this
same idea is excited within any one who hears me. So far the idea is simply there, and
as such it can neither be rejected nor does it call for any acknowledgment. But now the
question arises, “ What is the meaning of this idea ?” If I complete the proposition by
saying "the tower of Babel exists,” then I pass beyond the mere idea and state that the
then what I have rejected is not the idea of the tower of Babel, but the thought that
it is the idea of a visible and tangible thing. Thus what is acknowledged or rejected by
me is not the idea of the tower of Babel, but the thought that the given idea corre-
sponds to an actual thing—that is, a connection. On this whole question cf. my die
Impersonalien, p. 50 sq.
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S
possible for me not to be, or that the whole external world might not be;
it is quite superfluous to assert that I am, when neither I myself nor any-
one else doubts it. Only in an advanced state of reflection can we attain
to an express consciousness of our own being; at first my being is indis-
tinguishably included in the immediate consciousness of myself; the only
question is, in what state or activity do I find myself.
Immediate sense-perception does for external things what this immediate
self-consciousness does for myself. If we reflect, and consider what it is
that induces us to acknowledge the being of particular external things, we
find that it is sensation. That which we touch and see is there, and when
we try to realize what we mean by Being, we find that we connect with it
the idea of being perceived, and of the possibility of being perceived, the
capability of taking effect upon the sense-organs of a feeling subject. But,
being perceived is not Being itself, it is only its sign and consequence ;
Being does not begin with being perceived, nor does it cease when being
perceived ceases. That which is perceptible must be in order that it may
be perceived, and the perception of a thing is only the most direct and
irrefutable proof that it exists.
When we attribute Being to insensible or supersensible things, as in the
ontological proof of the existence of God, or in the conception of things
per se, we have always a difficulty in freeing ourselves entirely from the
spatial ideas which accompany the thought of being in the world of sense.
We say that “there is a God,” and when we try to impart greater reality to
the thought, we can only do so by including in it an effect upon a per-
ceptible world, in and through which there is an effect upon us by means
of which the non-sensuous reveals itself and may be known. But this
efficacy is not the origin of the thought “Being,” it is merely a conse-
quence of it, and hence the ground of our knowledge that the efficient
agent is.
Here we see clearly the peculiar difficulty which this concept of Being
brings with it. On the one hand, it cannot be spoken of at all without
presupposing a relation to me, the person who thinks of it. I have an
idea of the object because it has entered into some relation to me; that it
is, is my thought. But by this very thought I set aside this mere relativity
and declare that the existent is, apart from its reference to me or any other
thinking creature; that its being does not wholly consist in the relation of
being thought as an object of my consciousness. The Herbartian formula
of absolute position in its double meaning combines these two aspects, with-
SIMPLE JUDGMENTS
75
out however solving the difficulty ; but it has at least the merit of having
made clear what it is that our natural thought really means when, careless
of difficulties, it predicates Being.
If we wish to analyse and understand existential propositions, we must
start from this meaning which they have in common use, before they have
been critically approached ; and then the question arises : what do we
think when we say A exists, and in what sense do we declare the unity of
the subject and predicate ?
In order to answer this question, we must first see what is the general
presupposition which gives rise to the judgment " A exists," as a judgment
concerning a particular thing in the ordinary course of our thought.
Evidently this presupposition is, that some doubt has been or may be
raised as to the existence of the subject; and this is only possible when
that which the subject-word originally signifies is merely an idea, something
which appears in consciousness either in the form of memory or as occa-
sioned by communication from others. Concerning that which is immedi-
ately present, I cannot ask whether it exists ; certainty of its existence is
given by the way in which it is intuited. But I learn from my experience
of the passing and vanishing of things which I have previously seen in
definite places, and from my experience of being deceived by others, that
not everything of which I form an idea is also to be found in actual per-
ception. Thus I am driven to distinguish between the intuition of that
which is present and the mere idea, to which there is no corresponding
intuition present. When I have lost anything, when I fail to find what I
formerly possessed or knew, then, though I have the image of the thing in
my memory, the present intuition is wanting; it is not there, not forth-
coming, not to be found. It is only the idea of the thing which is present
in my consciousness as subject idea, and to this I seek the corresponding
perception. Only in reference to such an idea is it possible to raise the
question as to its existence, and the meaning of the question is whether
that of which I have an idea still forms a part of the perceptible world.
Thus in every existential judgment the subject-word becomes a sign of
something which is merely an idea, from the very fact that the thought of
its existence is withdrawn from it in order that it may for the first time be
expressly attributed to it. This happens as soon as I have found what was
wanting, i.e. as soon as I have experienced the corresponding perception,
or have convinced myself through some process of inference or through
information from other people that it is still perceptible somewhere. Thus
S
!
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all existential judgments within the sphere of the empirical world rest upon
the distinction between the merely inner idea (of memory or of fancy) and
present perception ; and what they assert is the identity of that which is
perceived and the mere idea which is named as subject.
This is especially clear when my idea of the object whose existence is
in question has only been communicated to me from other people. They
create in me the idea of a Hercules or a Theseus, of the Tower of Babel,
or of the magnetic mountain ; thus the question arises whether these have
existed, whether therefore the ideas connected with the words are ideas of
real beings or are mere imaginations, whether the information is based
This throws light again upon the proposition so strongly emphasized by
Kant : that the predicate “to be” adds nothing whatever to the content of
the idea as such. Whether I say “ A is ” or “ A is not,” my thought of A is
just the same; the meaning of the statement itself demands that neither
more nor less shall be present in the actual world than just the A thought
by me. Thus“ being” forms no part of the subject-idea, no “real pre-
dicate," as Kant says; it merely expresses the relation of the A which is
thought to my faculty of knowledge. The synthesis, then, which is
primarily contained in the existential judgment referring to the empirical,
is the identity between an object as idea and an object as intuited; it is
due to the fact that I may be conscious of the same contents in two forms,
in the form of the mere idea and in the form of intuition. The thought of
“ being” is immediately connected with the intuited object.
So far existential judgments reverse the process of denominative judg-
ments. In the latter the object is given as intuited, and is therefore thought
of from the first as actual ; to it is added an idea which was known before,
and the agreement of the two is declared in the denominative judgment.
In the existential judgment it is the mere idea which precedes, and it is
then said to agree with a particular object of intuition.
But while this relation—the agreement of the idea of a thing with a
possible perception-is its chief significance, the meaning of the predicate
“to exist " extends further. That which exists does not stand in this
relation to me alone, but to everything else which is; it occupies space
between other objects, it exists at a definite time before and after other
things, and it stands in causal relations to the rest of the world ; hence even
of the perceptible we may assert an existence which is merely inferred.
Herbart finds in the concept of Being complete unconditionedness and
SIMPLE JUDGMENTS
77
absence of relations, and against this Lotze rightly shows that what we
think of in the concept of Being is just this fact of standing in relations.
From this point of view the ever-present thought of an actual world
around me is presupposed in every existential judgment; such a judgment
merely supplies a definite subject for some place in this totality of the
existent. It is always assumed that there is something external to me;
the question is whether the object of my thought is to be found in that
which is given, or whether something actual falls under a certain concept.
This last train of our thought leads to those statements in which the
expression of being stands first, and which are thus akin to the impersonals.
To some extent also they assume the outer form of impersonal propositions
-OTi, there is, es gibt — these phrases first indicate something which
exists, which is, is there, is offered to us by the world which is presented, in
order to denote it more definitely afterwards. This form of the existential
proposition, then, is the natural one, when the question we are dealing with
is not whether a thing is present which we think of as definite and par-
ticular (perhaps because we knew it before) but whether a thing exists
which falls under a given concept and can only be denoted as “an A.”1
§ 13.
Those judgments concerning particulars in which the subjects are
abstract nouns and the predicates, adjectival or verbal, cannot be brought
under the categories of thing, attribute and activity. The first synthesis
upon which they are grounded is to be found either in the unity of the
attribute or activity with its modification, or in that view of a thing which
attributes a predicate to it merely because of some given attribute, activity
or relation.
1. The first, and, to an undeveloped thought, the natural way of
regarding perceived events, is to refer them to concrete things, and to
express everything which is and happens as attribute, activity and relation
of particular things; there are few propositions in Homer of which the
subjects are not particular persons or things. It is only when thought
comes to distinguish more accurately and compare more extensively that
we have any occasion to employ the attributes, activities or relations of
particular things as independent subjects of a statement. This may be
1 Cf. my Impersonalien, p. 65 sq.
LOGIC
exactly an event or attribute, or in order to refer a causal relation to one
definite element of a thing.
2. In judgments such as “this red is bright,” “ the gait of this animal
is a hop," there is presupposed the judgment of attribute or activity which
breaks up the presentation into a thing and its determinations. The
synthesis of the judgment consists partly in the synthesis of the attribute
or activity with its modification, partly in the naming of the latter (cf. $ 6, 2,
P. 32 sq.).
3. Before an attribute or activity can be the subject of a causal relation
the general idea of an efficient agent which is originally connected with a
thing as cause must have been more exactly determined by a process of
comparison ; so that a thing is regarded as taking effect only by virtue of
one of its attributes, or only in so far as it is engaged in a certain activity.
When we say that friction warms, and weight is oppressive, the true
subjects belonging to the verbs are the body by which the friction is pro-
duced and the heavy thing; these alone are capable of causing an effect.
But by comparison our thought distinguishes that element in the body in
virtue of which it gives rise to the effect, and expresses it by an abstract
noun, because in this way the event can be presented as the expression of
a general law.
4. Relational ideas also-such as distance, difference, etc.—can in the
same way appear as the subjects of adjectives or verbs which express an
effect. When the attraction of two bodies is diminished by their distance
the words in which the change is stated attrïbute an efficacy to a spatial
relation as if it were a substantial cause. But there is no need to prove
that this is a mere abbreviation.
We know from general laws, which include both the fact of the efficacy
and the conditions of its modifications, that a certain result will necessarily
follow upon the change in distance, and this result is stated as the effect
of the change itself. The higher the abstractions in which our thought and
knowledge move the more unsuited to them do the original meanings of
words and constructions become. Without our perceiving it, language,
chiefly by the aid of abstract nouns, abbreviates and leaves unexpressed
that which mental habits lead us to understand as a matter of course.
The complex relations of scientific laws, according to which the parti-
cular event depends upon many conditions, are forced into simple forms
of expression in such a way that the efficient cause itself appears
insignificant in comparison with the varying circumstances under which it
SIMPLE JUDGMENTS
79
takes effect. The original idea of efficacy is attenuated into the uniform
interdependence of different movements, and this is adequately expressed
by a mathematical formula, but can only be represented in words by the
aid of figures of speech and metaphors which we have ceased to feel
as such.
§ 14.
The unification of different ideas does not exhaust the nature of judg-
ment.; every complete judgment as such includes also the consciousness
of the objective validity of this unification.
But objective validity does not, as might be supposed, rest immediately
upon the fact that the subjective connection corresponds to the relations of
the corresponding existent; it rests upon the necessity of the unification.
This necessity has its root in the principle of agreement, and this again
presupposes stability in our ideas; but these logical principles can give not
assurance of the real identity of things.
1. Those definitions of the judgment which limit it to the merely sub-
jective connection of ideas or concepts, overlook the fact that the import
of a statement is never merely to assert the subjective fact that I, at the
moment, make such a connection. On the contrary, the judgment, by the
form it assumes, claims that the connection is true of the objects them-
selves, and that just for this reason it must be acknowledged by every one.
It is this which distinguishes the judgment from the merely subjective
combinations of ingenious and witty comparisons which assume the outward
form of the proposition, but do not aim, like the judgment, at making an
objectively valid statement. In the same way the judgment differs from
mere conjecture, opinions and probabilities.
2. But objective validity has more than one meaning. In the first place
we must distinguish a verbal, nominal validity, from a material, real validity.
When I say “this is red” the first question which may be raised is, whether
what I call red is what every one else calls red. Then the objective
validity, which may be denied of my judgment, refers to the general use
of language, which is opposed as an objective rule, or general law, to sub-
jective caprice. All verbal disputes turn upon the question of this validity;
such disputes are possible partly because the subjective meaning of words
for the individual differs from that which is generally recognised, partly
1 Ueberweg, for instance, $ 67, gives a correct definition from this point of view, when
he says : the judgment is our consciousness concerning the objective validity of a subjec-
tive connection of ideas.
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LOGIC
because language is not absolutely fixed even in its general use, and be-
cause the boundaries of particular words are fluctuating.
3. But when the nominal correctness which is implied 1 in every judg-
ment, inasmuch as it is spoken and meant to be understood, is present,
when the speaker connects the same ideas with his words which every one
else connects with them, then the point to observe is that the connection
of ideas is stated as objectively valid, and the spoken proposition as true,
so that every one is called upon to believe it and to judge in the same
way about the same subject.
To determine the meaning of this material validity is not so simple as
might appear when it is said that the same connection must exist between
the corresponding objective elements as between the elements of the
judgment; or, that what is thought must actually happen. For it is the
peculiarity of our thought, when judging, that its processes are incongruent
with the existent to which they refer. Let us confine ourselves to the
judgments so far considered : those which ascribe attributes and activities
to particular things, or denote things by a name. In the first place we
find that there is nothing existent which agrees with the predicate-idea in
the same sense as there is something which agrees with the subject-idea ;
for the predicate-idea, as such, is from its nature general and does not
refer directly to any particular thing which is thought of as having a
particular existence. All words (with the exception of proper names) are
the immediate signs of ideas which, though formed from intuitions of the
| Marty has made the following objections to the view that every judgment contains
the implicit statement that its terms are correctly used (Vierteljahrsschr. fiir wiss. Phil.,
1884, VIII., I p. 85). “When, in good faith, I state the proposition, “This is snow,' it
is, no doubt, presupposed that I believe what I call snow to be called snow by every one
else. But we cannot say that this judgment concerning language is implicitly contained
in the statement.” But suppose I say to some one, “ That is crimson,” and he replies,
“No, it is scarlet,” does he mean to say that I am wrong as to the colour itself, and see
a different colour from that which the object really has ? or does he not rather mean that
I am mistaken in my denotation, that I am calling crimson what, in the ordinary use of
language, is called scarlet ? Thus the judgment, “That is crimson,” contains the state-
ment that I not only see the colour rightly, but also give it its right name ; for to this
latter part only did the “ No ” apply. Marty goes on to say that there is no need for
the judgment as to language (the agreement of my use of language with the ordinary use)
to be present to consciousness in any form when I utter the proposition in question.
“It is enough that it has previously been there, and that a habit of speech, which can now
act by itself, has been formed on the ground of our confident assumption of it." Thus,
according to Marty himself, my judgment includes a confident assumption; all that he main-
tains is that it need not always come into express consciousness. But what does this
mean, if not that it is implicitly contained in the statement?
SIMPLE JUDGMENTS
81
existent, do not represent it as particular, nor as it exists in particular
given cases. Again, the judgment presupposes the mental separation of
subject and predicate; it takes place in the recognition of the unity of
two ideal elements which, for our consciousness, had formerly a divided
existence. There is no such separation in the existent to which our
judgment refers. The thing exists only with its attribute, the attribute
only with the thing ; the two form an undivided unity. In the same way
a body exists only as at rest or as moved, its state is not separable from it
in reality. Thus the general and the particular, predicate and subject,
with their preliminary separation and act of unification, find no counter-
part whatever in the existent; we cannot say that the connection between
the elements of the judgment corresponds to a connection between
analogous objective elements. Only when, by the act of judging itself,
we do away with the subjective separation between subject and predicate,
and thus think of the two as united, do we revert to the existent, which
itself remains an undivided unity and never undergoes an actual separation
corresponding to our mere distinction. There has been no “distinctio
realis” corresponding to the “distinctio rationis.” If, then, it is the
essential characteristic of judgment to be a function of a merely subjective
kind, its objective validity must have some other meaning than that of the
agreement between the connection in the judgment and an objective
connection; a meaning which can only be understood when we take into
consideration the peculiar nature of our predicate-ideas.
4. The simplest judgments are those which are merely denominative-
judgments, declaring the immediate coincidence of images, unmediated
by subsumptive inferences. Presupposing nominal correctness, it is
necessary to the validity of such a judgment, as ordinarily understood,
that intuition and idea should coincide—a relation which is purely mental.
It is also necessary that the subjective intuition, which claims to be the
copy of an objective thing, should really correspond to this; i.e., that the
subjective image which is present should be that which, according to the
general laws of our sensual intuition, would necessarily be aroused in
everybody by the same object. The judgment, “ This is snow," is
objectively valid when that which is seen coincides with the idea called
“snow” by every one, and when, moreover, it is seen distinctly by an eye
in a normal condition. Objective validity then reduces itself to this : that
both the process of forming the intuition and the act of judgment take
place in a way which is universally valid. When there is agreement as to
S. L.
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LOGIC
the meaning of the predicate, any dispute which may now arise can only
refer to the question as to whether the person giving utterance to the
judgment, “ This is snow,” sees correctly; i.e., sees in the same way as
every one else, and under the conditions of correct knowledge. In par-
ticular cases this is purely a quæstio facti which differs with the individual,
and cannot be determined according to any general rule. But the general
question as to what authority we have for referring our ideas to real
objects, and for attributing an existence independent of ourselves to what
we perceive, does not belong to logic. The presupposition, upon which
all ordinary thought is grounded, that we know an existent, may be
affirmed in the realistic sense; or it may have its meaning so changed in
the idealistic sense that Being merely denotes something which is thought
of necessarily and by every one in the same way. But in either case the
subjective functions, which are active in judgment, remain the same.
Concerning the metaphysical validity which we attribute to ideas, our
Logic need come to no conclusion at present; it investigates thought as
a subjective function, and can therefore decide nothing as to the signifi-
cance of intuitions. But when an intuition and a predicate-idea are there,
we cannot allow that it is possible for the inward act of unification to
differ, that one man should posit like ideas as unlike, another different
ideas as like; for we find within us immediate certainty of the necessity of
our unification and the impossibility of the contrary, and should thus be
forced to exclude from the community of thought any one who should
arrive at a different result. In other words, the judgment has objective
validity for us because it is necessary to unify ideas which coincide. 1
1 It might be argued by one conversant with objective logic that after all the judg-
ment, “ This is snow,” is intended to state something concerning the nature and constitu-
tion of a thing, and that the question as to its objective validity depends upon whether
this is really snow or not. This would remind us of the question of the clever critic,
“How do the astronomers know that the star which they call Uranus is really Uranus ? "
It is a necessary condition of all use of words that at any given stage of our knowledge
“snow” shall, by general agreement, denote some definite idea, and that when we
give names we shall be guarded from confusion by the fact that the distinctions in
that which is presented are not more numerous than those of the ideas named. This
being presupposed, then, however we may turn and twist the statement, that this is really
snow, the question as to its objective validity still demands the answer given above.
Instead of an idea like the above, which was sufficiently characterised by sense-intuition,
I might take as the ground of my statement an exact concept with accurately determined
attributes. Then the statement “ This is snow,” would mean, " This has all the
characteristics of snow; it is white, it consists of crystals whose angles of contact are
60°; it becomes water at a temperature of o degrees.” But this brings me no further
with the question of objective validity beyond the statements : (1) That at the moment
SIMPLE JUDGMENTS
83
5. We might be tempted to recognise the fundamental principle just
found as that known in the traditional Logic as the PRINCIPLE OF IDENTITY;
for this principle of identity is there regarded as the ground of validity in
all judgments attributing a predicate to a subject, and hence as a funda-
mental law of our thought.?
Unfortunately, the word identity has in the course of time received
many meanings, and the so-called law of identity has been made use of
in very different senses.
my perception is correct, my senses do not deceive me and convey impressions to me
different from those which the same object at other times gives to me and to other
people ; (2) That the elements which I distinguish in this image exactly correspond in
detail with the ideas-white, crystals, melt, etc.—with which I am thoroughly con-
versant, and which are denoted by me as by every one else by these words--the total
idea thus corresponding perfectly to what I am accustomed to think of as “snow.”
Further, I am certain, in the first place, that I have not forgotten what “white," etc.,
means; and, secondly, that I do not identify blue or red when seen with my idea of
white, that, on the contrary, it is necessary that I should unify my perception with the
idea. There is no other objective truth and subjective certainty for this proposition,
nor can there be so long as the universal-as such—has its existence only in my mind,
and only the particular in reality.
Again, it might be said that the proposition, “ This is snow,” means that the thing
present is like or similar to other particular things which I have previously perceived,
and that it is this material likeness of existing things which forms the contents of my
judgment. But though this is indirectly contained in the judgment, it is so only in so far
as these particular things are also stated to be snow; the judgment would only be
multiplied by this explanation.
But then, it may be asked, does all error in this department consist in verbal mistakes
in denotation and false perception ? May there not also be false subsumption of the
particular under the universal in such a way that in the synthesis of two ideas unlike
things may be held to be like? This certainly happens, inasmuch as in no stage of our
judgment have we a sufficiency of ideas which are fixed in meaning, clearly distinguished
and named, to correspond to the manifoldness of the particular. Tà Mèv yàp óvbuata
TTETTÉpavtai kal TÒ TÛV lóywv años, tà è a páyuata Tov åplo uòv átreipá totiv (Arist., de
Soph., el. 1). It is the difficult task of science to establish a complete system of predicate-
ideas which shall be clearly distinguished and unambiguously named, and which shall make
any error of subsumption impossible. So long as this ideal is not attained both in
general and by each individual, there will always be particular ideas which cannot find
their corresponding general idea amongst those which are known and familiar to us; and
these, as an immediate unification is not possible, will seek their names by inferences.
If these inferences are hasty, and are guided merely by analogy in extending the use of
names, there will be errors ; but it will in the first instance be a nominal error, antici-
pating the formation of concepts in a direction in which it will not follow, and it does
not refute the principle given above, which is valid only where the general idea which
corresponds to the particular is already formed. Only so far, again, is perfect certainty
possible. When we reach the predicate by means of mere inferences of the ordinary
sort, we may indeed state it in words, but we cannot attain to the certainty of the
necessity of the act of judgment.
1 Cf. with what follows my article in the Vierteljahrsschr. für wiss. Philos., iv., p. 482 sq.
84
LOGIC
* In the first place, under the formula A is A, it was interpreted as affirm-
ing that every object of thought is identical with itself, that it must be
thought as just this and no other.
Then, as the principle of all affirmative judgments, it was said to state
that subject and predicate must stand in the relation of identity if the
judgment were to be possible or valid; possible, when the principle was
presented as a natural law according to which we always do think; valid,
when it was presented as a normal law according to which we ought to
think. In the latter case it was the criterion of valid judgments.
stating that everything which exists is absolutely identical with itself, and
that Being can therefore be attributed only to that which is absolutely
identical with itself, hence only to the unchangeable which contains no
sort of plurality.
We may begin by trying to determine that meaning of the term identity,
which its etymology points to as the most original, and which, except in
connection with this logical question, is generally accepted. Here, then,
identity means that what is thought of at different times, or under
different names, or in different connections, is nevertheless not two, but
one and the same object; it is merely thought of twice. The term cannot
be applied to an idea which is quite simple and occurs only once ; like
every relational concept, it requires two points of reference. I cannot
even recognise the identity of something which remains absolutely the same
unless I am aware that I have thought of it at different times and compare
the recurring ideas.
Now when we say that something which is thought of twice is the same,
we may mean one of two things; we may mean either a real or a logical
identity. A real identity is stated when two ideas, two perceptions, two
accounts, two names or other denominations are referred to the same
person, thing or event. It is in this sense that I state that the tragedian
Seneca is identical with the philosopher Seneca ; that the Hermes found
in Olympia is identical with the statue of Praxiteles, mentioned by Pau-
sanias; that the solar eclipse, predicted by Thales, is the same which took
place, according to astronomical reckoning, on May 25, 585; that the
person who met me to-day is the same whom I saw years ago in such and
such a place. This real identity does not exclude difference in the object
at different times ; the tree, which I have formerly seen in foliage, is now
leafless; the man is now grey whom I knew in his youth. But where we
SIMPLE JUDGMENTS
85
are not concerned with the reference of our ideas to particular things or
events in space or time, the identity must be logical, i.e. it must refer to
the contents of the idea as such. We say that ideas which we have at
different times and on different occasions do not differ, but are absolutely
the same as to their contents; thus, different words or expressions denote
the same concept ; different formulæ the same number. In so far,
then, as we abstract the attributes of different things and compare them
only according to their contents, we can even say the colour of one material
is the same as that of another, the length of one rod the same as that of a
second; but the materials and rods are not therefore identical ; they are
only alike in the given respect. In the same way, we speak in diplomatic
language of identical notes ; for, when the contents of the notes are the
same, we disregard the plurality of the documents.
This is the extent to which we can apply the word identity, if its original
meaning-and, indeed, any definite meaning-is to be preserved. From
this, it follows that identity is either complete or not at all; that identity
has no degrees, and that the expressions “partial identity,” “relative
identity,” if meant to denote kinds or degrees of identity, contain a contra-
dictio in adjecto. We can speak of an identitas partium (e.g., of parts of
Europe and parts of the Russian Empire), but not of an identitas partialis.
To return to our Principle of Identity. In its first meaning, the formula
A is A certainly expresses a necessary presupposition of all thought and
judgment. No thought nor judgment is possible, except when particular
ideal-objects can be retained, and reproduced and recognised as the same;
for no definite relation could be established between ideas which were
always wavering and shifting. Thus, all thought depends upon the stability
of our particular ideal-contents as its condition. In so far as the stability is
always realized to a certain extent, we may speak of a principle of stability
in the sense that it expresses a fundamental fact; so far as it is recognised
as the condition of all true judgment, the formula A=A contains also a
precept, which must always be satisfied if our thought is to be perfect.
But this principle, which refers only to the stability of each idea in itself,
cannot serve also as a ground for the union of the subject and predicate
in the judgment. For judgments which are meant only to state the identity
of an object of thought with itself are quite barren. No one thinks of
stating that a circle is a circle, and that this hand is this hand; and in
propositions which apparently correspond to the formula A is A, the
subject and predicate-terms really refer to different things. In the
D
86
LOGIC
proposition “ children are children,” the subject-term means only the
age characteristic of childhood ; the predicate-term the other qualities
which are connected with it. By the proposition "war is war," we mean
to say that when once a state of warfare has arisen, we need not be surprised
that all the consequences usually connected with it appear also; thus, the
predicate adds new determinations to the meaning in which the subject
was first taken.
But in the case of simple denominative judgments, we cannot speak of
the strictly logical identity of that which is represented by the subject and
predicate terms. In a judgment concerning a particular thing the predicate-
idea is generally the more indefinite, and does not exhaust all the speciality
of the subject-idea ; we can only speak of the agreement of the two. I
find again in my subject-idea the thought denoted by the predicate; the
particular thing is like the general image of my idea. Thus, it would be
more correct to call the ground of these judgments the Principle of
Agreement; it states the necessity that there should be agreement of
ideal content between what we connect as subject and predicate; that the
consciousness of this agreement should be expressed in the judgment. It
implies, moreover, that no thinker can be mistaken as to whether there is
agreement between the ideas present to him as subject and predicate, in so
far as they are present. Thus, the principle states the immediate and
infallible certainty of the consciousness of agreement, both as a fundamental
psychological fact and as a necessary presupposition of judgment.
When the predicate of a denominative judgment is a proper name, or
any verbal expression which by its sound gives rise to the idea of a single
existing thing as such, and is used as a sign of the thing (this is Socrates, this
watch is mine), and if the judgment is based upon immediate knowledge,
then, in this case also, the agreement of the two ideas—the intuition and the
memory-image—is presupposed. But here again it is not necessary that
there should be absolute identity of the ideal contents. I recognise an
acquaintance even in a new dress, or when he looks paler than usual. But
this agreement is accompanied by the consciousness of the real identity of
the subject with the particular thing denoted by the predicate. This real
identity of the thing corresponding to the two ideas which have arisen at
different times, and which are both ideas of the same thing, is again funda-
mentally different from the agreement and stability of ideas ; it refers to a
determination of being as opposed to being thought. We can, however,
formulate a principle from this point of view also, viz. that in the concept
SIMPLE JUDGMENTS
87
*
A
of the particular thing itself there is included both its singularity and that
identity with itself, which alone gives a meaning to the idea of the duration
and permanency of the thing ; so that the very concept of a thing includes
the assumption of things identical with themselves. But in saying this, we
do not go so far as to state the Eleatic or Herbartian principle of absolute
indistinguishability, or of the identity and immutability of the what-in
(for instance) the formula “every thing is what it is.” On the contrary,
our conviction of the real identity of particular things with themselves
refers to their permanence during change of action, their duration under
different appearances; we constantly refer ideas having a partially different
content to one and the same thing.
In the judgment“ this is Socrates” we say that the person present is
really identical with the definite individual known as Socrates. Here again
the statement refers to the objective validity of this identity, for in making
it we are conscious of the necessity of referring the two ideas to one and
the same thing. To question its objective validity would be to say that
the thing referred to as subject and the thing referred to as predicate
may be, or are, two different things, and that it is not necessary to unify
them. The law of agreement among our ideas is not sufficient to prove
the necessity of referring two ideas to a single real thing, for this law only
guarantees the agreement of their contents ; it is here that assumptions con-
cerning the nature of the existent and the distinguishing characteristics of
real identity become important, and these the function of judgment does
not itself give us. Such is the assumption that all individuals, of certain
kinds, can be confidently distinguished, and that there are no two objects so
alike that they can be mistaken for one another if we examine them closely.
It is on this, for example, that our conviction rests of the identity of persons
known to us. When our recollection of the outward form fails to give
us certainty, we have recourse to the identity of consciousness with its
individual peculiarities, as Penelope did when she examined Odysseus as
to his knowledge of the arrangement of their marriage bed; but with out-
ward things it is by their spatial determinations and the principle of im-
penetrability that we finally establish their identity. The necessity of be-
lieving in real identity is the result of presuppositions such as these, which
arise from our knowledge of the nature of things. To these statements con-
cerning real identity, which are supported by considerations obtained from
another source, we may add the judgments which express the coincidence
of a certain subject with a given member of a series, or with any other
17
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LOGIC
1
particular thing which is determined by a relational predicate-Augustus
is the first of the Cæsars ; Aristotle is the teacher of Alexander.
6. With regard to the objective validity of the judgments which pre-
dicate attributes and activities, everything which has been said with refer-
ence to naming is, from one point of view, true of these also, because of
the twofold synthesis which takes place in them. The attribute or activity
which is thought of in the subject must agree with the general predicate-
idea. On the other hand, their objective validity can be maintained only
upon the assumption that the unity of thing and attribute, of thing and
activity, is a real relation, hence that we are able to know a thing by its
attributes, and to look upon a change in our idea as an alteration in it.
This relation of the thing to its attributes and activities has also been brought
under the concept of identity, though here again an elasticity has been
ascribed to the term which does not really belong to it. The thing is only
identical with itself as the permanent support of its attributes, as the subject
which in activity remains one with itself; it is not identical with its attri-
butes, nor with its activities, it is not the same as these. Cinnabar is not
identical with its redness, nor the sun with its shining ; and the principle
by which the judgments, “ Cinnabar is red," " the sun shines," are to be
justified, cannot be the principle of identity. The only general law of
thought which we can lay down,-and it expresses also a fundamental
fact—is, that we are able to distinguish, retain, and recognise anything
which exists by means of these categories of inherence and action alone ;
and that the Being of a thing is also the Being of its attributes and activi-
ties.
But even when we start from this law and hold that what we judge about
is the existent, all we can mean is that the existent concerning which we
judge necessitates this particular movement of thought by which we distin-
guish between it and its attribute, and then unify them again.
7. The general ideas of things which we use as predicates of denomi-
native judgments, are, to some extent, accompanied at every further de-
velopment of thought by those judgments of attributes and activities, of
which they have been the subjects. Snow, for example, may signify not
an unanalysed image, but a white, loose, cold thing; the general name has
thus become a summary of attributes. To this extent the relations of
inherence and action are implicitly contained even in denominative
judgments, as belonging to that meaning of the word which is present to
consciousness. When there is added the real identity of things which fall
SIMPLE JUDGMENTS
89
under different ideas (water, ice, steam-boy, man, old man), a substantive
may serve merely to denote a complex of attributes which express the
different temporal states of a particular kind of subject.
§ 15.
Everything which exists as a particular thing is given to us in time, it
occupies a definite position in time, and is intuited as lasting during a
period of time, as developing varying activities in time, and possibly as
changing its attributes. Thus a REFERENCE TO TIME is necessarily con-
nected with all our judgments concerning the existence, attributes,
activities, and relations of particular things, and all such judgments can
claim to be valid for a definite time only.
1. While this proposition is self-evident for activities the reference to
time seems wanting in some of the attributive-predicates, inasmuch as they
are regarded as invariable and given with the existence of the subject itself.
But while there is always the general possibility that attributes may change
in spite of the identity of the subject, this relation of permanence is to be
found only in exceptional cases; it is not contained in the form of the
judgment by itself; at the most it is found in the secondary relations
attaching to the meaning of the predicate, or in the predicate itself (un-
changeable, etc.). Only when we call a thing by a proper name do we
exclude all reference to time, and by the nature of our predicate refer to
the subject, irrespective of temporal relations. All other denominative
judgments admit of this limitation of their validity to a certain time, in so
far as in naming the predication of attributes and activities becomes pro-
minent (v. end of $ 14), and the same thing may thus be called first by
one name, then by another.
2. Thus the narrative-judgment is never completely expressed unless it
contains a statement of the time for which the unity of predicate and sub-
ject is objectively valid ; it must be expressed in the present, past or
future tense. The extent to which languages are capable of expressing
temporal relations in predications is one measure of their logical perfection.
It is only to the disconnected thought of the child, which is quite
absorbed in the interest of the moment, that everything which occurs to
it is present; the power of distinguishing times grows as self-conscious-
ness becomes clearer and more methodical.
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LOGIC
II. EXPLICATIVE JUDGMENTS.
§ 16.
The judgments we have so far considered make statements about par-
ticular things. Essentially different from these are judgments of which
the subject consists in the meaning of the subject-word, which do not refer
to the definite existence of particular things named by the subject-word,
though this existence is frequently presupposed by the nature of the idea,
or, as a consequence, of the source from which it is derived. Their objec-
tive validity is independent of time. As explaining the contents of a
general idea, they may be regarded as the indirect expression of a rule
which refers to the existent.
1. “Blood is red and snow is white,”—such judgments do not speak
of this or that particular thing, nor give expression to any perception
present at the moment. Since the subject-word is absolute, all that it can
express is that which constitutes its meaning; and this meaning is an ideal
content of indefinite generality which has been disengaged from the idea of
any particular existing thing, and which in its indefiniteness cannot be said to
exist. Hence all that the statement “ blood is red” can tell us must refer
to this ideal content, and it signifies nothing more than that the predicate
is thought of in connection with the subject. What sort of unity there is
between subject and predicate depends upon the nature of the ideas con-
nected. If both belong to the same category, then the simple coincidence
of the ideas is stated; that which is thought as a concrete thing has
attributes and activities predicated of it which are contained in the idea of
the thing itself.
It is in a similar sense that we make use of the article, particularly
where the subject-idea is the idea of a thing having an individual form (the
dog is a quadruped).
We must also include in the class of explicative judgments those which
seem, by means of the so-called indefinite article, to make a statement
concerning a particular individual, a particular state, etc.; such propositions
as “a fir-tree is a conifer, an ague is accompanied by high fever,” do not
refer to any definite particular thing; what they mean is, that that which
is a fir-tree is a conifer, and this statement can only be based upon the
relation between the general ideas fir-tree and conifer, not upon knowledge
of the particular.
2. The objective validity of these judgments has immediate reference
SIMPLE JUDGMENTS
91
only to the sphere of ideas; all that they tell us is, that when the subject
(presupposing nominal correctness) is thought, it will be thought together
with the predicate; that what I and every one else think of as “ blood ”
is thought of as red. It is only secondarily, when we pass from the
generality of the word to the actual things contained under it, that the
judgment refers to the Being of these things also; and states concerning
them the rule that when there is a thing which is denoted by the subject
the predicate belongs to it.
According to one view, such judgments are from the first general judg-
ments gained from experience by induction, having for subjects particular
things thought of as indefinite in number. But here it is forgotten that the
first essential for such an induction is that we should have some standard
according to which we may name particular things by the same word and
so comprehend them in a judgment common to all. Such a standard we
can find only in the meaning of the words we bring to our process of
naming; this meaning must be already to some extent fixed before there
can be any question of judgments of induction. It is perfectly true that
under the influence of progressive experience, which is always adding
something to our ideas, these ideas remodel themselves, and that it is
generally a matter of chance where common thought comes to a halt and
fixes the boundaries of its words.
The meaning of the word blood, for example, is formed in the first place
from the intuition of human blood and that of mammals and birds; hence it
may, and in ordinary language, does, include the colour red amongst its
contents; but by an extension of its original meaning it might also be
applied to the whiteish fluid in other kinds of animal organisms. At some
stage of formation, however, the meanings of words are a necessary prelimi-
nary to the judgment of the individual; whatever the stage at which they
stop this fixed meaning is preliminary to naming and to the possibility of
judgments of experience gained by induction. Thus if blood is the fluid in
the veins of mammals and birds, then “red” forms a part of its meaning,
and when we take it as fixed in this way we cannot use it to name fluids of
another colour.
Thus before we can give utterance to a judgment having the meaning of
a judgment of experience including many cases (of which we shall speak
later), a simple judgment must have preceded to unfold the contents of the
single idea denoted by a given word ; the general rule to be found herein
is, in the first instance, a rule of naming which forbids us to call anything
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LOGIC
S
blood which is not red. The inductive judgment first appears when a new
attribute is discovered common to all the things which are denoted by the
same name,—when we say that B is invariably connected with the attributes
which make up the contents of the subject idea A, B not having been pre-
viously connected in thought with A.
Such an explicative judgment can contain the statement of a rule con-
cerning things themselves only in so far as the idea of a permanent and
lasting thing, together with the possibility of variable attributes, is contained
in the substantival denomination ; and the rule is that the predicate always
and constantly belongs to the things which fall under the denomination,
and is invariably connected with their other attributes. When the judg-
ment extends to reality it is this invariability of the red colour belonging
to everything which can be called "blood” to which it really refers.
3. Verbs occupy a peculiar position here, Strictly speaking, the only
case in which a verb can be the predicate of a general subject is when we
are speaking of an activity which is continuous, and which lasts as long as
the thing comprehended under the subject-idea (fire burns, the wind
blows); when, on the contrary, the verb expresses a variable activity, begin-
ning and ending in time, it is only as a figure of speech that it can be
used as predicate (the sheep bleats, the horse neighs); what the expression
should really denote is merely a faculty or a habit, i.e. an attribute from
which the activity may proceed, and not the activity itself.
4. When we compare this class of judgments with those first considered,
we are chiefly struck by the fact that their validity does not depend upon
the existence here or there, at this time or the other, of a thing correspond-
ing to the subject-idea. Hence they are not valid for some given time,
but can claim unconditional validity just because they refer merely to ideas.
On the other hand, all merely narrative judgments are temporarily valid.
5. Here there appears a characteristic difference in the meaning of the
Present tense, according as it is used for the statement of unconditionally
valid judgments or of those amongst temporarily valid judgments which
refer to the present. When we think of a thing as presented and as
having a particular existence we have thereby assigned to it its place in that
time which embraces everything, and is the same for all; by its existence
it stands amongst other things which are contemporaneous, or precede or
follow it; and by its quality, concerning which our judgment is made, it
occupies a definite point of time and thus stands in a definite temporal
relation to the moment of our judgment.
SIMPLE JUDGMENTS
93
But when the subject of our judgment is the idea which constitutes the
meaning of the word, this idea is disengaged from the temporal com-
plex. Removed from the changes of time, it stands before us in a mental
present, in which there is no distinction of yesterday and to-day, but in
which the consciousness that our idea will be the same at every repetition
annuls all temporal distinctions between the particular occasions upon
which we actively think of it. When thought in this way the subject has
predicates which belong to it independently of time, which belong to it as
often as it is thought of. The proposition “the sky is blue” denotes the
state of the sky at the present moment, and is thus,—as a narrative judg-
ment,-- really in the present tense; but it may also have the completely
different meaning that the sky as I generally think of it, and as the fixed
object of my thought, is always blue. In this case no past nor future is
contrasted with the present. The validity of the judgment is not estimated
by my perception of the object in a given momentary state, but by the
invariability of the ideal content which I am connecting once for all with
the word-an invariability which is the condition of all my speech or
thought.
III. THE ACT OF JUDGMENT AS EXPRESSED IN LANGUAGE.
1. § 17.
The verbal expression of the unification of subject and predicate which
takes place in the judgment is to be found in developed languages in the form
of inflection of the verb, which has itself arisen out of what was originally a
mere juxtaposition. Even where the verb “to be”appears as the link between
a substantival or adjectival predicate and the subject, the act of judgment is
expressed by the verbal ending alone ; the verb “to be” forms a part of
the predicate.
1. Less developed languages, and, in simple cases, even advanced ones,
are content to express such a unification as takes place in the judgment by
the mere juxtaposition of the two words which stand for subject and predi-
cate. This juxtaposition must not only indicate that the corresponding
ideas are at the moment unified by the speaker, it must also express the
objective validity of the judgments. Accentuation alone can distinguish
the statement from the question, or from any other mode of connection,
such as the attributive which expresses a unity of two ideas which is already
present. When, on the contrary, the development of the linguistic forms has
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LOGIC
11
followed all the logical distinctions, then in the case of verbal predicates
the meaning of the personal ending (which blends the pronominal equiva-
lent of the subject immediately with the stem of the verb, thus making it
agree in person, number and gender) is to denote the connection of sub-
ject and predicate in judgment; and the indicative mood, combined with
the emphasis and arrangement which distinguishes the statement from the
question, states this connection as objectively valid. The tense, again,
indicates the time for which the judgment is to be valid.
That which logicians would denote by the expression copula, that element
of language which can combine words into a proposition, and so into the
expression of a statement, lies in the personal ending of the indicative, and
in this alone. The meaning of the unity of subject and predicate which is
expressed by this terminal inflection differs according to the nature of the
ideas connected.
2. Judgments in which the predicate is expressed by an adjective or
substantive are not generally formed by mere juxtaposition (as in ở mèv Bios
Bpaxùs, Ý de téxvn Makpń); the verb “to be” is employed. But this is not
by virtue of its meaning the element which expresses the formation of the
judgment; the function of judgment is contained in the form of inflection
alone. The verb “to be” is the means by which we give the form of a
verb to the predicate, and thus enable it to take the ending which is the
outward sign of its predicative relation to the subject. In the judgment
“cinnabar is red,” nothing is added by the meaning of the verb “to be”
which is not already contained in “red,” for as an adjective it involves
reference to a subject of which it is the attribute. As abstract nouns, “red-
ness” and “red-being” would have just the same meaning; the verb “to be”
is merely used to express the fact that“red” is not thought of as independent
and abstract, but is predicated of a definite subject. In this way the verb
“to be” certainly serves to facilitate the expression of this use of the word
"red,” and to show that it is a predicate, as contrasted with the merely
attributive relation which might be expressed by juxtaposition ; but in so
doing it is a mere vehicle for the copula, not the copula itself; it does not
constitute the judgment, but merely prepares the way for it. This function
of "to be,” to denote the meaning in which a word is to be used, appears
still more clearly in the case of substantives. These do not, like adjec-
tives, carry in their form a reference to something else, yet their meaning,
by its nature, enables them to fulfil the function of a predicate, whenever
that meaning is a general one and only appropriated to a definite particular
SIMPLE JUDGMENTS
95
by means of a denominative judgment. “Man” is not the name of a defi-
nite individual, although the idea of the figure of an individual is included
in its meaning ; it is not a name at all, but the sign of a definite ideal-con-
tent. Only the demonstrative adjective or the article converts the word
into the name of a definite man; the use of the verb “to be," on the
contrary, converts it into a predicate, and it cannot be a name before it has
been a predicate. Thus “ Mensch," as a general idea awaiting its refer-
ence to some definite individual, and “Menschsein ” have the same mean-
ing; the verb “sein” serves only as the outward sign of the function of
the idea as predicate, which might also be shown by its position and accen-
tuation. Thus its function is that of a formal element of language ; but it
is not that formal element which expresses the act of judgment and merits
the name of copula.
3. But how does it happen that it is just the verb “to be” which we
use in this way? and what connection is there between the meaning of “ to
be” as an independent verb, when it stands alone as predicate, and this
function, which it has in connection with adjectives and substantives?
In the fourth chapter of the first book of his Logic, J. S. Mill draws
attention to the ambiguity contained in the word “is," inasmuch as when
it is used as the so-called copula, it certainly does not state that the subject
exists, but only denotes the relation of predication. Such a sentence as
“A centaur is a fiction of the poets” directly denies the statement that a
centaur is; and he is surprised that this ambiguity should have been over-
looked by almost all authors, although existing in modern as well as in
ancient languages.
Mill has paid as little attention to Herbart as to other German philoso-
phers. Herbart, following in the footsteps of Fichte, has shown, with his
usual acuteness (Einl. in die Phil., § 53), that the judgment A is B, and
the question is A B? certainly do not contain the statement (which, though
commonly attributed to them, is really quite alien) that A is, for nothing
whatever is said about A by itself, nor of its existence or validity.
There is no doubt that this remark is correct, and should never have
been disputed.? A judgment of the form“ A is B” can never, by the
1 Grundlage der gesammten Wissenschaftslehre, part i. § 1, a passage of which I have
been reminded by Bergmann (Reine Logik, i. p. 235).
2 It is urged against this (cf. Ueberweg, p. 162) that propositions such as “God is
just," " the soul is immortal,” “true friends are to be valued,” must involve the state-
ment that there are such things as God, a soul, true friends; that this presupposition is
contained in the indicative mood; that any one unwilling to accept the presupposition
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LOGIC
mere fact that the subject and predicate are connected by “is,” include
the statement of the judgment "A exists.” The function of this “is” is
would have to add clauses to those propositions which should make them hypothetical :
" in case there is a God,” etc. Such a clause, it is said, can be dispensed with only
Sphinx, Chimæra), shows that the reality is merely feigned, or that the statement is
merely the explanation of a name. This objection is so far true that the reality of the
subject is generally presupposed by those who speak or hear such judgments; otherwise
there would be no motive present for uttering them. But this is quite another thing
from saying that the judgment itself, as it stands, involves the statement of the reality of
the subject, i.e. that this is necessarily stated by the words of the judgment, and more
especially by the indicative mood. If it were so, it would be incomprehensible how
there should be any exception to the rule, for if the indicative of the categorical judg-
ment containing "is” has the force of stating the reality of the subject, then it must
have this force always and under all circumstances. The exceptions which Ueberweg
admits themselves prove that it does not depend upon the form of the judgment, but
upon the ideas we unconsciously attach to the meaning of the subject-words, without
their finding utterance in the judgment, whether or not the presupposition of their existence
is “ as a rule" accepted. And, indeed, what meaning can the statement of existence
have when the subject does not denote individual beings as such—as in the proposition
"God is just,” or “ true friends are to be valued ”—but is of a universal form? When
snow exists ? Certainly not in the sense indicated by the present tense of the indicative
when used of definite things having a particular existence, for then the statement would
be that snow exists now at this moment. But the judgment, “snow is white,” is true
in summer and winter alike ; and yet it is not held that the judgment tells us that snow
always exists. Again, if the statement is said to be, that such bodies as those of which
I think when I say snow, have actually existed somewhere and at some time, it can be
only the existence of definite “snows” which is meant. This alone can be stated, nor
can it be said of snow in general that it exists. But the judgment, "snow is white,”
does apply to snow in general and not only to this or that snow.
Still it is true, that the recollection of actually perceived snow is always connected
with the idea which we attach to the word “snow,” and for this reason, because of the
way in which I have attained to the meaning of the word, it is presupposed that we are
dealing with something which exists. But suppose I take the analogous judgment,
6 Pegasus is winged,” the idea of wings is as firmly connected with the idea which I
attach to the word Pegasus as that of white colour with snow. So far, however, I
have never seen an existing Pegasus ; indeed, I know that it is a creation of fancy, and
for this reason the existence of Pegasus is not presupposed. But the judgment itself
tells me neither that Pegasus exists, nor that he does not exist ; only how the idea is
constituted which I connect with the word. Take the judgment, “ The branches of the
hyperbola are infinite,” it is undoubtedly a valid judgment, although it can have nothing
to do with the existence of the branches of this or that particular hyperbola. The
infinite branches of the hyperbola exist in exactly the same way as all other subjects of
my judgment, that is, they exist as objects of my thought, of which I assume that
every one else thinks alike.
W. Jordan has treated this question more carefully in his treatise, über die Zweideutigkeit
der Copula bei Stuart Mill (Stuttgarter Gymnasialprogramm, 1870). It is true that on
much wider scope than Ueberweg to this concept of existence, when on page 14 he says,
SIMPLE JUDGMENTS
97
exactly the same whether we are talking of existing or of non-existing things,
of subjects which are thought of as particular, or of subjects which are
thought of as general (to these, as general, particular existence cannot
“Whenever the thinking subject finds something present which is independent of his
act of thought, whether it is in the material or spiritual world, Logic will permit the
use of the “is.'” If we take this explanation literally, it is certainly true that every act
of judgment—so far as it presupposes, and does not create, the subject of the judgment
-recognises something which is independent of this act of thought, and this something
is the idea denoted by the subject-word. Such a reality of ideas is presupposed whenever
a judgment finds expression in language, and it is presupposed moreover that it is common
to many individuals. Thus the question would disappear if such were the reality
intended, and the “is ” would be justified wherever the subject-word, and therefore the
judgment, had any meaning. But just for this reason the judgment would have nothing
whatever to do with the statement of the actual existence of the thought denoted by the
subject-word, in the ordinary sense of existing.
However, this is not what is meant. Jordan attempts-in opposition to Herbart and
Mill—to preserve for “is” the meaning of real existence. This he does in the first
place by saying that the reality in question belongs to the predicate, but not to the
subject. In such propositions as “self-defence is forbidden,” “ moderation is difficult,”
there is no doubt that the existence of the subject-idea is left undecided, while in the
predicate, on the contrary, allusion is made to something which actually exists. The
whole is an existential proposition in disguise, i.e. there are laws, or grounds, which
forbid self-defence, circumstances which make moderation difficult. But if we once
begin to paraphrase like this, we shall find at last that even the proposition, "a square
circle is unthinkable,” is an existential proposition; “ there are logical laws which make
a square circle impossible.” This, however, is to abandon the ground of dispute, for
the question was, whether the reality of the subject is stated? We are far from denying
that every statement, just because it claims objectivity, contains the recognition of
objective “laws” and “grounds" ; but we do deny that for this reason the existence is
stated of a thing (or attribute or event) which corresponds to the subject-idea. Jordan's
other distinction, which he applies to Mill's example of the centaur, is better. Such a
proposition as “the centaur is a fiction of the poets ” approximates to a definition.
Now amongst definitions Jordan distinguishes a particular class which he calls “recti-
fying,” and these are the definitions which deny the idea which the subject stands for,
and replace it by another. The proposition says, “the centaur does not exist in the
sense indicated by the word of actually being, but the idea of the centaur is a fiction."
No doubt there are a number of such predicates which degrade the subject-word into
the sign of a merely mental thing, when, by its customary meaning, it might be taken
to denote an existing thing. But we must not forget that at the head of these predicates
there stands the verb to be—to exist. Whenever I expressly state of a subject that
it exists, the subject-word is, for me, the sign of an idea ; and my predicate states that
an actual thing corresponds to this idea.
The view that the meaning of the word "to be" is always the same has lately received
determined support from Fr. Kern (Die deutsche Satzlehre, p. 64 sq.), who pronounces
against distinguishing two meanings in it. “In the propositions wooden iron is non-
sense,'' a square circle is a contradiction,' the existence of the wooden iron and of the
square circle is stated with just as much clearness and emphasis as the existence of the
boy in the proposition the boy is in the garden.' But while ... the boy exists
outside my thought as well as within ... the iron and the circle exist only in my
idea. They exist, moreover, in connection with the property of being nonsense or a
S. L.
H
.
LOGIC
belong); of predicates which can belong to an existing thing, or of predi-
cates which deny existence by their meaning. In each case its one function
is to put the predicate into such a form that it can be used in the judgment,
and to enable it to take the personal ending. The nature of the subject and
predicate-ideas alone determine the sense in which subject and predicate
are unified, and whether the existence of the subject is presupposed, left
uncertain, or denied. “The square is a regular, four-angled figure” means
logical identity, “this is my watch," real identity ; “gold is a metal,” sub-
sumption under a more general idea ; "gold is yellow," the unity of thing
and attribute ; “A is a mile away from B,” a relation; "the movement is
slow,” the unity between a general idea and its more exact deterinination,
and so on. “Socrates is ill,” presupposes the existence of the subject,
because Socrates is the name of an individual who is thought of as existing,
and “ill ” is a condition thought of as actual at a given time. “Pegasus
is winged ” leaves the existence of Pegasus uncertain for any one who does
not know whether the name is that of an actual or of a merely fictitious
being. “Pegasus is a mythological fiction ” denies the existence of the
subject; in every instance our information is obtained only from the
meaning of the terms, either of subject or predicate.
4. With reference to the predicates we may here distinguish between
two classes.
contradiction, which property I have recognised and stated; and thus they cannot pos-
sibly be found in any reality which is independent of me."
But the ambiguity of the word is immediately granted by this distinction between a
subject which exists in a reality external to me, and one which exists only in my idea.
For when the word “is” stands alone in the sense of “exist” what it states is that the
subject does not exist only in my idea, but independently of it. In such a proposition as
“God exists—but only in my idea” the clause directly denies the meaning in which we
are, at first, impelled to understand the words “God exists.” But it is not even true that a
square circle exists “in my idea,” for who could imagine one? The contradictory is im-
possible in my thoughts, as well as in the reality which is independent of me. What the
predicate “is a contradiction” really tells us is, that I cannot think of anything corre-
sponding to the words “square circle”; it denies existence in thought as well as in reality.
In p. 74, it is brought forward as an instance, that to any one who doubts it we say
with emphasis “ A is the person who did it," this emphasized is being meant to lay stress
upon the existence of A as the person who did it. But it is obvious that the existence of
A was never called into question, hence that there is no reason to lay special stress upon
it. It was the action of A, and not his existence, which was disputed, and the question
whether we had any right to predicate of A (whose existence is undisputed) that he is
the person who did it. If this is not so, then the proposition “ A is not the person who
did it” must be meant to deny not merely the quality of agency, but the existence of A.
Concerning Bergmann's objections (Reine Logik, i. p. 235 sq.), cf. Vierteljahrsschrift für
wiss. Philos., V. 113 sq.
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99
All modal relational-predicates, which express a relation to my know-
ledge (with the exception of those appertaining to the senses, such as
visible, or tangible), by their meaning make the subject-term the sign of
a mere idea which does not involve real existence; and this is the case
whether the predicates themselves affirm or deny its existence, or leave it
undecided. When I use the predicates true, false, credible, incredible,
etc., of anything, I denote that it is only an idea, and that the predicate
is to give information concerning its relation to me and to my subjective
thought. Such propositions as “Tell's apple-shooting is a fact,” “ the
Trojan war is an historical event,” “atoms are bodies which actually
exist,” would be impossible if "is” and “are” could by themselves state
the existence of the subject.
But the verb “to be,” when used absolutely and as meaning “ to exist,"
is itself a modal relational-predicate. By expressly stating the existence
of the subject it determines the question whether that which the subject-
word first denotes merely as an idea is also an actual thing. Cf. above,
§ 12, 7, p. 72.
But with other predicates everything depends upon what the subject is
and the sense in which it is used ; and this cannot be seen from the mere
external form of the judgment and the use of the word “is.” If the
subject-term is used as general and is not introduced as the name of one
or more definite things, then the predicate which is formed by means of the
verb “to be” can state nothing but the contents of this subject-idea, and
nothing whatever is said as to the existence of the subject. When I say
"gold is yellow” or “atoms are indivisible,” the being yellow or indivisible
appertains to the idea which I denote by the subject-word; but the pro-
positions do not declare the existence of particular things. I must learn
from some other source whether or not the subject-term is applicable to
such things. But if the subject-term appears from the first as the name
of things which have a particular existence—e.g. “this piece of gold is
yellow,” “this horse is black”—then existence is presupposed; not in the
word “is” however, but in “ this.”
5. This “ambiguity of the copula” applies not only to the verb to be,
but to all predicates which can by themselves denote real states and
attributes, inasmuch as they sometimes state that which actually takes
place in a particular case and sometimes that which belongs as attribute
or activity to the subject-idea. Strictly speaking, it is only the present
tense which is ambiguous; for this sometimes expresses the empirical,
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temporal present, sometimes the general necessity of thought. The pro-
position "great souls pardon offences” states neither that great souls exist
-though this is presupposed in the act of pardoning-nor that some
great souls are at this moment pardoning. All it tells us is, that if a man
is a great soul he must pardon offences. But the proposition, "Socrates
speaks," states the existence of Socrates in the same way as the proposition
“Socrates is ill”; we can speak of him only just in so far as he exists,
because the word Socrates denotes an individual having a particular exist-
ence, and any attributes or actions which are ascribed to him must involve
his existence. 1
6. But how does it happen that the verb “to be,” which is the ex-
pression of actual existence, assumes a formal function whereby it loses
its meaning-nay, even seems to contradict it? The remarkable thing is
not that the ambiguity in this respect has been so little noticed, but rather
that all known languages agree in containing it. The explanation is not
difficult. As Ueberweg (p. 162) rightly notices, and, as we have empha-
sized above (p. 95 sq.), it is as a rule taken for granted that the things of
which we speak exist; there is no need of any express assertion ; we are
not interested to know that things are, but what and how they are. When
now, it is desired, not merely to express predication by mere juxtaposition,
but to give the form of the verb to the predicate, the verb “to be” offers
itself just because it is so general and has by itself no contents. It is
always presupposed; but in order that we may know what we wish to
know, we need to have it determined more exactly as “ being this” and
“being thus”; just as the statement of existence is determined more
exactly as “ being here ” and “being now.” The predicate “red,” which
by its form already denotes something appertaining to something else
which exists, now appears as a modification of Being, being red
Now as the present tense denotes on the one hand the empirical,
sensual present, and on the other the timeless present of our thoughts ;
so the meaning of being in this connection is also extended. The attribute
has the same relation to the thing which is thought, and to the thing
which in its existence is perceptible to sense; as the presupposition of
Being was only implied before, it can now be abstracted from. As objects
of my thought, things do not alter; their being may cease, their being-
this and being-thus remain so far as I retain them in thought.
1 The theory according to which the judgment “A speaks” is altered to “ A is
speaking,” in order to get the inevitable copula “is," may be held to be obsolete.
SIMPLE JUDGMENTS
ΙΟΙ
Nevertheless the verb has kept a part of its original meaning, and the
most important part. The verb "to be" originally implies real existence.
That which exists holds good independently of my thought, and holds
good for every one. This objectivity of the connection to which my
judgment gives utterance is an essential factor of the judgment itself.
This it is, and not the existence of the subject, which forms a part of the
statement; and for this “ Being” is a very suitable expression.
By this extension of its fundamental meaning it strengthens the assertion
of objectivity, of universal validity, already contained in the inflexional
form.
CHAPTER III.
HOW JUDGMENTS ARISE, AND THE DISTINCTION BETWEÉN
ANALYTICAL AND SYNTHETICAL JUDGMENTS.
§ 18.
IMMEDIATE JUDGMENTS are those which presuppose nothing but the ideas
connected in them, in order that these ideas may be united as subject and
predicate with a consciousness of validity ; MEDIATE, or MEDIATED JUDG-
MENTS are those in which some further element is necessary in addition to
these ideas.
Kant's distinction of analytical and synthetical judgments refers only to
the relation between the predicate and the concept which is denoted by
the subject-term and assumed as given. It is not applied by Kant to
those judgments in which the subject is a particular, intuitable idea. All
relational judgments, moreover, must be regarded as synthetical from the
Kantian point of view, even when based upon the analysis of a complex
presentation.
1. When, after analysing the functions through which the simple judg-
ment takes place, we ask about the origin of the judgment, we are not
concerned with the origin of the ideas—whether subject or predicate-
united by the judgment; in speaking merely of the analysis of the act of
judging we assume these to be given. The question concerns only the.
✓ genesis of the act of judging itself, and this has two aspects : that of the
connection or unification of subject and predicate, and that of the con-
sciousness of the objective validity of this connection.
This genesis may be either immediate or mediate. It is immediate
when nothing is presupposed in the judgment but the subject and predicate
ideas connected in it, in order that it may take place with a consciousness
of objective validity. It is mediate when this can take place only by the
addition of some other elements. It may be that without some mediation
the subject and predicate cannot even be referred to each other in such a
way that their union in a judgment might be thought of; or it may be
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HOW JUDGMENTS ARISE
103
that at least the consciousness of the objective validity of such unity must
be obtained elsewhere. Let us for the present call that which brings
about the unification of subject and predicate the Ground of the judgment.
Then the immediate judgment is one, the ground of which lies in the con-
nected ideas themselves, apart from anything else; the mediate judgment
is one which has its ground in these ideas only when taken together with
others; the mediation may at first merely relate subject and predicate to
each other by raising the question whether A is B; or it may at the same
time settle the question and guarantee the certainty of the validity of the
judgment A is B.
If the ground lie entirely in the ideas themselves which are connected
by the judgment, then, according to what we have said above, their relation
must be such that the unity expressed in the judgment can be immediately
recognised. In a denominative judgment I am conscious, without further
mediation, of the coincidence between the idea which is present and that
which is reproduced and denoted by the predicate-term ; when I say
“that is a fir-tree,” I find in present intuition just what agrees with the
general idea of the fir-tree. In immediate judgments of attributes and
activities the idea corresponding to the predicate is a part of the subject-
idea. I analyse the latter and emphasize a certain element, e.g. colour, and
this I recognise as agreeing with a colour already known. Here, again,
nothing beyond the complex idea given as subject is needed in order that
I may discover in it the element which corresponds to the predicate.
In the case of relational judgments, it is true that an analysis of the
subject-idea by itself cannot yield the element which agrees with the predi-
cate. I may turn and twist as I will the idea of the lamp which stands
before me, I can discover in it nothing which tells me that it stands to the
left of the writing desk. But in this instance that which is given is a com-
plex intuition containing two objects and their relation ; and by analysing
this into its elements I obtain the judgment, for which no more is needed
than the ideas connected in it. The complex presentation is the ground,
for the statement that the lamp stands to the left of the writing desk.
Thus all immediate judgments are of necessity analytical, if those judg-
ments are analytical which only re-unite the elements obtained by analysis
of a presentation, judgments, that is, in which either the contents of the
predicate are already presented in the subject, as in those of naming,
attributes or of activities ; or in which subject and predicate, together with
the relation between them, form parts of a complex presentation, as in
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relational judgments. If this is so, then synthetical judgments must be
those which are inferred, and those which need some other ground lying
outside the ideas given, in order that the synthesis of the judgment may
take place.
2. That all immediate judgments should be analytical in this sense in
no way contradicts the essence of the judgment, which is to be a cúvdeois
vonuárwv. For the analysis or decomposition is only the preparation for the
act of judgment, not that act itself ; the work of judgment is to restore
union between the elements which have been thus distinguished (cf. § 81).
3. Still, to use the terms analytical and synthetical simply in this sense
is forbidden by the use of them introduced by Kant. The above distinc-
tion between immediate and mediate judgments is based upon a ground
essentially different from that of the Kantian distinction between analytical
and synthetical. In the former case it depends entirely upon how the
judgment arises at any time in the judging subject, whether it is immediate
or mediate, and whether it has its origin in the separation or combination
of elements; and we cannot generally discover what this genesis is from
the verbal expression of the judgment. Kant, on the other hand, depends
in the first instance upon the presupposition of definite concepts which
are expressed by the terms appearing as subjects.
"In all judgments,” he says in the well-known passage of the Kr. d.r. V.
(ed. i., p. 6; ed. ii., Int. IV.), “in which we think of a subject as related to
the predicate, it may be related in two ways. Either the predicate B
belongs to the subject A as something which is contained (implicitly) in
this concept A, or else B, though connected with the concept A, lies quite
outside of it. In the first case I call the judgment analytical, in the
second synthetical. Thus analytical judgments (affirmative) are those in
which the connection of the predicate with the subject is conceived through
identity, but those in which this connection is thought without identity are
to be called synthetical. We might also call the former explicative, the
others ampliative, judgments, for the former add nothing by the predicates
to the concept of the subject, they merely break it up by analysis into its
component concepts, which were already thought (although confusedly) in
it; the latter, on the contrary, add a predicate to the concept of the sub-
ject, which was never included in the thought of it, and could not have
been obtained from it by any process of analysis." The two propositions,
“all bodies are extended” and “all bodies are heavy,” follow as examples.
In order to obtain the former judgment I need only analyse that concept
HOW JUDGMENTS ARISE
105
(of body), i.e. only become conscious of the manifold which I always
think in it, in order that I may find this predicate therein. On the other
hand, when I say “all bodies are heavy,” the predicate is something quite
different from that which I think in the mere concept of a body in
general.
Just for this reason, he adds in the Prolegomena, § 2, 6, all analytical
propositions are judgments a priori, even when their concepts are empi-
rical; e.g., gold is a yellow metal ; for in order to know this, I require no
experience beyond my concept of gold, as yellow and a metal, which is
just what constitutes the concept.
" Judgments of experience, as such,” continues Kant in the 2nd edition,
“are all synthetical. It would be absurd to base an analytical judgment
upon experience, for in order to form the judgment I have no need to pass
beyond my concept or to appeal to the testimony of experience. That a
body is extended is a proposition which is established a priori, and no
judgment of experience; for before appealing to experience, I have all the
conditions for my judgment in the concept, from which I can extricate the
predicate according to the law of contradiction, and at the same time
become conscious of the necessity of the judgment-a necessity which
experience could never have taught. On the other hand, though I do not
include the predicate of heaviness in the concept of body in general, still
this latter denotes an object of experience by one of its parts, and to this
I may add other parts of the same experience as belonging to the first. I
can in the first place know the concept of body analytically by the
characteristics of extension, impenetrability, figure, etc., which are all con-
tained in this concept. Then I extend my knowledge, and on referring to
the experience from which I had derived this concept of body, I find that
heaviness is always connected with the above characteristics, and hence I
add it synthetically as predicate to that concept. Thus it is experience
upon which the possibility of the synthesis of the predicate heaviness with
the concept body is based; for though the one concept is not contained
in the other, they still belong to each other, as parts of a whole—.c. of
experience, which is itself a synthetical connection of intuitions, although
merely accidentally."
We have given these passages in full, because of the importance of
realizing the presuppositions upon which this distinction rests. In the
first place Kant-according to the received way of regarding the judgment
-has in view solely the concept, which is denoted by the subject-word, and
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which constitutes its significance. The question is whether the predicate
is one of the characteristics which I think in the concept of the subject,
“ although confusedly,” or whether it is not yet contained in this concept
as I now think it. In the particular judgment also, “some bodies are
heavy,” which is used as an example in the Prolegomena instead of the
universal judgment of the Kritik, the point dealt with is only that the
predicate heavy “is not really thought in the general concept of body.”
Here Kant presupposes, in the examples chosen by him, that the concept
is derived from experience, but contains only a part of the experience of
this object; or, as he expresses it in the first edition, denotes the complete
experience by means of a part of it. This implies two things: first, that
the concept is formed through a process of abstraction, whereby its
characteristics (as common characteristics of the different things from
which it is abstracted) have already been fixed; and secondly, that we are
not dealing with an exhaustive concept which expresses the whole nature
of an object of experience, but with a purely subjective image, in which-
from causes which have no necessary connection with the nature of the
thing-one part of the characteristics actually appertaining to the given
class of things is made use of to denote the class itself. Thus the only
ground for calling the judgment, “all bodies are extended,” analytical and
the other synthetical, is a generally accepted meaning (actual or assumed)
of the word body.
From the Methodenlehre (p. 721 sq. ed. i.) it is no doubt evident that
Kant regarded it as a matter of chance, so far as empirical concepts were v
concerned, which characteristics are employed for their formation. It is
there shown that in the empirical domain there are no definitions in the
strict sense, since the characteristics which belong to the object--e.8. gold
or water-can never be exhaustively enumerated, and hence the rule that
the definition should be complete can never be complied with. In our
concepts we include such of the characteristics alone as are sufficient for
distinguishing the objects; it is never certain that a word, while denoting
the same object, does not mean for us more of its characteristics at one
time than at another. The so-called definitions are only verbal determina-
tions, nominal definitions. The same view is taken in SS 99-106 of the
Logic.
In calling the judgment, “all bodies are extended," analytic, and “all
bodies are heavy” synthetic, Kant has therefore no other ground than a
nominal definition, which happens to be universally received. This is the
HOW JUDGMENTS ARISE
107
main point against which Schleiermacher's criticism is directed when he
declares that the distinction between analytical and synthetical judgments
is only relative, because the concept is always in the process of formation.
The same judgment (ice melts) may be analytical when we have already
included in the concept of ice its dependence upon definite relations of
temperature, and synthetical when we have not yet done so; thus the
difference represents merely a different stage in the formation of the con-
cept. Apply this to the Kantian concept: before the experience which
justifies me in the proposition, “all bodies are heavy,” I have formed my
concept only from the characteristics of extension, etc.; but after it I can
and must include the characteristic heaviness in my concept in order that
it may express the complete experience, and my concept, “all bodies are
heavy,” thus becomes analytical. With this concept I might now proceed
to further experience, e.g. I might go on to say that all bodies are electrical,
all bodies are warm. If my concept were the expression of a complete
knowledge, which indeed were impossible before all knowledge had been
attained, then all judgments of this kind would be analytical.
This criticism is fully justified by Kant's own statements. I can never
determine whether a judgment concerning empirical objects is analytical
or not unless I know the meaning which the person making the judgment
connects with his subject-word, the sun total of the characteristics which,
at this particular stage of the formation of the concept, he has compre-
hended in it. His progress from one meaning of the word to another takes
place by means of a synthetical judgment. This judgment, we must be
careful to note, is the result of an inductive inference, the only possible
ground for a universal judgment drawn from experience; but for this very
reason (as the Methodenlehre expressly emphasizes, p. 721) it cannot be
necessary and apodeictic. In the case of mathematical concepts this un- v
certainty disappears, but only because these are formed for a purpose and
contain an arbitrary synthesis (ibid., p. 729).
Before a judgment, considered in itself and independently of all other
considerations, can be regarded as analytical, it must evidently be assumed
that there are no subjective differences between the concepts which differ-
ent individuals connect with one and the same word. Assuming, then,
that words have a completely fixed and circumscribed meaning, there may
be judgments which are certainly analytical; in this case they are to be
found in the accepted meaning of the word. The Kantian example is
strictly correct, if it is presupposed that with the word body every one
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always connects the characteristic “ extended," and no one ever connects
the characteristic heavy.
But it is just as evident that if this is the case I can no longer have any
rational motive in giving utterance to such judgments, which are mere
truisms and convey no information. Who would trouble himself with such
judgments as "all triangles are triangular,” “all squares are square”? A
judgment which is analytical in this sense can never be uttered except to
some one who is in danger of forgetting the meaning of a word, of think-
ing the characteristics of the concept only “confusedly,” of extending it
beyond its sphere, etc.—i.l. to some one for whom it is, strictly speaking, no
longer analytical; for so long as he himself thinks the characteristics only
confusedly, he cannot even make the judgment. Thus judgments which are
analytical in this sense lead naturally to those which impart the uncompre-
hended meaning of a word to the ignorant-to those which no longer
make statements about thought, but only about words. They are strictly
analytical for any one who is master of the language ; but any one who is
only learning it makes synthetical judgments; his judgments, however,
being grounded not upon his own knowledge, but upon a belief in the
statements of other people.
4. But so far both Kant and Schleiermacher have failed to tell us how
the matter stands with those judgments which are not covered by our pre-
supposition, judgments, that is, of which the subjects are not concepts
at all, and in which the verbal expression does not show what idea is
present to the speaker, inasmuch as he is speaking, not of the contents of
the idea denoted by the subject-term in its generality, but of a concrete
thing which, though it falls under the general concept, is particular and
concrete, and hence cannot be completely denoted by the subject-term.1
But all actual and primitive judgments of experience are of this kind. Our
experience is gained from the particular, and the synthesis in the synthetical
judgment “all bodies are heavy” is dependent on judgments of which the
subjects are definite bodies, and in the last instance on particular percep-
tion and observation. Let us realize the process which underlies any
judgment of perception, e.g. this rose is yellow, this liquid is sour. It is
quite evident, if we consider the words and their meaning, that there is a
synthesis here, for yellowness is no part of the concept “rose,” nor sourness
of the concept “liquid”; nor from the meaning of "this,” which expresses
a mere relation, can anything further be derived. But then we are not
1 Cf. Trendelenburg, Log. Unters., 2nd ed., ii. 241 ; 3rd ed., 265.
1
HOW JUDGMENTS ARISE
109
concerned with the meaning of words; these are always general. “This
rose” denotes a concrete thing which, in its concrete particularity, can be
only very imperfectly denoted by the word ; the demonstrative “this ”
serves merely to draw the attention of some one present to an intuition
incommunicable by words, and this intuitable thing is the subject of my
judgment; it is of it that I say : it is yellow.
I might content myself with saying: this is yellow. The subject of my
judgment would be the same, but would be still more indefinitely ex-
pressed in language. When I say, “this rose is yellow," there is, properly
speaking, a double synthesis. First, there is a denominative judgment,
“this is a rose,” by which I have subsumed my concrete idea under a
general image, finding that the concrete intuition agrees in the whole of
its form, structure, etc., with the general image. But this denominative
judgment is only incidentally made; it does not itself appear directly, but
only in its result the subject-word by which I denote this thing.
The actual judgment before us, however, states that this, which I call a
rose, is yellow. Upon what ground ? Not on the ground of a synthesis
between “rose ” and “yellow," but on the ground of an analysis of my
intuition, in which, together with form and structure, is included the yellow
colour in an undifferentiated unity. One element of my intuition is
identical with what I call yellow, and this I then predicate of the whole in
an attributive judgment.
Or, more exactly, if we describe the process from the beginning: in my
intuition I have first noticed those elements in which it coincides with the
general image of the rose, hence the naming of the subject; I have then
noticed one further element, which as yet is not expressed by the name,
and hence the judgment.
The relation between the concepts “rose” and “yellow” of course
comes into consideration as well. If "yellow” were analytically con-
tained in “rose,” as white is in snow, or cold in ice, then, generally speak-
ing, I should have had no motive for expressly stating it; it would have
been already expressed by the name “rose.” But since this is not so, I
must, in order to describe my intuition completely, add the predicate yellow
to the denomination “rose.” Whoever hears my judgment—in the course
of a description, say-performs a synthesis as he adds the particular de-
termination of colour to the image which the word rose has awakened in
him. But I, the person judging, have merely analysed my idea of the
subject.
ΙΙΟ
LOGIC
But the other example: this liquid is sour. Is there no synthesis here?
Certainly, but before the judgment, not by means of it. This judgment
is distinguished from the preceding one by the fact that different senses
are concerned in it. I am accustomed to determine by sight whether or
not anything is a liquid, and thus the denominative judgment that is
presupposed is confined to visual ideas alone. Now I put the liquid to
my tongue and discover its sour taste, and I express my perception in the
judgment “this liquid is sour.” Before I can make this judgment I must
have already referred my sensation of taste to the object which was known
to me by sight; I must be certain that what has touched my tongue is
what I saw before in the glass. Otherwise I have no subject for the
predicate “sour,” and cannot make a judgment, cannot refer the predicate
sour to the subject liquid, and express this reference in an attributive
judgment. Thus my judgment analyses an act of combination which con-
stitutes the process of perception ; but the function of the reference of
the sensation of taste to its object is not the same as the function of the
judgment. If we expressed the former in a judgment, it would run “ that
which tastes sour is the same thing that I saw before as a liquid”; the
latter, “this liquid has the attribute of being sour." I must have re-
cognised sourness as belonging to, and being in the liquid, before I can
predicate it.
5. To return to the Kantian example: if we look more closely, we
shall find that there is still a sufficient ground—though nowhere indicated
by Kant himself—to justify him in saying that the judgment, "all bodies
are heavy,” is synthetic. This ground lies, however, not in the concept
“body," but in the nature of the predicate. Looked at carefully, "heavy”
is really a relational-predicate; it refers not to what a body is in itself as
the isolated object of my intuition and my thought, but to what it is in
relation to other bodies. The judgment, “all bodies are extended," is
valid in just the same way of each particular one, even though I should
think of it as being alone in the world ; the judgment, “all bodies are
heavy,” expresses a reference of each particular one to all others, and
hence it cannot be already contained in the “concept of body in general.”
If, as I believe, this, together with the historical influence of the old
Cartesian definition of body, is the hidden ground of Kant's apparently
unmotived distinction, it throws light also upon his “synthetical judgments
a priori,” for the examples which he gives of these are all relational-judg-
ments. That 7+5=12 is a relational-judgment concerning the numbers
HOW JUDGMENTS ARISE
III
represented by 7+5 and by 12 ; the judgment asserts their equality. The
predicate “equal to B," can of course never be contained and thought of
in the subject A taken by itself, nor discovered by any analysis of it ; for
the idea of B is necessary as well as that of A in order that it may be
thought at all. It is quite true, again, that equality with 12 is not
analytically contained in the expression 7 + 5. but must be discovered by
an actual addition, by proceeding to a number which is 5 more than 7.
The judgment is impossible until the addition has been completed, and
two numerical expressions given thereby; but then it is analytical in so
far as the intuition of the equal number of units which may be reached
in either the one way or the other furnishes the ground of the judgment.
It is not in the judgment itself that we pass beyond the presentation 7 + 5,
but in what precedes the judgment and makes the comparison possible ;
so soon as this is possible the judgment becomes a mere analysis of the
given relation. It is the same with Kant's geometrical example: that the
straight line is the shortest way between two points. “ The shortest way"
is also a relational-predicate, which cannot be contained in the idea of the
straight line by itself; it presupposes comparison with other lines. But
the straight line can never be presented in intuition apart from the space
in which it is drawn, and which contains the possibility of other lines
beside it. That which forms the ground of the judgment and is analysed
by it, is the total intuition in which the straight line appears between
others connecting the same points. So that even these synthetical judg-
ments a priori, so far as they are immediate, are really analytical; they
are not concerned with the explication of the concept expressed by the
subject-word when taken alone, but with a complex object which, though
partly denoted by the subject-word, contains something beyond the subject
of the judgment. The ground of the judgment lies in that part of the
object which is not denoted by the subject-word.
Of the principle of causality we must speak later on.
6. In the sphere of empirical notions the Kantian division of judg-
ments into analytical and synthetical refers to judgments having different
kinds of subjects, and therefore having also a different ground for their
validity. His analytical judgments are those which merely unfold the
contents of a concept which has received some fixed meaning in a word,
without any regard to the existing object of intuition. His synthetical
judgments presuppose intuition, and the synthetical connection of intuitions
in experience; their subjects are " things,” which fall under the word but are
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LOGIC
only incompletely denoted by it.
narrative.
The former are explicative, the latter
ception—an analysis, however, not of the concept, but of the intuition which
was formed by a synthesis preceding the judgment and not in it. We
have still to test the Kantian statement that in analytical judgments we
think the connection of the subject and predicate through identity, but
not so in synthetical judgments. Accepting for the present the term
identity, which we showed above to be inappropriate, we still fail to see
how any (affirmative) judgment can be expressed without identity ; i.e.
without the consciousness of the unity of subject and predicate. The
relation between subject and predicate is the same in the judgment of
perception as in the judgment which deals with concepts; and the state-
ment that identity is absent from the judgment of experience is true only
if we look, not to the proper subject of the judgment of experience, but
to the meaning of the word by which this subject is denoted; or when we
arbitrarily limit the notion of identity to the sphere of mere concepts.
But Kant is so far right that there is a different ground for the validity
of his analytical, and of his synthetical judgments a posteriori. The former
presuppose only the habit of connecting certain ideas with a word ; hence,
in order that such judgments may be repeated, nothing is needed but
constancy of ideas and agreement in the use of language. The latter have
their final ground of validity in a fact of individual intuition, which cannot,
as such, be made common property. The necessity of the former judg-
ments has its ground in the stability which we find in our general ideas;
the necessity of the latter in the laws according to which we form ideas
of the particular, and are conscious of their objective reality. And here
again we come upon the difference in meaning to be found in judgments,
owing to the ambiguity of the copula. In the judgments which Kant
calls analytical, nothing whatever is said as to the existence of their sub-
jects, in those which he calls synthetical the subject-word denotes “objects
of a possible experience.”
§ 19.
Before a judgment can be passed in which the idea of the predicate is
not immediately recognised as one with the idea of the subject, we re-
HOW JUDGMENTS ARISE
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and a predicate which lies outside it, and to cause us to recognise this
relation as a unity in the sense of the judgment, and to be certain of it. .
1. The first and most familiar example of a mediated judgment by
which a predicate is, for the first time, added to a subject and compre-
hended in it, is the mental act of a person who hears from some one else a
judgment which he himself has neither occasion nor ground for making.
All real learning is mediated judgment. The Socratic Maieutic, indeed,
starting from the principle that there is no such thing as learning, nothing
but recollection, is content to call into consciousness the ideas of sub-
ject and predicate by means of questions. Thus the materials alone are
provided, the person questioned being left to form his judgments himself,
and his conviction of their validity being based upon his own discernment.
And if this process were perfectly carried out, then, indeed, all judgment
elicited by it would be immediate and analytical, finding the predicates in
the subjects without assistance. The questioner would merely take upon
himself the work of the psychological laws of reproduction, bringing to
the subject just that idea which is appropriate as predicate, for the mind
in its continual eagerness to form judgments to make use of.
But teachers and taught have seldom time for this process; it is nearer
the truth to say that all learning begins with tradition, where the learner
accepts the judgments he hears, and repeats them himself. In so far as he
learns, what happens is that he hears a proposition, the idea of a subject
is aroused in him by the subject-term, and he includes in it a predicate in
respect of which the subject had as yet been undetermined. When
any one learns that ice is frozen water, ice is given to him in intuition,
but its mode of formation was unknown, and no reference to water con-
tained in his intuition. For the person who learns that the earth moves, a
completely new determination is added to the idea of the earth—that of
movement, and he is called upon to unify subject and predicate in a way
contrary to his habit of thought. Not until he has understood what he
has heard, i.e. really made the synthesis demanded, does he reach as the
result of his mental action that from which the teacher set out the unity
of subject and predicate in the sense determined by their category. In-
deed, there will still be a difference between teacher and taught as indi-
viduals; for on the one hand the words are not absolutely fixed and equiva-
lent in meaning for both; on the other hand, even if they were, they leave
more or less room for choice between particular degrees of meaning in their
application to particular things.
S. L.
I14
LOGIC
In proportion as the individual is ignorant, and connects with his words
only meagre ideas based upon incomplete knowledge, he must have recourse
to such synthetical judgment; and by means of this his words become
ticular determinations. At the word “lion " the child at first thinks only
of the outward, visible form which his picture-book shows to him; from
tales and descriptions his idea becomes enriched with all the attributes and
habits of the animal ; while the zoologist possesses the idea complete.
The more perfect the knowledge, and the richer therefore the meanings
of words, the less room there is for syntheses such as these, in which some-
thing new is learned. In the end synthetical judgment would be limited
to that sphere which can never be denoted by words—to the particular
fact as it is for any one who has not observed it himself, and to the par-
ticular changes and relations which can only be expressed by temporarily
valid judgments. All judgments about the meaning of the word, the
general idea of the object, are then analytical. (This is what Schleier-
sphere of particular facts. Dialectik, $ 155, pp. 88, 105.)
2. In learning by tradition the ground which the learner has for the
certainty of the judgment is merely the authority of the teacher ; objective
validity is accepted from confidence in his knowledge and veracity; he is
believed. Since all narrative judgments are necessarily synthetical for the
hearer, they are those which, by their nature, appeal to and demand the
belief of the hearer. Besides one's own perception (and whatever may
be inferred from it) there is no knowledge concerning the particular ex-
cept by way of belief, which, in this case, is historical belief.
3. There is another process, similar to those of teaching and narrating,
which adds predicates to a subject capable of further determination, and
calls upon us to unify them. It is introduced by the inward play of our
ideas, as determined by the laws of associative reproduction, and the
activity of imagination as led by similarity. When we are conscious
of any object through perception or recollection it does not merely
call up those predicates which agree with its contents as now presented
and lead to immediate judgments. Recollection, association, and
analogy bring forward other ideas, which tend to combine as predicates
with the subject, although they are not as yet contained in the idea of
the subject now present. From one point of view the common case
already dealt with in $9, p. 55, is an instance of this the case in which
HOW JUDGMENTS ARISE
115
visual images of particular objects call up the recollection of their other
qualities, and these are forthwith attributed to them as predicates. (This
is a bunch of grapes—this is sweet; this is a stone-hard, etc.) But
though, in such instances, association takes place with such absolute
certainty that when the judgment is made the idea to which it refers is
already complete, we do find cases differing from these by imperceptible
degrees, in which the fusion does not take place at once, but the idea
called up remains-to use Herbart's phrase-in suspense, and only brings
the expectation of a judgment. This is most obvious when different and
mutually-exclusive ideas are excited at the same time, and a struggle takes
place between them, as, for instance, when I see a human figure at a
distance, and it excites in me the images of both A and B, seeming to
resemble first one and then the other.
Upon such associations are founded more particularly all judgments
which extend to the future. They can never proceed from analysis of the
present, but are mediated by some process of inference. “The snow will
melt.” I cannot tell this by looking at it, but, led by former experience, I
add in thought to the present intuition a predicate not yet contained in it.
4. The universal tendency to form judgments and to connect what is
new with what is familiar, is so strong that, when there is no check, the
same processes which suggest the predicate may also give rise to the
judgment; i.e., they may produce belief in the objective validity of the
proposed synthesis. In proportion as thought is undisciplined it is in-
cautious, and slow to recognise the difference between purely subjective
and psychological combinations and those which are objectively valid ;
there is a greater tendency to believe everything which occurs to one,
especially when strongly supported by a wish or an inclination. The
recollection of one or a few cases in which a predicate B belonged to a
subject A, is generally sufficient to make us attribute the predicate B to
every subject which at first sight resembles A; and we are often scarcely
conscious of the process of inference by which the synthesis of the judg-
ment has been brought about. This credulity of our natural thought, while
the source of many deceptions, hasty assumptions and superstitious opinions,
is at the same time the indispensable condition on which alone we can
profit by experience, and learn to pass beyond what is immediately given.
As we found with the generalization of ideas that the process has not to be
learned but rather to be checked, and the power of distinguishing cultivated,
so it is also with judgment when it passes beyond what is given. Our
116
LOGIC
natural tendency is always to think of many predicates and attribute them
to the subject; what we have to learn is caution and doubt, to distinguish
between the valid and the invalid, and to enquire as to which of these
syntheses are objectively necessary, and which are merely forced upon us
by nature and habit.
5. When some check prevents the judgment which passes beyond what
is immediately given from taking place, there arises the question. This
may be in two ways. In the one case we seek to complete a given idea
in accordance with some previous experience, the desired completion not
being offered by any absolutely certain association. Such is the case
when I cannot recall any idea agreeing with a new and unknown object-
what is that? Or when I seek the subject to a given attribute or activity
—who is speaking? What is that shining? Or again, when I am uncertain
what attributes or activities belong to a thing besides those perceived-
what does that taste like? In the second set of cases a completion is
offered by association, but the certainty of its validity is wanting; the
judgment is sketched out in thought, but is not passed as a judgment.
In this way there arises the question which seeks a decision as to the
validity of a given predication-is A really B?
6. Both the question which aims at completion, and that which aims
at confirmation, presuppose psychologically the simple and immediate
judgment which is inseparably connected with the consciousness of its
validity. I can only seek for that of which I have at least a general and
indefinite idea ; nothing but experience of perfect syntheses can create in
me the desire of completing an imperfect idea by the addition of some
further element. I must have acquired the habit of referring sensations to
definite things before I can arrive at the point of seeking the thing belong-
ing to a sensation which is presented without any certain reference.
In the same way the question which demands yes or no for an answer
ments before it can be sought. Its search for an answer implies the
thought of the certainty connected with predication in other cases.
In simple and immediate judgments—that is a tree, that is red, snow is
synthesis of subject and predicate. I cannot ask whether coal is black, or
snow white, whether the object before me is red or a tree. As soon as I
am conscious of the two ideas I am also conscious of the necessity of the
synthesis between them.
HOW JUDGMENTS ARISE
117
It is not until we attempt to pass beyond what is given, not until we
would unite with the idea of the subject an element not yet contained in
it, that the two elements which are united in the immediate judgment, the
simple or complex synthesis between subject and predicate and the con-
sciousness of its necessity and objective validity, can be separated. The
question “is A really B?” can only arise in that sphere of thought in
which judgments are formed by a process of mediation.
Hence it follows that the first stage in the formation of judgments—our
psychological starting-point-is not invariably (as e.g. Bergmann holds 1) a
“predication without quality,” a mere “idea” in which subject and
predicate are thought together, the judgment taking place only when the
“critical reflection” upon its validity is added. In the simplest cases the
two elements are not found apart, and we cannot show the meaning of
predication in general unless we start from objectively valid predication as
it occurs in the immediate positive judgment “ A is B.”
All such theories overlook the fundamental importance of the distinc-
tion between immediate and mediated judgments, a distinction which in
logic is not less important than that between analytical and synthetical
judgments in the transcendental philosophy.
7. In the question “is A B?" the elements and the connection
between them have the same meaning as in the judgment. The question
expresses the expectation of a synthesis between A and B, and moreover
of a valid synthesis, not merely of an arbitrary combination. The judg-
ment is already conceived, but it still needs the seal of its confirmation,
for the certainty of validity is wanting. This invention and essaying of
judgments which pass beyond what is given and the immediate judgments
based thereon, represents the active movement and progress of thought
in inventive action in the sphere of the judgment. We may say at once,
questioning is thinking. Doubt, conjecture and expectation are only
particular varieties of the same state. They differ in the degree to which
we are conscious of the absence of a ground for the completion of the
judgment; they are alike so far as concerns the meaning of the synthesis
between subject and predicate.
8. The decision of a question may sometimes come from the elucida-
? Reine Logik, 1879, p. 42, 169 ; cf. the objections raised by Schuppe, Vierteljahrsschr.
für wiss. Phil., iii. 484 ; my own article, Vierteljahrsschr. für wiss. Phil., v. I, p. 97 ;
and Bergmann's reply in the same journal, v. 3, p. 370. Brentano's view is dealt with
in my Impersonalien, p. 58.
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LOGIC
tion and completion of the subject-idea itself; when this idea is the
intuition of a particular object, we discover by means of more exact appre-
hension and observation what was not formerly observed. Such is the case
when, seeing a white powder, I ask whether it is sweet and put it to my
tongue ; I have then made an addition to my perception, and my answer
is an analytical judgment proceeding from the new perception. When my
subject-idea is not given in intuition, reflection may bring more complete
recollection, and again enable me to make an analytical judgment. But if
these attempts fail, then the only way of arriving at a decision is to seek
for mediations which may confirm the attempted synthesis, and the
mediation to which the spoken question appeals in the first instance is
information from some other person.
9. It may be that a ground for the desired synthesis, which would
enable it to take the form of a judgment, can be found neither by the
elucidation or completion of the subject-idea, nor yet by mediating ideas.
Then either the question remains unsettled and we fail to become conscious
of its objective validity, or else the negation arises, from the fact that the
subject-idea immediately or mediately repels the predicate-idea.
Reserving for a later investigation the former case—that of the falsely
called problematical judgment—let us now turn to the negation.
CHAPTER IV.
THE NEGATION.
§ 20.
THE NEGATION is always directed against an attempted synthesis ; hence
it presupposes some prompting, either from within or without, to connect
the subject and predicate. The object of a negation must be either a
completed or an attempted judgment, and for this reason we cannot regard
the negative judgment as a species equally primitive with the positive
judgment, and co-ordinate with it.
1. Following the example of Aristotle, many logicians have begun by
defining the judgment as either affirmative or negative, making this twofold
aspect a part of its definition. This is true in so far that judgments when
formed can be exhaustively divided into affirmative and negative, and that
when we form judgments, it can only be by affirming or denying a pre-
dicate of a subject. But the definition is false if it implies that affirmation
and negation as forms of judgment are equally primitive and independent
of each other, for the negative judgment presupposes the attempt, or at
least the thought, of an affirmation, i.e. it presupposes the positive
attribution of a predicate, and has its meaning only in contradicting or
annulling such an affirmation. Or rather, the primitive judgment should
not be called affirmative at all; it would be better denoted as positive.
The simple statement A is B is an affirmation only when opposed to the
negative judgment and in so far as it rejects the possibility of a negation ;
but that we should think of the possibility of a negation, or that a question
should be raised which must be decided by yes or no, is no necessary
condition of the judgment A is B.1
2. When we consider that only a finite number of predicates can be
affirmed of every subject, while an incalculable number can be denied, it
is at once evident that the negation has no meaning except in opposition
1 Cf. Beneke, System der Logik, 1, 140 sq.
119
I 20
LOGIC
to an attempt at a positive statement. No one would think of making all
the negations which in themselves would be possible and true; he could
have no motive for so doing. Before there can be any sense in saying:
this stone does not read, does not write, does not sing, does not think ;
justice is not blue, is not green, is not five-cornered, does not rotate, etc.,
there must be a chance that some one will attribute these predicates to the
stone or to justice.
All that the negation aims at is to confine within limits fixed by the
nature of the given ideas the subjective and fortuitous movement of
individual thought, which in fancies, questions, conjectures and erroneous
statements extends beyond what is objectively valid. Thus it presupposes
a subjectively arbitrary and contingent thought-the limitless sphere of the
false, which consists in just this deviation of individual thought from the
thought which is objectively necessary and universally valid, and it is a
matter of chance how the negation may arise with any particular individual.
It is impossible to lay down universally and exhaustively what must
necessarily be denied of any subject.1
3. We cannot further define and describe what we mean by “not,” nor
what is the significance of the negation; we can only recall what always
takes place in the process. The true meaning of the proposition A is not
B may, however, be elucidated by contrasting it with incorrect and artificial
interpretations.
In the first place subject and predicate, taken each by itself, are thought
in the negative propositions in exactly the same way as in the positive; the
words stand for the same ideas. When I say "snow is not black," snow
means the same as in the judgment "snow is white,” and black the same
as in the judgment "coal is black”; no effect is at present produced upon
them by the negation, they have their usual contents. The question raised
by Aristotle (De Interpr., 2 and 3) as to whether there is a ovoua åóplotov
(oủk ävOpwtros) and a Pñua åóplotov (oủ káuvel) which could appear as
subject or predicate of a judgment does not refer to the essence of the
negative judgment, but only to the nature of the subjects and predicates
which can be used in a judgment, and can be affirmed or denied of each
1 Kant, Kr. d. r. V. Methodenlehre, ed. 1, p. 709 (a passage which Windelband
points out in the Strassb. Abh., p. 169), says : In respect of the content of our knowledge
in general, negative propositions have the peculiar function of simply averting error ;
hence also negative propositions which aim at averting false knowledge when there is no
possibility of error may indeed be very true, but they are devoid of meaning, and for
that reason often very ludicrous.
THE NEGATION
I 2 I
other. A natural and primitive idea can never be denoted by the
expression not-A or not-B, but it is always possible that these expressions
may be serviceable as abbreviating formulæ, under which definite subjects,
or at least predicates, may be thought. But then they act as symbols of
these, and when a statement is possible at all some predicate is affirmed or
denied of such subjects, or such predicates of some subject; the judgment
not-A is B and the judgment A or not-A is not-B are affirmative, the
judgments not-A is not B and A or not-A is not not-B are negative.
Aristotle has given the right explanation of this. It is true he attempts all
possible combinations with unlimited subjects and predicates (De Interpr.,
10), but he does not make into a particular kind of judgment those in which
a subject or predicate of the form not-A appears. When, on the other
hand, Kant places the infinite 1 or limiting judgment beside the affirmative
and negative as a third kind (Kr. d. r. V., § 9)—the soul is not-mortal, that
is, belongs to the infinite sphere which remains when I take away the mortal
—then he starts from a view of the judgment which we shall have to oppose
later on, a view which takes its essential aim to be the placing of a subject
within the sphere of a concept. By this view he is enabled to bring out a
distinction between the propositions “the soul is not mortal,” and “the
soul is not-mortal”; he does not, however, thereby gain a third judgment
in addition to the positive and negative, but is himself obliged to allow that
in general logic there is no ground for considering a judgment of the form
A is not-B, in which a purely negative predicate is attributed to A, to be
anything more than an affirmative assertion.
4. In opposition to the attempts to regard all negative judgments as
affirming a predicate not-B of a subject is the largely accepted tradition
that the negation affects the copula, by which we are led to speak of the
affirmative or negative quality of the copula. This is so far true that the
negation does not lie in the elements of the judgment, but only in the
manner in which they are referred to each other. But it is incorrect to
oppose a negative to an affirmative copula. If by copula we understand
the expression of that mental act by which a predicate is referred in the
judgment to a subject as agreeing with it, as activity or quality, then a
unification is expressed by it. But that which holds subject and predicate
apart, and prevents the attainment of unity, cannot be a kind of unification.
1 The name comes from an awkward translation and application of the abpuotos,
which Aristotle had used, not of the judgment but of its component parts. Cf. Tren-
delenburg, Elem. Log. Ar., $ 5.
I 22
LOGIC
A bond which divides is nonsense. We should rather say that the proper
copula (in language the verb-ending) has exactly the same meaning in the
negative as in the affirmative judgment; that is, it expresses the positive
relation in judgment between subject and predicate, the attributing of the
predicate to the subject, and it arouses the thought that the predicate
belongs to the subject. For it is just this thought (which is also contained
in the question) which is declared to be false ; it is just this attempt at
synthesis which the negation prevents. The copula does not convey the
negation, but is the object of it. There is no such thing as a negative,
but only a negated copula.
Three elements, then, can be primarily distinguished in the simple,
positive judgment. These are the subject, the predicate, and the thought
of their unity (in the particular sense of the synthesis determined by the
categories), this latter being the object of the certainty which finds utterance
in the positive judgment. The same three elements are present, and have
the same force, in the negative judgment; but the negation is added as a
fourth in language as well as in thought. This prevents the completion of
the attempted synthesis as valid, and it opposes its “No” to the whole
proposition A is B. The object of the certainty, which gives to the negative
proposition as well as to the affirmative the force of a statement, is just this
“No." The judgment “A is not B” means, “it is false, it must not be
believed that A is B”: hence, immediately and directly, the negation is a y
judgment concerning a positive judgment that has been essayed or passed ;
only indirectly is it a judgment concerning the subject of this judgment.1
5. If the negation were formed by means of a negative copula—if, there-
fore, we had to regard the “is not” in the judgment“A is not B” as the ex-
pression of a simple act of thought,—then, to be consistent, those logicians
who ascribe to the “is” of the affirmative judgment the force of stating the
existence of the subject should hold that the “is not” in negative judgments
denies the existence of the subject. But this is certainly not the case. As
a rule, the judgment A is not B presupposes the existence of A in all cases
when it would be presupposed in the judgment A is B; i.e. whenever it is
part of the meaning of the words. But the negative judgment in itself
states no more concerning existence or non-existence than the affirmative
judgment. “Socrates is not ill” presupposes in the first place the existence
of Socrates, because only on the presupposition of his existence can there
be any question of his being ill. But since the negation only declares it to
1 See Appendix A.
THE NEGATION
123
be false that Socrates is ill, the presupposition contained in it is certainly
not so definite as in the affirmative judgment "Socrates is ill”; for this
may also be denied because Socrates is dead. (For further, see below,
§ 25.)
$ 21.
The negation follows the different forms of the positive judgment, and
has for its object those different relations between subject and predicate
which constitute the different meanings of the unity between them. Hence,
when the judgment contains a manifold synthesis, the negation is ambigu-
ous. Directly it can express nothing existent-neither attribute, activity,
nor relation.
1. In prohibiting an attempted statement, the negation adapts itself to
all the different kinds of propositions; and whatever these may state, it
declares to be false.
To the judgment which would allow two ideas to coalesce as wholes,
the negation opposes their difference. Such propositions as “apes are not
men,” “red is not blue," " freedom is not license” prohibit a threatened
confusion, or a conscious annihilation of the distinction fixed between the
objects. This negative judging brings into consciousness by an express
act what was already contained unconsciously in the formation of our
ideas and in their verbal denotation. That is, it makes us conscious of
that distinction between different ideal contents which, being always drawn
in the same way, gives us a fixed plurality of ideas to which the plurality
and difference of words corresponds. This act of distinguishing, through
which our ideas are formed, must have already taken place before it can
be brought into consciousness and confirmed by the negative judgment.
When opposed to the qualitative judgment, the negation prohibits the
relation of inherence between a subject and an attribute ascribed to it. The
relation of inherence in itself even forms the ground for the negative judg-
ment. The proposition "lead is not elastic” does not deny that the subject
is a unity of thing and attribute, but that the attribute, which really belongs
to the subject and which is not expressed in the statement, is the one in ques-
tion. I cannot find in the subject "lead” the attribute denoted by "elastic”;
the actual attributes of lead are other than elasticity. So that here, also,
what the negation finally emphasizes is the fixed difference of certain
qualitative ideas. The same holds good of judgments whose predicates are
activities.
I 24
LOGIC
2. Now according as the movement of thought (see $ 11) passes from
the attribute or activity to the thing to which it belongs, or the reverse, the
object of the negation also varies (the variation being expressed verbally
by emphasis or position). It may either lay stress upon the fact that a
given thing, with fixed determinations, does not possess the attribute or
activity in question, or emphasize the fact that it is not this thing to which a
given attribute or activity belongs. The judgment "I have shouted” is as
false when no one has shouted at all as when it was someone else who
shouted. In the first case, the reality of the predicate is denied, in the second
its relation to the subject; in the latter, the subject is generally emphasized,
or the negative placed before it (I have not shouted; it was not I that
shouted). Finally, the negation may mean that neither predicate nor
subject is to be found. Starting from the general view of the negation,
the proposition “the fire does not burn” is a contradictio in adjecto. How
can the predicate “ burn” be denied of the subject fire ? And yet we do
not hesitate to say it; we expect to find the burning fire, the negation says
“it is false that the fire burns," and this proposition is true when there is
no fire at all. This applies especially to the negation of the Impersonals.
“ It does not thunder" means either that the name given is false--that
what is heard is not thunder, or it denies the phenomenon itself, which is
indicated by the predicate—the negation extending also to the presupposed
reality of the subject.
3. Similar modifications appear in the case of relational judgments.
That is, the synthesis of the positive judgment being here threefold, we
cannot tell from the simple negation of the relational judgment what the
statement of the negation is primarily aimed at, nor what is the point which
the person making the negation has in view. If the judgment “ A is
walking home” be false, what is denied may be merely the direction in
which he walks, or it may be the kind of movement (if he is riding or
driving), or the fact that he is going away at all; or, finally, it may be
disputed that it is A who is walking home. The proposition “ A is not
walking home” may have any of these meanings. . This ambiguity of the
negation, which at best can only be dealt with by emphasis, is a new proof
that its only force is to state the falsity of the positive judgment as a whole,
and that it is unable by itself to constitute any definite relation. In
the case of causal relations, which are expressed by transitive verbs, the
negation may be directed merely against the particular object of the
activity, which itself really takes place, or against the activity itself, or
THE NEGATION
125
against the subject to which the activity is ascribed. “I have not written
this sentence” may either deny the whole fact that the sentence in question
has been written, or it may emphasize either this sentence, or I. “I
have written nothing" denies all writing whatever by the negation of every
possible kind of object of writing; “I drink no wine” denies only a
particular kind of object.
4. In the same way, when an unconditionally valid judgment is denied,
the negation merely tells us that the statement made by the unconditionally
valid judgment is false, the statement being that the predicate is contained
in the subject-idea, which constitutes the meaning of the subject-term
(plants do not feel ; light is not matter). How far such negations may be
ambiguous (e.g., the triangle is not equilateral) will be discussed below,
$ 25.
When opposed to temporally valid judgments, the negation applies only
to their validity for the time stated, and cannot therefore say anything as
to the condition of the subject at any other time. The judgment “this
watch is not going” declares that the temporally valid judgment “this
watch is going” is false; and what it means by that is that it is not going
now; this negation leaves it undecided whether or not the watch goes at
other times.
5. Attempts have not been wanting to supplement the poverty of the
negation as merely annulling some other statement by giving it the force
of a directly significant statement. In this way, what is stated by the
negative judgment would stand opposed as independent and valid in itself
to what is stated by the affirmation; and thus negation and affirmation,
as forms of statement, would occupy the same rank.
Aristotle himself has to some extent given a precedent for this. He
makes the affirmation and negation (particularly in the Metaph. ®, 10, 1051,
b 1 sq.) correspond to a unification (ovyktiobal) and separation (dypño bal),
and in so doing he makes it the primary meaning of the relation between
subject and predicate in the affirmative judgment to express something
compounded (from substance and accident). We have already (8 14, p.
80 sq.) shown this view to be impossible, since the predicate of the
judgment can never be looked upon as something existent; least of all as
an existent thing which can be thought apart from the subject. There is
no meaning in saying that, in the existent, “commensurable” is always
separated from the diagonal of the square ; separation and unification both
belong to thought alone. But, for the same reason, neither can the nega-
I 26
LOGIC
tion correspond to any separation. In the first place, elements actually
separate in the object could have no mutual reference whatever; and it
would be inexplicable how these separate elements should be found
together in one act of thought. Moreover, here again, since the predicate
never stands for anything but an idea, we cannot say that it exists anywhere
in such a way that it can either be united with the subject, or remain
separate from it. The view that the proposition “man is white” is the
expression of a unification of the substance “man” with the idea of “white,”
because the latter has an independent existence, would be impossible,
except as a consequence of the Platonic doctrine of ideas. It is due to
this alone that the relation between a thing and a predicate which is
incompatible with it can be denoted as a “perpetual separation.” 1
On the other hand, Spinoza's well-known proposition “Determinatio est
negatio” has been made use of to express a view which goes so far as
to transfer the negation into the nature of things themselves, thus ranking
the negative judgment as the original expression of knowledge of these.
Trendelenburg has rightly drawn attention to Thomas Campanella as one
of the most decided supporters of the opinion that all things consist in yes
and no, being and not-being; that everything is this particular thing only
because it is not something else. “Man is,” that is his affirmation. But
he is only man because he is not stone, not lion, not donkey; hence he is
at once being, and not-being. Spinoza has the same meaning when he says
“Determinatio est negatio”; a figure is determined in so far as it is not the
space surrounding it, and thus it can be thought of only by the aid of nega-
tion—as a limitation, i.e. negation of the infinite. But such views always
involve a confusion between the negation itself as a function of our thought,
and the presupposed objective ground of this negation-the exclusive
individuality and uniqueness of each one among the many things which are
real. That which they are not never. belongs to their being and nature ;
it is only our thought, which, in making comparisons, brings such alien
elements into contact with them. All that concerns us is to recognise why
we have need of these subjective expedients in order to know the world of
reality in which no counterpart of our negating thought is contained. It
is only by a constant confusion between negation in thought and those real
relations in being which are very imperfectly expressed by mere negation
.
1 Prantl has very justly noticed the deficiency of the Aristotelian theory in this respect
in his Geschichte der Logik, 1, 118, 144 sq. Elsewhere Aristotle expressly recognises
that the negation belongs only to the sphere of thought (Metaph., vi. 4).
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127
that the Hegelian logic succeeds in presenting it as a real power, and as the
nature of things; but unless we may admit this confusion once for all, as
may well be done after Trendelenburg's penetrative criticism, it must be
pointed out at almost every step of the Logic.
§ 22.
When the attempt to attribute a predicate to a subject is prohibited by
the negation, the ground for this prohibition lies either in the fact that the
predicate in question is wanting to the subject (or, in the case of certain
relational judgments, the subject to the predicate); or else in the fact that
the subject, or at least one of its elements, is incompatible with the predi-
cate. The mere statement of the negation does not show which of
the two it is.
Further, the negation is equally unable to explain, or even to give com-
plete expression to, those relations between ideas by virtue of which
they are incompatible (the so-called contradictory and contrary opposition).
I. When a negative judgment is not inferred—when, therefore, the
negation is not mediated by interposed terms—we have nothing but the
given subject, and the attempted predicate, as materials for our negation.
Hence the ground for prohibiting the predicate must lie in the relation
which is given between the ideas of subject and predicate.
There are two ways in which this may be. Either the predicate is
wanting in my subject-idea (or, in a relational judgment, one element is
wanting in the whole ideal complex), or it is excluded by the subject-idea
(or by the ideal complex present). The ground of the negation may be
either a deficiency (otépnous, privatio) or an opposition (évavtiórns,
oppositio).
2. It may be that the subject-idea is concrete and particular, an object
of intuition, and the attempted positive judgment a temporally valid one
which is to be denied in the same sense in which it was supposed to be
asserted. In such a case the negative judgment rests upon my conscious-
ness of not finding the predicate in my intuition of the subject-upon
immediate knowledge of the difference between the subject as it really is,
and another conceivable thing possessed of the predicate, upon my
consciousness, that is, of a deficiency of determination in the subject.
“This watch is not going,” “this flower has no scent,” “ the invalid is not
moving," “ the sun is not warm to-day,”—all these judgments proceed from
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LOGIC
my consciousness of difference between what is given and what is merely
thought of, between this watch and one which is going, between this flower
and one with a scent; it is the fact of my bringing a more fully determined
idea to what is actually given which gives rise to my judgment. In the
case of relational predicates, again (Socrates is not here), the complex of
things expressed by the attempted judgment (Socrates and myself in the
same portion of space) differs from the complex given to intuition
(Socrates is absent from the portion of space in which I am).
The deficiency becomes more striking in proportion as the more com-
plete idea is familiar and easily produced for comparison, and in propor-
tion as the missing predicate seems to belong more closely to the whole
complex. The absence becomes a deficiency in its narrower sense—the
absence of something which should be there—when reference to a purpose,
or an æsthetic law, demands the completeness of the predicates. Logic-
ally, however, such references, which give a colouring of disappointment to
judgments such as “he does not see," " he does not hear," "he will not
understand this," " the sentence has no meaning,” have no value except to
draw attention to the deficiency, and to enable us to realize the standard
of comparison. They form no ground for any particular kind of nega-
tion as such.
3. The same absence of a predicate takes place also in the case of
general ideas. The negative judgment may be based upon the fact that
the predicate does not form a part of the idea which constitutes the mean-
ing of the subject term : “plants do not feel,” “ water has no taste," etc.
Comparison with things related in other respects, of plants with animal
organisms and of water with other liquids, forms the ground for the priva-
tive judgment; something which, to judge from the nature of the subject
in other respects, might belong to it, does not belong.
4. The same ground for a negation would be present, if the attempt
were made to attribute to a more general idea predicates belonging only to
the particular ideas which fall under it, and are more fully determined. It
is no part of the general idea of the triangle that it is plane, nor that it is
spherical; nor is it part of the idea of the plane triangle that it is right-
angled or acute-angled. It is not contained in the idea of man in general
that he is either black or white, straight-haired or woolly-haired ; nor in the
general idea of motion that it is progressive or rotatory. Still, we cannot
express this mere indeterminateness of the subjective general idea by the
simple negation of those predicates. The propositions, “ the triangle is not
THE NEGATION
129
117
spherical,” “is not right-angled," “ man is not black," " motion is not
rotatory," would be understood in a quite different sense, as stating that
the predicate was wanting to all the objects denoted by the name. So
strong is the habit of passing at once from general ideas to the most
concrete and determined ideas in which they are contained, that the
proposition “the triangle is not rectangular,” though quite true in itself,
would be misunderstood. It must be expressed “the triangle is not
necessarily rectangular,” or “not all triangles are rectangular.” Cf. below,
§ 25.
5. With the negation which is based upon the privative relation, and
hence upon a simple difference, we may contrast that which arises from
the fact that one element of the subject-idea repels the predicate-idea.
Here we cannot even think, as we do in the case of privation, that the
predicate might belong to the subject. (The same thing takes place in the
case of relational-ideas ; it is false that A is to the left of B either because
A is not near B at all, or because it stands to the right of B; the one rela-
tion prohibits the other.) This brings us to those relations between ideas
by virtue of which they are able to exclude each other as predicates of one
and the same subject.
6. Suppose we are dealing with a denominative judgment, in which the
attempt is made to unify subject and predicate as a whole with a whole;
then the exclusiveness of the relation between different ideas is due to the
fixed determination and differentiation (within the different categories) of
our ideas-a determination and differentiation presupposed in all judging,
since it is the condition of the continuity and harmony of consciousness
itself. “ Socrates is not Crito,” “ wood is not iron,” “red is not blue,”
“seeing is not hearing,” “right is not left,"—such judgments are based
upon the fact that we have a multiplicity of ideas distinguished from each
other with certainty, and guarded against all confusion and mistake; and
all the judgments can do is to remind us that these differences are always
present (§ 21, 1). The knowledge that two ideas differ is, indeed, generally
earlier than the knowledge of how they differ; for in order to show
how they differ I must finally have recourse to elements of which I simply
know that they are different. I distinguish with certainty between my
friend A and my friend B before I realize to myself what it is wherein they
differ. Suppose I did realize it, and become conscious that the one is fair,
the other dark; the one of a round, plump figure, the other lean and
angular ; the difference between fair and dark, round and angular, lean and
S. L.
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LOGIC
plump would still remain ; and here all that I can finally say is that they
differ, not how.
In treating of the affirmative judgment we were obliged to lay down
(§ 14, p. 83 sq.), as the presupposition of its possibility, a principle of
agreement, according to which ideas are recognised as like with unfail-
ing certainty, and upon which all possibility of certainty in an affirmative
judgment depends. We may find a similar ground for the negation in the
proposition that different ideas are immediately and unfailingly recognised
as different, and that it is impossible that there should be any mistake as
to whether two ideas present in consciousness are different or not. If the
formula “A is not A” had not been misapplied to denote everything and
anything, we might make use of it to express that A is different from all other
ideas; that everything which is thought is just itself and no other. It
would then state both a law of our differentiating thought and a funda-
mental psychological fact.
Does any one appeal, in opposition to this, to the fact that we do confuse
many things, and so fall into error? Then we answer, first, that confusions
with reference to things take place because their differences are not repro-
duced by our momentary ideas; as e.g. when I mistake an artificial flower
for a natural one, because I have observed it superficially—in this case my
ideas do not differ as they would have done had my observation been more
complete. Secondly, that confusions take place in consequence of the
imperfect reproduction and constancy of our ideas, one substituting itself
for the other in course of time. Thus I may greet a stranger as an old
acquaintance because the image of my acquaintance has faded, and under
the impression of what I now see is represented as different. But this
does not mean that it is possible to hold that two ideas are not different
when they are present as different in consciousness, and are retained
undisturbed during an act of judgment. On the contrary, all unity and
clearness in self-consciousness depends upon this power of the negation to
hold asunder the manifold presented to us, and to guard it from blending
in confusion; and in the same way the one possibility of being certain of
the validity of a judgment, and hence the possibility of judging, depends
upon an immediate and perfectly certain consciousness of difference.
Where this could not be presupposed, -as, say, in a case of insanity,—all
community of thought would cease.
7. In the case of attributive judgments, it is more difficult to investigate
the conditions of the negation. The same thing may have different attri-
THE NEGATION
131
butes, and different things the same attribute; this simple difference in the
ideas of attributes affords no ground for denying attribute B of thing A
because it possesses the different attribute a; or for denying attribute a of
B because A has it; though there is ground for saying A is not B, a is not
B. The question is: what is necessary in order that we may say of a thing
A that attribute B cannot be united with it? Clearly it can only be said
when one of the attributes of A stands in such a relation to attribute B,
that they cannot both together belong to the same subject. Thus one par-
ticular colour on a surface—.g. white-excludes all other colours. The
fact that snow is white enables me at once to deny all other colours of it;
the fact that a line is straight enables me to deny the predicate curved of it;
and so on. This is true also of verbal and relational predicates. Sitting
and standing, standing still and walking, right and left, equal and greater
or smaller, are all mutually exclusive ; if the one is true of any thing, the
other must be denied of it.
8. The expressions “opposition” and “opposed” have, like that of
identity, become almost useless owing to the different meanings given to
them, and owing to the frequently vague relation between what was called
opposition and negation on the one hand, and difference on the other. The
conflict of particular ideas has been confused under the same name with
the contradiction of judgments; and with reference to the more special
relations of conflicting ideas there is confusion of language like that in
the Tower of Babel. Let us attempt to formulate the distinctions from
the nature of the case.
There can be no reasonable ground for denoting as conflict or opposition
the mere difference of ideas which is the condition of all thought. Just
as all sorts of things co-exist without conflict in space, and present in their
different attributes the varied image of the world, and its perpetual change
in their various activities, so our thoughts contain an incalculable manifold
of ideas between which there is no conflict, although each is looked upon
as particular and indeed differentiated. Negation distinguishes them and
suffices to give to each its due. In themselves there is no more conflict
between the ideas of man and lion than between those of black and red, or
black and white. Conflict arises only when rival claims are made upon
the same thing; and a relation of conflict between ideas is found only when
they meet as attempted predicates of one and the same subject. Thus
conflict can appear only in the sphere of subjective thought, which is
trenching upon the false, for in the truth every subject is in undisputed
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LOGIC
possession of one predicate. The members of definite, larger or smaller,
groups of ideas are related in such a way that, when tried as predicates of
the same subject, they repel and exclude each other; and this not because
of something peculiar in the nature of a particular subject, but because of
their own contents. We will call them by a current term "incompatible,”
for “ incompredicable,” which would most accurately express the case, has
too unfamiliar a sound. This relation exists originally between ideas of
attributes, activities and relations ; derivatively it exists also between ideas
of things, in so far as these appear as predicates in judgments of denomi-
nation and subsumption, for two substantival ideas are contradictory in so
far as they contain determinations which cannot be combined. 1
9. We cannot deduce from any general rule what ideas are incompatible;
this is determined by the actual nature of the ideal-contents and their re-
lations to each other. It is possible to imagine our sense of sight so con-
stituted that we should see the same surface illuminated by different colours
(as, indeed, it does emit light of differing refrangibility); just as we distin-
guish different overtones in one note, and the particular notes in one chord.
It is purely matter of fact that different colours are incompatible as predi-
cates of the same source of light, and that different sounds as predicates of
the same source of sound are not so, and that the tactile sensations of tem-
perature and pressure can be referred to the same subject in the most
different combinations (cold and hard, cold and soft, etc.).
Nevertheless a general statement can be made of the ideas in reference
to which we are most frequently conscious of incompatibility, and which
are most liable to come into actual conflict. Evidently they are those
which, because they are most homogeneous and most nearly akin, because
they belong to homogeneous and similar subjects, can be most easily tried
as predicates together; those which, just because they are akin, present
themselves together as the more special determinations and modifications
of a general idea. It is for this reason that the incompatibility with which
we are most familiar is that of different determinations which fall under the
same general idea ; such as the determinations of colours, of qualities in the
sense of touch, of forms, numbers, etc. It is the incompatibility of these
which is at once obvious to us because we have had most frequent oppor-
tunity of becoming conscious of it. No one thinks about the incompati-
bility of man and kangaroo, of melting and flying, because no one will ever
Plato, in the Phædı, ch. 52, 103 D. sq., investigates in a masterly manner tà
εναντία άλληλα ου δεχόμενα.
THE NEGATION
133
have occasion to ask whether a creature is a man or a kangaroo, or whether
something is melting or flying. The incompatibility between black and
white, young and old, standing and lying, strikes us constantly, for the cases
are innumerable in which the question may be raised whether something is
black or white, whether a person is old or young, whether something is
standing up or lying down. Hence the delusion of thinking that in the
different determinations of a general idea we come upon a specific relation
of incompatibility, which belongs to them quite apart from any judgments-
as if black and white, straight and crooked, had some special enmity to
each other as being sons of the same father.
10. Incompatibility has no degrees; and when we are dealing merely
with the ground of the negation, the relation between black and invisible
does not differ from that between black and blue, nor the relation between
black and blue from that between black and white. But with the relations
upon which incompatibility is based are connected others, which refer
merely to the magnitude of the difference, and are easily confused with
it-the relations which are commonly called opposites. Black and white
are opposed in quite a different sense from that in which black and blue
are opposed ; the difference between the two relations is based upon the
interval between homogeneous ideas, which interval gradually increases and
finally reaches a maximum. It is in this sense that we oppose day and night,
mouse and elephant, a drop and an ocean, to each other. For our feeling
there is a sharp distinction between the sudden transition from one extreme
to the other, and the transition to the idea nearest in similarity, particularly
where transitions constantly take place, and so establish a connection be-
tween the more proximate differences. And when the impressions upon
our feeling are themselves of an opposite nature, being beneficial and
pleasing on the one hand, painful and displeasing on the other, the im-
pression which is given of the magnitude of the objective difference is ren-
dered especially intense by this effect upon feeling. Thus it is that light
and darkness, good and bad, pain and pleasure, beautiful and ugly, are
opposed to each other; and we need not point out that it is always pre-
supposed that such ideas are homogeneous and fall under a more general
idea which is common to both. But we should prefer to call this relation con-
trast, to avoid confusing it with that of incompatibility. It was noticed even
by Aristotle, and has been shown with much acuteness by Trendelenburg,
1 Trendelenburg, Logische Unters., xii., 2nd ed., II. 151 ; 3rd ed. 171. Cf. El. Log.
Arist. with $ 10. Arist. Cat., 6. 6a 12, and the passages in Waitz with Cat., 11 b, 34.
134
LOGIC
that the increase of difference in such an ordered series of ideas, and
the position of the extremes of the series, is represented to us by a spatial
image. The spatial "opposite” represents geometrically a maximum of
difference in direction and gains a physical significance from pressure and
counter-pressure, action and reaction, and it finds itself re-echoed in our
own will as contrast is in feeling. But this relation also, like that of con-
trast, is distinguished from the many incompatibilities only by character-
istics which have no direct reference to the negation.
II. This is most obvious in the attempts to understand, or at least to
express, by means of the negation, those relations which go by the name of
opposition. Opposition was held to proceed originally from the negation, a
not-A taking up its place by the side of an A. By dragging in a term
which was originally framed to apply to two opposite judgments (v. below,
§ 23) a distinction was drawn between the contradictory and contrary
opposition of ideas. Ideas which are contradictorily opposed, we are
taught, are related as A and not-A, so that the one idea contains only the
negation of the contents of the other. Those which are contrarily opposed,
on the other hand, are so related, that though the one annuls the other, it
also contains a positive determination. Equal and not equal, white and
not white, are examples of contradictory opposites; white and black, good
and bad, of contrary opposites..
In order to test the truth of this theory, we must first insist that nega-
tion has no meaning except in the sphere of the judgment. Every negation
is the negative answer to a question, and prohibits a predication ; no and
not have no place except when opposed to a proposition, or in a proposi-
tion. Taken literally, the formula not-A, where A denotes any idea, has no
meaning whatever. There is no such thing as an idea which is only the
pure negation of the contents of another idea. If negation is to mean
putting aside (Aufhebung), then indeed an idea-man, heaven, blue, green
—may be there or not there, consciously presented or not presented at all,
and so far “put aside." But the fact that the idea of man is not present
is not itself an idea, and the formula cannot mean that oủk ävēpumos signi-
fies that the idea of man is not present, for in order to understand it the
idea of man must be present. Thus the formula fails of its purpose in
the same way as Kant's memorandum, “ Lampe must be forgotten.”
If not-A were taken to denote everything not present in our ideas when
we form the idea of A alone, everything therefore the idea of which is
1 odèy gàp evdexetal voelv un vooûvta šv. Arist., Met. T, 49. 100 b, 610.
THE NEGATION
135,
not immediately given with the idea A, then A and not-A would no longer
denote incompatible determinations, and it would not be true that they
are mutually exclusive. When the idea “white ” is present I have no-
thing before me but the colour. If everything which is not this colour
is not-A, then it includes round and square, heavy and soluble in sulphuric
acid. These are all “not white,” i.e. something other than “white.” But
these predicates are in no way incompatible with white, and form no
opposition in the ordinary sense of the term ; for that, we should have to
pass from “white” to all white things, but does the word "white" by
itself ever mean all white things?
But if not-A were a real negation, the idea A must be denied of some-
thing, and so pass, either expressly or tacitly, into a judgment. And this
is what is really meant; not-A is taken to denote that which is not A, that
of which A must be denied. Thus it presupposes a negative judgment,
or a number of negative judgments, concerning unnamed subjects
which can be denoted as not-A only upon the ground of these negations
and very indirectly. If, then, any idea is to be formed of not-A, these
subjects must come from somewhere ; the mere fact that we are called
upon to deny A does not cause them to be present. I must review in
thought all possible things in order to deny A of them, and these
would be the positive objects denoted by not-A. But even if there
were any use in this, it would be an impossible task, and Aristotle was
right in calling the expression an όνομα αόριστον.1
If we consult Kant's Logik we are told that not-A as a predicate indi-
cates that the subject is not contained within the sphere of a predicate,
but that it lies somewhere outside in infinity. The proposition “ the soul
is not-mortal ” places the soul among the unlimited number of undying
beings which remains from the totality of possible beings when I subtract all
the mortal. This seems to give a simple receipt for realizing what belongs
to not-A. But it is only applicable when we are dealing with predicates
which can be used to denote particular beings, for then we can look upon
the world as an infinite number of such particular beings from which we
subtract the number of the A's. But how shall we deal with concepts
which are of an abstract nature and whose extension can never signify a
number of beings? If A = mortal, and I divide the extension of possible
beings into mortal and not-mortal, where will justice, virtue, law, order,
1 With reference to this not-A compare also Prantl, Geschichte der Logik, i. 147.
Lotze, Logik, ed. 2, p. 61 sq.
LOGIC
distance, find a place? They are neither mortal beings, nor yet not-mortal
beings, for they are not beings at all; they are attributes and relations of
beings, and can belong to both mortal and immortal beings. If they are not
to be counted under not-A because they may belong to a mortal being, still
we cannot include them under A, and contrary to the presupposition from
which we set out, we are left in possession of a territory lying midway
between A and not-A. If A stands for man, then it seems easy to put
men on one side away from the rest of the world, everything which remains
-sun, moon and stars, minerals, plants and animals—all is not-man. But
where do the attributive concepts black, green, soft, hard, belong? to A or
tā not-A? The intended division of all possible beings into A and not-A
quite overlooks the fact that there are different categories; that every
concept stands in relation partly to concepts of like categories, partly to
concepts of differing categories, and that the lines which divide them cross
in all directions.
But even supposing it possible to think of all that which is not-A as
predicate, where should I find a reason for denying A of everything which
can be called not-A? Not in the fact that it is not-A ; this can only be
said indirectly and derivatively; but in that which it is, that which pre-
vents us from predicating A of it. The opposition said to be expressed
and made comprehensible by not-A is, on the contrary, the presupposition
of the not-A, which is itself merely a derivative sign of the opposition, not
its essence and ground.
The same indefiniteness into which contradictory opposition resolves
itself, attaches also to the contrary opposition of the ordinary doctrine. If
we say that everything which can be expressed by the formula not-A+B
is contrarily opposed to an idea A, then red and virtuous, black and im-
mortal enter into contrary opposition, not to speak of the strange confusions
which arise when A and B are taken from different categories. And this
is not excluded by the formula which denotes everything included in not-
A and denoted not merely negatively but directly; so that grass-green
and algebra, emotional and ellipse, fall into contrary opposition. The
examples must be excused; in no other way can we make obvious the
want of meaning in formula which are dragged over from one treatise
on Logic into another.
12. The view that negation can only take place where there is a reason-
able possibility of question and of affirmative answer has led others to
THE NEGATION
137
abandon not only this vague not-A, but also the common explanation of
contrary opposition as not-A+B. According to them, contradictory as
well as contrary opposition is to be found only when a general idea is more
fully determined by mutually exclusive differences; where, for instance, a
line is determined as straight or crooked by differences of direction, or
the state of a body in space is determined as rest or movement. Accord-
ing to this view contradictory opposition is found where only two deter-
minations are opposed to each other ; where therefore the negation of the
one definitely implies the other--a line which is not straight must be
crooked ; while contrary opposition is found where several determinations
appear on an equal footing, as in the case of colours. Thus, under the
names of contrary and contradictory, the distinction is again introduced
which Aristotle made (Categ., 10. 11b, 33) between opposites which
admit of no intermediates, such as even and uneven in the case of whole
numbers, illness and health in a living being; and opposites which admit
of an intermediate, such as black and white.
This way of putting the doctrine is more rational because it at any rate
gives us a subject for the negation in the general idea. But in return it
conceals another danger, that of believing it possible to produce opposite
concepts—and something positive therefore--by determining a general
idea by A and not-A. But the general idea does not exist before its deter-
minations, but only together with them. There is not first a line in
general, which we could determine to be straight or not straight; it is part
of the nature of the space containing the line that both straight and
crooked lines are possible in it. Thus, it always depends upon the nature
of the objects comprehended in a general idea what are the determina-
tions they permit, and whether another predicate is permissible together
with one which we recognise as possible. In the same way it depends
upon the nature of the objects how great the range is of these compatible
determinations. Here again the negation and the formula framed from it
1 Some have even gone so far as to confine the name of contrary opposition to those
terms in such a series of differences which are furthest apart ; thus, in the case of colours,
only black and white are said to be in contrary opposition, while red and yellow are
merely disjunct, not contrary. This was the view taken by Trendelenburg in his Log.
Unters., chap. xii., in accordance with Aristotle's dictum (Categ., 6, 6a, 17, and elsewhere ;
vide the passages in Waitz, Org., 1. p. 309)-i.e. that the εναντία are τα πλείστον αλλήλων
diegtnKÓTA TÛV ¿v tự aút@ yėvel. But this, according to p. 180, introduces a new point
of view, that of a comparison of the intervals between our ideas, and with this we have
nothing to do when considering the grounds of the negation.
138
LOGIC
can only interpret for us that which lies in the nature of ideas; it cannot
determine this nature beforehand. On the contrary, the incompatibility of
certain ideas continues, for our present observation, to be an empirical
relation, which Logic, strictly speaking, has never done more than describe.
The import of the procedure by which we give expression to differences
in a general idea, as A and not-A, can only be treated of under the
doctrine of the Concept.
13. In one case, however, it seems undeniable that opposition has its
origin in negation : when, that is, one term of the opposition has really a
purely negative significance. Straight and crooked are two different
intuitions, each in itself definite and positive ; and it may at least be
questioned whether in the case of rest and motion the one is the mere
negation of the other or not,2 either the one or the other being taken as
positive. But how about blind, deaf, unhappy, unreasonable, unwise,
speechless, unfeeling, and all the numerous epithets formed with “un-” and
"-less”? Can the relation between seeing and blind be expressed except by
saying that blind means not-seeing, the simple privation of sight? and is
not this an opposition which has arisen entirely from negation and one
term of which means nothing but a not-being? And has not language, by
thus blending the negation with the predicate, justified the not-A of
logical theory beforehand ?
If this were so, then it must be fully equivalent whether I deny the one
term of the opposition or affirm the other ; whether I say “this does not
see,” or “this is blind,” “ A is not happy,” or “ A is unhappy.” No proof is
needed that this is not the case. If all we know is that the judgment "A
sees” is false—and the mere words “ A does not see" never tell us more
then it is not said why he does not see. But blind denotes a definite
state of the subject, an organic change of the apparatus of sight, in con-
sequence of which seeing does not take place. By denying sight, then,
we do not affirm blindness, as must be the case did these so-called pri-
vative predicates really contain nothing but the expression of a negation.
Here again, then, negation is not sufficient to explain opposition. It is
only because our negations are almost always based upon such oppositions
that negation, working according to psychological laws, excites mainly the
idea of opposition. Language, which makes use of psychological forces,
and arbitrarily curtails the original meanings of words, is able to turn this
1 Spinoza tells us (Tract. de Deo, ii. 19) that rest is not a mere negation (nothing), and
upon this proposition the whole of his physics is based.
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139
habit to account, and to denote oppositions by negations. But language
always means more than it says, and logical analysis intervenes to dis-
tinguish between the necessary meaning of the negation in itself, and its
ordinary meaning which attaches to it only from association and on the
ground of the known relations of the predicates.
8 23.
The PRINCIPLE OF CONTRADICTION refers to the relation between a posi-
tive judgment and its negation; it expresses the nature and meaning of
the negation by saying that the judgments “ A is B” and “ A is not B”
cannot both be true together. This statement differs essentially from the
proposition usually known as the principium contradictionis (A is not not-A),
which refers to the relation between a predicate and its subject, and forbids
that the predicate should be opposed to the subject.
We give the name of αντίφασις, contradictio, to the relation between a
positive judgment and its negation (and hence also to the two judgments
which stand in this relation). They are contradictorily opposed to each
other (αντιφατικώς αντικείσθαι, contradictorie oppositum esse).
I. A confusion similar to that concerning identity and opposition exists
with respect to the so-called principium contradictionis. Aristotle, in a
familiar passage, 1 formulates it as follows: “It is impossible that the same
1 Metaph. Γ, 3. Ιοο5 ο, 19 : Το γάρ αυτό άμα υπάρχειν τε και μη υπάρχειν αδύνατον
το αυτό και κατά το αυτό (και όσα άλλα προσδιορισαίμεθ' άν, έστω προσδιορισμένα προς
τάς λογικές δυσχερείας) αύτη δή πασων εστι βεβαιοτάτη των αρχών . . . αδύνατον γάρ
οντινούν ταυτον υπολαμβάνειν είναι και μή είναι, καθάπερ τινές οΐονται λέγειν Ηράκλειτος
ουκ έστι γάρ αναγκαίον, άτις λέγει, ταύτα και υπολαμβάνειν ει δε μή ενδέχεται άμα
υπάρχειν τω αυτώ ταναντία (προσδιωρίσθω δ' ημίν και ταύτη τη προτάσει τα ειωθότα)
εναντία δ' έστι δόξα και της αντιφάσεως, φανερόν ότι αδύνατον άμα υπολαμβάνειν τον αυτόν
είναι και μή είναι το αυτό άμα γάρ αν έχοι τας εναντίας δόξας ο διεψευσμένος περί
τούτου. Διό πάντες οι αποδεικνύντες εις ταύτην ανάγουσιν εσχάτην δόξαν : φύσει γάρ
αρχή και των άλλων αξιωμάτων αύτη πάντων. 4 10ο6 6, 33 : ουκ άρα ενδέχεται άμα αληθές
είναι ειπείν το αυτό άνθρωπος είναι και μή είναι άνθρωπον (cf. also Μetaph. β, 2,996 6, 31 :
λέγω δε αποδεικτικάς τάς κοινάς δόξας, εξ ών άπαντες δεικνύασιν, οίον ότι πάν αναγκαίον ή
φάναι ή αποφάναι, και αδύνατον άμα είναι και μή είναι). Here Aristotle makes use
of the phrase that contrary attributes (έναντία) cannot belong to one subject both
together, and he seems to employ it as a proof that one and the same person cannot
believe that anything both is and is not at the same time. But he must not, of course,
be understood as intending to lay down a principle higher than, or independent of, the
principle of contradiction ; he not only denies this in the same passage, but refers again
to it afterwards (Metaph., iv. 6. 1011 0, 15) :-έπει δ' αδύνατον την αντίφασιν αληθεύεσθαι
άμα κατά του αυτού, φανερόν ότι ουδέ ταναντία άμα υπάρχειν ενδέχεται το αυτό; here
stating that the principle of contradiction is the original principle upon which the other
depends. The above proof should rather be called a mere συλλογισμός εξ υποθέσεως in
the Aristotelian sense ; i.e., an argumentatio ex concessis, which is intended to show that
140
LOGIC
(predicate) should both belong and not belong at the same time in the
same way to the same thing.... This is the most certain of funda-
mental principles ... for it is impossible for any one to believe that
the same thing both is and is not (as some think Heraclitus says, for
a man does not necessarily really believe what he says) ... Hence
every one who brings forward an argument, falls back in the last instance
upon this proposition, which by its nature serves also as the principle upon
which all other axioms depend.”
That is to say then: the proposition A is B.and the proposition A is
not B cannot both be true together. If we state the proposition A is not
B, we must declare the proposition A is B to be false ; and if we state the
proposition A is B, we declare the proposition A is not B to be false.
2. This is nothing but a statement concerning the significance of the
negation. Its nature and meaning are laid down in a proposition which
cannot itself be expressed without negation, and which is, therefore, only
of value as making us conscious of our own act when using the negation.
If we connect the same meaning as every one else does with the word
“not,” we may indeed say both that A is B and that A is not B, but we
cannot believe it and maintain it seriously. Or, again, we may by our
words make it appear that both are true together; but only by using the
words in different meanings, or by speaking of different times. It is for
this reason that Aristotle guards his proposition so carefully by the
determinations “at the same time” and “in the same sense.”
That Aristotle intended his principle to have immediate reference only
to the nature of our thought is as certain as it is that the negation has its
sole origin in a movement of thought which extends beyond that which is,
and endeavours to combine incompatible things. This is shown by his
argument" it is impossible that any one should believe that the same thing,
at the same time, both is and is not.” It is shown again (Metaph., iv. 4)
when he says that those who say that it is possible for the same thing both
to be and not to be, and that it is possible to believe this, do away with all
possibility of thought and of mutual understanding; for these require that
every word should have definite meaning, and that the speaker should
keep to this meaning, and not contradict it.1
the recognised proposition “contradictory attributes cannot belong to the same thing”
involves the proposition “No one can believe that the same attribute can both belong
and not belong to one and the same thing.”
* Cf. Prantl, Gesch. der Logik, I., 131 sq., 134 : The corresponding principle with refer-
ence to objectivity always arises out of the relation which exists in subjective speech
THE NEGATION
141
!
3. If this is what Aristotle meant by his principle of contradiction, then
the positive interpretation of it is also obvious. It can be none other
than the proposition that every one who consciously makes a statement
states just that which he does state; that what he says must have a
fixed meaning, because, if another meaning is substituted whilst he speaks
and thinks, he does not really say anything. It must be true that “what
I have written, I have written; what I say, that I do say." But it is
evident that this is only a corollary to what we have called above the
constancy of ideas; it is the unambiguity of the act of judgment. This
unambiguity of the act of judgment would form the content of a principle
of identity which would be the positive rendering of the Aristotelian
principle. But it is through the rejection of simultaneous affirmation and
negation that we first become conscious of this unambiguity, and it tells
us nothing which is not already stated in the principle of contradiction.
It is then quite natural that only the principle of contradiction should be
ranked by Aristotle as a principle, while its positive rendering finds merely
an incidental expression." For a long time indeed it was the Aristotelian
principle of contradiction which was meant by the principium identitatis.
ID
and belief, and this is in accord with the subjective origin of human judgment. No
doubt when the principle takes the form “it is impossible that the same thing should
both be and not be” it does seem as if we had to do with a principle which is
primarily metaphysical, and logical only in a secondary manner; Ueberweg, for instance,
takes this view when he divides the sayings of Aristotle into those which state the
metaphysical, and those which state the logical principle. But there can never have
been a division such as this between metaphysics and logic as Aristotle understood them,
if only because he regards the true judgment as always the expression of Being, and,
indeed, frequently denotes the èotiv of predication simply as a being. Nevertheless, if
we remember his express statement (Metaph., vi. 4) that truth and falsehood appertain to
thought, and not to things, a proposition which declares that of two propositions one
must be false can only refer originally to the activity of thought in its oúveous and
dialpeous. It follows from this as a matter of course that the same thing cannot both be
and not be at the same time, nor the same attribute both belong and not belong to the
same (objective) thing at the same time ; for if this were not so, then, owing to the Aris-
totelian conception of truth, the logical principle would also be without validity. For
Aristotle, both modes of expression are ultimately exactly equivalent in meaning. Cf.
Zeller, Phil. d. Gr., II. 2, 174. .
1 Trendelenburg, Elem. Log. Arist., § 9, quotes from Anal., 1, 32, 47a, 8: Acî mây
Td ålnoès aútd è avt@ ouoloyoúuevov Elvai trávrị ; but this is introduced for the sake of
the later doctrine, and where it stands has not the significance of a principle. Such
significance can be attributed only to the propositions in the Metaph., p. vi. 4 sq., and the
contents of these are correctly formulated by Prantl, Gesch. der Logik, I, 131, as the
statement that every assumption concerning a υπάρχον (I should only have said υπάρχειν).
remains constant with itself; and this again is only possible on the assumption that our
verbal denotations are conceptually determined. Baumann has lately endeavoured
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LOGIC
4. The principium contradictionis of modern logicians (particularly
Leibnitz and Kant) in the formula A is not not-A, differs entirely in mean-
ing and application from the Aristotelian proposition. This latter refers to
the relation between an affirmative and a negative judgment. According to
Aristotle, one judgment contradicts another. The later proposition refers
to the relation between subject and predicate in a single judgment; the
predicate contradicts the subject. Aristotle states that one judgment is
false when another is true; the later writers state that a judgment is in
itself and absolutely false, because the predicate contradicts the subject.
What the later writers desire is a principle from which it can be known
(Philosophie als Orientierung über die Welt) to re-establish the true Aristotelian meaning
of the logical principles, but he nevertheless diminishes the importance of the law by
making it refer to the merely empirical fact that something has been thought of (“ Es
drückt nichts aus, als dass die Thatsache des Vorstellens stattgefunden hat in der Weise,
wie wir sie vollzogen haben"), and by stating it as merely a special case of factum
infectum fieri nequit. The law is not intended to establish in a subsequent judgment
the fact that something has been thought; for this subsequent judgment itself is governed
by the rule that it must have a definite meaning, its meaning being that just this mental
act and no other has taken place. It is really intended to show how any act of judgment
has taken place, that it contains one definite single meaning, that if we affirm anything
we can affirm it in one sense only, and cannot in the same act of judgment hold the
opposite view also.
1 I do not know when it was that the name of principiun identitatis was first given
to the formula A est A, or Ens est Ens, instead of to the Aristotelian principle, which
was so denoted throughout the Middle Ages (see Prantl's References); nor when the
principium contradictionis (and the princ. exclusi tertii) received its altered meaning ;
the two changes were no doubt connected. We can see very clearly how Leibnitz passes
from the one rendering to the other. In the Nouveaux Essais, iv. 2 (Erdm., p. 338, 9),
we find as the principle of identity A est A, “chaque chose est ce qu'elle est”; while
the principle of contradiction, on the other hand, is : “une proposition est ou vraie ou
fausse.” This, he tells us, contains two propositions : 1. “que le vrai et le faux ne sont
point compatibles dans une même proposition, ou qu'une proposition ne saurait être vraie
et fausse à la fois ” ; 2. “ que l'opposé ou la négation du vrai et du faux ne sont pas
compatibles, ou qu'il n'y a point de milieu entre le vrai et le faux, ou bien il ne se
peut pas qu'une proposition soit ni vraie ni fausse.” Here, as in the Theod., 1, 44,
Leibnitz is in essential agreement with Aristotle. But his first example is “ce qui est
A ne saurait être non-A”; and though we may still recognise in this the two judgments
“the same thing is A and is not-A," the use of the term non-A has very nearly con-
verted it into the formula A is not non-A. This formula actually appears together
with the other in the Nouviaux Essais, I, § 18 (Erdm., p. 211): “il est impossible
qu'une chose soit et ne soit pas en même temps.” In the Princ. phil., on the other hand,
he states that the import of the principium contradictionis (8 31) is to enable us to say
that everything which contains a contradiction is false, and that everything which
is opposed to the contradictory or false is true. Here, then, the contradictio is in the
predicate. Finally, in $ 45, it is said that the opposite of an identical proposition
contains an express contradiction, so that “ A is A” and “ A is non-A” are opposed
to each other as necessarily true, and necessarily false.
THE NEGATION
143
whether certain propositions are in themselves true. From the Aristotelian
proposition we cannot immediately infer the truth or falsehood of any
particular proposition, but only the impossibility of believing both
affirmation and negation at the same time.
Kant's polemic against Aristotle is then quite misdirected. According
to him (Kr. der r. Vern., Hart, p. 166 sq.) the fundamental principle is :
“ To no thing can there belong a predicate which contradicts it.” It is a
universal—though indeed, merely negative—criterion of all truth. It is
valid of all knowledge whatever, irrespective of its contents, and states
indeed, as a rule, go so far as to guarantee the truth of a proposition, for
a judgment may still be false or groundless even when it is free from
internal contradiction ; nevertheless it may be of positive use towards
knowledge of the truth, for when the judgment is analytical, let it be
affirmative or negative, the principle of contradiction always affords a
sufficient test of its truth. We must always be right in denying the reverse
of whatever is contained and thought of in the concept of the object as
given to knowledge, and we must necessarily affirm the concept itself,
since its opposite would be in contradiction to the object.
It is from this point of view, then, that Kant rejects the formula, “it is
impossible for anything at the same time both to be and not to be," as
containing a synthesis which has slipped in from carelessness and quite
unnecessarily. The proposition, he says, is affected by the condition of
tine, and as much as to say: “a thing A, which is something=B, cannot
at the same time be not-B; but it can very well be both (B as well as
not-B) one after another.” “But the principle of contradiction, being a
purely logical principle, must in no way limit its statements to time-
relations ; such a formula, then, is entirely contrary to the intention of
this principle.” The misunderstanding, he goes on, is due entirely to the
use of synthetical propositions. A predicate (e.g. unlearned) is synthetically
connected with the subject (man); if, at the same time, an opposite pre-
dicate (learned) is attributed to the subject, then a contradiction arises ;
but the contradiction is between the one predicate and the other, not
unlearned man is learned,” the truth of this negative proposition is obvious
from the principle of contradiction, without the addition of “at the
same time” as condition. In his Logic, also, Kant deals in the same
way with the principle of contradiction.
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LOGIC
Little is needed to show that Kant is speaking of something quite
different from the original principle of contradiction. Leibnitz divided
truths into necessary and matter of fact, and offered a special principle of
truth for each of the two classes: the principle of contradiction for neces-
sary truths, which are all of them in the last instance what are called
identical propositions; the principle of sufficient reason for truths of
matter of fact. Kant proceeds in the same way with his two classes of
analytical and synthetical judgments; what he is looking for is a principle
for the truth of analytical judgments. Now analytical judgments are
always concerned with subjects which are concepts, and they state what is
thought in these subjects as concepts-hence quite independently of time;
the predicate of an analytical judgment is always already contained in the
concept which forms its subject. But what the principle of contradiction
in the Kantian sense states is, “to no concept must a predicate be at-
tributed which contradicts it.” In so far, then, as other judgments express
their subject by means of a concept (in “this man is learned,” the object
is known by the concept man), the principle applies to them also ; they
would be self-destructive if they attempted to attribute to a subject a
predicate contradictory to the concept under which that subject falls.
We will investigate hereafter what is meant by contradicting a concept,
and whether a universal logical principle can be grounded upon this con-
tradiction. At present it is clear that, starting from these premises, Kant
is certainly right in excluding time-determinations from his principle.
But when he accuses the Aristotelian formula of a misconception in
in thinking Aristotle's meaning to be the same as his own; for it is
certain that Aristotle meant to prohibit, not indeed contradiction between
two predicates, but contradiction between the affirmation and negation
of the same predicate.
5. It may fairly be asked here, “How is it possible that two principles,
differing so greatly as do the Aristotelian and the Kantian, should be
generally regarded as one and the same fundamental law of human
thought? And is there really no connection between them?” Some
connection there certainly is. The ordinary principle of contradiction
aims at giving a rule by which the validity of negative judgments may be
tested. It is seen that a negation generally rests upon the exclusion of
patibility rests again in its turn upon the negation; hence it is thought
THE NEGATION
145
that universally valid negations are all reducible to contradiction. But in
this way we see that the formula really “moves in a circle."
But what can be the meaning of saying that a predicate B contradicts
a subject A? That a proposition which attributes a predicate B to a
subject A involves a contradiction? The only way in which a contra-
diction can take place is when the judgment which attributes this predicate
B to a subject A contradicts another judgment (presupposed, if not ex-
pressly stated) which denies the predicate B of the subject A. This latter
judgment (A is not B) being accepted as needing no proof, or as known
from some other source, the contradiction certainly annuls the first
judgment; and it does so, moreover, according to the proposition laid
down by Aristotle, that they cannot both be true together. Why is the
proposition in Kant's example, “an unlearned man is learned,” a con-
tradiction? Because the predicate “ learned” is attributed to a subject
which is denoted by the subject-term “unlearned man,” a term which
implicitly contains a judgment stating that the subject is not learned. In
this way the proposition may be reduced to the two judgments, X is
learned, and the same X is not learned. These two judgments are both
stated by the proposition, which therefore contains a contradiction, and
therefore is false, i.e. it is false that the same man is learned and not
learned ; and if it is true that he is not learned, it is false that he is
learned.
A contradiction, then, can only take place in so far as a judgment
is already implied in the subject. This is certainly the case both with
the analytical propositions which Kant has in view, and with those pro-
positions of which alone the school logic is accustomed to treat. As we
have seen above, Kant's analytical propositions are possible only on the
presupposition of concepts which are the same for every one; i.e. on the
presupposition of universally valid judgments concerning the meaning of
words; judgments which state that body means the same as extended
thing, that the idea denoted by the word “body” contains the idea “ex-
tension.” If I say, “all bodies are extended,” then that means “every-
thing which I call body I must also call extended”; the denotation of
any X as body contains the judgment, “ X is extended.” If now I say
“ a body is not extended,” or even “ this body is not extended”-then
there is a contradiction : “this is extended, and this is not extended”;
and as it is absolutely established that anything which is body is extended,
the contrary is necessarily false.
S. L.
L
146
LOGIC
So far the opposition has been between affirmation and negation: A is
B and A is not B. But now, instead of contradictory propositions, there
appear the contradictorily opposed predicates B and not-B; and the con-
tradiction between affirmation and negation is transferred to the two
affirmations "A is B” and “ A is not-B”; if it is true that A is B, it is
false that A is not-B.
On these presuppositions alone can a contradiction take place between
subject and predicate; and we cannot recognise the falsity of a proposi-
tion from the contradiction between its predicate and the concept forming
the subject, unless it is presupposed that the process by which concepts
are formed is infallible, and their denotation by words absolutely fixed;
and, when we are treating of the particular, that the process of the sub-
sumption of the particular under the concept is also infallible. Now, so
long as we have to do merely with the subjective image upon which Kant
bases his analytical judgment (v. p. 104) no doubt it is easy to form a
concept and to combine in it certain characteristics—to say “body
is extended thing." Then the judgment “bodies are extended” is
equivalent to “the extended is extended.” Here, as Hobbes holds, we
have only equations between the arbitrarily framed meanings of words.
Even the statement "all bodies are extended” involves an unauthorized
assumption, for it tacitly assumes that my concept is applicable to
possible things, and that I can safely make this application in any par-
ticular case—for this is the only meaning of “all.” Finally there can be
absolutely no question raised as to whether I should say more concerning
what I call body than is already contained in the name; all propositions
become identical, i.e. without meaning or importance.
But it is just at this point that the formula “ A is not not-A” appears
as the expression of the principium contradictionis. The contradiction
between a predicate and its subject is reduced to this formula by the
assumption that all true judgments must admit of being finally reduced
to “ A is A," and that our absolute measure of truth lies in the finished
system of concepts in which alone our thought and knowledge move.
But the first weak point in the formula is its åóplotov non-A. An attempt
might indeed be made to explain this away. Starting from the so-called
principle of identity, the proposition can be made, “it is false that A is
not A”; because, that is, it contradicts the true proposition, A is A. By
a slight perversion of language this may be contracted into the proposition :
non A non est Al; the given A still remains subject, and it is denied
THE NEGATION
147
that A as predicate can be denied of it. In the same way the formula
would have a meaning if A were taken as the sign of a proposition. But
this is not what is meant. Non-A is introduced deliberately: the contra-
dictory opposition of concepts is substituted for the contradiction of
propositions, and what is now prohibited is that non-A shall be predicated
of A. From some points of view we might be content to accept non-A,
and to acknowledge the formula as theoretically correct; but it is useless
in practice. We seldom meet with the contradiction in such a crude form
as “gold is not-gold,” “green is not-green,” “Being is not-Being.” Gene-
rally speaking it must be discovered under disguises. Would that it were
so easy when A is given to decide what determinations are included in
non-A and therefore contradict A!
But now we see that, like a proper oracle, the principium contradictionis
gives us no answer to the question, “what is it which may not be stated
of A?” If we take refuge in saying that A as a concept contains the
characteristics a, b, c, d, and that therefore non-a, non-b, non-c, non-d
must not be attributed to it, the difficulty of the non-A is only multiplied;
and if we are content to say a, b, c, d must not be denied-well, that is the
Aristotelian principle applied to judgments, which we already acknowledge
to be valid.
But the Kantian Logic can contain no universal formula by which to
determine what is opposed to a subject; for our concepts, according to
Kant's express teaching, generally denote the nature of their objects by a
part only of our experience of them. Hence we can never conclude from
the fact that something is not contained in the concept that it does not
belong to the thing; it never follows that because something does not
contradict the concept, it does not contradict the thing. It is moreover a
fiction that all the relations of concepts are known to us so far as opposi-
tion and exclusion are concerned.
It is because the Aristotelian principle refers only to what we know-
the function of negation—and does not confine itself to judgments having
concepts for their subjects, that it is a first principle, absolutely uncondi-
tioned and applicable to all our judgments. Because, moreover, there is
contained in it—so far as we have any knowledge of the relations of op-
position and incompatibility among concepts—the ground of the impossi-
bility of attributing to a concept a predicate excluded by it.
But all that the ordinary principium contradictionis can say is, that a
proposition is false if its predicate is incompatible with some determination
.
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LOGIC
of the subject; and it therefore prohibits us from attributing to it an in-
compatible predicate. Thus it presupposes a knowledge of what is incom-
patible and cannot be an unconditioned first principle sufficient in itself
to establish the falsity of a proposition (by doing which it would also,
according to the principle of the excluded middle, establish the truth of
its contradictory opposite).
$ 24.
To interpret the nature of the negation completely we must add to the
principle of contradiction the further principle that the negation of the
negation is affirmative, that to deny a negation is equivalent to affirming
the same predicate of the same subject.
I. It is strange that logic has found no place for the proposition
“duplex negatio affirmat,” which has been abstracted by grammar from
frequently recurring forms of speech. Probably it has been looked upon
as a consequence of the principle of excluded middle; but its position
is rather that of the indispensable link leading from the principle of con-
tradiction to that of excluded middle. The principle of contradiction
states that it is impossible for affirmation and negation both to be true
together; in this way, if the affirmation holds good, it leads to the falseness
of the negation. But in so doing it does not state what is meant by stating
that a negation is false. Only because the denial of the negation is the
affirmation itself is there no medium between affirmation and negation.
Aristotle lost sight of this simple connection between the two by treating
affirmation and negation from the first as completely parallel and co-
ordinate forms of statement. Owing to this he failed to give a satisfactory
account of the negation itself, and, strictly speaking, left no room at all
for the negation of a negation. But as soon as we see that every negation
presupposes a previous synthesis, its only object being to declare this
synthesis invalid; as soon as we see that the negation is a particular act in
which the “not” has the force of a judgment concerning a judgment
(either attempted or complete)--then it becomes clear how far the nega-
tion of a negation is possible. “A is not B” contains the statement that
the proposition A is B is false, that other determinations than B-determi-
nations incompatible with B-belong to A, that it is impossible to unify B
with A. This statement, or the attempt at such a statement, may in its
turn be denied. “It is false that A is not B,” says that it is impossible to
state that the proposition “ A is B” is false, to ascribe any other predicate
than B to A, to prevent the unification of A and B. And if the objections
THE NEGATION
149
to the synthesis A is B are impossible, then this synthesis must hold
good.1
2. It is in this property of the negation, that when directed against a
negation it is to that extent a positive statement, that we first become fully
aware of the completely subjective character of the whole movement of
thought when concerned with negation. By the process of negation no
truth can be produced and nothing can be created which did not exist in-
dependently of it. The presupposition of its validity is that a combination
should be attempted which is merely subjective and peculiar to the indi-
vidual, and which is prohibited by the immovable necessity of thought ;
and when the negation has been attempted without sufficient ground it
vanishes, leaving no trace behind; the repeated “not” only serves to
indicate the circuitous way which the thought of the individual has taken,
in order to reach a truth which might have been reached directly. For in
the last instance it is always out of some positive knowledge that we declare
a negation to be false, and in this positive knowledge is contained the
ground for the overthrow of the negation.
3. But it is not altogether to no purpose that this circuitous route is
taken. In grammar it has already been recognised that resisted attacks
increase the psychological firmness of conviction ; the affirmation which
has fought through a negation seems to stand firmer and to be more
certain. So much it may gain; but it can never gain so as to contain more
than before, or to be richer in meaning. “A is B” gives just the same
information whether it is known directly or is the result of the negation of A
is not B-that is, so long as A and B keep the same meaning, and we do
not substitute the affirmation of a positive characteristic opposed to B for
the mere negation “ A is not B.” If we did this, we should of course have
gained something new, inasmuch as A would have come into relation with
a new predicate. Is it false that light is not a kind of motion, then
the proposition we have gained tells us no iota more than the propo-
sition “ light is a kind of motion.” If for our first proposition we substitute
another “light is a kind of matter," on the ground of a disjunction accepted
for other reasons, then the denial of this might give us new information, i.l.,
a distinction between “light” and “matter” ; but this would not be due to
the twofold negation.
1 Cf. Bradley, The Principles of Logic, 1883, p. 149 sq. ; special weight is laid upon
the position that every negation must be based upon positive knowledge ; the only ground
upon which we can deny that A is not B is our knowledge that A is B. This knowledge
is therefore included in the double negation.
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LOGIC
§ 25.
It follows of itself from the principles of contradiction and of twofold
negation that of two contradictorily opposed judgments one is necessarily
true ; hence that there is no third statement besides affirmation and negat
tion which would imply the falsity of both. This is the PRINCIPLE OF THE
EXCLUDED MIDDLE, which, like the two previous principles, aims only at
interpreting more fully the nature and meaning of the negation.
The ordinary interpretation of the principium exclusi tertiï is by the
formula omne A est aut B aut non-B, according to which every subject
possesses one of two contradictorily-opposed predicates; but this is as
different from the original and genuine principle of excluded middle as the
ordinary principium contradictionis is different from the principle of con-
tradiction.
1. The principle of contradiction tells us, that of two judgments “ A is
B” and “A is not B” one is necessarily false, because both cannot be
maintained together; and by so saying it fixes the meaning of the negation.
But it follows immediately that one is necessarily true because both can-
not be denied together. If I deny that A is B, then by so doing I main-
tain that A is not B ; while if I deny that A is not B, that again is only
maintaining that A is B. If then I attempted at one and the same time
to deny both that A is B and that A is not B, I should by one negation
say that A is not B, and by the other that A is B, thus falling into a con-
tradiction. Thus there remains no middle statement between affirmation
and negation, which could contain any reference of the predicate B to the
subject A ; and any judgment which tries to combine B and A as predicate
and subject, must either affirm B of A or deny B of A.
2. Aristotle repeatedly states this principle, and in the most important
passage (Metaph., iv. 7) he attempts a proof of it (one, however, which
contains a petitio principii); elsewhere he gives it as needing no proof.1
1 Arist., Metaph. I, 1011 6, 23 : 'AMà une oudè uetatù årtiođOEWS EVOExetal Elvai oudèy,
αλλ' ανάγκη και φάναι και αποφάναι έν καθ' ενός ότιoύν δήλον δε πρώτον μεν όρισαμένοις τί το
αληθές και ψευδος: το μέν γάρ λέγειν το ον μή είναι και το μη όν είναι ψεύδος, το δε το όν είναι
και το μή όν μή είναι αληθές, ώστε ο λέγων τουτο είναι η μη αληθεύσει ή ψεύσεται" αλλ' ούτε
TÒ Öv Néyeral un Elvai, Elvai, oŰTE TÒ un óv. This passage has received various interpre-
everything must be either affirmed or denied of everything. This is obvious as soon as
we define what true and false mean. To say that the existent is not, or that the non-
existent is, is false; while to say that the existent is and that the non-existent is not, is
THE NEGATION
151
7
Its close connection with the principle of contradiction is shown by the
fact that even Aristotle gives formulæ containing both, while Leibnitz ex-
pressly includes them both in the formula : “A proposition is either true
or false.”1 But the “either-or” conceals an ambiguity in an apparently
simple expression, and the dependence of the derivative proposition is lost
sight of. It is therefore more natural to give the principle of excluded
middle a special place as a corollary to those principles which immediately
unfold the meaning of the negation; but it is incorrect to rank it beside
the principle of contradiction upon which it depends, as if it were equally
immediate, especially as its application is less easy and evident than that
of the fundamental principle.
3. It is owing to the weakness of the mere negation, and the incom- .
pleteness of the information which it gives us as to the meaning of its
denial, that difficulties seem to arise in applying the principle of excluded
middle.
The more familiar difficulties, arising from continuous transitions and
the many-sidedness of the subjects, are indeed easily solved. When the sun
is rising, either of the two propositions “it has risen" or "it has not risen”
may be true, according as we apply the term “risen” to the elevation above
the horizon of the upper or lower edge. It may be said that in the moment:
non-existent) is or is not, we speak either truth or falsehood. But if we suppose a middle
statement between affirmation and negation, it tells us neither that the existent, nor that
the non-existent, either is not or is; for if any one of these statements were made, it
would be an affirmation or a negation, and either true or false. The middle statement
could say nothing either of the existent or of the non-existent, nor could it therefore be
either true or false. But that which is neither true nor false is no statement at all, for it
is a part of the nature of a statement to be either true or false (ώστε ούτε αληθεύσει τις, ούτ'
oủk åndevoel, 1012 A, 6). Ueberweg gives a similar interpretation, ed. 3, $ 79, p. 216.
It is obviously presupposed in the definition of the true and the false judgment, and in
the classification of judgment into affirmative and negative, that there is no Meta&ú, if no
more can be stated than that the existent or non-existent is or is not. The passage can-
not therefore be regarded as a proof; it serves merely, together with the rest of the
chapter, to point out that it is always presupposed that there is no middle course.
Categ., 10, 13a, 37 : "Ooa de ús katápaois kal år bpaois årtikelta! . . . ÉTÈ MÓVW TOÚTWY
åvaykalov åel TÒ Mèv ålnoès tj dè yeúdos aŭtwv Elval. -This is repeated in 13 b, 27-33.
- Metaph., 1, 7, 1057 a, 33 : TÛV O’ ÅVTIKELMÉvwv åvtipáoews MÈY Oůk ČO TL METAĞú• TOÛTO Yáp
έστιν αντίφασις, αντίθεσις ής οσοούν θάτερον μόριον πάρεστιν, ουκ εχούσης ουθέν μεταξύ.
K. 12, 1069 a, 3 : åvtipárews oŮdèv åvà ućoov, there is a similar passage, Phys, ausc. v. 3,
227 a, 9.
In the Analyt. post., 1, 2, 72 a, II, the opposition which excludes a third is even used
as the basis upon which to explain what a judgment is : απόφανσις αντιφάσεως όποτερονούν
Mbplov, åvrida ous dè årtideois ħs oủk čOTI METAČŮ kad' aŭtnv. Cf. De interp., 9, 18 a, 28.
1 See note, p. 142.
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LOGIC
of death it is equally false to say “he lives," and " he does not live”; but
this again is incorrect, for "life" expresses a state which continues, and the
dying man in articulo mortis does not live. And all cases in which we
have to deal with spatial and temporal limits may be similarly treated.
Still more clumsy are such examples as “it is false that a chess board is
black and false that it is not black”; if the predicate applies to the whole,
then the negation is true ; if not, then the subject is not the same in the
two propositions. But these are not the only difficulties which arise.
Aristotle himself raised the question as to what is the relation between
the two propositions “Socrates is ill,” and “Socrates is not ill,” when
two is necessarily true. The decision he comes to is, that in this instance
the two propositions expressing the material opposition, “Socrates is
ill” and “Socrates is well,” would indeed both be false; but that the mere
negation “Socrates is not ill” remains true even in this case, thus pre-
serving the universality of the principle. This solution does not, indeed,
seem perfectly satisfactory; for, as commonly understood, the proposition
“Socrates is not ill” means that Socrates does live but is not ill. If we
answer the question “is Socrates ill ?” by yes or no, then-according to
our usual way of speaking—we accept the presupposition upon which
alone the question is possible ; and if we say of a dead man that he is not
ill, we are guilty of using our words ambiguously. It may still, however,
be claimed that, by calling such an answer ambiguous, we admit that the
words do not, in themselves, exclude the other meaning; and that form-
ally, therefore, the truth of the proposition is incontestable.
4. We may admit this justification, and nevertheless draw from it the
lesson, that in the sphere of temporally valid judgments there is not much
to be done with the principle of excluded middle. The question is not
as to whether Socrates existed at all; if it were, then, of the two propo-
be true. His existence is presupposed in the proposition, but existence
at a previous time, and the difficulty applies to the present. Because
temporally valid judgments state their affirmations only for a given point of
time, it remains uncertain whether the negation of such judgments applies
only to this point of time, or to the subject throughout its whole exist-
1 With reference to these and similar objections cf. Ueberweg S8 78-80, more especially
p. 205 sq. ; Drobisch, Logik, $ 60, p. 66.
2 Categ., 10, 13 a, 27-6 35.
THE NEGATION
153
ence. It is uncertain, therefore, whether what is false is only present,
past or future, or the predicate altogether and at all times. Of the two
propositions “he will die—he will not die,” one is necessarily true, the
other false. But the proposition does not tell us whether she will not
die ” is true because he is already dead, or because he will be carried
up to heaven in a whirlwind like Elijah.1 When, therefore, we can attain
by means of the principle of excluded middle to the truth of an affirma-
tion, the principle has its value even in the case of merely temporal judg-
ments, for affirmations are not ambiguous. But it is not worth while to
use it for the sake of mere negations.
5. There is less difficulty with respect to judgments of unconditional
validity. Since these apply to the contents of the subject-idea, there
would seem to be no room for ambiguity in the negation of them. In
such judgments as “matter is heavy” and “matter is not heavy," "space
is infinite” and “space is not infinite,” neither affirmation nor negation
seems to be ambiguous. But here a difficulty of another kind presents
itself, one which we have already touched upon above ($ 22, 3, 4, P. 128)
and which rises out of the generality of the subjects. Owing to this
generality we are constantly tempted to extend our judgments to all the
definite particular things which fall under the subject-idea ; but though the
Predicates of affirmative judgments are of course true both of the general
idea and of the particular objects which fall under it, we cannot in like
manner deny of the particular objects everything which does not form part
of the general idea. It is no part of the general idea triangle to be
equilateral, nor of the general idea man to be white; but we cannot on
that account deny that any triangles are equilateral or any men white.
· Aristotle makes a strange exception with reference to the future when he says (De
interpr., 9, 18 a 27) that when one person says that something will happen, and another
person denies it, it does not follow that one necessarily speaks the truth, for if it did all
the future would be necessary and deliberation would be superfluous. But here-as
Zeller allows (Gesch. der griech. Phil., II. 2, p. 157)—the Stagirite has committed an over-
sight. He confounds the statement that it is necessary that the one or the other should
be speaking the truth, with the statement that one or the other speaks necessary truth,
i.e. speaks the truth because what he says is necessary or necessarily not ; while all that is
necessary is that the actual, perhaps fortuitous result should prove one of the two to have
been right. What Aristotle means is that the statement that one is necessarily speaking
truth involves that the truth or untruth is already determined, while really the one state-
ment is as uncertain as the other, and neither Čotal nor oỦK čoral can be properly used in
the sense of knowing. We see here how he, with his habit of referring every proposition
to Being, can find no correlate for a statement which leaves the alternative between
Being and Not-being undetermined.
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LOGIC
Hence there is something wrong about the opposition between the
judgments “ triangles are equilateral—-triangles are not equilateral.”
The negation is again ambiguous, for now it only denies generality, and
is not meant to state that the predicate cannot be united with the
subject. It is at this point that first the divisive judgments, and then
the disjunctive judgments grounded upon them, appear; the former
stating the compatibility of different predicates with the general idea, the
latter their incompatibility amongst themselves.
6. According to the ordinary formula of the principium exclusi tertii
the proposition that of two contradictory judginents one must necessarily
be true (either A is B or A is not B, holds good) is rendered as follows:
“of two contradictorily opposed predicates one must belong to every con-
ceivable subject A” (A is either B or not-B). In this way the negation is
transferred to the predicates, and strictly speaking we obtain two affirma-
tive judgments, which allow of no third intermediate. After this transi-
tion had been made by the Wolffian Logic, Kant made use of it for
his own purposes. He showed that since, when all possible pre-
dicates are compared with their opposites, one of each pair must belong
to every subject, this principle passes beyond the sphere of the merely
logical, and as the principle of complete determination presupposes a
totality of all predicates as the total possibility. We need not here enter
upon the question as to whether this transition does not contain a
quaternio terminorum in the “all,” which in one place is used as a completely
indefinite generality, in the other as a definite number. At any rate, it
shows clearly how Kant understood the principle-i.e. as concerned with
the reference of a subject to all possible positive and negative predicates,
in order to see by which of these it is to be determined. Thus the propo-
sition “A is either B or not-B” instructs us to substitute for B all conceiv-
able predicates one after the other. But even apart from the question as
to the justification of not-B this is a barren task; we never gain any deter-
mination in this way, since it always remains undecided whether B or not-
B, X or not-X belongs to the subject. Even if we could decide between
the alternatives, still, so far as the great majority of such predicates was
concerned, no conceivable combination would enable us to try the
affirmative form of the predicate, and thereby challenge a negation. As
regards general concepts the difficulty would still remain that with them
both B and not-B are compatible; so that for this reason also the value of
the principle is considerably lowered.
THE NEGATION
155
7. But the principle of excluded middle really derives its reputation
mainly from the fact that it is a special case of a relation which is certainly
most important and rich in consequences—i.e. the relation of disjunction.
It is due to the nature of ideas that we are often in a position to limit our
choice among different statements concerning the same subject to a few,
often to two only. We are able, on the ground of our knowledge and of
the particular contents of our subjects and predicates, to frame two
positive statements, of which we know that they are so far related like
contradictorily opposed judgments that while both cannot be true to-
gether, neither can both be false ; and in this case we gain, by denial of
either member of the disjunction, a definite, unambiguous affirmation.
Now the principle of excluded middle is apt to make us think that we
can attain easily, and at little cost, to such fruitful disjunctions as these ;
we need but say that every proposition is either true or false, and there
we have an incontestable truth and a sure basis for strict investigation.
But the opposition of predicates has substituted itself unnoticed for the
mere negation, and the negative statement seems to tell us more than it
really does; it is understood as if it applied to the truth of the proposition
with the opposite predicate, this being what it is as a rule really based
upon. If we could solve all difficult questions by starting right off with
“It is either so or so ” (a proceeding of which we might use the phrase
“ trancher la question” even more fitly than the French themselves use it)
_“he is either mentally healthy or diseased in mind,” “the number is
either odd or even,"—then indeed the principle of excluded middle
would be an invincible weapon. But in itself it can never really do more
than oppose the affirmation by the negation in its poorest and most
barren form; and though the view that there is no intermediate between
affirmation and negation is important as interpreting the meaning of the
negation itself, yet the proposition cannot be dignified as a special
principle.
8. The indirect proof, again, does not really derive its cogency from •
the Principle of Excluded Middle. It is true that it ends by inferring an
affirmation from the falsity of a negation ; but the falsity of this negation
must have been shown by substituting for the purely negative and there-
fore indefinite contradiction one which was definite and based upon a
disjunction, and this disjunction was in itself sufficient to support the
proof.1
1 While reserving a fuller treatment of the question for a later section, we may, in
156
LOGIC
passing, show by an example that the principle of excluded middle is unnecessary for
the indirect proof. In Euclid 1. 29, it is proved that when a straight line falls on
parallel straight lines the alternate angles are equal. For if the angles were not equal
it would follow that the inner angles were together less than two right angles, therefore
that the lines-according to the accepted postulate-were not parallel. The contradiction
of this with the hypothesis from which we started shows that it is false that the alternate
angles are not equal ; true, therefore, that they are equal. Expressed in this form, the
proof seems to rest upon the principle of excluded middle. But it is not really so.
Unless we substitute the statement “one angle is greater than the other” for the
"angles are not equal,” we can get no further with our proof. The hypothesis which
proves to be false is that one angle is greater than the other; and it is from the falsity of
this that we get the truth of the proposition. The ground of the proof, therefore, is not
that of the two propositions : the two angles are equal
the two angles are not equal
one must necessarily be true; but that of the propositions :
the two angles are equal
the one angle is greater than the other
one must be true.
The disjunctive proposition includes the mere negation, but the negation does not in.
clude the disjunctive proposition, and it is upon the latter that the proof rests.
CHAPTER V.
PLURAL JUDGMENTS.
By Plural Judgments we mean those which, in one proposition, state one
predicate of a plurality of subjects.
1. AFFIRMATIVE PLURAL JUDGMENTS.
§ 26.
When simple judgments repeat the same predicate of a number of
subjects, and the person judging expresses his consciousness of this
agreement by making one verbal act of predication refer to several sub-
jects, then the first form of judgment which arises is A and B and C are
P (Copulative Judgments).
When A and B and C fall under the same denomination N, so that we
are enabled—or induced-to enumerate them as several N's, then there
arises the Plural Judgment in the narrower sense, which, with a definite or
indefinite statement of the number, includes the plurality of subjects in
one verbal expression (several N's are P).
I. Our desire to form judgments exercises itself according to the
material and occasions offered psychologically. The first result is a series
of acts of judgments, connected only by the fact that they follow one
upon the other in the judging subject, and are comprehended by one
consciousness which, in passing from one to the other, does not im-
mediately lose sight of the previous acts. The verbal connection of
propositions by “and,” of all forms the most primitive and least signifi-
cant, states originally nothing but this subjective fact of co-existence in
one consciousness. Thus it has no objective significance ; "and" serves
equally to connect the most heterogeneous and the most closely allied.
But according to psychological laws those judgments tend to group them-
selves together which either state different predicates successively of the
same subject, or the same predicate of different subjects. Judgments of
the former kind, which presuppose that the attention lingers over one and
157
LOGIC
the same subject-idea, link themselves naturally into the conjunctive form,
A is B and C and D, etc.; and this does not merely imply that the predi-
cates one and all belong to the subject, but also expresses the conscious-
ness of this co-existence of different determinations. To this extent the
conjunctive judgment tells us more than its component parts taken
singly. But there is no occasion at present to consider this form more at
length. It becomes important only when applied with a consciousness of
logical claims either to narrative judgment, when it serves as a description,
or to explicative judgments, when it serves as a definition.
2. The combination of judgments which ascribe the same predicate to
different subjects presupposes that our attention is fixed upon the predi-
cate, that factor of the judgment which is present in the mind as a general
idea. This further implies that our thought is actively comparing ideas
and referring them to each other; seeking to connect particulars and to
recognise agreement in difference. Thus the judgment of the form A and
B and Care P has the same end before it as all judgment; it attempts to
appropriate the manifold and new by the aid of ideas which are already
present and firmly established, and it therefore represents a higher
3. The simplest case in which we have a repetition of predicates is the
intuition of a plurality of like or similar things which are named by the
same word. These things may be perceived as discrete, and form a
spatial or temporal series ; or they may be recognised as differentiated
parts of a whole, as members of a group. The repetition of the same
intuition and the same denomination comes into consciousness in the
distinction of the many A's from one A ; verbally in the formation of the
plural. When we are interested merely in the question what it is which
we have seen, there follows a denominative judgment in the plural (those
are sheep, those are letters). But by every plurality of the homogeneous
we are instigated to count and to make numerical comparisons, and an
indefinite or definite numerical expression appears in answer to the
question “how many.” In the judgment “ these are three shots” either
the numeral or the noun is the real predicate, which is emphasized by
the speaker, according as the name or the number precedes.
4. As a rule the act of naming takes place so rapidly and unconsciously,
that we form no special judgments in the process, but merely assert the
name in the word by which we denote the subject. Generally also the
distinction of unity and plurality, the counting of small numbers, and the
PLURAL JUDGMENTS
159
estimation of different degrees of plurality-few, some, several, many, etc.,
-pass as quickly. We make special predicates of these only when
the question arises how many there are, or when we wish to establish a
doubtful or disputed statement; then the synthesis which is contained in
the judgment is between the plurality which is presented and now counted
and the definite or indefinite numerical idea.1 Generally this again finds
expression only as part of the denotation of the subject, as a completed
result; and what we are concerned with is the statement to be made about
such and such a number of subjects.
5. What is the nature of the function of judgment, when there arise in
this way such judgments as “hail-stones are falling—some stars are be-
coming visible—many trees are rooted up-fifty men are wounded”? .
The first view is that which regards the plural of the verb—and there-
are summed up in one common expression. Before I can say, “some
stars are visible," I must have seen one here, one there, another there.
The predicate belongs to each one, but either I do not know their names,
or I do not wish to name them ; instead of saying a Lyrae and a Cygni
and a Bootis are visible, I denote the particular individuals by their
common name only; but it is these definite particular stars to which I
refer. It is only in one set of cases, however, that the plural judgment
arises in this way. In others the subject is perceived as a plurality, as it
were, at one glance, and the predicate is stated of this plurality; the
in judgments where the predicate cannot belong to the particular subject
by itself. “Numberless birds fill the wood with their song "_"the trees
grow thickly together”_these are not judgments which can have arisen
from a summation of many judgments.
It is different when the numerical term is the real predicate. The
Those logicians who see in every judgment a subsumption of the subject under a
more general predicate concept which is its genus, might be puzzled to say what the
particulars are in respect to which three, or seven, or a hundred are general and what
extension is to be ascribed to these concepts. Does the extension of “three” comprise
everything in the world which I can enumerate as one, two, three? Or must we not
rather say that three is in itself a fully determined idea, in which there can be no question
of extension, because, as we always count in the same way, the number itself is always
absolutely the same? Again, when it stands as predicate is it really the predicate of the
things concerning which the statement is made, or is it not rather the predicate of their
number, this number owing its existence to the fact that I am at the moment grouping
together and counting just these things and no others ?
160
LOGIC
proposition “many men are short-sighted” is not intended to inform me
that A and B and C, etc., are short-sighted, nor indeed is it meant as a
statement about definite individuals. The information offered is the
lamentable fact that the short-sighted are many—i.e. many, comparatively
speaking, in comparison with the total number. When news arrives from
the battle field it is taken for granted that some have been killed, or at
least wounded; the question is how many, and the construction of the
telegram, “Dead 10, wounded 50,” is logically the most correct.
We need not point out that repeated activities give occasion in the
same way as things for plural judgments.
It is true, no doubt, that several particular judgments must precede all
such statements of number ; before I can count, each particular one must
have been observed, A is short-sighted, B is short-sighted, etc. But in
counting them I disregard everything which distinguishes them ; I forget
who is short-sighted, I know merely that I have made my observations
upon people, and retain the definite number of repetitions of the same
observations upon homogeneous individuals, determining its relative
magnitude. I proceed like the statistician, who fills his schedules with
numbers only, and who cares nothing as to who are the subjects of the
enumerated births, deaths and suicides; the predicates of his judgments
also are numbers.
It is necessary to treat of these obvious points at length, in order to
throw some light upon the obscurities of the traditional doctrine of uni-
versal and particular judgments.
§ 27.
The “all” by which the subject of the so-called universal judgments (all
A's are B) is bound together, signifies, according to its original meaning,
a definite number, and a judgment beginning with "all” presupposes a
limited number of particular objects which can be counted. Thus,
according to its original meaning, “all A's are B” can only be said in
reference to definite particular objects. And here from a logical point
of view the “all” is the predicate (the A’s which are B are all A's).
We must carefully distinguish between this EMPIRICALLY UNIVERSAL
JUDGMENT and that which is UNCONDITIONALLY UNIVERSAL. In the latter
we attempt inadequately to express the necessary connection between the
predicate B and the subject-idea A, by falling back upon the unlimited
number of the particular. (If anything is A, it must also be B.)
PLURAL JUDGMENTS
161
I. According to its original meaning "all” presupposes a definite num-
ber, for it expresses the fact that two definite numbers are equal to each
other. Before I can pass a judgment of the form “All A's are B,” I must
undertake a twofold process of counting. I must first count the things which
are A, and then the A’s which are B ; then if the two numbers are equal I
express it in the proposition “All A's are B” (such phrases as-—"all four,"
“all nine,” remind us directly of this process). If I say “they are all
there "-e.g., the guests invited—then I know how many I invited,
count those who are present, and the numbers being equal, the “all” re-
sults. If I think that a card is missing from a pack, I count them, and
if the number of cards which I hold in my hand is equal to the number
which belongs to the pack, they are “all there."
It is not necessary that the definite number should be expressly known
and named, in order that a judgment may be stated as to "all." When
a room has been emptied, and I say "they are all gone out,” there is no
need for me to know how many people were there. It is enough that
none have remained behind, that I have reviewed in thought all who were
present, and now know that each particular person who was present must
also have gone out; hence that the predicate is wanting to none.
Under any circumstances “all” has always passed through this twofold
negation. It arises out of the assumption of a possible difference between
one number and the other,-out of the question, therefore, whether there is
no exception. “All” denies the exception; and by whatever method I may
assure myself that there is no exception, whether by directly counting them
or only by taking one after the other with the certainty that none escape me,
- I am equally sure of my “all.” Thus the formula nemo non, nullus non, etc.
is really the primitive one, and not a circumlocution ; it exactly expresses
the process gone through, and it is omnes which is the secondary expression.
2. Strictly speaking the real statement is concerned with the “all.”
It is this which is the predicate from a logical point of view, even though
it may not appear as such grammatically. The proposition is “those A's
which are B are all A's.” It is implied by the plural that there are many
A's, it is also implicitly stated that there are A’s which are B; but the
question to be dealt with and to be answered by the judgment is, whether
the A's to which B belongs are all-whether there is no exception. (When
we are dealing, not with things which can be counted side by side in space,
but of states or activities which take place at different times, then what we
have said applies to the “always” and “every time.”)
S. L.
M
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LOGIC
3. From this it is clear that in a judgment concerning "all,” the words
originally apply to particular things ; that these particular things must be
present in a definite and limited number which can be counted, and that
only upon this presupposition can a judgment concerning “all” be the
adequate expression of my thoughts.
In other words : The words “all A's are B” are originally the expression of
an empirical generality only, i.e., a generality attainable by actual counting;
and they can only be used in reference to subjects which are forthcoming
in a definite number which can be counted, and of each of which the
predicate can be stated. They are the expression of a definite limited
comparison of the cases before us, and they presuppose that I am certain
that the judgment is true of each particular one before I can state it of all.
4. How then are such judgments as "all men are mortal," "all bodies
are extended,” etc., related to these? Their meaning is not that before
making the judgment we have gone through all men or all bodies one by
one and counted them; but that the predicate, mortal or extended, belongs
to whatever is a man or whatever is a body.
But there are two senses in which such judgments may be really valid.
They may, in the first place, be explicative judgments (analytical in Kant's
meaning of the word), because based upon the recognised meaning of the
subjects-term. I can state with perfect certainty that “all animals feel ”
without having enumerated the particular animals, if feeling is contained in
my idea of animal—if therefore I should not call anything an animal to
which feeling was wanting. In this case it is only in a secondary way that
the thought is expressed by “all.” The expression results simply from
the analysis of the idea which I connect with the word animal. The
meaning of the word determines the limits within which it is applicable,
and hence I can foretell from the meaning that the predicate to feel must
be present wherever the denomination animal is justified (p. 9 sq. above).
Because animal feels, all animals feel. The analytical proposition express-
ing the meaning which the words have in our thoughts is translated into
the more familiar language of narrative judgment concerning particular
things, and by my passing from the general thought to individuals it
becomes more intuitable. This is why the expression “ all ” has become
naturalized where it is not original; where, that is, we only anticipate an
experience of all the particulars, and anticipate it even where, from the
nature of the case, it can never be completed.
In other cases the predicate is not analytically included in the meaning
PLURAL JUDGMENTS
163
of the word. The word “ man,” for instance, may include only the par-
ticular formation of the body, life, ability to speak, etc. ; a definite length
of life is not necessarily included in it; every one at one stage of his life is
able to distinguish men from everything else with confidence, before he
thinks of asking how long they live or whether they all die. When this is
the case the judgment“ all men are mortal "—is not analytical. Nor is it
a judgment of experience in the sense that “all men” denotes only those
whom I know and in whom my experience has taught me that I shall find
the predicate. But this makes it only the more certain that it is the
result of an inference ; either of an inference from all observed cases to all
others, of which there is an indefinite and incalculable number; or else of .
an inference from the determinations which are understood as expressed by
the word to others which are necessarily connected with them. If we
really form the judgment, and do not merely repeat it after some one else,
it can only be as the result of some such inference.
We can never tell at all from the verbal expression of the judgment in
which sense it is to be taken ; whether it is to be understood as an empiri-
cally universal judgment which presupposes a definite number of subjects,
or as an unconditionally universal judgment; and, if the latter, whether as
analytical or synthetical. The ordinary doctrine does not hesitate to
regard every judgment beginning with "all” as belonging to the same
species.
5. If a judgment concerning “all” is unconditionally universal, then it
is clear that no direct statement is made about the actual existence of the
subjects, though this is most certainly presupposed by empirical judgments
if they refer to actual things at all. “All A's are B” means only " what is
A is B”; or “if anything is A it is B.” It is, indeed, indefinitely pre-
supposed that some existing particular thing is recognised and called by
the name A, but this is not stated in the judgment. Just for this reason
the plural, and indeed the whole mode of expression, is, strictly speaking,
inadequate, a μετάβασις εις άλλο γένος, a relapse from the sphere of the
free and independent thought which moves among our firmly-established
ideas into the habits of intuition, which deals with the particulars. The
adequate expression is simply A is B, man is mortal, a square is equi-
lateral, etc.
6. The traditional doctrine finds no difficulty in introducing the
universal judgment. What is generally said is that if a predicate B is
stated of the whole extension of the concept A which forms the subject,
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LOGIC
then the judgment is universal ; if a part only of the extension, then it is
particular. If the subject-term is a nomen proprium, or an equivalent
expression, then its extension is exhausted by one individual ; thus the
judgment “ Callias is rich" has so far the character of being universal.
Nevertheless this simple doctrine contains—besides the doubtful use of
the nomen proprium as the sign of a concept-an obscurity of which the
consequences are constantly recurring. It is generally taught that the ex-
tension of a concept is made up of the concepts contained under it as species,
inasmuch as we can form a plurality of more definite general ideas by means
of the differences admitted by the higher concept. But in the discussion of
the universal judgment it is generally assumed without hesitation that the
extension of a concept consists of particular existing things, and that there
is no difficulty at all in reviewing, establishing, and recognising this exten-
sion, because it is presupposed that our concepts are already all that they
should be that is, the expression of the nature of things according to
their fixed specific differences. Hence Logic does not as a rule distinguish
between those judgments which are based upon the Concept alone (i.e.,
the meaning of the subject-word), and which in unfolding this meaning
attribute a predicate to every thing which is named by the subject-word
and thus forms a part of the "extension of the concept"; and those which
-perhaps on the ground of unanimous experience—state a predicate of
all known things which fall under the same denomination because they
have the same attributes. By neglecting this distinction Logic obscures the
most important point, the transition, namely, from an empirically universal
to an unconditionally universal judgment, the process by which concepts
and judgments are formed from experience. The judgment “all planets
move round the sun from West to East” is originally empirically universal;
any one giving utterance to it before 1781 meant by all planets, all six ;
between 1781 and 1801 Uranus was counted amongst them, and all seven
were included ; from 1807 till 1845 all eleven was what was meant; and
to-day we mean in the same way all the two hundred or whatever the
number may have become. But what is meant is always all that are
known, the same movement in its orbit being attributed to each. The
proposition says that all the bodies which I call planets have a common
direction of movement from West to East; that I know of no exception.
But suppose that I had recognised it as necessary—upon the ground, say,
of the hypothesis of Kant or Laplace—that all compact bodies moving in
constant orbits around our sun should move in the same direction, because
PLURAL JUDGMENTS
165
no reversed movements were possible within the space which can contain
them; then I should have to include movement from West to East in the
meaning of the word planet—e.g., to distinguish them from meteors—and
then my judgment, “all planets move from West to East,” would be
analytical in the Kantian sense, and would extend to the unenumerated
planets still to be discovered. It would mean that whatever can be called
a planet moves from West to East; from which it follows that anything
moving in the reverse direction would not be a planet.
7. The difficulty of finding a place for the so-called Singular Judgment
in the classification which distinguishes universal and particular judgments,
arises—as is clear from what has preceded—from the fact that the former
is in no way comparable with the latter. For in the case of universal and
particular judgments we have to do with a predicate which implies an
absolute or relative numerical statement; their genus is not the judgment
in general, but judgments whose predicates are numerical ideas. But in the
case of the so-called singular judgment we are dealing with the question of
what belongs or does not belong to a certain particular subject, and not of
how many subjects are forthcoming which possess one predicate.
In the first place, then, we cannot regard the division of judgments
into singular, particular and universal as correct and exhaustive. In the
second place, we have no ground for treating particular and universal
judgments as special kinds ; there is no more reason in the ordinary Logic
for regarding judgments having “all” for a predicate as a special kind
than there is in mathematics for regarding judgments having the predicate
“equal ” or “ infinite” as a special kind. Hence it is an arbitrary pro-
ceeding on the part of the traditional Logic to ask of every judgment
whether it is particular or universal. Singular judgments concerning the
particular and concrete have been treated as universal (in spite of the fact
that there are three kinds generally called singular—the individual judg-
ment "Callias is rich," the numerical judgment “one planet has a ring," and
the particular judgment of the next section “there is a comet which has
broken up”); while plural judgments have been regarded as particular,
although in no sense comparing what is given with the “whole extension of
the concept”; and simple explicative judgments, even definitions, were
without a place until they consented to pass as universals. Generality
plays an important part in human thought ; nevertheless in the last
instance it borrows its importance from necessity.
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LOGIC
§ 28.
The so-called PARTICULAR JUDGMENT as given in the common formula
“some A's are B” may be an empirical judgment concerning particular
things. In this case it differs from the merely plural judgments only when
it aims at establishing an exception to the universal, or at preparing the
way for a universal judgment.
When the subject is not to be taken in an empirical sense it is a
completely inadequate expression for the thought which it is meant to
denote, and confuses the important distinction between empirical and
unconditionally valid judgments.
1. To the universal judgment the traditional Logic opposes a Particular
Judgment having for its formula “some A's are B," and in so doing it
follows Aristotle, though his meaning was not the same. This particular
judgment, as ordinarily treated, is one of the most unfortunate and incon-
venient creations of Logic. So far as the words go, its meaning is quite
indefinite, and as a rule it is incongruent to the thought which it should
express and which it really obscures. It is true that the difference
between the universal and particular judgments is generally elucidated by
pointing out that in the former the concept which serves as subject is
taken in its whole extension, while in the latter it is taken in a part of its
extension only (év uépei). If we allow that the extension refers to the
totality of particular individuals, then this distinction holds good on the
assumption that we know the whole extension and that therefore all the
parts of the extension are actually given to us. This distinction between
the universal and the particular judgment was rational enough according to
the view of Nature taken by Aristotle ; a view which starts from the idea
that a system of fixed and immutable concepts has realized itself, and is
constantly realizing itself, in the fixed forms of Nature, and that our
empirical knowledge surveys this realisation of the concept in all its
essential differences. And the distinction was all the more rational
because Aristotle never actually applied it except when it was justified.
But when later Logic dealing only with conceptual relations, and totally dis-
regarding the material realization of the concept, took up the Aristotelian
distinction, and made use of its formule-or rather of a bad translation of
them—the result was a host of absurdities, rendering the ordinary doctrine
completely false if the words are understood in their ordinary meaning.
2. The Aristotelian τινί υπάρχειν μή παντί υπάρχειν is generally translated
PLURAL JUDGMENTS
167
by the formula “some A's are B," but the plural here can have a meaning
only when applied to things which are particular and definite, and can
therefore be counted, in which case it presupposes a narrative judgment
treating of the actually existent. And, in the same way, when the
particular judgment is contrasted with the universal, the plural has a
meaning only when it is presupposed that the extension of the concept
is divided into parts, each of which itself contains a plurality of indi-
viduals ; whereas there seems no reason why a single individual should
not suffice to form a part of the extension of the concept.
The first condition is present in all cases where a particular judgment
is opposed to an empirically universal judgment--all planets move in
ellipses, some planets have moons. But when we are dealing with abstract
subjects, whose extension does not consist in a plurality of things, the
formula leaves us in the lurch. Must we say "some virtue is justice” or
“some virtues are justice"? "some love is calf-love," or—but there we
have no plural ! Even in cases where number is not contrary to sense,
the use of the plural shifts the ground of the judgment. Such judgments
as “some parallelograms have equal diagonals," "some conic sections are
parabolas," have a very strange sound from the point of view of geometry ;
for in geometry we do not think of its constructions as spread abroad in
the world in a plurality of instances, so that we can speak of them as of
some cats which have blue eyes and some quadrupeds which can fly. The
universal judgments, “all parallelograms are divided by the diagonals into
congruent triangles,” “all conic sections are curves of the second degree,”
sound less strange, because “all,” when used in the unconditional sense,
extends beyond the empirically known. But this privilege does not
belong to the particular judgment; this necessarily imprisons the thought
within the sphere of the particular. 'H karà uépos eis aio now televtậ.
But on the second point the customary plural is false and misleading ;
"one man is sinless” is as much a particular judgment as “some men are
sinless” would be; and Aristotle himself included the singular in his tus
ävOpwnos leukós. Herbart is quite right in his correction of the ordinary
doctrine on this point (Einl. $ 62).
3. When a judgment of the form “one A is B,” or "some A's are B,”
is a narrative judgment of empirical origin, then it seems to have no other
meaning beyond that of stating a definite predicate of one or more
subjects which are denoted indefinitely by a general word instead of being
1 Even Kant makes the category of plurality correspond to the particular judgment.
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LOGIC
named one by one. The second judgment does not seem to differ in its
plurality from a number of judgments concerning single subjects, since the
numerical determination is not emphasized.
Still in the judgment "some men mistake red for green” there is some-
thing more implied than in the copulative judgment "John and Peter and
Paul mistake red for green.” The individual definiteness of the statement
is indeed lost by denoting John and Peter and Paul, as “some men.”
But through being denoted by the general name they are placed in a
relation to the whole of mankind which challenges a comparison ; and the
meaning of the judgment indicated by the indefinite denotation of the
subject, is that those who as men are like all other men differ from others
and possess some peculiarity in this respect; in other words, that differences
of colour-sensation are contrasted with the assumed likeness.
In so far as it thus aims at emphasizing differences and exceptions the
plural judgment becomes particular. But it is clear that this aim is
attained just as well by a singular judgment whenever its subject is
denoted by the general name instead of the proper name. The judgment
“there is a comet which has broken up into two ” is particular in this
sense.
4. But the traditional logic teaches that the particular judgment is
not meant to exclude the universal ; “some A's are B” does not tell
us that not all A's are B. This is a new proof of the ambiguity of the
formula, for, generally speaking, it is certain that what we do mean to say
is just this—that some A's are distinguished from the other A's. Still the
former interpretation has an element of truth in it, which is, that the
plural judgment may both be proceeding towards a universal judgment to
which it is preliminary, and be cut off from a universal as an exception to
it. As a proof against the apparent immobility of the fixed stars, it was first
shown that some of them have a motion of their own, and the copulative
judgment "a Centauri, and 61 Cygni and Sirius have a movement of
their own,” was expressed as “some fixed stars have a movement of
their own.” It was meant by this not that these three are on this
account not fixed stars, but that while leaving them amongst the fixed
stars, we have—contrary to our old belief-perceived movement in certain
of them; the judgment was opposed as an exception to the proposition
“all fixed stars are absolutely immovable.” It was a particular judgment
meant to express a distinction amongst the fixed stars.
But as the number grew and progress was made with observations the
PLURAL JUDGMENTS
169
same judgment "some fixed stars have a movement of their own” was able
to take the new meaning that it is known certainly of some and is probable
of all. The former judgment presupposes the knowledge complete that a
predicate belongs to some A's and is wanting to others, while the latter
presupposes that our knowledge is only in a state of growth, and the par-
ticularity of the judgment is merely provisional.
5. But the school logic does not generally take any notice of this pro-
gress of knowledge through experience of the particular; its particular
judgments presuppose fixed conceptual relations and are only adapted
to the interpretation of these. But this logic falls into difficulties when
called upon to show the truth of its propositions by means of the prin-
ciples of identity and contradiction. Whence do I obtain the knowledge
that “some parallelograms have equal diagonals ” ? Not from the concept
of the parallelogram, for this contains nothing about right angles; and
even if I add “some” to “ parallelograms,” though by so doing I take
only a part of the extension of the concept, the concept itself has become
no more definite than before, and I cannot upon the strength of this
addition say of the part anything which was not contained in the concept.
If then no particular judgment can proceed from a mere explication, it
must be possible for us to define the idea of the parallelogram more
accurately and conceive it in a form which implies the predicate and is
one among a number of other possible forms, or else this form must be
present in thought as constituting the subject of my judgment. I do not
however state it in denoting the subject ; I mean right-angled parallelo-
grams, but denote them merely as some parallelograms.
The more adequate expression would then be the " parallelogram can
have equal diagonals” and “one kind of parallelogram has equal
diagonals.”
Still we should certainly not banish from logic its formula "some A's
are B” in the sense that “some A” denotes a part of the possible A's,
were it not for the constant danger of unwittingly substituting actual
things for possible things, for it is actual things which are indicated by the
plural in the first place.
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LOGIC
§ 29.
II. NEGATIVE PLURAL JUDGMENTS.
Exactly the same rules hold good when one and the same predicate is
denied of a plurality of subjects; and it is particularly to be noticed that
the judgment which denies universally may be either empirically or uncon-
ditionally universal, just as the affirmative judgment may.
1. The COPULATIVE NEGATIVE JUDGMENT,1 “neither A nor B nor C
are p” leads, when A and B and Cfall under a common genus,
to the plural negation “Several N's are not P." This again leads
to the statement which refers to the number of the N's, “the N's which
are not P are many, are a hundred.” The relation between this statement
and the negation concerning a single thing is exactly the same as was
explained with reference to the affirmative judgment ($ 26).
2. The UNIVERSAL NEGATIVE JUDGMENT-“those A's which are not B’s
are all A's”—is originally obtained by the same process of reviewing a defi-
nite number as that by which the universal affirmative judgment is obtained.
When I examine a definite number of trees one after the other to see
whether they bear fruit, and must answer in the negative as to each one, up
to the last, then I obtain the universal negation, which is appropriately
expressed in the words “none of them bear fruit.” 2 For by means of this
“none” one after the other is brought before me ; there is not one, oùdè eis,
1 This must be distinguished again from the conjunctive negation of different predicates
with respect to the same subject (A is neither B, nor C, nor D); the import of this
judgment cannot be made clear until later on. I consider it a burdensome superfluity of
terminology to make use of the expression remotive judgment for the copulative
negation.
2 Thus “no person"_" no one "_"nothing, etc.,” are not negative subjects such as the
Aristotelian oủk öv@pwTos; I make no statement about "nothing”_"no one.” When I
say “no one is good except God alone,” the subject of my judgment is “human beings,"
and their goodness is denied ; what I mean is “there is none who is just, not even one."
When I say “nothing hurts me," I do not mean that a thing called nothing hurts me,
but that everything that might perhaps hurt me does not hurt me. But the appearance
of the negation in the subject is most expressive of the way in which I seek, as it were,
a subject for my predicale and find none. It is the same when “no one"-"nothing”—
“none," stands in the accusative, e.g. “I see no one going, no one coming,”-gramma-
tically the “coming no one," appears as object of my seeing, actually it is the sight of a
coming person which is denied. Again, in the proposition “I hear nothing," not only
the object, but the hearing itself disappears—“it is false that I hear anything.” From
this it follows that “nothing” (as well as "no one,”) has no meaning except in a
proposition ; to use it out of a proposition as the independent symbol of a concept, as
in the famous Being, Nothing and Becoming, must lead to mere playing with words.
PLURAL JUDGMENTS
171
ne unus quidem, to which the essayed predicate belongs. A single A
which was B would prohibit the universal proposition. This explains also
the ambiguity of the negation, and the different meanings which may belong
to judgments of the form “no A is B.” For on the one hand they pre-
suppose the existence of a number of A's, and what they are meant to tell
us is that the predicate B is absent from all existing A's,-no tree bears
fruit. On the other hand, they may be meant to deny the very existence
(within the given spatial or temporal region) of subjects to which the
predicate might belong-no tree is casting a shadow, no spring breaks
through the sand. When I deny that an A exists which is B, it is pre-
supposed that I am trying to find a subject A of which the predicate B
may be affirmed. It may be that I succeed in finding one, or some A's,
but without the predicate B; or that I find no A at all, which will be the
case when the predicate B could not be absent if an A were there (cf.
" the fire is not burning," p. 124).
Thus the judgment "no A is B,” has for its immediate meaning the
denial that an A which is B exists. It is only secondarily, and in cases
where the predicate might be absent from A, that the proposition might
be expressed as "the A's which are not B are all A's.”
3. From this it follows again that this formula “no A is B," is
adequate only when particular A's are in view, and as the result of
judgments concerning particular A’s ; when therefore it represents a
narrative judgment. But if we wish to say that the predicate is excluded
by the subject-idea, hence that anything which can be named as A is on
that account not-B, then the adequate expression is “ A is not B,” or
“it is impossible for A to be B." It is only our habit of always return-
ing to the concrete and intuitable, which makes us use the uncondition-
ally negative judgment (as well as the universal affirmative) with reference
to particular things, even in cases where no question is directly raised
either as to their number, or even their existence. Instead of saying
"no man can know the future,” it would be more correct to say “ man
cannot know the future”; for my judgment denies the possibility, not the
existence, of the prophet. This is obvious when modal predicates
question the existence of any particular thing corresponding to the
subject-word. We do not say “no ghost exists,” “no murder is com-
manded,” but “ghosts do not exist,” “ murder can never be com-
manded.”
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LOGIC
III. THE NEGATION OF PLURAL JUDGMENTS.
$ 30.
When a universal judgment is denied, the negation applies to what
is actually stated in the judgment; viz., that the subjects to which the
predicate belongs or does not belong are all which fall under the subject-
term. The negation of “all A's are B,” means “the A's which are B
are not all A’s ”; and the way in which we understand the negation must
depend upon whether the judgment was intended as empirically or as
unconditionally universal.
The negation of the empirically universal judgment tells us that there
actually is an exception; that of the unconditionally universal judgment
only that an exception is possible.
Aristotle taught, and logic is constantly repeating his teaching, that
universal affirmative and particular negative judgments, and universal
negative and particular affirmative judgments, are contradictorily opposed.
This doctrine leads to false conclusions unless attention is paid to the
difference between empirically valid and universally valid judgments.
1. The real character of the judgments we have so far considered is
brought out most clearly by the negation. The negation of a copulative
or plural judgment has more than one meaning, inasmuch as that which
is false may be merely the plural, or the whole connection between
subject and predicate. The difficulty is especially great in obtaining any
definite statement from the negation of a negative statement. If it is
false that neither Peter nor Simon Magus were ever in Rome, that does
not tell me whether both were there, or which of the two; from the
statement that it is false that several comets have brought misfortune I
do not know whether only one has brought misfortune or none at all.
The negation of a numerical predicate disputes the numerical predicate
itself in the first place, but it is left uncertain whether it does not extend
further. If it is false that ten houses are burnt down, then either more or
less or none at all are burnt down.
2. A more definite value attaches, according to the ordinary doctrine,
to the negation of a universal judgment—whether affirmative or negative.
When a negation is advanced against an affirmative judgment concern-
ing “all” it annuls the statement that the number was complete without
exception; the universality is denied. Since the affirmative universal
judgment says, “ there is no exception,” its negation says, “there is an
79
PLURAL JUDGMENTS
173
exception.” If I know it to be false that all ravens are black, then there
is at least one which is not black; hence I can say “one raven is not
black.”
Suppose the negation is directed against the proposition “no A is B”;
according to what was said above this means “there is not an A that is B,”
so that as a consequence of the negation it must be true that there is an A
which is B. If it is false that no raven is white, then there is a white
raven.
Thus, the principle of contradiction and of the twofold negation being
applied to propositions with the predicate “all,” the teaching of Aristotle
(De interpr., 7, 17 b, 16) follows directly from the meaning of the universal
judgment, i.e. : évtikalo bal katábaciv åtopáoel åvtipatikās try tò kalónov
σημαίνουσαν το αυτό ότι ο καθόλου, οιον πας άνθρωπος λευκός-ου πας
ävOpwnos deucós, oïdes äv@pwnos LEUKÒs— ČOtu tus ävópwnos deucós. This
formula is perfectly correct, and has not yet been falsified by the thoughtless
habit of substituting the plural “some” for où tâs and ris. 1
3. But it is correct only so long as we avoid passing from uncondition-
1 The ordinary doctrine is that there is :
Contradictory opposition between, All A's are B
Some A's are not B
and between, No A is B
Some A's are B
And contrary opposition between, All A's are B
No A's are B.
These two latter propositions cannot both be true, but may both be false.
Of the judgments “some A's are B-some A's are not B,” Aristotle rightly says
(Anal. Y., II, I5, 63 6, 27) Tò Tivi Tộ oỦ TUì The AểẸP LUTiKeyTac uºp ov->because the
subjects are quite different. To these judgments modern terminology has given the absurd
name of “sub-contrary" ; both, it is said, may be true, but both cannot be false. (If we
assume that in the proposition "some A's are B-some A's are not B” the subjects are
the same, the denotation alone being indefinite, then the propositions would naturally
be contradictorily opposed; but the expression leaves it undecided which A's are meant.)
A difficulty into which the ordinary doctrine seems to lead us bears witness to the
justice of our view as given above ; viz., that the contradiction between universal and par-
ticular judgments of opposed quality is the simple consequence of regarding “all” as the
predicate. As an instance of this difficulty, the two propositions " light is matter-light
is not matter" are contradictorily opposed and one is necessarily true ; while the equiva-
lent propositions “ all light is matter--no light is matter” are said to be in contrary
opposition only, and may therefore both be false. The difficulty is solved when we
notice that in the second pair of judgments an entirely new subject is introduced, which
involves the assumption that we are speaking of light, not according to its unity but
according to its differences. From this it follows that the proposition “all light is
matter" is after all an inadequate and not completely equivalent expression for “light is
matter."
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LOGIC
ally valid judgments to judgments which are empirically valid and vice
versâ.
The negation may be directed against an unconditionally universal
judgment, which is intended by means of the more intuitable universality
to state, when affirmative, the necessary connection of subject and predicate;
when negative, the necessary exclusion of the predicate from the subject.
In this case it can deny only what was meant, and says that in the first
case it is not necessary, in the second that it is not impossible, for the
predicate to belong to the subject. But this negation, which has nothing
to do with the presupposition that particular subjects have been enumer-
ated, must not be taken to mean that the predicate B belongs or does not
belong to one or some actual A's; it would be quite inadmissible to apply
the relation of contradiction here. The statement that it is false that all
men are sinners (in the sense of the sinfulness inherent in their nature) does
not tell us that some men are actually not sinners; and the empirical
judgment "all men are sinners” might still be true, " because all have
sinned.” If it is false that no man is entirely bad, in the sense of the
negation of an impossibility, it would not on that account be true that one
or some were in reality entirely bad.
On the other hand, the negation of an empirically valid particular judg-
ment can never be the ground of an unconditionally universal, but only of
an empirically universal judgment. If it is false that there is anything
living which has not had its origin from something living, then the propo-
sition omne vivum ex vivo is true in the sense that everything living which
is known to us has had its origin from something living. Bu twhether it
follows from this that the proposition states an absolute necessity, is still
disputed. It may be false that there are men who live over 200 years,
but this gives no ground for the judgment “no man lives over 200 years”
in the sense that it would be impossible to be a man and still to be more
than 200 years old.
It is characteristic of the inferences of empirical science that they pass
from empirically valid judgments to universal judgments which are un-
conditionally valid. But their justification for so doing can be found
neither in the doctrine of the contradictory opposition of universal and
particular judgments, nor yet in the ambiguity of the “all”; and it is
the difficult task of a theory of induction to determine under what con-
ditions the transition may be made from an empirical judgment to one
which is universally valid.
PLURAL JUDGMENTS
175
4. The real import, then, of the universal and particular judgment with
which Aristotle and the traditional logic were concerned, and to which
they attributed so much importance, was not that of the ordinary theory,
viz., “ that a predicate belongs to the whole extension or to a part of the
extension of a concept,” but that the connection of a predicate with the
subject is necessary or possible. The whole interest attaching to the
absence of an exception lies in its indication of a binding law; the whole
interest of the exception in the fact that it points to a plurality of possi-
bilities.
This brings us naturally to the closer investigation of the necessary
and the possible with reference to judgments.
CHAPTER VI.
POSSIBILITY AVD NECESSITY.
It is necessary for our immediate guidance, and before proceeding to
treat of the logical questions referring to the possible and the necessary, to
lay down a fundamental distinction. The statement that a judgment is
possible or necessary is not the same as the statement that it is possible or
necessary for a predicate to belong to a subject. The former refers to the
subjective possibility or necessity of judgment; the latter to the objective
possibility or necessity of what is stated in the judgment. The Kantian
distinction of the differing modality of judgments, according to which they
are problematical, assertorial or apodeictic, applies to the former; the
Aristotelian proposition : Târa apóraris éotiv û Toll Ünápxelv ñ Toll
ảoáyK7s tmcpxetv n Toũ vềéxcodau jaspxetv (Anal pr, I, 2, 24h, 3 ) to the
latter.
I. THE SO-CALLED MODAL DISTINCTIONS.
§ 31.
The so-called PROBLEMATIC JUDGMENT “A may be B” (meaning that
A is perhaps B) in so far as the consciousness of objective validity is absent,
cannot properly be called a judgment; i.c., it is not a judgment concerning
that which is denoted by the subject of the proposition. It is a judgment
only in so far as it states that the speaker is uncertain as to whether A is B.
The so-called ASSERTORIAL JUDGMENT (the simple statement Ais B) does
not differ essentially from the apodeictic judgment (it is necessary to affirm
that A is B); for every judgment of which we are completely conscious
when we give utterance to it, includes the affirmation of the necessity of
its utterance. It is true that the judgments differ with respect to the way
in which the certainty is attained, whether it is immediate or mediate; but
if we were to ground the distinction between assertorial and apodeictic
judgments upon this difference, then the apodeictic would take the
subordinate place, as having only a derivative certainty.
176
POSSIBILITY AND NECESSITY
177
1. The distinction between a statement which is merely possible and one
which is necessary, does not appear in the case of immediate judgments
where subject and predicate are found to agree without further mediation.
Such judgments are formed according to the principle of Agreement with
a confidence which is not the result of reflection. But it is different
with mediated (synthetical) judgment such as takes place when we form
ideas of syntheses between definite subjects and definite predicates not
yet contained in the subject-idea before us. These ideas may be due
either to external stimulus, the questions or statements of other people,
or they may arise internally from psychological combinations. But in
either case there may be no ground capable of yielding a consciousness of
objective validity in the synthesis, and then what we have is merely the
idea of a synthesis which remains in suspense as a question or conjecture,
and awaits some decisive certainty to confirm or deny the predicate.
Here the judgment is thought of as possible; and this means that it is not
necessary at the moment for the person thinking about it either to affirm
or to deny it. Such a judgment (A is B) which is merely thought of as
possible and not yet affirmed, may be briefly denoted as the hypothesis A is
B, and the simplest expression of this stage between synthesis and
judgment is the question. This is genuine only when expecting yes or
no for its decision ; when asked by one who has already made up his mind
for the sake of testing some one else, it is not a question, properly
speaking, but an imperative. But while the question expresses the first
conception of the hypothesis which seeks confirmation or rejection, it is
followed—if neither is found-by the consciousness of indecision which is
expressed in the formula “A is perhaps B, A is perhaps not B." (The
formula so often used " A may be B” is ambiguous and misleading, for it
expresses both the objective “can” (dúvaobai) and subjective hesitation.)
This form of statement, then, differs from the question only by expressing
our consciousness of inability to decide the question. While the question
contains the wish for decision, this form denotes the resignation which
is obliged to remain in uncertainty. Both really express the same
thought—that of a synthesis concerning the validity of which we are
undecided.
2. This expression of uncertainty is generally called a Problematical
Judgment, and Assertorial and Apodeictic Judgments are opposed to it as
expressing different degrees of certainty.1 Kant himself, indeed, gives a
* Cl. e.g. Ueberweg, Logik, ed. 3, $ 69, p. 164 sq., ed. 5, p. 207; Drobisch, $ 61, $ 62.
S. L.
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LOGIC
somewhat different meaning to the problematical judgment. He tells us
(Kritik d. r. V., 89. 4) that modality contributes nothing to the contents of
the judgment, but is concerned only with the value which the copula has
for thought in general. Problematical judgments are those in which we
accept the affirmation or negation as merely possible (a matter of choice).
Assertorial judgments, those in which it is regarded as actual (true).
Apodeictical judgments those in which we look upon it as necessary. The
arbitrary acceptation of the problematical judgment Kant extends to
judgments which are obviously false ; they have a problematical signifi-
cance if it is thought that some one might perhaps for a moment accept such
a proposition. On this view, which compares the problematical judg-
ment to the Aristotelian Útóbeous, 1 every judgment is problematical
when its validity is not at the moment expressly stated. But this may
mean one of two things, between which we must distinguish. The reason
why nothing is stated concerning the validity of a judgment in Thought
may be that nothing can be stated, because the speaker has not yet come
to a decision; or it may be that the speaker will not state anything
concerning its validity, some ulterior purpose leading him for the time
being to treat a valid judgment as invalid, or an uncertain judgment as
certain. On this point the traditional Logic has not followed Kant, and
Kant himself in his Logic (Intr. ix.) means by the problematical judgment
nothing more than an uncertain acquiescence.
3. But the custom of denoting the proposition “A is perhaps B”
as a problematical judgment, threatens to destroy the concept of the
judgment itself, and to fall into contradiction with all other teachings.
The essence of the judgment is to present a statement which claims to
be true, and calls for belief. An utterance therefore which states nothing
and leaves it open for the opposite to be true, is not a kind of judgment.
If every judgment is either the affirmation or the negation of a question,
then an utterance which neither affirms nor denies cannot be a judgment;
for to leave the question undecided is no decision, and to be uncertain
is not a degree of certainty. The law of contradiction notwithstanding,
11
1 According to Aristotle, the 'mbOeois is a merely assumed judgment concerning some-
thing which is or is not ; the judgment is not certain, or at least it is not proved to
be certain, and it must be conceded if it is to be used in conversation or proof. Cf. my
Programm : Beiträge zur Lehre vom hypothetischen Urtheile (Tübingen, Laupp, 1870),
p. 2. A justification may also be found here for the use of the word which I have
introduced above.
POSSIBILITY AND NECESSITY
179
A
the two propositions “ A is perhaps B” and “A is perhaps not B,” would
both be true together.
So far, then, as concerns A, the so-called problematical judgment is
not a judgment at all; it is only the thought of one, the unfinished
attempt at a judgment. The only real statement made in the formula “ A
is perhaps B” is, “the hypothesis A is B is uncertain.” Immediately,
and in the first instance, this is nothing but a judgment concerning the
person who is speaking, concerning his relation to the hypothesis A is B.
The formula says: I do not know whether the hypothesis is valid or not,
I have no ground either for affirming or for denying it; it states the pre-
sent condition of my thought, but nothing which could have objective
validity with reference to A.
We might try to give a wider meaning to the formula by taking it to
mean, not merely that I do not know whether A is B, but that it is not
known whether A is B; thus regarding the uncertainty as something more
than a fact peculiar to the individual, as always attaching to the proposi-
tion. But apart from the fact that the words do not mean this, even
this statement could not lead to a judgment concerning A which might
be co-ordinated with positive and negative judgments. We still have
only a statement concerning a subjective attitude, though an attitude not
peculiar to the individual but due to the present position of the sum total
of knowledge, or, which is still more general, due to the limits of human
intelligence. It is quite true that with reference to many questions we
can get no further than stating the impossibility of a decision, and that
such knowledge has its value when we are measuring our human capacity by
the ideal of knowing. Nevertheless it states nothing which could be taken
as a judgment concerning A. For an ideal consciousness, an omniscient
intelligence, the one proposition is true, the other false ; not until we are
certain of the one or the other have we realized the aim of thought, a
judgment which is objectively valid. Until then, the hypothesis remains.
an unsettled problem, and it is only confusing to subsume the expression
of subjective uncertainty and the expression of the certainty of the
objective validity of a proposition, under one concept as judgments.
Hence the only possible negation of the problematical judgment is
“the person forming the judgment is not uncertain whether A is B,
but is certain either of the affirmation or of the negation.” 1
1 Not only Wundt (Logik, 1, p. 197, cf. my reply in the Vierteljahrsschr. für wiss.
Phil., iv. 473 sq.), but Windelband as well (Strassb. Abh., p. 185 sq.), has defended the
180
LOGIC
We must, then, cease to teach that the so-called problematical judg-
ment is a kind of judgment, if we hold that the concept of the judgment
problematical judgment against this view. The latter endeavours to show from the
position which has been discussed above, p. 122 sq. that the problematical judgment is
co-ordinate with the affirmative and negative judgment; that it is a third kind of the
" practical relation” which is expressed in the criticism of a given combination of ideas.
“The critical judgment, like all other functions of approval and repudiation, is capable
of gradual variations.” The gradation of certainty appears in the different degrees of
probability ; these represent different intensities of the feeling of conviction, a feeling
which applies both to negative and to affirmative propositions. “We may think of
these different intensities of probability as represented by a line ; at each end we have
complete certainty, of affirmation at the one, and of negation at the other; and these, by
a gradual diminution of the certainty, approximate to a point of indifference where
there is neither affirmation nor negation.” This zero point has two meanings, for the
indifference between positive and negative reaction may be either total or critical. Total
indifference occurs, first, in all those trains of thought which are accompanied by no
estimation of the truth ; secondly, in the question where ideas are combined without any
decision as to the truth of their combination, but still with the desire for such a decision.
Now since the question contains no decision as to the validity of the thought, Windelband
does not co-ordinate it (as Lotze attempts to do) with the affirmation and negation as
another kind of judgment. But when we are led by consideration of the ideas combined
in a question to the conclusion that there is no sufficient ground for certain, or even
probable affirmation or negation, then we get the problematical judgment, which signi-
fies that nothing is to be said concerning the validity of the ideal combination A-B.
This is intentional suspension of criticism, critical indifference. Such conscious refusal,
to come to any conclusion is, says Windelband, quite decisive as to the position assumed
by the person judging towards the combination of ideas, contained in the question ;
therefore, when we divide judgments according to their quality, the problematical must be
co-ordinated with affirmative and negative judgments.
Of course I fully recognise the truth of what is here said as to the import of the so-
called problematical judgment and acknowledge my obligation for the distinction (which I
have adopted) between the problematical judgment and the simple question. But I cannot
help drawing an exactly opposite conclusion from it. Even from Windelband's point of
view, that affirmation and negation are both alike criticisms of the value of an ideal com-
bination, I fail to see that the suspension of criticism is a kind of criticism. The relation
between the three “ forms of judgment” cannot be that of co-ordination. Either I cannot
come to any decision or I can; if I do come to a decision, I must decide either in the
affirmative or in the negative. Thus it is only affirmation and negation which are co-
ordinate because they are divergent kinds of decision, and both are opposed to indecision ;
this is what I wished to show. If I have no knowledge on any matter unless I can either
affirm or deny, then the knowledge that I can neither affirm nor deny is only a knowledge
of my subjective inability; it is therefore a judgment about myself and not about the
subject of my proposition. Nor can I agree that because certainty is a feeling and all
feelings present differences of intensity, therefore there are degrees of certainty. Cer-
tainty, if we take the word in its strict sense, is either present or not; anything which is
not absolutely certain is uncertain. It is true that certainty manifests itself immediately
in consciousness, that there is a feeling of certainty; just as uncertainty, the wavering
between opposite probabilities, manifests itself in feeling. But then the opposition is not
between certain affirmation as one extreme and certain negation as the other, with un-
certainty as a transition between the two ; it is certainty and uncertainty which are
POSSIBILITY AND NECESSITY
181
includes the affirmation of the truth of the statement made, and if we
teach that a judgment must be either true or false.
4. The traditional doctrine is not much more successful in its distinction
between Assertorial and Apodeictical Judgments. Kant says (Krit. d. r.
V., § 9. 4; Logik, $ 30) that the assertorial judgment is accompanied by
the consciousness of the actuality of judging, the apodeictical judgment by
the consciousness of its necessity; and according to this all that is needed
in the assertorial judgment is that a statement should find utterance in
words, the consciousness of the necessity of the judgment being unessen-
tial. In the introduction to the Logik, ix., again, the assertorial judgment
appears as the expression of a merely subjective belief, which is valid only
for me; while, on the other hand, that which I know is said to be
apodeictically certain, i.e. necessarily having a universal and objective
validity for every one—even though the object of this assured conviction
should be a merely empirical truth.
According to this distinction the assertorial judgment would also be
excluded by our definition of the judgment; for in this we make the claim
to objective validity an essential characteristic. Indeed, from this point
of view the judgment has but one meaning, that every one must affirm and
believe the same, because it is necessary to affirm and believe it. Our
speech would lose all serious meaning, and degenerate into mere child's
play or lies if, when we stated a proposition, we did not also mean to say
that its negation is false, and that any one making an incompatible state-
ment is wrong; i.e. if the distinction between an assertorial and an
apodeictical judgment were that while the latter is necessary the former
is not, that while the latter is true for every one the former is true only for
me. Truth has no meaning except this necessity of our subjective action.
Even the merely temporal statement concerning the most casual particular
phenomenon—this iron is hot-presupposes that at the moment it is
necessary to judge in this way and not otherwise. My sensation makes the
connection between this subject and this predicate inevitable, and if the
question were raised whether or not the iron is hot, I should maintain
against all contradiction that in no other statement could I find expression
for my sensation.
opposed, and certainty belongs both to affirmation and negation. If the doctrine that
certainty has degrees were consistently carried out, we must regard the distinction
between opinion and knowledge as merely relative. It is really only the hope of certainty
which has degrees.
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LOGIC
5. Here, then, there disappears all essential difference between the
assertorial and apodeictical judgment. When I say “this is so,” it is not a
perfectly complete judgment unless it means “I must of necessity judge
that this is so"; the certainty of my statement rests entirely upon the pre-
supposition of this necessity.
All that remains of the distinction is that the necessity rests upon
different grounds in different cases, and that we become conscious of it
in different ways.
6. With reference to the first point, we may begin by distinguishing
between immediate and mediate judgments. In the case of immediate
judgments (in specie analytical) the necessity of affirming (or denying)
the predicate of the subject is grounded upon the principle of agreement
(or of difference); in the case of mediate judgments, either upon
authority or upon some process of inference. Immediate judgments
depend either (as in perception) upon individual experience as the ground
for attributing a predicate to a subject, or upon the generally recognised
meaning of a word. The same distinction between a ground peculiar to
the individual and one accessible to all, divides mediate judgments into
those which depend upon authority and those which depend upon a process
of inference. The fact that I take some one as an authority is a ground
which holds good only for me as an individual, so long as his credibility
is not established and proved as universally valid ; but a process of infer-
ence cannot be binding upon me unless it is binding for every one who
starts from the same data.
In this way the distinction has been made between immediate certainty
(which is grounded upon perception by ourselves or by others), and
mediated certainty which is grounded upon proof-though really the
certainty grounded upon the perception of others ought rather to be
counted as mediated, and immediate certainty is not confined to percep-
tions alone. The assertorial judgment has been reserved for the former
kind of certainty ; the apodeictical (Tpótaois åtodelktiKÝ) for the latter.
The distinction is borne out, moreover, by the customary formulæ, “A is
B,” and “A must be B” (“must” being taken as the expression of that
which is merely inferred, as in the proposition" it must have rained last
night.”) But then it becomes necessary to give up the ordinary notion
that the apodeictical judgment denotes something higher than the asser-
torial; and that in passing from the problematical to the apodeictical
there is an increase of certainty, and therewith of the value and dignity
POSSIBILITY AND NECESSITY
183
of the judgment. For every mediated certainty must ultimately rest
upon that which is immediate ; every proof upon premisses which need
no proof themselves. It is curiously at variance with the emphasis laid
upon apodeictical certainty that in ordinary life the “apodeictical” judg-
ment "it must be so," " it must have happened so,” denotes only a very
moderate degree of confidence ; and this because we have good grounds
for distrusting the certainty of ordinary inferences, and prefer to trust to
that which is immediately perceived. But even when the most rigid
proof is presupposed that which is proved can never claim a higher degree
of certainty than the data from which it is proved.
Other writers seem to have in view rather the difference between
propositions which hold good with absolute universality, and those which
necessity of reason is characterized as apodeictical, in opposition to
matter of fact. In this way Leibnitz distinguished between necessary
truths and truths of matter of fact.1 Necessary truths are those whose
opposite contains a contradiction ; truths of matter of fact are those
propositions; the latter rest upon immediate sensation. This way of
formulating the distinction fails to show that the subjects referred to by
necessary truths, and those referred to by truths of matter of fact, are
not of the same kind. Necessary truths of reason set forth comparisons
between concepts, which are assumed to be the unalterable possession
of all. It is only upon this presupposition (according to § 23, p. 145 sq.)
that it can be said of a proposition that it is contradictory, hence that its
opposite is true; such truths correspond to Kant's analytical judgments.
existence, and truths of matter of fact, so far as they have reference to
existence and to changeable events, certainly tell us something which is
not contained in the concept of the thing ; for it is no part of the concept
of the thing that it exists, nor yet that it happens to be constituted in one
Leibnitz, Princ. phil., § 33 (Erdm., p. 707): Il y a deux sortes de vérités, celles de
raisonnement et celles de fait. Les vérités de raisonnement sont nécessaires et leur
opposé est impossible, et celles de fait sont contingentes et leur opposé est possible.
Quand une vérité est nécessaire, on peut en trouver la raison par l'analyse, la résolvant
en idées et en vérités plus simples jusqu'à ce qu'on vienne aux primitives... 35 :
ce sont les énontiations identiques, dont l'opposé contient une contradiction expresse.
Nouv. Ess., iv. § 1; Erdm., 340 : Pour ce qui est des vérités primitives de fait, ce sont
les expériences immédiates internes, d'une immédiation de sentiment. Cf. De scientia
universali, Erdm., p. 83.
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LOGIC
particular way. To deny them, therefore, involves no such logical con-
tradiction as to say that a triangle is not triangular. But because the
opposite of a truth of matter of fact is not a priori impossible, it does
not follow that it is not necessary for me to state the fact after it has
happened ; or that the opposite statement would be possible for any one
knowing the fact. Even truths of matter-of-fact are truths only because
it is impossible to state their opposite ; but with them the impossibility
rests upon the ground of individual experience, not upon the ground of the
unalterable concepts from which I start. Even when immediate conscious-
ness is translated into a proposition of objective validity, it is presupposed
that the sensation is referred to existence and an existing thing according
to universally valid principles. Truths of reason are contained even in
truths of matter of fact, inasmuch as no true judgment can arise out of
individual experience except in accordance with general principles (e.g.
the principle that every change presupposes a permanent subject in
which it takes place). On the other hand, our possession of general
concepts upon which identical propositions are based, is in the last
instance matter of fact, something which must be there before the
principle of identity can be applied and give rise to a necessary judgment.
Thus the necessity of both kinds of truths is, finally, hypothetical. If I
think in definite concepts, I must predicate of them what I think in them ;
and if I have certain perceptions I must predicate of the perceived
subjects what these perceptions force me to predicate. Even this dis-
? It may be objected here that the senses deceive us, and that while it is impossible to
doubt the proposition A= A, it is possible to doubt the existence of the whole material
universe. This is quite true, but in no way invalidates the proposition that judgments
are true only in so far as they are necessary. For if we assume that our empirical
sensations are purely fortuitous, differing for each individual and as inexplicable as
dreams in their occurrence, we could make no statement as to an existent, or indeed any
universally valid statement at all, but then neither would any empirical judgment, except
such as referred to our momentary affections, be possible. If, on the other hand, we
assume that though sensations are indeed subject to a necessity which is the same for
every one, yet both this necessity and its law are unknown to usthen again we can
form no judgment concerning external existence. This is really the case so far as
concerns the question as to the ultimate nature of the existent which we feel, and for
this reason we get here only conjecture and hypothesis, not judgments which can be
announced as true. But wherever we are persuaded that we recognise necessity, in the
processes by which we form judgments from sensations, there we find judgment which
is assured and accompanied by a conviction of its truth. We know that we have a
sensation of this or that colour, that we are obliged to assign to it a definite position in
space and that we must regard it as the colour of some definite phenomenal object;
whether this object is mere phenomenon or the phenomenon of something existent and
POSSIBILITY AND NECESSITY
185
tinction disappears so far as the nature of the necessity is concerned, and
it is only the ground of the necessity which differs because the subjects of
the judgments differ.
There is no doubt that our consciousness of the necessity of connecting
a subject with a predicate may arise in different ways. Many immediate
judgments are affirmed by us unhesitatingly and without reflection, without
a suspicion that we may be wrong, or that the facts may be otherwise.
Absolute certainty and unalloyed confidence in our act of thought is here
inseparable from that act itself, and with such judgment our thought always
begins. The announcements of immediate self-consciousness, -as well as
statements of what is immediately evident, whether in intuition or universal
judgments—are accompanied by no feeling of constraint, such as we might
expect from the necessity of which we have spoken, nor yet by the thought
of the possibility of the opposite ; not until some attempt is made at con-
tradiction are we conscious of this. With other judgments we are con-
strained to certainty because all other possibilities are cut off ; and in the
consciousness of this constraint the judgment and its certainty present
themselves together. If we define necessity as the impossibility of being
otherwise, then we may say that only the latter judgments are accompanied
by a consciousness of necessity, not the former.
But it is that immediate security and certainty which is the original and
genuine form which necessity assumes in the sphere of thought; in it we
see thought at work in its most active and powerful form. And nothing
can completely replace this immediate self-evidence. The attempt to
maintain a contradiction may indeed serve to confirm the sense of security,
and to measure the force which is exerted in a statement; but the validity
of the original proposition must, generally speaking, be presupposed before
we can see that its opposite is impossible. Only when it has been es-
tablished that A is B, is it immediately clear to us that the proposition A
is not B contains a contradiction. The twofold negation does not create
the proposition, it merely circumscribes it by cutting it off from its
opposite; still it is in this form that we become expressly aware of the
truth by withdrawing from it and again returning to it. Just as we first
become explicitly conscious of identity through negation of the other,
of affirmation through negation of the negation ; so also we become
what the nature of this existent may be-all this is matter of dispute, and the view
which is taken determines the sense in which a judgment concerning matter of fact is
true.
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LOGIC
conscious of necessity through the impossibility that it should be otherwise.
But necessity is already contained in the thought which elucidates it; the
negation of the negation confirms the affirmation only because this process
is itself immediately certain in every step it takes. The true and original
necessity is that unreflecting necessity which predominates in all our
thought, and just for that reason cannot be brought into consciousness at
every point
We might distinguish between assertorial and apodeictical judgments
by saying that in the case of the latter we are expressly conscious of their
necessity, which therefore finds expression in words; while in the case of
the former the necessity is undifferentiated from the act of judgment itself.
Then we should have hit upon a really existing difference, which attaches,
not indeed to the degree, but to the kind of certainty belonging to a
proposition. But it is a difference which is entirely psychological, and
which shows how that which is dependent upon conditions peculiar to
the individual may—though accompanying the same judgment-appear
now in one way, now in another. It is a difference, moreover, which
signifies the exact opposite of what we mean by the ordinary expressions,
for the apodeictical form “A must be B” reminds us of the doubt,
and of the conceivability of the opposite; it proceeds with circum-
spection from A to B, while the assertorial judgment makes straight for
its mark. It is just when the judgment is an inferred one that the asser-
torial form expresses more complete confidence than the apodeictical,
which seems to challenge us to test the proof. Thus the former is always
the more natural, because the more direct expression of apodeictical
certainty ; even logic states the conclusions of its syllogisms in the asser-
torial form.
It might be objected to this that many statements are made at random,
the speaker troubling himself but little as to the necessity of his statement.
This is true, as true as it is that many lies are told. But it does not
refute the proposition that the act of which the sober statement is the
adequate expression involves the declaration of the necessity of the judg-
ment, and that it is in this way that every one understands the statement.
Else would speech be without thought, using words without meaning; or
burdened with falsehood and presenting as certain that of which the speaker
is not certain. It has nothing to do with logic that many falsehoods are
thus spoken in the strife of interests and party; for logic presupposes the
desire of speaking, as well as of thinking, in accordance with truth. We
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187
T
grant also that it is only gradually that this desire of speaking and thinking
the truth becomes conscious; at first it is merely an impulse unconscious
of its aim. But before this consciousness is clear the speaker knows not
what he is doing ; judgment is indeed there, but it is not free and conscious
and has not yet come to full maturity.
8. The necessity of thought which is manifested in the certainty of par-
ticular acts of judgment owes its distinctive character in the last instance
to the unity of self-consciousness. Every particular judgment may be
repeated with the consciousness of the identity of subject and predicate
as well as of the act of judgment; starting from the same data it is always
the same synthesis which takes place, and our self-consciousness cannot
exist apart from this invariability. Thus our judging ego, with its un-
varying activity, is opposed to particular acts of judgment as a universal,
as the same and the permanent which binds together the different and
temporally separated acts of thought. With the confidence of the move-
ment in each particular case is connected the consciousness of unvarying
repetition, of return to the same point. In this constancy, which presents
a general law in contrast with the particular act, we are conscious of
judgment as something withdrawn from the sphere in which we have a
subjective choice and are free to bring about alterations; we are conscious
of it in the same way as when it maintains itself in some particular act
against contradiction. Because this identity and constancy of our action
is the condition of our consciousness as one and undivided, it is also the
final and fundamental basis upon which we can fall back. While this
consciousness, in its completeness and comprehensiveness, is not yet
there—as in immature childhood so long the psychological conditions of
judgment are not yet fully developed. The case is the same in dreams,
where only a few trains of imperfectly coherent ideas are aroused.
From this it follows that each single act of judgment points, by its
meaning, to necessary and universally valid laws; laws, that is, which are
universally valid both for the single subject in his temporally different
moments, and for the various thinking subjects with whom we stand in one
community of thought; laws which, at first unconscious, serve only to bring
about the certainty of the judgment, but which, when raised into conscious-
ness, give us our fundamental intuition of something which is necessary.
9. The necessity of thought, which first becomes apparent in the cer-
tainty of the particular act of judgment and the invariability of its repeti-
tion, is something essentially positive ; it is the immediate expression of
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D
intelligence, the form of self-consciousness itself, and when brought into
consciousness it is as much an immediate intuition as the thought of the
ego, or of being. For this reason, it is also the measure of the further
concepts of possibility and impossibility. In the sphere of judgment the
possible is that which it is not necessary either to affirm or to deny; it is
the suggestion, the attempt of a judgment, which is never decided and
completed, and cannot be taken into the unity of self-consciousness, or
woven into the lasting fabric which is as certain as my own existence.
Mere possibility is a privation. The impossible, on the other hand, has
two meanings; that which it is impossible to think, would never be
thought, at the most it might be spoken in words. There can be no
thought corresponding to the words “the circle is square," and this is
what Aristotle means when he says that it is impossible to think of the
same thing as at the same time being and not being—"for it is not
necessary to accept what we say as true.” On the other hand we have
the possible which must necessarily be denied, the hypothesis which is
quite feasible when taken by itself, but the affirmation of which would
conflict with a valid proposition, and so place thought at variance with
itself. This impossible is to be found only in the sphere of the mediated
judgment; the predicate may be thought of as compatible with the subject
because their incompatibility is not known analytically, and thus the pro-
position may be temporarily accepted so long as the truth opposed to it
escapes consciousness; only a thorough comparison between all our judg-
ments brings about the negation of the possible. It is in this sense only
that Leibnitz's distinction is correct, when he says that the negation of
necessary truths is impossible, that of truths of matter of fact possible.
We may attempt to state them, but our experience refuses to confirm, and
forces us to deny them.
10. From what we have said, it follows that an actual affirmation or
negation—i.e. a judgment which we utter with a consciousness of its
validity—is only possible for those to whom it is necessary; as far as
the judgment itself is concerned possibility and necessity coincide. On
the other hand the hypothesis is possible if—and so long as—it is not
necessary, and therefore impossible, either to affirm or deny it. As the
expression of a subjective state of indetermination it may certainly be
said to take a third place beside affirmation and negation ; but just for
that reason it is not a judgment.
POSSIBILITY AND NECESSITY
189
$ 32.
The so-called LAW OF SUFFICIENT REASON, as originally conceived by
Leibnitz, is not a logical law at all, but a metaphysical axiom, which is
applicable to a part only of our judgments.
· Inasmuch as every judgment presupposes the certainty of its validity,
we may lay down the proposition that no judgment finds utterance which
has not some psychological ground for its certainty ; and inasmuch as it
is justified only when it is logically necessary, every judgment claims to
have a logical ground which makes it necessary for all who think. But
it does not do more than raise a claim, the justice of which it falls to logic
to investigate.
The nature of necessity in thought is expressed by the proposition that
when the ground is affirmed its consequences are also necessarily affirmed,
and that when the consequences are denied the ground also is denied.
This principle of Ground and Consequence corresponds to the principle of
contradiction as a fundamental law of the operation of thought.
1. The results of the preceding paragraph seem to find their natural
expression in the proposition that judgment cannot take place without a
ground, for by the ground we mean just that which makes a judgment
necessary. Thus an analysis of the import of every judgment framed and
spoken would give us the fourth of the so-called laws of thought; it
would express the characteristic common to all judgment whatever--i.l.,
that belief in the validity of the judgment involves belief in its necessity.
2. But the law of Sufficient Reason has had various meanings assigned
to it, and in this has shared the fate of the other so-called laws of
thought. Leibnitz was the first to give it a co-ordinate place as a first
principle with the law of contradiction. “Our inferences,” he says,
? Frinc. phil., 31 sq. ; Erdm. 707: Nos raisonnements sont fondés sur deux grands
principes, celui de la contradiction .. . et celui de la raison suffisante, en vertu
du quel nous considérons qu'aucun fait ne saurait se trouver vrai ou existant, aucune
énontiation véritable, sans qu'il-y-ait une raison suffisante pourquoi il en soit ainsi et non
pas autrement, quoique ces raisons le plus souvent ne puissent point nous être connues.
In the de Scientia Universali (Erdm., p. 83), Leibnitz formulated the same principle as
follows: Omnis veritatis (quæ immediata sive identica non est) reddi posse rationem,
hoc est, notionem prædicati semper notioni sui subjecti vel expresse vel implicite
inesse. It is evident, therefore, that the principle as he understood it here was a
purely logical one, according to which all propositions which are not identical are true
only in so far as their necessity is syllogistically proved. On the other hand, there are
places in which he emphasizes only the metaphysical aspect, e.g. in the Theod., 44
(Erdm., p. 515): . . . l'autre principe est celui de la raison déterminante, c'est
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“are based upon two great principles, that of contradiction ... and
that of the ratio sufficiens, by virtue of which we assume that no fact is
true or actual, no proposition true, unless there is a sufficient reason why
it is this and not something else, although in most cases these reasons
may be unknown to us." It is not difficult here to distinguish the two
sides of the question, and to see that he is speaking partly of the actual
existence of real things and events, partly of the truth of propositions. But
we must remember that Leibnitz intends this principle as the ground for
truths of matter of fact alone, i.e. for the truth of propositions which state
a fact, while necessary truths rest upon the principle of contradiction;
and that with him the ultimate ratio sufficiens is always the Divine Will.
Then it becomes evident that this distinction signifies nothing, and that
the principle of Leibnitz is no other than the principle of causation in
the real world ; the principle, that is, that the existence of every real
thing, and the reality of every event, must have a cause. The truth of
propositions which state facts is based upon the reality of those facts, their
truth being thus dependent upon the reality of the fact stated and this
reality upon the sufficient cause; so that in giving the real ground of a
truth of matter of fact, I name the cause which has given rise to the
actual event or thing. But this just shows how little we are justified in
regarding this principle as an absolutely universal logical law, which
should rank beside the law of contradiction as valid in reference to the
same propositions, or in trying to find in the Leibnitzian proposition a
logical ground distinct from the real cause. Such an interpretation is
indeed excluded by the repeated remark that the ratio sufficiens may
frequently be unknown to us. This is true only of real causes. A
logical ground which we do not know is, strictly speaking, a contradic-
tion ; for it only becomes a ground through our knowing it. Unless we
believe in the fiction that a judgment can be true apart from any intelli-
gence by which it is thought, we cannot believe that its ground has an
independent existence of its own.
que jamais rien n'arrive, sans qu'il-y-ait une cause ou du moins une raison déterminante,
c'est-à-dire quelque chose qui puisse servir à rendre raison a priori, pourquoi cela est
existant plutôt que non, et de telle plutôt que de toute autre façon. Ce grand principe
a lieu dans tous les évènements ... Pr. de la Nature et de la Grace, $ 7 (Erdm., p.
716): rien ne se fait sans raison suffisante. Cf. Trois, écrit à Mr. Clark (Erdm., p. 751).
While yet again in the fifth letter to Clark, § 125 (Erdm., p. 778) we find the full
formula : Ce principe est celui du besoin d'une raison suffisante, pour qu'une chose existe,
qu'un évènement arrive, qu'une vérité ait lieu.
POSSIBILITY AND NECESSITY
191
If therefore we lay it down as a logical law that nothing should be
thought without a ground, we must certainly mean something quite
different from what Leibnitz meant.
3. If we distinguish between the Real Cause and the Ground of the
Judgment, between what makes it necessary for an existing thing or event
to be actual in a given way, and that upon which the judgment is based
as an act of thought, there still remain two very different meanings in
which the word "ground” may be taken..
From one point of view every judgment, as an actual psychological
event in a thinking individual, may itself be regarded as something
existent, and the conception of the causal relation and its fundamental
principle is so far applicable that every event must have its sufficient
cause. The cause of an act of judgment must be sought, in the first place,
amongst psychological facts, for no judgment is possible unless certain
ideas are present to consciousness; thus the psychological cause of a
judgment is the sum total of the necessary conditions of this particular
gether with its faculty of thought, and the laws which govern the manifes-
tations of this faculty ; and it further consists in those states and preced-
ing acts out of which this given judgment arises. Amongst these are the
following conditions :-
a. The ideas both of subject and predicate must have been present in
consciousness; (this presence in consciousness implies causes which are
still further removed, and which we may call the cause remotiores of the
judgment, one of the most important being the will, as led by some interest
b. A synthesis must have taken place between the ideas of subject and
predicate, either because of an agreement which has led the activity of
thought, in accordance with its laws, to connect them, or because their
synthesis was suggested by the manner of their entrance into consciousness,
which gave rise to the thought of their possible connection.
C. In the latter case something must have occurred to bring about a
decision-either affirmative or negative, and, inasmuch as every judgment
includes the consciousness of its validity, to afford a psychological explana-
tion of the certainty as an actual state of mind.
From this point of view a distinction must be made amongst immediate
judgments between those which connect mere ideas and those which con-
tain a reference to the existent. With immediate judgments of the first
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kind the principle of agreement (as expressing a law of motion for thought)
is sufficient to explain both the synthesis and the certainty attaching to it;
while statements which refer to the existent, as e.g: judgments of percep-
tion (it lightens; this iron is hot) depend upon more complicated pre-
suppositions. Their occasion is a momentary feeling, or complex of
feelings, which in its turn points to a number of causes which have brought
me into a position in which my senses may be thus affected. But, besides
an actual matter of fact, we must include amongst the causes of the judg-
ment the sum total of all the psychological forces which are incessantly
re-creating the ideas of actual things and their attributes out of sensations,
and bring about in each particular case the certainty that we perceive and
know the existent. The principle of agreement explains only the way in
which we identify present perception with a former idea; it can never
explain the general conviction of the material reality of things, nor the
conviction that what we say at the moment is a true judgment concerning
matter of fact. While then the merely explicative judgment is sufficiently
explained by the causes which give rise to the ideas and our consciousness
of them, together with the principle of agreement, the other judgments
see the Kantian distinction between analytical and synthetical judgments
(in the Kantian sense) are possible becomes obvious. It is clear also that
recognition of the existing causes which give rise to our belief in reality,
and in the actual validity of our judgments of perception, can tell us
nothing as to the correctness of this belief; it is due, for instance, to
existing causes that sun and moon appear larger to all of us when rising
than when in the meridian.
In mediated judgments, however, the mediation which brings about a
decision need not consist solely in premises which can themselves be stated
in the form of judgments; it may also consist in unconscious habits of
combination, and in the influence of authority which is rooted in un-
analysable impressions,
Amongst the totality of psychological conditions we may now dis-
tinguish : 1. the occasion, which brings subject and predicate into con-
sciousness, thus giving rise, in the case of mediated judgments, to the
question ; 2. the ground of decision which enables us to affirm the
judgment, and to state the subjective synthesis as objectively valid, and
which is therefore the ground also of the subjective certainty of the judg-
POSSIBILITY AND NECESSITY
193
ment. The change in the objects concerning which we judge depends
upon the occasion, which may, so far as the content of thought is con-
cerned, be quite a matter of chance, and come entirely from without; but
the ground of the decision always brings us back, in the last instance, to
a psychical force working in accordance with laws, and any particular
psychological event can only be called the ground in so far as it introduces
the judgment by virtue of a constant connection. Thus in all immediate
analytical judgment the ground upon which we attribute the predicate is
the subject-idea, but only inasmuch as, in accordance with the principle of
agreement, the presence of subjects and predicates which agree necessitates
their synthesis.
5. Of this psychological ground of certainty the law holds good that
no judgment can be made without a ground, i.e. unless the conscious-
ness of its validity has in one way or another been produced ; and thus
without violence to veracity no proposition can be stated which is not
accompanied by the consciousness of the validity of the judgment. This
is involved in the nature of the judgment itself, as maintaining the validity
of a synthesis, and in the fact that a purely arbitrary act, a sic volo, sic
iubeo, could not produce that consciousness of validity which implies that
the synthesis is not arbitrary. We do not, however, mean by this that we
are always conscious of the ground as soon as we have uttered the
judgment.
6. But the necessity asserted by every judgment stated with a full
understanding of its meaning is not this psychological necessity, but
objective truth; and the ground of its certainty, which is implicitly
affirmed with it, is not one peculiar to the individual, but a universal
ground which must make the judgment necessary for every one, and can
lie only in the ideas themselves as such, since these only and not the
individual frame of mind, etc., can be common to all. This alone is the
logical ground, the ground of truth as distinguished from the ground of
certainty. All error and strife are due in the last instance to a difference
between the psychological ground of certainty and the ground of truth; to
the possibility that momentary belief may err, and the temporary feeling
of certainty deceive us. So far the law holds good that no proposition is
true without a ground; but just for this reason the investigation of what is
a logical ground, and what the conditions are which justify us in affirming
a proposition, falls beyond our present task. The object of our analysis of
the judgment was only to show that every statement claims by its meaning
S. L.
S
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LOGIC
to have a logical ground, and that this also involves the problem of how
the ground may be known.
7. A further distinction is called for here, which arises from the fact that
in thought we always start from data which have arisen involuntarily and
without reflection. Absolute necessity would belong only to judgments
necessarily developed in every being capable of judgments as such, both
the ideas connected and the connection itself being inevitable; and this is
what is presupposed in every theory which is based upon innate ideas (in
the older and original sense) and innate truths. The ground of these
judgments is reason itself, and so far as they are concerned there can be no
difference between logical and psychological ground. But other judgments
have only a hypothetical necessity, i.e. it is logically necessary to maintain
them on the presupposition that something else has preceded in con-
sciousness. So far, then, as it depends upon external conditions what ideas
arise in a subject and come together in thought, the judgment A is B is
indeed necessary so soon as we are conscious of A and B as agreeing; but
that it should come into thought at all is not universally and absolutely
necessary. Only when we assume an ideal thought, comprehending all
truth, is the logical necessity a material necessity also, giving rise to actual
thought. For the individual whose voluntary thought aims at this ideal,
the necessity is moral and conditioned by his ability.
From one point of view, then, we can accept as a ground in its fullest and
truest sense only that which must itself of necessity be thought. But from
another we may look upon every actual premise as a ground so far as we
acknowledge that a further judgment results from it with logical necessity.
We may indeed go a step further and find a relation of ground and
consequence between propositions which we think of only as hypotheses,
and in reference to which therefore there is not even a psychological
certainty. To say that a hypothesis is a ground with respect to another
hypothesis means, that if the former is accepted as true, then the latter
must also be accepted as true. Thus in the first case ground signifies
that which compels us to complete a judgment so soon as it has actually
come into conscious thought; here it means the hypothesis which, when
accepted as valid, forces us to maintain the validity of another hypothesis.
It is of the ground in this latter sense that the law holds good which
was formulated by Aristotle,1 and which in later times has ranked only as
1 Aristotle, Anal., Pr. II., 4, 57 b. 1: "Otav dúo éx? Oűtw mpos &Xinda Cote DatÉpov
POSSIBILITY AND NECESSITY
195
1
'the principle of hypothetical inferences; the law, that is, that when the
ground is affirmed the consequence is also affirmed, when the consequence
is denied the ground is also denied. All that is expressed by this formula
is the nature and meaning of logical necessity, just as the nature of
the negation is expressed by the principle of contradiction. It tells us that
if the proposition A is recognised as the ground of B, then the affirmation
of A involves that of B also, the negation of B that of A also. This law
alone deserves to rank beside the principle of contradiction, for, like it, it
applies to a fundamental form in which thought moves, a progress accord-
ing to necessary connections. But just as the principle of contradiction
leaves it undecided which of the opposed statements holds good, so also
this law leaves it undecided whether either ground or consequence is
true.
8. Material causality must in no way be confused with the logical
relation of ground and consequence. The proposition that every thing,
or every change, has its cause, stands in just the same relation to the
logical necessity of our judgments as every other general proposition which
serves as a ground for extending our statements, or enables us to pass with
logical necessity from one proposition to another. If we use the expression
“ground" of material causality also, and say that the attraction of the
earth is the ground of the falling of bodies, all that we are immediately told
by this is, that the one produces the other realiter. But so far as the causal
relation when recognised enables and forces us to infer from the fact
that the cause takes place that the effect also takes place, so far that
recognition is a logical ground; and only by assuming the causal relation
can we pass from the truth of one fact to that of another distinct from
it. Thus the propositions which state causal relations play an important
part amongst our logical grounds; but it is far from being true that every
logical ground is based upon a causal relation, and still less true that the
way in which our judgments depend upon each other at all resembles that
in which material causality takes effect. The distinction still remains
between the ground of knowledge and the material ground, and it becomes
obvious whenever an effect leads to recognition of the cause.
9. Finally, we must distinguish between logical grounds and grounds of
probability. These give the preference to one of several hypotheses, none
of which we have sufficient ground for affirming ; and this they do by
όντος εξ ανάγκης είναι θάτερον, τούτου μη όντος μεν ουδέ θάτερον έσται, όντος δ' ουκ ανάγκη
είναι θάτερον.
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LOGIC
intensifying the expectation that this one is, and will prove to be, valid.
Thus their value is in the first instance only psychological, but they have
sometimes a practical significance ; e..., when it is necessary, upon practical
grounds, to come to some decision even in the absence of certainty. The
significance which they have for the growth of knowledge cannot be in-
vestigated until the third part of the book.
II. POSSIBLE AND NECESSARY AS PREDICATES OF ACTUAL
JUDGMENTS.
$ 33.
In its objective sense, “necessary” is always in the last instance a pre-
dicate of that which is expressed in a judgment. It is necessary either that
a thing is, or that it has certain attributes, or exerts certain activities, or
stands in certain relations. This necessity is either internal and due to
the nature of the thing, or external and due to causality. In either case
it is hypothetical. It is knowable only in the form of general rules, which
govern the particular; while, on the other hand, it is the aim of uncon-
ditionally universal judgments to express this necessity.
1. While the assertorial judgment is separated from the apodeictical
by no essential, inherent difference, the statement that something must
be or must happen differs in its contents from the statement that it is or
happens when these statements extend beyond the sphere of our ideas to
the existent, and refer to a material necessity. No doubt, wherever the
“must” and the “necessity” appear in merely explicative judgments—such
as “all bodies are necessarily extended,” and “an effect must have a cause”
--what is meant is the logical necessity contained in the fixed meanings
of our words which compels us to connect a predicate idea with a subject
idea, and hence to predicate the former of everything to which the latter
can be applied. The judgment “ bodies are extended” makes the same
statement as the judgment “ bodies must be extended ”; the only differ-
ence is that the latter expressly reminds any one who may be in danger of
forgetting it of the meaning of the words.
But when we are speaking of the existent as such, then our statements
concerning its necessity refer to something which is binding upon the
existent itself, and not merely upon our judgment. “Necessary” then
becomes a significant predicate which is affirmed or denied in just the
same way as any other predicates of actual judgments.
POSSIBILITY AND NECESSITY
197
It is true that of things as such necessity in its proper sense cannot be
used as a predicate ; it is not an attributive word. Such phrases as “God
is a necessary Being," "the world is not necessary,” are no adequate ex-
pression of our thought; what we mean is, that God necessarily exists.
Just as dei or oportet require a proposition to follow, and "must" is a so-
called auxiliary verb, so also it is only what is stated in a proposition-
the existence of a thing, its possession of a quality, its development of an
activity—which can be predicated as necessary. Only to abstract nouns
which take the place of a proposition can “necessary” be attributed as a
predicate; e.g., the existence of God is necessary. (The necessity of the
judgment is no exception to this; it is necessary that I, and that every
thinking being, should judge thus.)
This introduces a new class of statements—those in which the subject
is that which is stated in a judgment (not the judgment itself, as in the
case of the predicates true, false, credible, logically necessary). Thus we
can only speak of material necessity in so far as a material unity, that of
the thing with its attribute and activity, corresponds to the synthesis of
the judgment.
2. What is it which connects existence with an object of thought, an
attribute or activity with a definite existing subject, or different things in
one relation? If we disregard for the present necessity of existence and
assume that certain things are, there remains for investigation their kind
of being and their mode of action. This appears to us primarily as merely
matter of fact and empirical, and what we want is to see that it is also
necessary, since thus alone can it be understood and penetrated by
thought. The ground of the subjective necessity of that part of our judg-
ment which refers to the matter of fact in our knowledge must be found
in material necessity. What we are investigating here is not the origin of
the attempt to find such a bond of necessity in the world, and to attain,
beyond the knowledge that something is and happens, to the insight that
it must be so; nor do we seek a metaphysical justification for this
assumption. It is enough that the attempt is there and governs our
popular as well as our scientific thought, so that the problem arises of
establishing its meaning.
Here we must begin by distinguishing between the presupposition which
guides all our thought, that there is necessity in the world, and the ground
of the statement that this or that particular thing necessarily is. Necessity
is knowable only where there is an invariability of connection in the
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LOGIC
existent like that which governs the connection between thoughts in the
sphere of logic (S 31. 8); when therefore the particular event results in-
variably and with infallible certainty from what has preceded it, as the
judgment always recurs in the same way when the same data are present;
and when therefore a complete coincidence of material with logical ne-
cessity is possible. In such invariability alone do we find the ground of
the necessity that something is. That which is to be a material ground
must have the invariability and universal validity which belongs to the
logical ground; it must be universal as opposed to the particular case,
and invariable as opposed to mutability in time. To know something as
necessary always means to know it as the consequence of something
which is constant and universal. For this reason it is that we can never
see the necessity of that which is purely individual, and as such incom-
parable with anything else, even though we may believe that it is
necessary.
3. We regard the necessity which binds together subject and predicate
as sometimes internal, sometimes external; and the distinction reminds us
of that between analytical and synthetical judgments. When a subject is
in itself sufficient to make its determinations necessary, we look upon the
necessity as internal ; when something else must supervene in order to give
rise to a determination, we look upon it as external.
It is for us an internal necessity that the spirit is self-conscious and
thinks; it is external that a body moves when it is pushed. In the first
instance the attribute and the activity result of themselves from the subject
alone so soon as it is there, in the latter case not until something else is
there also.
4. When we speak of internal necessity, we contrast the unity of the
thing with the plurality of its attributes and activities, and regard the
former as the permanent ground, unaffected by temporal distinctions,
which makes the attribute or activity necessary, either as constant or in
a fixed order of change. In so far as the unity of the thing involves the
necessity of certain attributes it is called the essence (the nature) of the
thing, and everything which proceeds from its essence alone is essential
to it. In no philosophical conception has this thought played a more
important part than in the doctrine of Leibnitz that there is none but
internal necessity, and that each particular monad develops its series of
activities from its own inner nature alone. Here the nature of the par-
ticular individual is the sole ground of necessity, and the whole course of
POSSIBILITY AND NECESSITY
199
S
S
.
its existence is only the unfolding of this nature. It is recognisable partly
in immutable attributes and permanent activities, partly in the law of
development which prescribes that one activity shall give rise to another.
It is this idea of a permanent ground governing the manifestations of a
thing in which the thought of a thing as being identical with itself and yet
having changeable attributes and varying activities culminates. If we want
to establish the full identity of the thing, we must look deeper than its
actuality at any given time. Here we find change; and since attributes
are not external to the thing, the thing being what it is through its attri-
butes, the identity of the thing itself seems in danger of disappearing if
there is no basis permanent in change and giving rise to that very change.
And the unity and identity implied in a thing can be represented in thought
only if one and the same ideal content, which recurs always in the same
way, may be taken as the counterpart of a real existence identical with
itself.
This same thought of the nature of the thing as the permanent, timeless
ground of its varying, temporal actuality, affords an objective justification
for our primarily subjective general ideas. The comprehension of spatially
and temporally different things under one general idea, and their denota-
tion by one and the same word, is an arbitrary act guided only by sub-
jective caprice or grounds of expediency, unless there belongs to the
various things something really common to all and identical in all beyond
the similarity which appears to us. But this common element lies behind
the distinguishable and particular phenomena, with their individual peculiari-
ties, and must be found in the fact that a common nature necessitates
uniformity in attributes and activities, and that variations are looked upon
as due to external causes, as accidental, and not essential.
5. External necessity is opposed to internal, and determination by cir-
cumstances to the development of nature. Every particular phenomenon
is this because another is that; every change in a particular thing takes
place because a certain change has taken place in another thing. Things
have the power of mutually prescribing each other's action. The order of
the world consists in this necessity which passes from one to the other,
and which is causal necessity in the narrower meaning of cause as causa
transiens. The knowledge that something is what it is, and happens as it
happens, from external necessity, is made up of two elements—the general
law and the particular datum to which this law is applicable. It is neces-
sary for the planets to move in ellipses round the sun : our knowledge of
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LOGIC
this rests on the one hand upon our knowledge of the general principles
of mechanics, on the other hand upon our knowledge of the actual mass
of the sun and the planets and of the relation between tangential velocity
and attraction; a different relation would give rise to different orbits. We
cannot get rid of this purely empirical element, and for this reason our
knowledge of the necessity as such is expressed in hypothetical forms
only, which state that if this or that occurs something else necessarily
occurs. The occurrence of the former is again necessary from other
causes; but in explanation of these we always come upon some further
empirical fact, and so on ad infinitum.
Thus the necessity of each particular phenomenon is never more than a
conditioned necessity, an ανάγκη εξ υποθέσεως. When something is said
to be necessary, it is not the cause, but the fact that it results from the
causes present, which is called necessary.1
6. The hypothetical necessity of the existent due to its nature and its
cause seems distinct from necessity due to the end. Man must breathe in
order that he may live; to maintain peace we must be prepared for war.
But if we look more closely, this teleological necessity may be analysed into
logical and causal necessity. Only as the thought of an actual, thinking
and willing being is the end something actual which can be a ground of
necessity. It is something which is thought of as in the future and willed,
and the realization of which is intended, though, according to the causal
order of nature, which connects every given result with given causes, it can
be realized only by means of given causes. Hence whoever wills the end
must also will the means; assuming that we will a definite end, it is neces-
sary that we will definite means. The connection between the thought of
the end and the thought of the means as objects of our will is logical; but
the necessity of thought rests upon our knowledge of the causal necessity
of being. The facts presupposed in the final cause are on the one hand
that the end is willed, on the other that efficient causes are present which
cannot be arbitrarily changed or multiplied. From our knowledge of these
we may infer with logical necessity the means for a given end, which must
be willed if the end is willed. But in our interpretation of nature we look
upon results as ends even where there is no reference to the will of any
thinking subject and its realization, because the end here serves as the
point of connection for a plurality of causes; and hence arises the appear-
ance of a special kind of necessity, distinct from that which is logical or
These concepts will be more fully explained in Part III.
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201
causal. “Man must breathe in order that he may live”--this expresses
nothing more than our recognition of the fact that the order of nature has
connected death inevitably with the cessation of breathing, and that breath-
ing cannot be replaced by any existing contrivance. Should life be willed
as an end, breathing must also be willed as a means.
Suppose again that the thought were in itself creative ; then it would not
be an end, needing the means for its realization ; it would be simply a
cause having the power to produce a material reality, so that here again
there would be no teleological necessity.
The same considerations apply to what has been called moral necessity.
There are certain normal laws which a rational being with a will is forced
to recognise as principles valid for his will, and by which he feels himself
bound; and the recognition of such obligation is a necessity of his nature
which is regarded as an essential characteristic of the rational subject. If
these normal laws are actually willed and accepted as a highest end, then
it becomes logically necessary to apply them to the particular, to transfer
the obligation to particular cases. But to regard the obligation itself in
the light of a necessity because it brings with it a feeling of constraint, is
to confuse our conceptions and to conceal the cleft which divides the
recognition of obligation and actual willing.
7. When the necessity refers to existence itself, then, from the point of
view of external causality, it is obvious that in affirming the existence of
any particular thing to be necessary we assume a creative power which
produces it either from blind necessity or for the sake of some actual end.
We may, for instance, try to understand the existence of the world by
explaining it as the self-manifestation of God; in so doing, we derive its
existence from a higher cause, and thus attribute to it a conditional
necessity.
But suppose it is maintained that something has of itself necessary
existence, as in the ontological proof where existence is said to belong to
the essence of God, and to proceed necessarily therefrom, an attempt
being thus made to convert hypothetical into absolute necessity; then
the light leaves us which the experience of our own self-consciousness
had thrown upon the thought of necessity, and which had shown it to be
merely a bond of connection between distinguishable data, either of
thought or of being. It is a bond which breaks away as soon as we attempt
to connect the existent with a mere concept, a concept, moreover, which
belongs to no one's thought; and if the idea is that something already
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LOGIC
existent undertakes the superfluous task of making itself necessarily
existent (although existence is already presupposed in such necessity), then
there is nothing left for the bond to connect. Just as we cannot speak
comprehensibly of logical necessity without presupposing an existing,
thinking subject whose nature it is to think, so also an ultimate and
simple being is always presupposed in necessity of existence. In the rest-
lessness of our questioning, we imagine that we must have necessity even
in the first member of our series ; and when we accept the answer that
God is causa sui and has the grounds of His being in Himself, we allow
ourselves to be misled by words into stating empty formulæ,1 the fictitious
value of which is nowhere more obvious than when they are taken seriously
and lead to the metaphysical myth of a ground distinct from God Him-
self. Somewhere or other we must end with simple being. That view
of the world which confines itself to the cycle of finite causes must
regard the whole complex of mutually conditioned beings as something
simply existent; while, if we would understand the world as necessary,
we make it dependent upon God, where it is even more certain that
all distinction between being and necessary being absolutely fails us.
8. Mathematical necessity is often taken as the most perfect type of
what we call necessity. Spinoza's standing illustration of the material
necessity in the production of an effect by its cause is “in the same way
as it follows from the nature of the triangle that its angles are equal
to two right angles.” This is not the place to investigate the nature of
mathematical knowledge, or to determine the question whether its necessity
is logical or material. It is, however, clear from what has been said that
the very nature of mathematical objects involves that constancy and in-
variability by virtue of which they are always presented in the same way,
and because of which every particular has the significance of a general in
that it may be repeated in the same way in actual intuition; while in
material objects we are forced to seek for a constant element and dis-
engage it from casual and varying connections. Space and plurality, our
intuition of space and counting, are all no doubt given in the first instance;
but they are given in such a way that we are certain of their absolute
immutability.
9. Now it is none other than this objective necessity which our
universal judgments are meant to express; the necessity, that is, of the
union between the subject and definite attributes, or of the connection
1 Cf. Arnauld's criticism of Descartes in the Objectiones Quarta.
POSSIBILITY AND NECESSITY
203
between definite attributes, activities, and relations, and other attributes,
activities, and relations. Only when we are convinced of this necessity is
the unconditionally universal judgment justified. The judgments - all
matter is heavy," " that which is matter is necessarily heavy," "it belongs
to the nature of matter to be heavy,” are all equivalent. The connection
of the predicate with the subject is necessary from the nature of the sub-
ject; whenever the subject exists, its predicate is actually combined with
it. The judgments “every thrown body describes a parabola," "a body
when thrown necessarily describes a parabola,” again state the same
thing; the universal judgment tells us nothing but the causal necessity of
forces working according to fixed laws.
When such a judgment is denied, then the necessity is denied ; and it is
said that the subject might be without the predicate. This is expressed in
the traditional doctrine by the particular judgment "some matter is not
heavy."
10. When universal judgments express the essential predicates of things,
they coincide with explicative judgments, and the logical necessity of the
judgment with the objective necessity which finds utterance in it. The
explicative judgment, while it states the contents of an idea, has also re-
gard to the things corresponding to the idea, and thus it gains an objective
significance whenever the idea comprehends the permanent and invariable
elements necessarily involved in the existence of a given subject or sub-
jects, when, therefore, the idea corresponds to the essence of the things.
The explicative judgment “water is fluid” expresses only the contents of
the idea of a thing which has been noticed in certain casual states. It
does not represent the essential nature or the kind of matter which we call
water, for this is also found in a solid or vaporous state; fluidity is not
a part of its essential nature. The judgment "water is a compound of
oxygen and hydrogen” is both explicative and an expression of the essen-
tial nature of water. It is the attempt to bring the two into perfect har-
mony which guides the problem of definition.
D
§ 34.
That alone is possible in the completely objective sense which is
removed from the sphere of necessity as the manifestation of free subjects.
Within the sphere of necessity we can speak of possibility only under two
suppositions. Either we must think of things as removed from the
temporal course of their actual existence and thus isolated from the con-
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LOGIC
ditions of their actual being, in order that we may represent as grounded
in their permanent nature predicates which really belong to them only
when co-existing with others; or else we must isolate in thought a part of
the conditions upon which the actuality of what is stated in a proposition
depends. When in the latter case we are ignorant of the conditions, the
judgment passes from objective possibility into the subjective possibility of
conjecture, and thus into the expression of uncertainty.
The judgment “it is possible that A is B” stands in contradictory
opposition to the judgment “it is necessary that A is not B.”
1. In investigating the many meanings of the expression “possible," we
will first distinguish between the possibility of being something which is
stated of a subject and the possibility of its mere existence. The former
finds expression in the propositions "A is possibly B, A may be B,”
the latter in the propositions “A is possible, A may be.” The former
judgments, again, may be sometimes stated of the particular as such, their
subjects being definite things (or attributes, activities, and relations of
definite things); sometimes of subjects which are thought as universal.
2. If we state of a particular thing that it can or may, we make a state-
ment originally connected with a presupposition from which alone it
derives its full meaning ; the presupposition, that is, of free subjects
which, as such, have the power of acting in different ways, but which
exert this power only at the command of the will and upon the ground
of a choice between doing and not doing, doing this and doing something
else.
We have first the thought of different activities which the will alone is
able to realize ; which of them it will realize depends upon a decision
which is neither externally necessary, nor yet a necessary consequence
of former activity. Opposed to this freedom, we have on the one hand
inability, when the material causality which could realize the thought is
wanting to the will; on the other hand there is the “must," when choice
is cut off, and necessity prescribes the path of action. On closer inspec-
tion, however, inability proves to be only another form of “must”; it is the
necessity of not-doing.
3. The position of a free subject towards the activities between which
it has a choice, strikingly resembles the position of the judging subject
towards different hypotheses, neither of which it finds itself forced to
affirm or deny. In both cases an act is planned in thought, but not yet
actually realized ; in both cases the question arises, “what should I do ?”
POSSIBILITY AND NECESSITY
205
But affirmation or negation can enter only when necessity appears, and
the matter is removed from the sphere of free action ; while in the other
case it is the undetermined and arbitrary act which realizes one of the
thoughts and thereby refuses reality to the other. We are not dealing
here with the metaphysical truth of this view, but with the presuppositions
which determine the thought of the possible in this direction. While in
the one case the different hypotheses cannot become actual judgments,
and so long as the choice remains the judgment is impossible, in the
other the power of realization lies in the will, and stands in the same
position with regard to either alternative, thus causing them to appear
as really possible. Thus we speak of the real possibility of a scheme or
plan, when we have convinced ourselves that all the conditions of its
realization lie in our power, and that this realization depends upon our
will alone.
The opposite, therefore, of the materially necessary, is that which
results from freedom; here alone we find the absence of necessity. It is
not without reason that language has combined the ideas of "will" and
“can” in the meaning of the word “may.”
4. But the idea of the possible extends even to that which is not
free. This also may be regarded in such a way as to make it comparable
with the free. Even the thing which is not free acts in different ways
in so far as it is changeable, and is not constrained to be and to do the
same thing at all times. When we look to its future a number of
different predicates lie before us, and the thought is aroused of a choice
between them. The sun will alternately shine and be concealed by
clouds; the brook will at one time freeze, at another be dried up; our
thought in picturing the future wavers between different predicates. But
it does not depend upon the decision of the thing itself which of these
predicates shall actually appear at a given time; this is determined by
necessity. The necessity may be merely that of its own nature, which
prescribes a certain development through different stages, and in this case
it must become all that it can become; and it is only a distinction of time
which makes us speak of the future, not as something which is, but as
something merely possible. Or the necessity may appertain to both the
nature of the thing and its circumstances; and when we are ignorant of
the manifold combinations of circumstances and their changing course,
or, disregarding them, comprehend in one thought that which in time is
successive, then the thing is to us like a free being of whose future
i
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LOGIC
decisions we are ignorant, and its actual states appear to issue from its
arbitrary will and caprice.
It is in the former way that we regard the totality of the universe so far
as we think of it apart from freedom. It contains the whole ground of
everything which in the future will be and happen, but which is not yet
actual. This is full possibility, potentia in its most significant mean.
ing.
We regard in the second way the particular things or events which take
their place in the order of the world, and which are both determined and
hindered by circumstances in their natural development. In so far as the
particular thing contains the partial ground of that which will be, there
belongs to it the mere possibility of future states. Thus the seed contains
the possibility of becoming a plant.
But this “can” has a perfectly objective and material significance only
when we are certain that the predicate will actually appear under certain
circumstances, because it depends upon the nature of the subject what
series of predicates it will assume under different circumstances. As a
rule we gather our knowledge of that which a thing may be from our
experience of the past; but we mean it as a statement of certain know-
ledge when we say that the moon can be eclipsed.
5. This meaning of “can” is particularly obvious when we make
general statements concerning our subjects : “water may freeze or
evaporate”; “iron can be melted”;"cooking-salt is soluble in water,” etc.
Here we have perfectly definite and positive statements, referring to an
attribute of the subject. Indeed, there is no way of making general state-
ments concerning changeable attributes except by passing beyond the
subject to the conditions and causes which determine its varying states.
When I isolate the idea of a thing and disengage it in thought from the
conditions of existence under which the actual always stands, retaining it
by itself, then there remains to it at first nothing but those attributes
which cannot be separated from it because they are essential. But as
thought surveys the cycle of changes which must and will be introduced
by varying relations and refers them merely to the general thought of the
thing, it makes use of expressions such as “can," "faculty,” “capability,"
etc., to turn the subject into a permanent ground for the changeable. This
ground, however, is not in itself sufficient to bring about actuality; it
must be supplemented by circumstances. But in proportion as all know-
able attributes of things resolve themselves into relations with other things
POSSIBILITY AND NECESSITY
207
we are able to express their unchangeable nature only as that which they
may be under varying circumstances.
Judgments of possibility, which state the further determinations that a
general idea admits of, are analogous with these. That which in the
previous case falls asunder into the temporal series of successive states
here breaks up into the plurality of ideas which contain a common element
needing further determination before it can agree with any definite
thing or can even be thought as particular. A triangle may be acute,
right-angled, or obtuse. No intuitable figure contains only the properties
which I think under the word triangle. Before I can form the image of
one, some definite relation of sides and angles is necessary; and when in
constructing it I try different determinations or recall them from memory,
the general idea presents me with a choice of various closer determinations.
No definite colour is necessarily connected with those attributes of an
animal which constitute the contents of the idea horse. The horse can
be black, white, brown, etc. So far as concerns the content of my idea,
these judgments are perfectly definite statements concerning the plurality
of differences. So far as they are intended to apply to the nature of the
existent, they express in the same way a material possibility which con-
nects variation of colour with the organization of a certain animal. Only
when applied to a definite particular thing does the judgment take upon
itself the problematical significance of ignorance. When all I know of a
thing is that it is a horse, I cannot state of it that it is black or white;
when I know only that something is a triangle, I do not know whether it
is right-angled or not.
When we are dealing with subjects thought of as general, then the
judgment " A can be B,” etc., is the adequate expression of the so-called
particular judgment.
6. It follows from the meaning of the judgments so far considered that
even when they apply to the particular they are intended as universally
valid, and their validity is not limited to any given time. Possibility and
“can” take on another meaning when we speak of a particular instance,
and state what may be and happen here and to-day. When we say, " it
may freeze to-night,” “the invalid can be saved,” “the answer may come
to-day," then our thought does not weigh the future by isolating its sub-
ject; on the contrary, it reviews the present circumstances and undertakes
to calculate from them the result. But such certain prediction is pro-
hibited by our want of knowledge, whether of all the circumstances, or of
CD
208
LOGIC
the exact laws according to which they take effect. All that the judg.
ments mean is, the sick man will be saved if the right cure is applied, if
no unexpected disturbance appears, etc. Thus some of the conditions
upon which the actual result depends are known, and form the ground of
the judgment; and in estimating the known and certain conditions in
comparison with the unknown and uncertain we enter upon the calculation
of the probability of that which we call possible. Still it is our ignorance
alone that makes it possible for us ; and thus these judgments lead im-
perceptibly to those which merely state the subjective impossibility of a
decision. While they appear to be concerned with things, they are really
only concerned with the measure of our knowledge of things; and they are
the expression of the resignation of our limited knowledge. This is proved
by the fact that exactly the same expressions are used of that which already
exists or is past. When the historian attempts to clear up a fact from
fragmentary or contradictory information, or the judge in taking evidence
endeavours to discover from clues exactly what has happened, then differ-
ent combinations offer themselves; it may have happened this way, but
then it may also have happened that way. This “may” or “can” is the
expression of subjective indecision; and its significance lies in its refusal
to allow the opposite alternative to be decisively established. When it is
said that the accused may be innocent in spite of weighty evidence, this
means only that the evidence is not sufficient to prove the guilt; that the
judgment "he is guilty” is not necessary, nor, therefore, possible. But
there is no question as to “can” in the objective sense, since objectively
it is already absolutely determined whether affirmation or negation is true.
But the statement that such and such a thing is possible becomes the
more empty and insignificant according as the extent of our ignorance is
greater, and we have fewer positive grounds to give as a reason why our
conjecture should come to pass. When we say that spontaneous genera-
tion is possible, this is true in so far as we cannot prove that it is im-
possible. But all the grounds contained in the order of nature as known
to us speak against it, and it is a possibility which lies only in the dark
regions into which our knowledge has not yet penetrated.
7. Only in this subjective sphere does it hold good that everything is
possible which contains no contradiction, nor leads to any. Every hypo-
thesis accepted as possible breaks down at once if it falls into contradiction
with a proposition recognised as valid ; hence it can be assumed only so
long as we do not find it to be contradictory to a valid truth, i.e. so long as
POSSIBILITY AND NECESSITY
209
1
its opposite remains unproved. But this absence of contradiction has
nothing whatever to do with the question as to what may happen in
reality.
8. Nevertheless the attempt has been made to find, in the absence of
contradiction, a criterion of possibility in the other sense also, particularly
where the question is not as to the possibility of being this or being that,
but as to the possibility of being in general. This is what Leibnitz under-
stood by the possible. It is that which is thinkable (conceivable) because
it contains no contradiction; and it was in this sense that he demanded
that the proof of the possibility of God should precede that of His ex-
istence. But this absence of contradiction is meaningless unless it be first
established what is contradictory when thought of as the determination of
one and the same thing, and what is not ($ 22, p. 127 sq.). Moreover, Leib-
nitz has to secure a relation to reality for this abstract determination by
postulating that everything possible demands existence, and will therefore
exist if nothing prevents it. It is against this forced transition from the
merely conceivable to something of which we can state that it is possible
for it to be that Kant's criticism (Postulate des empir. Denkens überhaupt)
is directed, which limits the conception of the possible by the formal con-
ditions of experience. But Kant himself allows too much scope to the
concept, inasmuch as he would still use it as a predicate of things, in the
same sense as Leibnitz. Against his view we must here again insist that
possibility can only be stated of that which finds utterance in the judgment,
hence that all possibility, as well as all necessity, is hypothetical, and pre-
supposes an existent. The statement that it is possible for something to
be has no meaning, if it lays claim to material validity, unless it points
out some power which can produce the thing and shows that the existing
order of the universe raises no conclusive objection against it. This alone
distinguishes the possible thing from the possible idea or possible concept.
A bare possibility is self-contradictory.
9. The possible stands in a somewhat special relation towards the
negation.
It would seem to be a matter of course that when we state the possibility
that A is B we include the possibility that A is not B; for the opposition
between the merely possible and the necessary lies just in the fact that it
may not be as well as may be. But on closer inspection it becomes
necessary to impose important limitations on the proposition that every A
1 De Verit. Primit., Erdm., p. 99. Cf. Princ. Phil., $ 45, Erdm., p. 708.
S. L.
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LOGIC
potest esse B is accompanied by an equally valid A potest non esse B; if,
that is, we would deal with significant propositions, and not with empty
formulæ.
For instance, our thought, in its function of comprehension, predicates
of the different phases of that which is changeable, capable of development
or of being determined from without, that they are possible. Then the
statement that the negation is also possible either has no meaning, or when
opposed to the original proposition alters the meaning of this. The
judgment "cooking-salt may be dissolved in water" is intended to state
an attribute of cooking-salt. What then is the meaning of the proposition
“it is possible that cooking-salt is not dissolved in water"? The proposition
that a pair of mice may have millions of descendants in a few years is meant
as an estimate of their power of increase, and hence as the statement of an
organic law; but what about the proposition that the pair may also not
have these descendants ? When the positive statement expressly isolates
its subject from varying conditions, there is no sense in returning to these
and suddenly resuming the standpoint of the multiplicity of actual events.
When, however, we are speaking of the particular case in temporally
valid judgments, then the possibility of not-being accompanies that of
being, and has the same significance. The answer may come to-day, but it
niay also not come till to-morrow, or not at all; it may freeze to-night, but
then again the frost may keep off. The ground of the negation is the
presupposition that, besides the known relations which would bring about
the result, there may be others also to counteract or prevent it; in the
first instance there may be delay on the part of the writer or the messenger,
in the second the introduction of a warmer current of air. This relation
between causes which bring about a result and causes which counteract
and prevent it, is presupposed when the possibilities of being and of not-
being are opposed as equally justifiable propositions. But its ground is
only our ignorance as to whether the causes actually present and taking
effect are favourable or counteracting.
The case is the same when we state the relation between a generic
concept and its mutually exclusive specific determinations. A triangle
may be equilateral or not equilateral. If all I know is that it is a triangle,
I have no ground for either affirming or denying that it is equilateral ; the
general idea leaves both possibilities open.
10. The negation of possibility leads to necessity, the negation of
necessity to possibility.
POSSIBILITY AND NECESSITY
211
a. It is possible that A is B contradicts
It is not possible that A is B, and this is equivalent to
It is necessary that A is not B.
b. It is necessary that A is B contradicts
It is not necessary that A is B, and this is equivalent to
It is possible that A is not B.
Thus there arises the twofold contradictory opposition which runs
parallel to the contradictory opposition of the universal affirmative and
particular negative, and the universal negative and particular affirmative
judgments.
But in both cases we can only avoid running into absurdities if we are
careful to interpret the formulæ always in the same sense.
These formulæ hold good when possible and necessary are used in the
subjective sense of a hypothesis ; they hold good also when necessary
and possible are uniformly used of the essential necessity of some deter-
minations and of the material possibility of others which are opposed to
each other; they hold good, finally, when possibility and necessity are
stated of some particular case in temporally valid judgments.
II. On reviewing all the questions to which the concepts of the possible
and the necessary have led us, we see that the function of judgment has
undergone a further development in two directions. On the one hand, the
different stages in the formation of the judgment which were traversed by
the immediate judgment with one step have been definitely separated by
the mediated judgment. The mere attempt at a judgment—the question--
has appeared upon the scene, and has led us to reflect concerning the
relation of the judging subject to this question; and by means of the
antithesis between the question and the decision, NECESSITY, the innermost
and essential meaning of all judgment, has been brought to light. On
the other hand, judgment has advanced a step further in that particular
simple subjects, or a number of these, have been replaced by the statement
of the judgment itself, the material unity of subject and predicate, which
has become the subject of new predicates, primarily of the necessary
and possible. In this way new categories have become manifest which
rank above those first discovered, inasmuch as they are founded upon the
earlier ones and place them in relation to each other, thereby enabling
us to know not only particular phenomena, but also their connection.
Thus they afford a positive counterpart to the mere negation, which, like
them, has reference to the synthesis of judgment.
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LOGIC
If we thus look upon the progress of thought as pressing onward from
the mere attempt, the hypothesis, and the possible to the necessary, we
can give their natural significance to the special forms which are generally
co-ordinated with the judgment which states or denies a definite predicate
of a subject, that is, to the hypothetical and disjunctive judgments. The
former is the simple expression of necessity, the latter the complete ex-
pression of mutually exclusive possibilities. The former shows a necessary
connection between possibilities, and in this way limits the sphere of
possibility by necessity; the latter is the preliminary step towards establish-
ing the necessity of one possibility by the denial of certain others.
CHAPTER VII.
HYPOTHETICAL AND DISJUNCTIVE JUDGMENTS.
From the point of view of what is called relation, modern logic generally
classifies judgments as CATEGORICAL (A is B ; A is not B), HYPOTHETICAL
(if A is, B is), and DISJUNCTIVE (A is either B or C). But this is not in ac-
cordance with the Aristotelian logic, nor are there any grounds for regarding
it as an exhaustive division of the forms of judgment. It often happens that,
so far as concerns the matter of the statement, categorical and hypothetical,
or hypothetical and disjunctive propositions express the same thought
with a difference which is merely grammatical. If, on the other hand, it
is the verbal expression to which we look, then the hypothetical and dis-
junctive forms cannot be co-ordinate with the categorical form of judgment,
since this is contained in both of them. If, again, the ground of distinction
is sought in this circumstance, and composite judgments, which are ex-
pressed in complex propositions, are opposed to those which are simple,
then we shall find that there are many other complex propositions besides
hypothetical and disjunctive judgments, and there will be no apparent
reason for excluding them from logical treatment.
As a matter of fact, logicians did for a long time follow the example of
the Stoics in distinguishing the composite judgment from the simple
judgment which is expressed in a single proposition; and this custom,
which had fallen out of use more particularly since Kant's time, has been
lately revived (e.g. by Ueberweg).
In an investigation of which the chief aim is to analyse actual judgment,
and which must therefore begin by investigating the expression of that
judgment in language, we must begin by reconsidering this former custom.
This is the more necessary because a number of misconceptions concern-
ing the hypothetical judgment have arisen owing to insufficient reflection
on the logical significance of the forms of language.
1 With what follows cf. my Programm : Beiträge zur Lehre vom hypothetischen Urtheil
(Laurp, Tübingen), 1870.
213
214
LOGIC
I. THE DIFFERENT WAYS IN WHICH PROPOSITIONS MAY BE COMBINED
AND THEIR LOGICAL SIGNIFICANCE.
$ 35.
There are certain forms of speech in which different propositions are
connected by particles, conjunctions, and relative pronouns. This con-
nection may be such as to express a relation between complete propositions,
which state definite judgments and are comprehensible by themselves; or
it may show that the one proposition is essential to the completion of
the other.
In the first case the relation may be merely verbal, as in relative propo-
sitions; or it may express a subjective relation of the propositions peculiar
to the individual speaker; or it may be equivalent to another judgment,
having for its predicate either the logical relation between the syntheses
expressed by the propositions, or the relation between the facts stated in
the propositions (states, events, etc.).
In the second case we may either make a statement by means of modal
relational predicates concerning the grammatically dependent judgment,
or we may make a statement concerning the fact expressed in that judg-
ment.
1. The simplest complex propositions, and the most easy to analyse,
are those in which two propositions, each comprehensible by itself, and
expressing an independently valid judgment, are placed in such a re-
lation to each other that more is expressed by the two together than by the
simple utterance of the one proposition after the other. The verbal forms
expressing this relation are the particles, and it is of their significance that
we must speak.
a. We have already seen (p. 157) that the particle “and,” and all
equivalent expressions, can do no more than tell us that the two judgments
are, at the moment of speaking, both present in the consciousness of the
speaker ; and since this subjective fact is already established by the utter-
ance of both propositions by the same person, such mere links have in them-
selves no objective significance, though they may assume the function of
indicating a corresponding connection in the objects of thought (e.g.
temporal succession when some event is being narrated). These particles
therefore are not equivalent to a judgment.
b. Nor can the adversative particles be taken as the signs of a definite
objective statement. It is true that in conversation they are often directed
HYPOTHETICAL AND DISJUNCTIVE JUDGMENTS 215
against some spoken proposition, which they confront with an objection,
limitation, or contradiction. Still they have not the force of a negation, for
it happens just as often that they only repudiate what might have been
conjectured or inferred from the proposition by means of some combina-
tion. When used by one person speaking alone they serve on the one
hand to contend in this way against some looked-for statement, and on the
other merely to introduce some contrasting or unexpected element, such
as an affirmative proposition after a negative, or an unexpected predicate.
Thus, while the negation denies a definitely uttered statement, the
adversative particles often anticipate tacit combinations merely assumed
as possible; the negation, therefore, which these express, is indefinite, and
cannot take the form of a proper judgment.
C. It is different when we come to the so-called causal particles and
particles of inference. Where these express the logical relation of the
judgments connected, they state that the one judgment is the logical
ground (or consequence) of the other ; but when they are meant to express
the relation between the facts stated in the judgment, they tell us that the
fact stated in the one judgment is the real ground (or consequence) of the
fact stated in the other. Thus the relation they express is that of a logical,
or material, necessary connection ; and to that extent they have all the force
of a proper definite judgment. “It is getting cold, for the thermometer
is falling”; “it is getting cold, therefore the thermometer is falling";
here we have in each case three complete judgments : “it is getting
cold; the thermometer is falling ; the former proposition is inferred from
the latter”; “it is getting cold; the thermometer is falling; the former
change is the cause of the latter."
d. With the causal particles expressing real necessity may be classed
all determinations which express real relations between the states, events,
etc., spoken of in the propositions, such, for instance, as the temporal
relations in a narrative-contemporaneousness, succession, etc.—and rela-
tions of place. These also stand in place of definite relational judgments,
by which they might be expressed.
e. Under the name of exponible judgments, the older logic has
included judgments which, while apparently making only one statement,
really contain several. Chief amongst these are the judgments containing
restrictive words—“only,” “none but,” etc. The proposition “only the
the man who is not wise is not happy, or that all the happy are wise.
216
LOGIC
2. Grammar distinguishes between the co-ordinate and subordinate
connection of propositions ; but in this general form the distinction
corresponds to no essential distinction in thought. The grammatical
form, it is true, seems to signify that the speaker is mainly concerned
with the statement of the principal proposition, for the sake of which
alone the dependent propositions are introduced; that is, the speaker has
no object in stating the dependent propositions except for the sake of
reminding us that they are accepted truths. But language as actually
used has not retained the distinction between co-ordinate and subordinate
propositions in all its strictness; it uses conjunctions and co-ordinating
particles in the same sense, and the utmost distinction made is a slight
difference in the subjective emphasis laid upon the propositions con-
nected by them—a difference which has no objective significance with
respect to the matter of the statement. The particles “for” and “because”
are used to denote one and the same relation; and the relation ex-
pressed by " at the same time” may also be announced by “whilst.”
The significance of relative connection is especially susceptible of
manifold gradation. When relative pronouns follow a term which is
already fully determined as it stands, they serve merely to enable us to
make a further statement concerning some portion of a given statement.
The relative pronoun, whilst obviating the express repetition of the
definite denotation, gives more prominence to the identity of the two
elements than would be attained by mere juxtaposition ; but the relations
between the two propositions thus connected may vary greatly. The
most decided subordination takes place when the proposition introduced
by the relative enables us to recognise one element of the main proposi-
tion more easily by reminding us of something we already know; and
in this case the statement introduced has no independent value whatever,
but is more in the nature of an attributive adjective, or an apposition.
There is complete equality of position, on the other hand, when the
relative proposition introduces a new and independent statement (this
happens most frequently in Latin). But here the relative does not take
the place of a proper judgment. It tells us nothing which is not already
stated in the two propositions connected by it, and its function is merely
verbal—that of establishing the identity between the verbal denotations.
The proposition “A, which is B, is C," tells us no more than “A is B,
and A is c”; all that it does is to leave no room for doubt that the
A of the one proposition is the same A as that of the other.
HYPOTHETICAL AND DISJUNCTIVE JUDGMENTS 217
Relative propositions have quite another function when an element of
the proposition which is in itself indefinite receives through them its
e
subject or predicate, and limit a more general denotation to a definite
sphere; that is, they are determining. In the proposition “men who
live in cold climates need more nourishment than others,” the subject is
incomplete without the relative proposition, which plays the same part as
a determining adjective in other cases-e.g. "elastic bodies are resilient.”
In this way simple denotation by a definite word may be paraphrased by
a relative proposition; the phrase "parallelograms, which are right-angled
and equilateral,” is a synonym for “squares.”
Here we must also add the indefinite relatives (“any one who," "any-
thing that,” őOTIS. àv, quisquis), which tell us nothing but that subjects
of which the one predicate is true have the other predicate also. The
expression is then equivalent to a universal judgment, and, like it, may
have either an empirical or an unconditional universality; while, again,
any universal judgment may be expressed in this form. The propositions
“man is mortal” ; “all men are mortal"; "anything which is a man is
mortal,” all mean absolutely the same thing—the necessary connection
between humanity and mortality. The only difference is that in the form
"anything which is a man is mortal” the act of naming, which has already
taken place in “all men,” now takes place before our eyes; and it is left,
moreover, an open question as to what particular thing, if any, can be so
named. The formula "all men are mortal,” on the contrary, although it
does not actually state that subjects are forthcoming, still presupposes
them if we understand the words in their ordinary sense.
Much the same may be said of “when” (wenn) and “where” (wo) as
relatives of time and place. The use of " when ”to denote one definite
point of time in the past, while still retained in English, is lost to the
German language. Here it is used principally of the future, and hence
to whether the future will really come to pass ; and this may be, although
perhaps in a very slight degree, even where there is no intention of ex-
pressing anything more than that one event will happen at the same time
as another (when it strikes twelve o'clock, the new year will begin ; when
the war is ended, we shall return). Where, again, it stands as a general
relative (whenever=as often as), its only direct meaning is the universality
of the co-existence of two states or events ; this universality being either
218
LOGIC
merely empirical, as expressing a perception to which there has been no
exception, or absolutely universal (when it grows dusk, the bats begin to
fly). But we cannot state that two events will happen together in the
future, nor that they will always and unconditionally take place together,
unless there is some necessary connection between them. To this extent,
therefore, the meaning of what was originally no more than a temporal
the conditional conjunction in the hypothetical judgment, of which we
through the same process.
3. From connections such as these we must distinguish others in which
a proposition as such forms part of another proposition, either as subject,
or as part of a relative predicate (object). The proposition may then
represent either the judgment as a subjective thought or utterance, or the
fact expressed in the judgment; and this again may be sometimes merely
thought or assumed, sometimes objectively valid as matter of fact.
a. Those statements in which modal relational predicates refer to
judgments have propositions for their component parts. The statements
that a judgment is true, false, credible, doubtful, possible, or necessary ;
the statements that I believe, repudiate, dispute, or doubt something—all
these have reſerence to a hypothesis which is expressed in a proposition,
and they state how the hypothesis is related to my thought or to thought
in general. All final propositions belong to this class. When I do
anything in order that something else may happen, the purpose makes
its first appearance as my thought; and the statement refers to the relation
between a result as expressed in the form of judgment and my thought
and will, with the action to which it leads.
Since every judgment as such must stand in definite modal relations,
these may always be predicated. To say that the judgment“ A is B” is true
or necessary means no more than the simple statement “ A is B.” To
say that I maintain, I know, I am certain that A is B, only gives special
emphasis to the certainty already contained in the fact of the statement
“ A is B.” But in such a rendering the proposition “A is B” becomes
the expression of a merely conceived judgment or hypothesis ; the com-
pletion of the judgment is transferred to the modal predicate.
b. Statements of which the component parts are states or events ex-
pressed in the form of propositions differ only verbally from those which
contain adjectival or verbal abstract substantives amongst their elements.
HYPOTHETICAL AND DISJUNCTIVE JUDGMENTS 219
The thought remains the same whether I say, “the greater warmth of the
summer is due to the higher position of the sun,” or, " the fact that the
summer is warmer is due to the fact that the sun stands higher”; all that
is necessary to such a statement is that fresh predications can be made
concerning what is originally expressed in a judgment.
4. Although this brief survey lays no claim to completeness, it may at
least suffice to show that the manifold grammatical forms in which propo-
sitions are connected together are no ground for special kinds of function
in judgment, which are not forthcoming in simple judgments. The mean-
ing of such forms can always be expressed by the predicates of simple
statements, and logical theory has therefore been fully justified in leaving
such connections as those of time and place to grammar, which treats of the
expression of thought in language. The expression “compound judgment”
is misleading and inappropriate; that which is composed of judgments
may be a combination of judgments, but we cannot therefore say that this
combination is itself a judgment. The fact is that when the component
parts of a judgment are propositions these propositions are not themselves
judgments; that is, they are not at the moment intended as statements :
they enter into new judgments, either as hypotheses, or as the results of
previous judgment, and therefore as an indication of what is meant in the
judgment.
5. Amongst all the different combinations of propositions conventional
logic has distinguished only what are called hypothetical and disjunctive
judgments, and in so doing has rightly judged that all other forms deal
only with definite statements, however varied ; that is, with the attribution
of definite predicates to definite subjects. But in these two forms we
have to deal with such statements concerning hypotheses as are of
direct importance for the final aim of all thought-progress from the
subjective to the objective, from the possible to the necessary—and there-
fore of universal importance for all kinds of statement. Reflection con-
cerning the value and significance of hypotheses is always necessary where
we cannot straightway form a definite judgment, but must endeavour to
arrive at truth by way of a preliminary experiment. Thus hypothetical
and disjunctive judgments rank with the negation, which, like them, is a
judgment concerning a tentative judgment; they both apply to that stage
of thought which lies between the question and decision.
220
LOGIC
II. THE HYPOTHETICAL JUDGMENT.
§ 36.
The HYPOTHETICAL JUDGMENT states that two hypotheses are related
to each other as GROUND and CONSEQUENCE ; its predicate is “ NECESSARY
CONSEQUENCE.” “If A is true, then B is true,” means, therefore, “B
is the necessary consequence of A.”.
1. The ordinary expression of the hypothetical judgment, and that in
which its meaning is most obvious, is a combination of propositions of the
form “if A is B, then C is D.” More briefly, and taking A and B as signs
of propositions, “if A is true, then B is true.”
2. In grammar such propositions are generally called conditional, and
in giving them this name we take what seems to be the most natural view,
i.e. that the point in question is the validity of the consequent. This
validity cannot be directly stated, but presupposes the validity of the ante-
cedent, the whole being thus a conditional statement of the consequent,
hence a statement concerning the subject of the consequent." But the
consequent is not to be stated until the antecedent has been confirmed,
and a conditional proposition is therefore an expression of uncertainty with
reference to both antecedent and consequent. Both, as the expression
goes, are problematically stated, or, as we should say, express mere hypo-
theses. So far as concerns the two propositions themselves, therefore, there
really seems to be no judgment at all in the proper sense, no utterance,
that is, which is stated as true and necessary; and this view is confirmed by
the fact that conditional propositions are sometimes stated with the avowed
consciousness of the falsity of both antecedent and consequent (si tacuisses,
philosophus mansisses).
3. Nevertheless such a combination of propositions does contain a state-
ment which is a judgment in the proper sense of the word, and this the
Stoics? were the first to recognise definitely. Such a combination tells us
that antecedent and consequent are related io each other as ground and
consequence (p. 195), that to accept the antecedent makes it necessary to
accept the consequent, and that the validity of the consequent is infallibly
connected with that of the antecedent. It is this relation of necessary
consequence which is the true predicate of the hypothetical judgment, and
1 This is how Wolff defines the hypothetical judgment in his Logik. See my Programm
mentioned above, p. 23 sq.
2 Cf. my Programm, p. 12.
3 J. S. Mill, Logic, bk. 1, ch. 4, $ 3.
HYPOTHETICAL AND DISJUNCTIVE JUDGMENTS 221
the two points of reference for the relation are antecedent and consequent.
So far as concerns the statement of this necessary connection, the question
as to the validity of the antecedent and our conjectures as to its truth,
probability, improbability, or falsity, are of no importance, just as in a
simple judgment concerning some object of thought it is quite immaterial
whether we regard the object as existing, as possible, or as merely fictitious.
In this way we may explain how it is that judgments beginning with“ if”
(wenn) seem sometimes to express uncertainty alone, and at other times
to be the expression of sequence amongst actual phenomena.?
This necessity, which in hypothetical judgments refers to propositions
which are merely assumed, is also stated with reference to valid judgments
by the so-called causal connection of propositions. Bis true because A is
true, a judgment which may refer either to the ground of our knowledge
or to the material ground. (It is warmer because the thermometer is rising ;
the thermometer is rising because it is warmer.)
4. The nature of the statement remains, of course, the same whether the
judgments which appear as antecedent and consequent be affirmative or
negative, universal or particular, narrative or explicative. The attempts to
find differences of quantity, etc., in the hypothetical judgment are based
upon a confusion between hypothetical judgments and statements concern-
ing mere time-relations or some purely empirical and casual coincidence.
No one would maintain that judgments such as “whenever it strikes
twelve some one dies” are hypothetical. The confusion is especially
apparent in the judgments which have been called particular hypotheticals :
“when it is fine the barometer generally stands high.” If the connection
is not invariable, it cannot be necessary, and such judgments can never
express more than empirical or casual coincidence in a relatively greater or
smaller number of instances. The proposition “sometimes when a triangle
is right-angled it has two equal angles" tells us only that the attribute
right-angled is occasionally to be found together with, and does not exclude,
equality of the two remaining angles. The phrase "sometimes when”
does not connect ground and consequence; it only states the coincidence
of attributes or events in the same or different things, the statement being
merely empirical, and saying nothing as to the ground of the coincidence.
(Cf. my Programm, p. 45, and Vierteljahrsschr. f. wiss. Phil. v. 1, p. 109 sq.)
5. The co-ordination of the hypothetical with the categorical as a
special kind of judgment, distinguished by the difference of its logical
1 See Appendix B.
222
LOGIC
function, may be said to date from Kant. In the categorical judgment, he
says, ideas are subordinated to each other as predicate to subject, in the
hypothetical as consequence to ground (Krit. der r. V., § 9. 3 ; Hart., p.
106). The necessary sequence thought of in hypothetical judgments,
corresponds to the copula in categorical judgments : it is that which unifies
the different ideas. Thus the category which corresponds to the logical
function of the hypothetical judgment is that of causality.
But the classification is throughout superficial and inadequate, if only
because the ideas which are related as subject and predicate are, in the
Kantian phraseology, concepts, while the ideas which are related as
ground and consequence are judgments. Kant's distinction gave rise to
the further doctrine—which he, however, did not himself teach--that cate-
gorical judgments are the expression of the relation of inherence, hypo-
thetical judgments of the relation of causality, a doctrine which is quite
untenable if the expressions hypothetical and categorical are taken in
their ordinary meaning. The judgment "God is the cause of the world”
is certainly categorical in the ordinary sense, nevertheless it expresses
causal relation; the judgment "if the soul is material, it is extended," is
hypothetical, yet it treats entirely of relations of inherence. When, again,
we disregard the verbal form and distinguish between judgments of quality
and relational judgments (as, e.g., Drobisch does), we may find some justifi-
cation for the division, so far as concerns the meaning of definite state-
ments. But in this classification the true hypothetical judgment is not
included at all, and only by straining a point can it be subsumed under
those relational judgments which are statements of real relations between
things.
6. The exact meaning of the hypothetical judgment differs according
to the nature of the propositions related by it as ground and consequence.
When two propositions, which standing alone would express unconditional
validity, are connected by "if—then,” the statement is merely that if we
accept the one, we must also accept the other. “If the soul is corporeal,
then it is extended ”; “if the soul is simple, then it is indestructible”;
“if God is almighty and good to all, then the world is perfect ”—such
propositions make the truth of the consequent depend as necessary con-
sequence upon the truth of the antecedent, and state that whoever accepts
the one must also accept the other. The ground of this necessity is not
apparent in the hypothetical judgment. It may consist in the simple
relations of the ideas (corporeal and extended) by virtue of which predica-
HYPOTHETICAL AND DISJUNCTIVE JUDGMENTS 223
tion of the one involves predication of the other; or it may consist in
assumptions concerning the nature of things, such as “the simple is in-
destructible," or in assumptions concerning the necessary mode of action
of certain causes; the hypothetical judgment does not tell us which.
From this point of view we may draw the distinction between analytical
and synthetical judgments. If the second proposition is contained in the
first in such a way that the generally recognised meanings of the words
enable us to infer the one from the other, then the judgment is analytical.
But if the connection must be mediated by a ground of necessity derived
from some other source, then it is synthetical. This, however, is a dis-
tinction which cannot be more exactly defined until we come to the
doctrine of inferences. We find instances of a similar nature in applica-
tions of a general rule to a particular case : “if death be the penalty of
murder, then this murderer must be punished by death.” Such proposi-
tions express the logical necessity by which the particular instance is
contained in the general rule.
7. When antecedent and consequent refer to the particular and are
statements having a temporal validity only, there are two cases to be
distinguished. Here, again, we may find that the second synthesis is
contained in the first, and follows from it by virtue of the meaning of the
predicates, these being invariably connected : “ if this man is drunk, he is
irresponsible.” Or the necessary sequence may be due to the special
circumstances of the case before us, and inferable from it according to
certain laws ; necessity of connection is found here also, but its conditions
are not contained in the antecedent. When we say, "if the sky clears, it
will freeze to-night,” we presuppose the given temperature, etc. ; the neces-
sary sequence depends upon the laws of the radiation of heat, but these
will not produce the result except at the given tenperature.
8. There is a special application of the hypothetical judgment in which
the propositions connected by it have no definite subjects. The subjects
themselves are left indefinite; either absolutely indefinite, when they are
denoted by some such word as “something," or partially indefinite, when
they are denoted only by a general term. “If anything is corporeal, it is
extended”; “if any one is just, he gives to every one his due”; “if a
triangle is equilateral, it is equiangular," etc. Here not only is the validity
of a given statement left in suspenso, its necessary consequence alone
being given; we are also left uncertain whether there is any subject be-
longing to the predicates, or where it may be found. But as it is stated
224
LOGIC
that any subject in which the one predicate is found must contain the
other as well, it is essential that in these judgments the antecedent and
consequent should have the same subject-in meaning, if not in words.
In the judgment " if a triangle has equal angles, its sides are equal,” there
are, no doubt, two grammatical subjects ; but the second refers by means of
the possessive pronoun to the first, and it is the first of which the state-
ment is really made.
They are then precisely equivalent to universal relatival propositions :
"he who is just gives to every one his due”; “every triangle which is equi-
lateral is also equiangular.” Propositions such as these state the identity
of the subjects to which the two predicates belong, but they can do so
only because the second predicate is necessarily connected with the first ;
this necessity shows itself in the fact that the two predicates are always
and without exception found in the same subject.
The course of thought presupposed by these modes of expression is
clear. We find them where particular things, whose existence is for the
time assumed, are being characterized. With the definite predicate of
the antecedent in our minds, we look abroad into the manifold; and in the
expectation that the predicate will be somewhere applicable, we state that
if it is, then the other predicate must be necessarily connected with it.
9. But these judgments tell us absolutely nothing which is not contained
in the unconditionally universal categorical judgment. “All bodies are
extended” does not refer to any limited and definite number; it merely
states that “whatever is a body is extended,” or that “if anything is a
body it is extended.” The word by which the subject of the statement
is denoted contains by implication the antecedent of a hypothetical
judgment. Such a proposition, therefore, as “the good man thinks
of himself last” is as truly hypothetical as if the subject were intro-
duced as “a good man” with a view to leaving it an open question
whether and where such a subject is to be found—though not when it is
merely the incomplete denotation of a definite subject. (The distinction
may be seen from the examples, “an emperor must die standing”; “an
emperor was a Stoic.")
This, then, is the answer to the much-disputed question as to the rela-
tion between hypothetical and categorical judgments. All categorical
judgments which are unconditionally universal are exactly equivalent in
meaning to hypothetical judgments, for (see § 27, p. 162 sq.) they state
nothing whatever but that subject and predicate necessarily belong to
HYPOTHETICAL AND DISJUNCTIVE JUDGMENTS 225
each other, so that to predicate the subject of a particular thing neces-
sarily involves the predication of the predicate. Inasmuch, indeed, as the
“all” is ambiguous, and may introduce either a judgment which is em-
pirically universal, or one which is unconditionally universal, the hypo-
thetical form is the more accurate and adequate expression. On the other
hand, judgments in which definite predicates are attributed to definite
particular subjects naturally resist the attempt to convert them into the
hypothetical form. The hypothetical judgment, moreover, has a wider
meaning and application than can be naturally expressed in the categorical
form.
10. It is different when the antecedent predicates changeable attributes,
activities, and relations of a subject which is only indefinitely denoted.
“When the temperature of water falls below zero, it becomes solid”;
“when a body projected with a given velocity is subject to the action of
a force which varies as the inverse square of the distance, it describes a
conic section”; “illumination is strongest when the rays of light fall per-
pendicularly on a surface "—such statements may refer either to repeated
instances in which the subject remains the same, or to instances where the
subjects are different; and for this reason they would be inadequately ex-
pressed by a universal categorical judgment. If we are to express the
necessity as unconditional universality, we must make use of the general
relatival phrases "every time that,” “as often as”; and from this it follows
that here the hypothetical judgment is also subject to time-relations.
Changes must take place at definite points of time, and to limit the
validity of the antecedent to a definite period of time is to appoint a
definite time for the validity of the consequent-either the same time, or
the moment immediately before or after. It is these judgments which
are, from the nature of the case, based upon causal relations whenever
their subjects are to be found amongst real things; for when change in
one thing involves a second change in the same (or another) thing, it must
be due to causal connection.
II. Amongst hypothetical propositions having indefinite subjects we
must also include those equations of analytical geometry and mechanics
which contain variables. The equation of the parabola ya =px is not an
equation in the ordinary sense—i.e. a judgment that two lines, numbers,
or figures are equal, because of the indefinite value of the variable. It
states only that if the abscissa has any definite value, then the ordinate
belonging to it has a value which is determined by its arithmetical rela-
S. L.
226
LOGIC
tion to the constant. In the same way all algebraical formulæ contain-
ing general symbols may be translated into hypothetical judgments, e.g.
a(b+c)=ab + bc.
12. Passing to hypothetical judgments containing negations, we find
that the form "if A is, B is not,” represents the negation of a proposition
as the necessary consequence of an affirmation, thus affirming that the
hypotheses A and B are incompatible. This incompatibility may be due
either to the incompatibility of certain predicates, or to the real relations of
hindering or counteracting causes. The relation is always mutual. If the
negation of B necessarily follows from the affirmation of A, then (according
to the law of ground and consequence) the negation of A follows necessarily
from the affirmation (i.e. the denial of the negation) of B ; and this is true
whether A and B represent universally and unconditionally valid judg-
ments or temporally valid judgments concerning the particular, or whether
their subjects are indefinite (when the sky is clouded no dew falls; when
dew falls the sky is not clouded). To such a hypothetical judgment there
corresponds the categorical judgment, which is universal and negative.
The proposition “no right-angled triangle is equilateral ” makes the same
statement as the proposition “if a triangle is right-angled, it is not equi-
lateral”; the negation of the predicate equilateral is stated as the neces-
sary consequence of the determination right-angled. 1
When a negation appears as the necessary consequence of another nega-
tion (if A is not, B is not) the ground of the relation must be the necessary
connection between the corresponding affirmatives. This is the sole
condition upon which the negation of the one can have the negation of
the other for its consequence. The invalidity of A is an infallible ground
from which to infer the invalidity of B only when A is the necessary con-
sequence of B. I cannot say that when the sky is not clear no dew falls
unless I am certain that when dew falls the sky must be clear; only if it
1 The difficulty raised by Twesten (Logic, 8 64) against the view that the hypothetical
judgment with a negative consequent is affirmative is easily removed. If the categorical
judgment "no equilateral triangle is right-angled ” is negative, how, he asks, can the
corresponding hypothetical “if a triangle is equilateral, it is not right-angled,” be affirma-
tive? It certainly could not if the hypothetical judgment were a statement about the
equilateral triangle, and not about the necessity of a consequence; but why should we
be unable to affirm that a negative proposition is a necessary consequence? The very
possibility of the unconditional negative “no A is B” depends upon our knowing that
the determinations contained in the thought of A necessitate the negation of B; and
this, which is the meaning of a universal negation, the hypothetical judgment expresses
by affirmation of this necessity.
HYPOTHETICAL AND DISJUNCTIVE JUDGMENTS 227
is true that every equiangular triangle is equilateral can it be said that if a
triangle is not equilateral, it is not equiangular. From the proposition “ if
A is, B is,” we may always deduce the other proposition “if B is not,
A is not,” according to the principle that the denial of the consequent
involves the denial of the ground—the principle, that is, which expresses
the meaning of the necessary consequence stated by the hypothetical
judgment.
When an affirmation appears as the consequence of a negation—if A is
not, B is—the judgment is always immediately or mediately grounded
upon the position that of different possible hypotheses which are mutually
exclusive one must necessarily be valid ; the position, that is, which finds
utterance in the disjunctive judgment. But it is not true that the judg-
ment “if A is not, B is” is, as it stands, equivalent to the disjunctive
“either A is or B is.” 1
13. The negation of a hypothetical judgment can take place only
through the denial of its predicate—that is, of the necessary consequence
stated by it. The contradictory opposite of the judgment "if A is, B is,"
is the proposition “ B is not the necessary consequence of the proposition
A”; i.e. B is not true because A is (even if A is, nevertheless B is not).” 2
In the same way the negation of the statement “it does not follow that
because A is, B is ” leads to the judgment "if A is, B is.”
14. Hypothetical judgments of the form “if A is, and B is, and C is,
then D is” should not be called copulative hypothetical judgments; they
do not state of different relations that they are all necessary consequences,
as in the judgment "both when A is and when B is, C is.” The latter
judgment is copulative, but the former gives only one ground consisting
of several conditions, and therefore it cannot be resolved into several
hypothetical judgments.
15. The possibility of the consequence can be connected with each part
of the ground, but only when we understand this possibility as having
reference to the partial ground ($ 34, p. 208). “When the moon is in
1 Vide my Programm, p. 54 sq. The proposition when the centre of the moon is
not in the plane of the ecliptic it forms a triangle with the centres of the sun and the
earth” does not mean the same as the proposition “either the centre of the moon is in
the plane of the ecliptic or it forms a triangle with the two other central points.” For i
may also form a triangle when it is in the plane of the ecliptic, but the node does not
fall upon the straight line passing through the centres of the sun and the earth.
2 This shows also the logical position of the so-called concessive propositions, their
meaning consists in their rejection of some immediate or mediate consequence which
might be inferred from the antecedent.
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LOGIC
conjunction or opposition, and at the same time the lunar node is in a
line with the sun and earth, then there must be eclipses," the proposition
may be resolved into the two judgments “when the moon is in conjunc-
tion or opposition there may be eclipses,” and “when the lunar node is
in a line with the sun and the earth there may be eclipses.” We find the
same “may” when the antecedent expresses the invalidity of a judgment
which would annul the consequent; “if the radiation of heat from the sun
does not diminish, organic life may have an unlimited duration upon the
earth."
III. THE DISJUNCTIVE JUDGMENT.
$ 37.
The DISJUNCTIVE JUDGMENT states that of a definite number of mutually
exclusive hypotheses one is necessarily true. When it does not refer to
the two members of an antiphasis as in the principle of excluded middle,
it always presupposes a simple judgment upon which the different
hypotheses are based, and which, by its contents, determines and limits
the range of possibilities. Most frequently it happens that either the
subject or the predicate admits of a closed series of mutually exclusive
determinations, and these are enumerated by the divisive judgment.
1. The simplest way of expressing that a hypothesis A is B is uncertain
is to say that neither its affirmation nor its negation can be asserted; I am
confronted by an undecided alternative. But I know that if the affirmation
is true the negation is false, and vice versâ; and that if the affirmation is
false the negation is true and vice versa.
But it is not only between affirmation and negation that such a choice
amongst different hypotheses may be presented. Various hypotheses may
be possible in reference to the same subject-A is perhaps B, perhaps C,
perhaps D. Where these predicates B, C, D, are quite independent of
each other there is no further relation between the hypotheses (thus I
might say of Queen Semiramis that she was perhaps tall, perhaps black-
eyed, etc.) ; but if the one predicate necessarily involves the other, then
there arises the hypothetical judgment. If again they are incompatible,
to accept the one predicate is to exclude the others, and I am confronted
by irreconcilable propositions, each of which by itself is a possible
hypothesis.
When irreconcilable propositions such as these are both equally un-
HYPOTHETICAL AND DISJUNCTIVE JUDGMENTS 229
7
1.
1
certain, they are connected by the particle “or.” Such hypotheses are
not necessarily predicates of one and the same subject, but may be any
assumptions whatever which for some reason are mutually exclusive, and
the relation between which can therefore be expressed in a hypothetical
judgment connecting the affirmation of one with the negation of the other.
Thus the particle “or” contains two statements—that the propositions are
uncertain, and that they are mutually exclusive. “ Ä is B or C” means
that A is perhaps B, perhaps C; if it is B, it is not C; if it is C, it is not B.
2. A similar juxtaposition of predicates occurs in judgments, which state
a possibility. The judgments “water can be liquid, solid and vaporous-
man can wake and sleep” may also be expressed, when any one point of
time is referred to, in the form “water is liquid, solid or vaporous-man
sleeps or wakes.” We find the “or” again when a general idea admits of
further determinations : “the triangle is plain or spherical, etc.—a plane
rectilinear figure has three, or four, or five angles, etc.” Whenever anything
is denoted only by a general term there is room for further determination
by means of mutually exclusive predicates. When all I know and say of a
thing is that it is a triangle, there are many different and incompatible
determinations, any of which may belong to it.
3. When we say of a number of such hypotheses that one is necessarily
true, the statement implies that all the mutually exclusive predicates which
are subjectively or objectively possible are included in the enumeration.
Then we have the disjunctive proposition : either A is B or C is D; A
is either B or C or D. Thus in stating a disjunctive judgment we have
in view the necessary validity of one out of a given number of possible i
and incompatible hypotheses.
4. The simplest case of such a disjunction is to be found in con-
tradictory opposition of judgments, so far as it is subject to the law of
excluded middle. Of the two propositions A is B, and A is not B, one
is necessarily true, the other false. But just because this disjunction is
so self-evident it is of little value (see § 25, p. 154). The important dis-
junctions are those which limit our choice amongst positive judgments with
definite predicates.
5. First amongst these are the disjunctions which state the limited
number of mutually exclusive attributes by which a general idea may be
further determined. A line is either straight or crooked; a triangle is either
right-angled or oblique-angled ; a human being is either male or female;
water is either Auid, solid or vaporous. The kind of possibility possessed
230
LOGIC
by the single members of the disjunction is that discussed in § 34, 5, p.
206–7. The meaning of the disjunction is that a thing known to me only
as falling under the general idea A must have some one or another of
the various attributes possible in A. This meaning is most obvious in
the hypothetical expression, which gives the full force of disjunctions such
as these; if anything is a line, it is either a straight line or a crooked.
Here then there is presupposed both a judgment ascribing a general
predicate to the subject, and the knowledge of a closed series of mutually
exclusive determinations which are possible to that predicate.
6. When we have in our minds all the particular subjects which may
be included in A, thus thinking of the different determinations as actual,
this relation may be expressed also in what may be called the DIVISIVE
JUDGMENT. “Lines are some of them straight, the others crooked”;
“human beings are some of them male, the others female.” When we
review a complete series of changes in the same thing the corresponding
form is “water is sometimes liquid, sometimes solid, sometimes vaporous.”
Here we must notice that the relation between divisive and disjunctive
judgments varies according to circumstances. When our knowledge
is derived from experience alone, the disjunctive judgment is grounded
upon the divisive ; since it is a matter of fact that all human beings may
be divided into males and females, we infer that a third kind is impos-
sible; and upon this inference we ground the disjunctive judgınent “every
human being is either a man or a woman.” In mathematics, on the
other hand, the disjunctive judgment comes first; only after the judgment
that a triangle is either right-angled, or acute-angled, or obtuse-angled, are
we certain that our enumeration of the kinds of triangle is complete. It
is the same with the judgment “ a plane which intersects a right cone is
either parallel to the base, or not; if not parallel, it either intersects
all the generating lines, or not all; and in the latter case it is either
parallel to one generating line or not.” This judgment comes first, and
only when we know that it exhausts all the possibilities do we obtain the
division of conic sections into circles, ellipses, parabolas, and hyperbolas.
The divisive judgment may also be expressed in the form of a copulative
judgment "the circle, ellipse, parabola and hyperbola are the conic sec-
tions,” the definite article indicating the identity of extension of subject
and predicate.
7. The need of expressing the completeness of the enumeration more
definitely than by the use of "some” has led to the divisive judgment
HYPOTHETICAL AND DISJUNCTIVE JUDGMENTS 231
being expressed in the form of a disjunction : "all lines are either straight
or crooked”; “human beings are either male or female." But this mode
of expression is ambiguous. The judgments said to be disjunct are not
“all lines are straight-all lines are crooked”; as, for instance, in the
judgment " the human race is descended from one pair or from several,"
where the disjunction is between the propositions “the human race is
descended from one pair,” and “the human race is descended from
several pairs.” In the former instance the disjunction applies to each
particular line; so that here again, if we would avoid ambiguity, we
must make use of the hypothetical form "anything which is a line, is
either straight or crooked.”
8. These disjunctions have for their members the more exact determin-
ations of the subject, and may therefore be reduced to divisive judgments
which divide the subject-concept into its species. From them we must
distinguish judgments which unfold the different possibilities in the predi-
cate of a given subject.1 When we say that the planets either shine by
their own light or derive their light from the sun, we do not mean that
the fact of being a planet includes both possibilities, and that some shine
by their own light, while others are illuminated by the sun. What we
really do is to start from the judgment “the planets shine,” and to inves-
tigate the exact nature of their light and the possibility of finding an
explanation amongst the given circumstances. Take the proposition "the
world has either existed from eternity, or has had a beginning; and its
beginning was due either to a free cause or to blind necessity.” In the
first disjunction we start from the existence of the world as datum, and
enquire as to the duration of this existence; in the second, our datum is
the beginning of the world from a cause, and our enquiry concerns the
different kinds of causes. When we say “he is either a hypocrite or a
fool,” it is presupposed that he behaves unreasonably, and the question is,
as to the source of this behaviour. A further distinction may be made
according as the closer determinations of the predicate form a part of its
meaning, or are gained from a consideration of the concrete possibilities
of the particular instance.
1 Trendelenburg's doctrine that the disjunctive judgment is a statement of the exten-
to changeable states, and it is not applicable in this sense when the concept of which the
possible determinations are developed is predicate. Cf. my Programm, pp. 60, 61.
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LOGIC
9. Judgments such as “either the wicked will be punished, or there is
no divine justice,” are grounded upon hypothetical judgments, and are
governed by the principle that the denial of the consequent involves the
denial of the ground, taken together with the principle of excluded
middle. If there is a divine justice the wicked will be punished-either
the wicked will be punished or not—if not, the supposed ground of their
punishment cannot exist.
10. It is of course true that the disjunctive judgment “ A is either B
or C,” may be resolved into two hypotheticals “if A is not B, it is C”
and “if A is B, it is not c”; but it does not follow from this that the
disjunctive judgment has no importance of its own independently of the
hypothetical judgment. We cannot state a negation as the ground of an
affirmation, unless the disjunction has already been established. The
judgment that if light is not matter it is motion, cannot precede the know-
ledge that light is either matter or motion.
II. It follows from the nature of the statement contained in the
disjunctive judgment that the propositions “ A is either B or C-
A may be either B or C—A must be either B or C,” are all exactly
equivalent.
§ 38.
RESULTS.
THE FUNCTION OF JUDGMENT is always the same in so far as it always
states categorically that a predicate belongs to a subject. The differences
which we find depend partly upon whether the synthesis between subject
and predicate is simple, as in the denominative judgment; or complex as
in judgments governed by the categories of attribute,' activity and relation.
Partly, again, upon whether the subject of a judgment is a simple idea,
or is itself a synthesis of the nature of judgment, or a combination of
such syntheses of which we may predicate that it is false, possible,
necessary, etc.
The distinctions generally made are based upon differences of predicates
and subjects, and not upon differences in the function of judgment; any
real variations in function are to be found in one class alone, that of
categorical judgments.
For this reason the importance of the predicates presupposed in all
judgment becomes more evident; to recognise these as remaining the
HYPOTHETICAL AND DISJUNCTIVE JUDGMENTS 233
same throughout changing subjects is the essential characteristic of
judgment.
1. So far our investigation has shown that the customary classification
of judgments, which has been established mainly by the authority of
Kant, is inadequate.
The basis and presupposition of all judgment is the judgment which
is immediate, simple and positive; and this consists in the synthesis of
a subject and predicate accompanied by the consciousness of objective
validity. The meaning of this synthesis and of its objective validity
depends upon the nature of the ideas connected in the judgment; it is
simple when the act is merely one of denomination, complex when it is
grounded upon the categories of attribute, activity and relation. That
which takes place in judgment is always the recognition of the agreement
between an idea previously known and one element of the subject; and,
according to the original meaning of “to know,” every judgment is the
cognition and recognition of something in the subject which is already
known. But it does not follow that every judgment consists only in this
knowledge, and is nothing more than the statement of a subsumption.
In one class of judgments it is just as indispensable that there should
also be present the consciousness of unity between attribute or activity
and thing, or the consciousness of relation between two things; and sub-
sumption cannot take place in judgments concerning attributes, activities,
and relations without the differentiation and synthesis of different elements
in a presentation.
Even the judgments which have numerical determinations for their
predicates show no essentially different function. It is not peculiar to
the numerical judgment that it must have been preceded by other judg-
ments; every judgment which refers to the particular, and names it by
the subject-term presupposes a previous judgment. All that is peculiar
to numerical predicates is the nature of the preliminary operations which
they necessitate, just as other relational predicates necessitate preliminary
operations appropriate to their peculiar nature-e.g. equality and inequality
presuppose measurement; the number given is compared with a number
previously known.
2. But the course of thought extends beyond immediate knowledge,
and leads us to think of judgments which might take place as distinct from
actual judgments. Then new judgments arise having reference to these
ideas of judgments or to the relations between them.
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LOGIC
Every statement contains the judgment that the synthesis expressed by
it is necessary or true, and in the negation this judgment is contradicted
by the statement that the synthesis is false. Besides this affirmative or
negative decision, we find on the one hand the judgment that a hypothesis
is possible--i.e. that it is not subjectively necessary either to affirm or to
deny it; on the other, the judgment that it is the necessary consequence of
another hypothesis, or that amongst a number of given hypotheses one
must necessarily be true.
These judgments all resemble simple judgments in that they state simple
modal predicates concerning a subject; their peculiarity lies, therefore,
not in the synthesis, but in the nature of their subjects and predicates.
Since, however, these subjects form an essential element of the function of
judgment, and since the predicates refer to just that characteristic of the
function which expresses its relation to the final aim of all serious thought,
such judgments are in an eminent degree logical. Indeed, there could be
no conscious judgment at all unless some account were taken of this re-
lation between the originally subjective combination of subject and predi-
cate and these modal determinations. We are therefore justified in giving
special attention to negative, hypothetical and disjunctive judgments; not
because they are special kinds of the judgment, but because they have
reference to hypotheses and to their logical value and significance.
Thus there is really only one sort of judgment, the categorical statement
that a predicate belongs to a subject. If any distinction at all is made
between the Form and the MATTER of the judgment, then by form we
must mean that mode of activity in thought through which a judgment as
such is formed; and this mode of activity is in all cases essentially the
same. The diversity which is generally represented as attaching to the
forms of judgment is really a diversity of matter, and depends upon the
nature of subjects or predicates. As this nature varies, we certainly find a
modification, sometimes in the movement of thought which precedes the
judgment, sometimes in the meaning of the predication-that is, in the
meaning of that unity between subject and predicate which is the thought
present in all judgments. The conventional doctrine of the different
“ forms” of judgment (due in part to the importance generally attached
to the verbal expression) loses sight of the one idea which is the sole
reason why we give the name of judgment to all the different kinds.
All judgment, therefore, presupposes first of all the presence of a
number of predicate-ideas which may be recognised in the subjects. It
HYPOTHETICAL AND DISJUNCTIVE JUDGMENTS 235
requires, moreover, that we should have ideas of different kinds of synthesis
between subject and predicate; these differences being determined by the
nature of the subjects and predicates, and constituting the meaning of the
simple statement that the predicate belongs to the subject.
If, however, we still continue to denote the resulting kinds of synthesis
as “forms” of judgment, it is after all a question as to the use of language.
But in so doing we must guard against thinking that the name "judgment”
denotes a number of originally different and co-ordinate acts of thought,-
a mistake which is constantly made when affirmative and negative judg-
ments are distinguished as opposite forms. Unless we do so we are in
danger of losing sight of the one concept which should correspond to the
term, and the term itself becomes a mere homonym.
PART II.
REGULATIVE.
237
INTRODUCTION.
$ 39.
In order that the function of judgment may actually succeed in attaining
to certain and universally valid judgments, it is before all necessary that
the certainty of the particular judgment in question should be invariable,
and accompanied by the consciousness of its universal validity. Two
conditions are essential to this. In the first place the person judging must
be conscious of the logical ground of his judgment; and secondly, the
elements of the judgment itself must be completely determined and con-
stant, and thought by every one in the same way.
For the latter condition to be fulfilled it is necessary that the elements
of our judgments, and more especially their predicates, should be logically
perfect concepts ; for the former, that the judgments themselves should
be grounded in accordance with universally valid and necessary laws of
thought.
1. In Part I. we have taken thought as we actually find it, and have
analyzed the function of judgment in which it always manifests itself when
aiming at truth and universal validity. We have sought to show the
meaning and significance of the judgment in all its relations, and we have
found that one essential element of every statement is its claim to be true,
i.e. necessary and therefore valid for all thinking beings.
We must now test this claim, and investigate the conditions under
which judgment attains its end. The conditions, that is, under which the
momentary certainty which accompanies every actual judgment involves
no delusion, but is the expression of objective necessity; and under which
the universal validity of the individual act of judgment is guaranteed.
2. In order that a judgment may be perfect, it is necessary in the first
place that it should remain unaltered for the person who judges; that he
should always repeat it in just the same way whenever the same subjects
and predicates recur; and that its certainty should therefore also be in-
variable. If the same synthesis were for him at one time certain, at
239
240
LOGIC
anothei uncertain ; if the same subjects and predicates were not always
connected in the same way within the limits of one and the same con-
sciousness ; if I thought it possible that, starting from the same data I
might judge otherwise in the future than I now do—then the act of judg-
ment must have failed, for its success involves confidence in the irre-
fragable validity of the judgment.
But the certainty that a judgment is permanent, that the synthesis is
irrevocable, that I shall always say the same,--this certainty can only be
forthcoming when it is known to depend, not upon momentary psycho-
logical motives, which vary as time goes on, but upon something which is
immutably the same every time I think and is unaffected by any change.
This something is, on the one hand, my self-consciousness itself, the cer-
tainty that I am I, the same person who now thinks and who thought
before, who thinks both one thing and another. On the other hand, it is
that about which I judge, my thought itself as far as regards its unvariable
content, which I recognise as identical each time, and which is quite in-
dependent of the state of mind of the individual thinker.
The certainty that I am and think is final and fundamental, the con-
dition of all thought and all certainty whatever. Here there can be none
but immediate and self-evident certainty ; we cannot even say that it is
necessary, for it is prior to all necessity. In the same way the certainty
of my consciousness that I think this or that is immediate and self-evident;
it is inextricably interwoven with my self-consciousness; the one involves
the other.
If now we can say that there is a necessity which obliges me to judge of
an idea in one particular way so soon as I am aware of it; if I can know
that as surely as I am I, I must connect subject and predicate in this way,
for no other reason than that I have thought of them, then my discernment
of this necessity is the ground of certainty for every judgment. This con-
stitutes my consciousness of its logical ground, and a connection is thus
established between the judgment and my self-consciousness itself ; I know
that so surely as I myself continue the same I must always repeat the judg-
ment in the same way.
This then is the first condition: for a judgment to be perfect the person
judging must be conscious of its logical ground.
3. What conditions must be fulfilled in order that we may attain to this
consciousness?
If an A of which I am conscious is to be the ground which makes a
INTRODUCTION
241
74
judgment B logically necessary, then this necessity must rest upon a con-
stant law, according to which B always and invariably follows from A;
and only in so far is the necessity knowable; the presence of A however
is pure matter of fact, without which the necessity cannot take effect.
Thus the consciousness of the ground resolves itself into consciousness of
the law according to which В follows from its premises, and consciousness
of these premises.
It may be that these premises are not themselves judgments, but objects
of consciousness of another kind, of which nothing more is known than
that they are at the moment present; such as sensations, reproduced ideas
of all kinds, or concepts which are present to consciousness. Thus so far
as concerns logical necessity we have arrived at an ultimate fact which
must be regarded as pure matter of fact; all we can ask is : what is its
necessary consequence? The judgment that the diameters of a circle are
equal is based upon our concept of a circle ; this concept however, or the
intuition which gave rise to it, is in the last instance matter of fact. No
universal logical necessity can be shown why this geometrical image should
appear in my consciousness at all, either from intuition of external objects,
or as the result of inventive construction. Every judgment of perception
includes amongst its premises the immediate consciousness of a sensation,
and this again is purely matter of fact. It is true that the question may
be raised as to whether its conditions are normal, and whether, therefore,
it justifies a judgment concerning the existent—i.e. it may be asked what
necessary and universally valid inference can be drawn from the simple
act of a subjective sensation. But that the sensation is there has nothing
to do with logical necessity, we know it by our immediate consciousness of
a simple fact.
When, on the other hand, the premises are themselves judgments, then
the consciousness of necessity resolves itself into the consciousness of the
laws according to which from certain judgments other judgments follow
(i.e. the rules of inference), and the consciousness of the validity of the
premises. Here again the same conditions apply; we must be conscious
of the grounds of these judgments. No judgments are exempt from these
conditions unless their certainty is so self-evident that it must be regarded
as immediate matter of fact, no less than the “I think," or the presence of
definite ideas; the certainty of these judgments cannot be further analysed
by a consciousness of their necessity. To them we must add the judg-
ments whose contents constitute the fundamental laws of all necessity,
S. L.
0
S
242
LOGIC
according to which anything is necessary, and the validity of which there-
fore cannot be seen to follow necessarily from some other judgment, but
can only be recognised—judgments, that is, which are as necessary as the
proposition “I am” itself, or which can be shown to have a certainty which
is necessarily involved in the certainty of this proposition.
Thus no logic which is to lay down rules for thought is possible unless
such ultimate laws can be known by us, and shown to be absolutely cer-
tain and self-evident. Our first task is not to trace the inexhaustible
phenomena of matter of fact and of individual experience which constitute
the given premises of our judgments in particular cases, but to lay
down the laws according to which certain ideas and judgments make other
judgments logically necessary, and constitute a ground for their certainty.
This involves what we have already claimed as a postulate in the Intro-
duction, $ 3: that we are able to distinguish objectively necessary thought
by the evident certainty with which it manifests itself, and by analysing the
conditions of this certainty to discover such universal laws. Our success
in carrying out this task must show whether or not there is any ground
for the postulate.
4. In order that a judgment may be always valid and immutably cer-
tain, other conditions must be fulfilled which apply to an earlier stage in
thought, and are not fulfilled in its natural course. The ideas denoted by
subject and predicate terms must be constant and completely determined.
The consciousness of the identity of a judgment attaches in the first
instance to its verbal expression, to the fact that the same statement is
made about the same thing in words, and the predicate must always have
this verbal expression, the subject at least in explicative and universal
judgments. Unless every word always keeps exactly the same meaning,
the meaning being thus perfectly definite and fixed, we cannot possibly be
certain that the repetition of the same proposition is also the repetition of
the same judgment, and the meaning of the judgment itself becomes
uncertain. Indeed, the very act of judgment tends to bring about this
confusion by a sort of shifting amongst our predicate ideas, for on ordinary
occasions we are often guided by what is no more than a vague similarity
between the new and the familiar (see 7, 8, p. 44). When the Marco-
manni mistook the lions which were let loose upon them by Marcus
Aurelius for dogs, and slew them without ceremony, their judgment " these
are dogs” meant only that the lions were more like dogs than any other
animals known to them. Even while they were judging, their idea of the
INTRODUCTION
2:43
dog and the meaning of the word was changed, and a new image com-
prised in it.
Again, although the necessity of judgments is a sufficient guarantee for
their universal validity, this only means that every one who starts from the
same premises must synthesize in the same way. But if the primary data,
the ideal elements between which the synthesis takes place, were different
for every individual and absolutely incommensurable, so that every one
connected a different meaning with a given word, then, however small the
difference, our judgments would never actually attain to universal validity,
they would at the most approximate thereto. That community of thought
which we endeavour to reach by means of language, and which is the
condition of higher mental development, more especially of all science,
would never be fully realized.
We saw, in $ 7, that in the natural course of thought the ideas of the
individual are not constant nor completely determined, and that different
individuals do not have the same ideas nor denote them by the same
words. On the contrary, the very laws which govern the natural formation
of ideas necessitate both their variability in the individual and their
difference in different individuals, thus prohibiting a completely fixed
verbal signification.
Hence we cannot speak of the complete logical certainty of a judgment
nor of its invariable validity unless we assume that whenever a judgment
seems to be the same as another, because clothed in the same language, it
is really the same; that the same statement is made about the same
subject. And before we can say that any given judgment is universally
valid-in concreto, therefore, comprehensible and convincing for all-we
must assume that the ideas contained in it are common to all and the
same for all. The anarchy of natural thought is completely excluded by
the ideal of perfect thought, and a logic which is to contain the rules of
perfect thought must begin by determining what are the conditions to be
fulfilled by ideas themselves as elements of the judgment.
5. This brings us to the two main problems of this part of our
work.
(a) The conditions upon which perfect judgments are possible are, that
the ideas which enter into the judgment as subject or predicate should be
absolutely constant, completely determined, the same for every one, and
denoted by unambiguous terms. An idea which fulfils these conditions
we call a concept in the logical sense of the word. One part of our task,
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LOGIC
therefore, will be to investigate the conditions necessary in order that our
ideas may be logical concepts.
(6) The condition of the logical necessity and universal validity of judg-
ments is that they should have a ground. A second investigation must
therefore discover the rules according to which a judgment follows
necessarily from its premises.
One part of this investigation will be concerned with the laws according
to which immediate judgments find their ground in the ideas of which they
are composed; the other part with the laws according to which mediated
judgments are grounded upon other judgments.
CHAPTER I.
THE CONCEPT.
$ 40.
THE LOGICAL CONCEPT differs from the general idea which has developed
in the natural course of thought, and is denoted by a word, in its constancy,
in the completeness and immutability of its determination, and in the
certainty that every one will employ the same term to denote it. It differs
from the concept in its metaphysical meaning as the adequate thought
of the essence of an object in that its only aim is the complete determina-
tion of our predicate ideas, and this aim has no direct connection with
the question as to whether the concept corresponds to any real object,
or whether it adequately represents such an object. The quality of
generality it has in common with every idea. It is the fact that it is
strictly defined, and clearly distinguished from all other ideas, which
forms the distinguishing characteristic of the concept, and in the construc-
tion of logical concepts our aim is to establish one mode of arranging
their manifold ideal contents for all thinking beings, and so to com-
plete systematically the process which begins without conscious purpose
in language.
1. In speaking of “concepts," we must distinguish three meanings of
the word. It may denote a natural psychological production, and here
it is the simple correlative of the "term" as used in ordinary natural
language. It is the idea at the stage where it has become a mental
possession, and has gained the generality explained in § 7, which belongs
to every idea as such. It is now qualified to become an element of the
judgment, more especially a predicate. Such ideas, as we have already
seen, are different for different people, and are still in the process of
formation ; even for the individual himself they change, so that a word
does not always keep the same meaning even for the same person.
Strictly speaking, it is only by a fiction which neglects individual
245
246
LOGIC
.
(D
peculiarities that we can speak of the concepts denoted by the terms
used in ordinary language.
2. In contrast with this empirical meaning the concept may be
viewed as an ideal : it is then the mark at which we aim in our endeavour
to attain knowledge, for we seek to find in it an adequate copy of the essence
of things. The concept in this sense must enable us to penetrate into
the very heart of the thing, to understand it ; i.e., to see that its particular
determinations as connected in it are the necessary consequence of its
nature as a unity. The concept of life, in this sense, would be the key-
stone to physiology ; that of matter, to chemistry and physics ; that of
mind, to psychology; and all knowledge in this direction would be
complete when we could exhibit a system of concepts comprising the true
counterpart of every existing thing. When we try to think of an absolute
and divine knowledge, we define it by saying that in the absolute intelli-
gence, concept and being are one. In this sense we may indeed speak
of the truth of our concepts; they are true when they are in themselves
the exhaustive expression of the nature of things. The true concept of
God would comprise in its determinations the thought of the real nature
of God in all its aspects.
3. Between these two meanings of the word, which may be called the
empirical and the metaphysical, there lies the logical, which alone concerns
us here. This has its origin in the logical demand for certainty and
universal validity in our judgments. All that is required is, that our ideas
should be absolutely fixed and determined, and that all who make use
of the same system of denotation should have the same ideas. In what
relation our thought stands to the existent, and whether there is absolute
agreement or not, is not determined here—or at least not directly. We
must indeed suppose that as knowledge is always growing, less is con-
tained in our ideas at any given time than in the existent; at the best
our ideas are representations which correspond to the existent so far as
they go, they are never exhaustive. If our judgments could never be
universally valid unless their elements were perfect concepts in the
metaphysical sense, and if it were as difficult to get rid of individual
differences and indefiniteness in our ideas as it is to overcome their
inadequacy to the existent, then we should be debarred even from
approximating to the goal of knowledge by the gradual progress of science,
for science always presupposes uniformity in the construction of concepts.
It is necessary, therefore, to distinguish between the formal sufficiency
0
THE CONCEPT
247
0
of concepts for the purpose of judgment, and their metaphysical
adequacy; and we must assume that it is at least possible to attain the
former before the latter has been reached.
4. Finally, we must distinguish between the logical perfection of the
concept and the appropriateness of its construction to some end, the
latter being connected with the problems of classification within some
given sphere of things (objects, actions, crimes, etc.). A concept may be
completely determined, and hence logically perfect, and yet not so well
adapted as some other to meet the requirements of science. For the
aim of science is to attain, by means of concepts and the terms which
denote them, the greatest possible simplicity and brevity in our know-
ledge; and it therefore asks, “How must our concepts be formed to
enable us to give the simplest expression to the most important and
comprehensive universal judgments ?” By this aim we must be guided
in methodology, which has its origin in the problems arising out of the
nature of the conditions of our knowledge.
On the other hand, if we are really to attain logical perfection in our
judgments, it is necessary that we should always have a sufficient supply
of logically perfect concepts to enable us to express and determine every-
thing which becomes subject to our judgment. In judging we do not
merely repeat what is already known; we are constantly appropriating
something new. In this sense the possibility of perfect judgments is
determined by the extent to which the raw material of all human ideas
has taken permanent form in concepts. We must always be prepared
with concepts in which to express our knowledge; or we must at least be
sure of being able to create them from elements which are already
conceptually determined. We may compare this ideal with that of a
universal alphabet which comprises generally accepted signs for all the
distinguishable simple sounds possible to the human organs of speech.
From this point of view Leibnitz's idea of the characteristica universalis
was a most appropriate expression for that at which we should aim in the
logical construction of concepts. 1
1 Cf. Trendelenburg : “Ueber Leibnizens Entwurf einer allgemeinen Charakteristik.”
Histor. Beiträge zur Phil., iii. p. I sq. And Descartes, Ep., I, III, where a similar
thought is developed : “ Ejusmodi linguæ inventio a vera Philosophia pendet. Absque
illa enim impossibile est omnes hominum cogitationes enumerare, aut ordine digerere ;
imo neque illas distinguere, ita ut perspicuæ sint et simplices ... Et si quis clare
explicuisset, quales sint ideæ illæ simplices, quæ in hominum imaginatione versantur,
et ex quibus componitur quidquid illi cogitant, essetque hoc per universum orbem
receptum, auderem demum sperare linguam aliquam universalem,” etc.
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LOGIC
5. The essential characteristic of the concept is generally said to be its
generality.1 Connected with this is the doctrine that concepts are gained
by abstraction, i.e., by a process which separates the common characteris-
tics of particular objects from those by which they are distinguished from
each other, and gathers together the former into a unity. But the sup-
porters of this view forget that, in order to resolve an object of thought
into its particular characteristics, judgments are necessary which have for
their predicates general ideas (or, as they are commonly called, concepts),
and as these concepts make the process of abstraction possible, they must
have been originally obtained in some other way. They forget, moreover,
that the process presupposes that the series of objects to be compared is
already in some way determined, and a tacit assumption is made of some
motive by reason of which we group together just these objects, and seek
their common elements. If we are guided by any motive, and not by
mere caprice, it must be found ultimately in the fact that the objects are
from the first recognised as similar, because containing certain elements
common to all ; that is, a general idea is already there, by means of which
these objects are selected from amongst all others. There is only one
connection in which the doctrine of the construction of concepts by com-
parison and abstraction is at all appropriate, and that is when we elucidate
the actual meaning of a word by enumerating the common characteristics
of the things which, as a matter of fact, are always denoted by the
word. In explaining the concept of animal, gas, theft, etc., we might
See Kant in the Transcendental Æsthetic, § 2, 4. Every concept must be thought
of as an idea which is contained in an infinite number of different possible ideas (as the
element common to all), and therefore as comprising these ideas under it.
2 Drobisch is quite consistent in admitting that this selection is arbitrary (Logik, edn.
3, § 18, p. 20). It is in itself a completely arbitrary matter what objects we choose to
compare with each other; we may compare a raspberry cane with a bramble, but we may
also compare it with a penkniſe or a turtle. When, however, the Linnean system, which
classifies together widely different plants, is cited as an example of this “far-fetched
comparisons,” it is overlooked that the concepts by which the Linnean classes are deter-
mined are not due to this simple and direct method of comparison. In this method it is
the common element of objects which are chosen at random which is selected, while the
Linnean classes, on the contrary, are the result of an endeavour to find simple distin-
guishing characteristics whereby to divide into definite groups the incalculable varieties
of plants. First it was seen that plants differ in the number of stamens, etc. ; then
followed the methodical grouping together of those which agree on these points. Of
course, this distinction was itself based upon a comparison in the wider sense, but it was
first employed to discover differences, and not the common element, of the objects com-
pared. (The last two sentences refer to the contrary view expressed by Drobisch,
edn. 5, p. 21.)
THE CONCEPT
249
attempt to select the common characteristics of all the things gene-
rally called “animals," or of all the bodies called “gas," or of all the
actions called “theft.” i Whether or not we should succeed, whether it
is possible to carry out such a recipe for the construction of a concept
--that is another question. There might be some chance of success
if we could assume that there is never any doubt as to what we ought
to call animal, gas, theft, etc. ; if, that is, we already possessed the
way is to look for the spectacles we are wearing by the aid of the spec-
tacles themselves.
6. Nevertheless, there is some truth in this doctrine. So far as con-
cerns the generality of the concept, we may find it first in the fact that as
a rule logical concepts merely complete ideas which have arisen naturally;
they do not supersede them ; we cannot change the nature of ideation,
a natural development. Now every idea naturally possesses generality,
inasmuch as it is detached from the original particular intuition or par-
ticular function, and has been made our own as a reproducible object;
nor can any arbitrary action on our part deprive the idea of this natural
generality. But this generality in no way depends upon whether an idea
has been formed from one intuition, or from many similar or dissimilar
intuitions ($ 7); all that we learn from it is, that the idea—as Kant
guardedly expresses it-is contained in an infinite number of possible ideas.
1 The Socratic method of determining concepts is in the main the same as this. It
always starts by assuming that definite concepts correspond to the current meanings of
words, and it proceeds to find the right explanation of the word by comparing particular
examples of that which it denotes, and contrasting with these examples of that which it
does not denote. The only difference is that Socrates does not aim at surveying every
particular thing, but contents himself with a few examples. To the present day the
doctrine of the concept is really based upon this Socratic method of always presupposing
that there must be concepts corresponding to words; and to this method is due the
general failure to distinguish between the concept of psychology and the concept of
logic. The method finds its justification and importance in the fact that in language as
customarily named by certain words, and as we come gradually to understand a word,
the idea of a number of particular objects is connected with it before we are conscious of
its general meaning as such. A typical instance of this is to be found in the answer of
Theætetus to the question: What is érrlotņun ?-it is mathematics, etc. Children and
those without scientific training will always answer by giving an instance instead of a
definition. The primary service rendered by the Socratic method was that it pointed out
the meaning of the word as such, that meaning upon which particular acts of naming
are based.
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LOGIC
Whether or not it is contained in many actual ideas, is immaterial to the
nature of the idea or concept, and it makes no difference whether it has
been derived from one or from many.
But we may find a further justification for the importance attached to
the generality of the concept in the fact that it necessitates a complete
separation of the meaning of the word from particular intuitions, thus
securing for the judgment a clear and definite meaning, and substituting for
a vague comparison a real statement of unity between subject and predicate.
When we see a palm for the first time, and call it a tree, we are led to do so
by its general similarity to the firs and beeches, which we know, and the
images of which are connected with the word “tree," although we may not
have noticed exactly wherein the similarity consists. “The palm is a
tree" is not strictly justified as a proper judgment unless the word "tree"
means nothing but what the palm has in common with firs, beeches, etc.,
then only can we take the judgment in its strict and proper sense, “I find
in the palm everything which is contained in my thought of the tree,”
instead of the vague and inaccurate meaning, “The palm is like a tree.”
This process certainly involves a conscious selection of all the characteris-
tics common to the objects which I call trees. But the chief object of
the selection is not to find a general idea comprising the particular; it is
to obtain a firm grasp of the general idea which is already indefinitely and
confusedly contained in the thought of the particular, and, by sharply
defining it, to give a definite meaning to the judgment, thus completing a
process which always begins unconsciously. The involuntary action of
psychological laws is sufficient to give rise to generic images formed from
manifold similar intuitions, the differences of the particular images being
lost sight of, and leaving shifting schemata to correspond to our words.
Thus we do, no doubt, drop the distinguishing elements, and retain those
which are common, but the process is incomplete because it is not
grounded upon any conscious comparison and distinction of the parti-
cular characteristics. To supplement this process is the aim of conscious
comparisons (S 7, 11, p. 47). It is true again that in the involuntary
formation of our ideas we find what alone should be called abstraction,
the abstraction which separates. It is by means of this that we break up
the undivided whole of intuition into thing, attribute, and activity, and
that by detaching them from this unity we form those abstract ideas
which enable us to compare different things, finding them alike in some
respects, different in others, and which alone can supply predicates for the
THE CONCEPT
251
judgments in which conscious comparison and distinction take place. It
is true, also, that a comparison of partially resembling objects taking place
under these conditions may become the more or less fortuitous occasion
for the formation of new concepts." If visible objects always presented the
same cornbination of colour and forni, we should have much more
difficulty in constructing separate ideas of colour and form—that is, in
abstracting them from the given whole; but a conscious comparison of red
things as to their colour is only possible after such an abstraction has
taken place, or, at least, simultaneously with it. A comparison of the
horse, the dog, and the lizard, may perchance lead us to form the concept
of four-footed animal, if we happen to be struck by their similarity in
having four feet (though more probably we should proceed by differentia-
tion, finding that quadrupeds differed from men and birds, beetles and
flies, on the one hand, and from snakes and snails on the other); and
many generalizations arise in this way. But the processes, when thus
carried out, are not the result of intentional skill, nor is their product such
as to satisfy logical requirements. The characteristics found upon com-
parison to agree are always subject, when selected in this casual way, to
that natural indefiniteness and absence of limitation which arises from the
elasticity of our ideas and their tendency to annex what is similar to them-
selves and place it under the same denotation ; and the whole process
lacks a solid basis when the characteristics which form the predicates of
judgments of comparison are not themselves perfectly definite and deter-
mined by every one in the same way. It is one of the chief failures of
the ordinary doctrine of the concept that it proceeds as if these
characteristics were given ready made, and such as to need no further
elaboration. Really, the enormous difficulty of passing beyond the
natural state in which every one speaks his own language consists much
less in the processes of comparison itself than in establishing accurate
and generally accepted standards of comparison ; i.e., the difficulty is to
determine conceptually the attributes which are to be used as charac-
teristics.
7. The logically perfect idea is distinguished from the idea which has
developed naturally and is the basis of ordinary speech by the fact that
in it the natural tendency of ideas to expand in the process of formation
has been counteracted by an activity which negates and limits, and thus
gives form and consistency. If we disregard for the moment the demand
that ideas should be the same for all, we may say that the essential char-
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LOGIC
acteristic of the concept is the constancy and complete distinction of the
ideal content which is denoted by any given term.
This constancy presupposes that a definite ideal content and its appro-
priate verbal sign have been consciously fixed by us in order that we may
always be able to reproduce it as the same, and be conscious every time
of its strict identity. Complete distinction requires a comprehensive
survey, in the first place, of those objects which most resemble each other
and are most liable to confusion, and further of the whole range of the
possible objects of our ideas. It depends also upon conscious acts by
which we become aware of the differences between the ideas A, B, C, D,
etc., retaining as clear an idea of the intervals between them as of the
determinations themselves. This act, which first makes us expressly,
conscious of the identity of the same content by its negation of a
different one, aids and completes the determination of our ideas,? while
at the same time we are enabled to arrange them according to the degrees
of difference.
8. Suppose that all the ideas which we have occasion in the course of
thought to consider and manipulate as units, and which are destined to
become elements of judgments, were capable of being produced by an
indivisible act, either of intuition or of relating thought; suppose, further,
that the objects of which we form ideas were limited in number and easily
surveyed, with such marked differences between them that we should be as
conscious of the transition in passing from one to the other as in passing
1 The view that an idea owes its first determination to distinction overlooks the fact
that distinction itself is only possible when different ideas are present, and that dis-
tinction does not therefore create the contents which are different. Ulrici, for instance
(Compendium der Logik, edn. 2, p. 60), says, “Red is the particular colour we call red
only because, being red, it cannot also be blue, yellow, etc.—without its difference from
blue, etc., it would be quite indefinite, mere colour-in general, an absolutely indeter-
minate quality of which we should know nothing because, as we have shown, we are
aware of colour as colour only by means of distinctions in colour.” This I cannot allow.
The sensation of red-more accurately, of a particular shade of red—is a positive datum
with a content peculiar to itself, and it would continue to be so even though it should be
accompanied by the sensations of fewer colours than are perceived by all normal eyes.
Colour sensations are not less definitely determined for any one because it may happen
that many colours have never been seen by him at all. The variety of his colour sen-
sations would be the smaller, and he would have a poorer supply of ideas, but that
would be all; no doubt to any one feeling red only, red would mean the same as colour
in general, but this is only equivalent to saying that the idea colour would comprise no
plurality of distinguishable qualities, not that it would be absolutely indefinite. The con-
ditions which enable us to retain a plurality of sensations in consciousness are not those
upon which the definiteness of particular sensations depends ; on the contrary, this de-
finiteness is rather presupposed by such ability. Cf. Lotze, Logik, edn. 2, p. 26.
THE CONCEPT
253
from one to two, from two to three, then the logical task of constructing
concepts would come to an end with the functions we have mentioned
and with the establishment of a generally accepted system of names; no
more would be needed but a memory able to retain what had been gained
from the general survey. If, for instance, our world of ideas were limited
to the twelve simple notes of the octave, then everything necessary to give
the definiteness of concepts to our ideas would be that we should re-
member each particular note and distinguish it from the others with
sufficient certainty to guard against confusion. The ideas of the particular
notes and the consciousness of their differences would yield us the whole
material for our concepts arranged in a fixed order.
But both assumptions are incorrect. The first, because the ideas which
we treat as units and denote by one term can generally be resolved into a
plurality of distinguishable elements; they prove to be products com-
pounded from simpler ideas which the mind can grasp by themselves.
This makes them more difficult to retain in thought, for in a compound
idea both the particular elements and the manner of their composition
must be retained; while, on the other hand, the difficulties of distinguishing
are greater and more special in nature, inasmuch as a compound idea may
resemble another in some of its elements and differ from it in others.
When, for instance, I try to keep before my mind the idea of a horse, I
can do it only by a process of mental construction, piecing together the
parts of the figure in a given manner; when, again, I wish to distinguish
it from some other idea, such as that of the donkey, I find that while
it agrees with it in most respects it is distinctly different only in a
few.
The second assumption is also incorrect. Throughout the materials
collected in memory we come upon numbers of imperceptible differences
which obliterate the marked intervals for which we look when trying to
give definite form to our ideas. This continuity, moreover, applies to
the simpler elements of our ideas as well as to compound images. In the
sphere of colours, red passes by imperceptible degrees through violet into
blue, through orange into yellow, through pink into white, through dark
red into brown. A similar continuity is found in the sphere of spatial
magnitudes and forms, and hence there arises such an unlimited number
of scarcely distinguishable objects that it is impossible to differentiate them
and to retain them in their differences. It is the same with intuitable
things themselves. Intermediate terms intervene everywhere as know-
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LOGIC
ledge extends between objects which were at first sharply distinguished;
between snow and hail, tree and shrub, horse and ass, negro and
European.
§ 41.
Since the greater number of our ideas are composite—.e., have their
origin in distinguishable acts—we cannot determine their content except
by a conscious determination of their elements (characteristics, or com-
ponent ideas) and of their manner of synthesis. Thus the conceptual
determination of the content of an idea presupposes first of all its analysis
into simpler and unanalysable elements, the same analysis determining
also the form of their synthesis.
This analysis could not be completely carried out unless based upon a
perfect knowledge of the laws which govern the formation of ideas, and
such a knowledge alone could assure us that the elernents were the same
for all thinking beings. But our analysis can never arrive at elements
which are completely isolated as products of independent functions ; it
always ends in a system of connected functions which are related to
each other, and which comprise the various forms in which the manifold
is synthesized. The functions by which we think the logical categories
(unity, identity, difference) are connected with the spatial and temporal
forms of intuition; and when referring to that which is thought of as
existing both are connected with the real categories (thing, attribute,
activity, relation); and all are again connected with the intuitively given
contents of immediate inner or sense perception. The perfection of our
ideas as concepts presupposes a complete system of these elements.
As we have in intuition an unlimited multiplicity of ideas which are
separated by imperceptible differences, our conceptual determination of
them must be limited to establishing definite boundaries within the gradual
fusion of differences.
1. The problem to which the first of the facts mentioned in $ 40, 8—
the composite nature of ideal objects-gives rise was familiar to the tradi-
tional logic. Here we are taught that the thought which is contained in
a single idea and denoted by one term must be defined by its charac-
teristics, that a concept must be resolved into its component ideas or
concepts. These are thought in the concept and form its content. Thus
the characteristics heavy, yellow, bright, metallic, etc., are thought in the
THE CONCEPT
255
concept gold; the attributes bounded, four-sided, equilateral, rectangular,
plane surface in the concept square ; and in the concept murder the
illegal, intentional, deliberate slaughter of a human being. This content is
represented as the sum or product of the particular characteristics. It is
generally held, moreover, that this analysis into characteristics solves also
the further problem of distinction, these characteristics constituting just
that whereby different ideas are distinguished. 1
The question as to how it is possible to distinguish different charac-
teristics in the totality of an idea is generally treated as if it were already
settled, and were evident from the examples cited. Attention has been
repeatedly called-especially by Trendelenburg—to the need of a more
exact determination of the relation between the characteristics. Are they
all homogeneous? and if not, how do they differ? are they indifferent to
each other, or are they mutually dependent ? and finally, in what relation
do the component parts stand to the whole ? For in borrowing terms
from spatial or temporal relations, and speaking of concepts or ideas as
component parts, we are only using figurative language. We do not mean
that the component ideas are ideas of the parts of a whole (as head, neck,
trunk, are ideas of parts of an animal), standing in the same relation to
the idea of the whole as the parts do to the whole ; we mean that they
are elements of the idea in the same way that the particular attributes are
of a thing
2. We cannot analyse a given idea into its parts or characteristics
unless it has been in the first instance developed by means of distinguish-
able functions out of different elements. If the idea was originally simple
and produced without a succession of acts, it would show no joints into
which the analysis could penetrate, nor would there be any justification for
such an analysis; it would at best be no more than an arbitrary breaking
up of the idea.
As a matter of fact the ideas which most naturally occur to us in this
connection, the ideas of intuitable things, have arisen through an un-
conscious synthesis. When we become conscious of them they are com-
plete as wholes ; but psychological analysis gives irresistible evidence of
the processes by which the whole has been developed from particular
elements. The image of an apple does not penetrate through the doors of
the senses to the tablet upon which our ideas are depicted at one flash, as
1 Ueberweg, e.g., writes, $ 49, p. 103: “The characteristics of an object consist in
such of its elenients as distinguish it from other objects.”
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LOGIC
if conveyed by a kind of enchantment, or by the mechanism of a psychical
photography. Analysis of sense-perception shows how the sensation of
colour must be connected with the movements of the eye in following the
outline; how one perspective view must be combined with others, and
these again with particular tactile sensations of the hand, mentally grouped
into the form of a stereometrical image ; how one psychical function must
construct from the sensations the idea of an external object, and another
assign to this object its position in space. It shows, again, how the idea
of the visible and tangible thing is enriched by sensations of smell and
taste, the reference of these to the visible and tangible object presuppos-
ing fresh functions appropriate to the combinations of the impressions of
different senses. Finally, it shows how such impressions when partially
repeated are continually supplemented by reproductive imagination, and
become associated with the word apple, in connection with which we easily
reproduce a kind of mental abbreviation of these processes; and all this
takes place so rapidly and unhesitatingly that the result appears in the
mind without our being conscious of the steps by which it has been
formed.
3. That which is true of ideas of things applies also to the ideas of at-
tributes, activities, and relations. Equilateral is a composite idea, for it
presupposes, first, the apprehension of the particular sides—and for the
recognition of a line as a side we need a relational idea—and then a
measurement of the sides and the judgment that they are equal. In the
same way the idea of movement, the simplest activity, requires the ap-
prehension of different positions and of the transition from one to the
other. The idea of murder is a relational idea, and includes in addition
to its two points of reference—the murderer and his victim—a whole series
of determinations, such as the conscious and deliberate intention of the
one, his action, and its effect in destroying the life of the other; so that
the idea as a whole can only be produced by a series of acts. This is
doubly true of ideas which contain the thought of a plurality of independent
objects connected by one or more relations, the so-called collective concepts
in the widest sense : people, family, etc.
4. So far as an idea is composite we can only determine it by con-
sciously attending to its particular elements and their manner of synthesis.
Thus the formation of concepts always presupposes, on the one hand,
analysis into simple, indecomposable elements; and, on the other, a re-
constructive synthesis of these elements. Here the form of the synthesis
THE CONCEPT
257
may itself be called an element and characteristic of the concept in the
wider sense of the term, and we shall in future denote it as such.
The concept thus is related to the naturally developed idea as the
conscious construction of an object is related to its unconscious and
involuntary formation; it presupposes that we are able to bring into
consciousness the complete process of the formation of the idea. This
takes place by means of judgments, which assign particular characteristics
to the object as its predicates, and the concept therefore presupposes these
predicates—i.e. the ideas of the characteristics—which must themselves be
conceptually determined if the composite idea is to be so. We thus find
that we need a number of simple characteristics, i.e. of ideal elements
which cannot be further analysed, but which are nevertheless perfectly
definite, fixed, and distinct.
5. But the concept must fulfil yet another condition; it must be such
as to serve for universally valid judgments. That is, every one who shares
in the community of thought must connect the same ideas with the same
words, and be able therefore to analyse them in the same way, and reduce
them to the same simple elements. We can communicate a composite
concept by enumerating its elements, and the manner of their synthesis ;
but these elements must be the same for every one, and be combined in
the same way if our concepts are to agree. There is presupposed, there-
fore, a store of ideas formed by every one according to exactly the same
laws; and we can be certain that our concepts agree only to the extent in
which we are certain that our ideas are formed according to laws which
are the same for all. Thus completeness and perfection in the formation
of our concepts depends upon our having complete insight into the pro-
cesses by which our ideas are formed, and upon our consequent ability to
arouse the same idea in every one else. If we could assume that all our
ideas are innate and possessed by every one alike, as was assumed by a
former theory of knowledge, at any rate with reference to a part of our
concepts; or if we could assume that the same world when presented
always produced the same system of ideas, with a mechanical certainty like
that with which equally tense strings give out the same note when struck
with equal force; then the assumption of the traditional logic that the char-
acteristics of concepts present themselves, as it were, spontaneously might
be justified. But in proportion as the process by which our ideas are formed
is complicated and dependent both upon external conditions which must
differ with the individual, and upon internal laws, it becomes more difficult
S. L.
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LOGIC
to recognise and lay down the conditions upon which every one will form
exactly the same ideas, and to recognise what elements agree or differ in
the ideas of different people. The difficulty, which is often great, of as-
certaining whether two people understand exactly the same thing by the
same word, is due to the difficulty of finding ideas which are the same for
every one and are called by the same name.
6. Since we are only laying down the conditions of an ideal perfection
in the logical formation of concepts, we cannot undertake to present a com-
plete theory of the formation of our ideas. Such a theory belongs to the
work of the future.1 But the results of our investigation so far show that
the problem of resolving a given idea into simple characteristics which are
the same for every one is much more complicated than would appear
from the formulæ which tell us that a concept A contains the character-
istics a b c d, and that these are its constituent ideas. As if A were a
kind of mechanical or chemical compound of familiar elements, all
different, isolated, and of equal importance, in the same way that a
syllable, to take the example given in the Theætetus, is a compound of
letters.
7. The first question which arises, then, is whether we may assume
any such simple ideas as isolated elements, which, like the letters of the
alphabet, might each be expressed and retained by itself. If we return to
our fiction of a world of ideas consisting solely of twelve notes, which only
need to be fixed, distinguished and named in order to be conceptually
determined, then we might say that composite ideas correspond to the
various chords. But it was a fiction even to assume that the idea of a
simple note is really simple, homogeneous and incapable of being further
resolved or differentiated. To have the idea of any given note as such, we
must think of it as one, identical with itself and differing from others; in
no other way can it enter into consciousness at all, for consciousness itself
is inconceivable without a plurality of distinct objects. The thought of
the note A therefore is inseparable from the idea of unity and of identity
with self; it involves moreover the idea of difference from others, and hence
of a plurality of these others. All this points to functions by which we
think of something as one, identical with itself and different from others;
thus thinking also of plurality as distinct from and related to unity. A
clear consciousness, therefore, of all that is involved in forming the idea of
1 Here our views coincide with those enunciated by E. Zeller in his Berliner
Antrittsrede.
THE CONCEPT
259
A shows us that, in addition to the audible note, it comprises these various
determinations; and the idea proves to be already complex as it comes
into consciousness. 1
We cannot, however, regard these determinations—unity, identity and
difference, on the one hand, and the sense-given note on the other-as the
ultimate and isolated elements for which we are looking. Unity, identity
and difference cannot be thought in absolute independence. Not only is
it impossible to think of identity without unity and negation--for these de-
terminations are inseparably interwoven—but they necessitate also the
thought of a something to which the unity, identity and difference belong.
Nay, so soon as we attempt to think of these determinations each by itself
the same story repeats itself; we can only keep these concepts themselves.
before the mind by placing them under the determinations of unity, identity
and difference. Thus our analysis never arrives at the absolutely simple,
inasmuch as it finds certain elements included in every idea, even the
simplest, which are due to the mere fact that it is thought at all, and that
any judgment is to be made concerning it. These elements are therefore
the necessary and constantly recurring products of the various functions
by means of which we are able to grasp an idea and to turn it to account
as the subject or predicate of a judgment. Thus, instead of the isolated
letters we sought, we find a complex of functions, dependent upon, and
mutually conditioning, each other, and manifesting their activity in what
we may briefly call the FORMAL LOGICAL CATEGORIES. They are related
in the same way to all objects of thought, being the conditions upon which
any idea can be consciously retained in the mind.2
8. But more yet lies hidden in the note of our hypothesis. We can-
1 Cf. Lotze, Logik, ed. 2, p. 26.
2 Amongst these formal categories, without which nothing whatever can be retained in
thought, we include also number, in the sense that these most general conditions of
thought involve the functions upon which all counting is based. That is, they involve
the positing and distinguishing of unities, the consciousness of progress from one unity to
another, and from that to a third, and the unity of the consciousness of these steps. We
allow that further development of counting, and the more complicated operations of
arithmetic are due to the relations of intuitable things in space and time, and that frac-
tions especially presuppose that divisibility of a whole which is originally found in space
or time only ; but it does not follow from this that number is altogether dependent upon
the conditions of intuition. Counting stands in no other relation to time than that in
which all our activities stand, that is, a succession of them can take place only in time;
but it is in no way essential that in counting we should be aware of time. The idea of
time is even dependent upon the idea of number, of a plurality of distinguishable acts.
Cf. $ 6, 36, p. 36.
260
LOGIC
not have an idea of a note or of a number of notes, except as in time ;
just as we cannot have an idea of a colour except as in space. Full con-
sciousness, therefore, of what is present to our minds when we form the
idea of a note includes the idea of time. And, again, when we try to set
aside time as a simple element, not to be further analysed, we find that
we can form no idea of time as absolutely isolated. We must combine it
with the idea of something in time, something, moreover, which is various
and manifold; just as we must think of space in connection with different
things in space. Thus here again the nature of our ideas will not admit
of our finding the absolutely simple and isolated; we can indeed find
elements which are distinct, but they always involve each other. More-
over, the relation in which time and space stand to their intuitable contents
is essentially different from that in which identity, etc., stand to their
objects. Hence we get fundamentally different syntheses of the different
elements of an idea, and we may express this difference, as Kant did, by
speaking of space and time as FORMS OF INTUITION, in contrast with the
formal categories.
9. When the concepts we are forming refer to the existing, then, in so
far as we think of it as actually or possibly existing, there appear new
elements again. Our only idea of the existent is of a thing with attributes
and activities, and we can have no idea of particular existence which is not
related to something else; at the very least it must be related to us as our
object. Thus all our ideas of the existent, or possibly existent, include
isolated characteristics, and which involve a third kind of synthesis of the
manifold, that of the thing with its attributes and activities. We cali these
elements the REAL CATEGORIES.
Traditional Logic generally chooses for its examples the concepts of
characteristics of the concept “gold” are heavy, yellow, shining, etc.).
But in addition to these, there is a distinct kind of synthesis among the
characteristics—that of attributes in a thing. This synthesis is essentially
site concept of attributes or activities, and it differs again from the syn-
thesis of particular things to a whole by means of the definite relations
connecting them. It can only lead to confusion if we express everything
-three-sided figure, dark red, rotatory motion, yellow body, a kernel sur-
rounded by a shell, etc.-all without distinction by the same formula A=
THE CONCEPT
261
I.
a b c d; as if this juxtaposition were the expression of a mode of con-
nection which is always the same.
If these real categories are indubitably elements of our ideas of the
existent, then it follows that in conceptual determination we must, first
of all, determine these categories themselves as concepts. The popular
distinctions between thing, attribute and activity, guided as they are by
the forms of words, and vaguely and waveringly applied, must be de-
veloped into clearness. Thus the determination of any concept which
refers to the existent presupposes a recognised theory concerning the
nature of these categories. It is logically complete only in so far as this
theory is logically complete, and will hold good only to the extent in which
it is generally accepted. And the possibility of such a theory depends
again upon the possibility of producing generally accepted concepts of the
categories themselves. It depends, therefore, upon an analysis of our
mental processes which shall make us conscious of what it is which every-
one must think in accordance with necessary laws, when thinking of any-
thing as existent.
. 10. The universality of such elements of our ideas as we have noticed
so far is ultimately due to their derivation from functions which always
recur in the same manner, however varied the matter of thought or in-
tuition to which they refer. The nature of our spatial and temporal
ideas is the same, whatever the particular objects thought of as in space
or time may be. No matter how varied the ways in which our senses are
affected, and the particular affections combined amongst themselves, the
process of referring the sense-given to things with attributes and activities
remains the same. The possibility of presenting a complete system of
these elements depends upon whether, as Kant assumes, they are given
entirely a priori, as forms which lie ready in the mind, and are therefore
discoverable by a complete analysis ; or whether the nature of our sensuous
affections themselves determines what formal elements are developed.
In the former case an organized and unalterable system meets the affec-
tions of the senses as they successively appear; in the latter, the categories
would be the result of a development determined by the particular kind
and order of our sensations. We need only mention these possible alter-
natives to show that the final determination of our concepts depends upon
a clear insight into the genesis of our ideas themselves.
11. Different from these elements of our ideas are the elements which
are given in intuition by immediate sensation or inner perception. From
262
LOGIC
the subjective psychological point of view there is no doubt that we have
something simple and ultimate, really elementary, in particular colours,
notes, odours; and again in the immediate consciousness of inner events-
of pleasure, pain, desire. The white of this paper, the black of these
letters, cannot be further analysed; it is given immediately by the affection
of our sense-organs. It recurs in the most varied combinations and
spatial forms ; but it is always the same and cannot be resolved into sim-
pler elements. Here, then, it seems easy to set forth elementary charac-
teristics, which cannot indeed be thought of as isolated-colour is never
without space, and so on—but can at least be easily retained in the mind as
distinct from their form and from each other; odours from colours, colours
from notes. Here, if anywhere, we have something which can only be
named and not explained, something analogous to the letters of the
alphabet; and if it could be shown that all our ideas were formed from
these elements given in immediate intuition, from the forms of intuition,
and from the real and formal categories, then the circle of ultimate
characteristics would be complete.
But here we come upon the second of the difficulties noticed in $ 40, 8.
Every definite sensation, every particular feeling of pain, is something
simple and elementary; but the number of these distinguishable simple
sensations is infinite. It is absolutely impossible that every particular
degree of light and warmth, each of which comes into consciousness as a
simple presentation, should be fixed in memory and kept distinct from all
others; by no expedient could language be made to suffice for all this
multiplicity. Language takes advantage of the fact that similar sensa-
tions are separated by imperceptible differences, and denotes a whole
series of approximating degrees by one word. But similarity by itself is
indefinite, it is of no use for conceptual determination, for it implies
difference without stating its degree. The only way of attaining the
definiteness of a concept here is to start from a comprehensive survey of
the whole series formed by these imperceptible differences, and in this
continuum to draw boundaries within which a given name shall hold good.
Thus we get what we have called the generality of the word in distinction
from the generality of the idea (S 7). The names of the colours, for
example, are not conceptually determined until the whole series of shades
has been exhibited, and it has been settled within what limits the names
green, red, etc., shall apply. Our means of carrying out this determination
must be left for Part III. Here it is sufficient to point out that “red” is
THE CONCEPT
263
not general in respect to dark-red and rose-red, in the same sense as
“extended” is general in respect to different bodies. It is not the same
red in different combinations which we think of in dark-red and rose-red;
each sensation is absolutely simple, and cannot be resolved into one
element which is the same in all and one which is different.1
From this we may learn also what is the import of such words as colour,
note, odour, etc. According to the ordinary theory, as colour is the
general idea corresponding to red, blue, and yellow, the concept of
colour should be one element of the concepts red, etc. But red, blue,
yellow, are simple, and we cannot say what colour is except by an enumera-
tion of the particular colours. If the word colour is to have over and
above this enumeration any definite conceptual meaning, it must be in the
fact that by grouping together a whole series of ideas it presents them as
clearly marked off from others which are incomparable with them, such as
notes and odour. But if we try to express the common element of these
ideas, we can do so only by means of a relation, which does not directly
denote the ideal content, but only a reference which red, blue, yellow, all
contain, and by which they are distinguished from other simple sensations
-reference, that is, to sight and to the eye. In such relations alone is a
common element to be found, but these relations are not elements of the
ideas themselves. This distinction between words which are merely
common names of simple characteristics, and words which really denote
simple ideal elements, must be constantly borne in mind; otherwise, the
1 Cf. Werner Luthe, Beiträge zur Logik, p. 2: “We cannot distinguish in any given
shade of red that element which is common to all red.” In Lotze (Logik, ed. 2, p. 27
sq.) there is only apparent contradiction to what is said above. True, he says at first
(p. 28), that in several distinct impressions there is something common to all which is
conceivable apart from their differences, and to which (p. 29) the differences peculiar to the
particular members of a series attach (light-blue, dark-blue, etc.). But he recognises that
the general blue cannot be realized in the same way as the elements of other concepts
which we compound from known particular ideas, and he adds that the presence of a
common element can only be felt or experienced, that the common element does not
form the content of a third idea of a like nature and species with those compared, and
that it cannot be independently intuited.
This is what we wished to express above, and it would be more correct not to speak of
a common element at all, but only of an unanalysable impression of similarity. This im-
pression is present in very different degrees, and guided by it, we arrange our simple
sensations in a series of diminishing similarity, so that we may fix limits in the series
within which to apply a definite denotation (red, yellow, etc.). It is different with differ-
ences of intensity, e.g., of warmth, or of notes of the same pitch; here we can form an
idea of the common element, because the differences are based upon the excitation of
feeling, and are not differences of an ideal content.
264
LOGIC
doctrine of the characteristics of concepts, together with the accompany-
ing doctrine of their subordination to each other, will fall into confusion.
Nevertheless, even common names such as these may be looked upon as
the signs of characteristics inasmuch as they indicate a common element
which is the ground of the reference which they all contain.
Intensity of sensation and its differences, however, are true general
concepts; for they refer to the excitation of feeling which accompanies the
sensation, and which changes in the same way, although the objective
elements differ.
12. What we have said of sensuous qualities seems to be true also
of forms and movements, since these, too, appear as immediately intuit-
able. Here again we have infinite multiplicity and imperceptible degrees
of difference; here again we seem to start from the particular sense-intuition,
and the general idea (form or motion) appears to possess a generality of the
word alone. But it only appears to be so. The idea of a given form--
a triangle, square or circle—is far from being given so immediately and
directly as the sensation of a sound or a smell. Perception of form
necessitates movement of the eye or of the hand; and this movement,
returning into itself and thus limiting a body in space in a definite manner,
is really from one point of view, as this kind of action, the same in every
perception of form; from another point of view it is differently modified
according to the course it takes. It is the same with the idea of objective
movement. The process by which it is perceived, the comparison of two
positions, recognition of their difference and the idea of continuous tran-
sition from one to the other, is always the same; but the path, velocity, etc.,
are variously modified. Movement and form are true general concepts ;
colour and sound (as the expressions of something immediately given, not
in the physical sense) are general words or common names. For this
reason one example suffices to show what movement is, but not so with
colour. This explains also why every theory which starts from sensations
as the only primitive elements of our ideas must tend to regard all gene-
rality as only that of common names; and why it extends this view to all
things which it regards as sense-given, ignoring the processes by which we
form ideas of them. Sensationalism and nominalism always accompany
each other.
THE CONCEPT
265
§ 42.
The analysis of objects into their final elements gives rise to series of
concepts in which each successive member is determined by a new distin-
guishing characteristic, and thus has a fuller intension than the preceding
member. The analysis of a single object may form as good a ground for
such a series as comparison between different analysed objects. The
poorer concept with fewer determinations, which is included in the thought
of the subsequent concept, is called the super-ordinate, higher, or generic
concept; the richer concept, with more determinations, is called the subor-
dinate, lower, or specific concept; their relation is that of SUBORDINATION.
The relation of subordination exists only between concepts of the same
category; for it is the category which determines the sense in which
their characteristics are synthesized, and through it alone they are com-
parable.
The extension of a concept is the sum-total of lower concepts which are
subordinated to it. Within the same series of subordinated concepts the
extension is greater as the intension is less, and vice versa. We must
distinguish between the logical extension of a concept and its empirical
extension; and again between the empirical extension of the concept and
the extension of the name.
We can speak of essential and unessential characteristics only in reference
to objects in their relation to a given concept.
1. Let us suppose that the most important part of conceptual determi-
nation--the survey of characteristics in their different classes—has been
carried out in accordance with a complete and universally valid theory of
the formation of ideas ; let us suppose further that we have thus discovered
what characteristics presuppose and are dependent upon others (e.g. colour
upon extended surface, a point which is generally overlooked), and that
we are also clear as to which terms denote definite ideal contents, and
which are only common names. Then the question arises how our uni-
verse of concepts will shape itself under these conditions.
In all conceptual determination we have to work upon ideas which are
already given as material, and our first task is to reconstruct and determine
these. Moreover, the constant supply of ideas which arise naturally and
without reflection always has its origin in the particular, and we are
constantly called upon to form judgments determining the particular by
predicates. For this reason our explanation of the further relations of our
266
LOGIC
concepts will be facilitated if we begin by the conceptual determination of
some idea excited by a particular thing.
2. When we wish to retain the idea gained from any particular thing-
that is, when we wish it to be securely committed to memory, and recog-
nised as the same when reproduced the merely involuntary function of
reproduction is not sufficient. This function, which we find aimlessly
active in, e.g., dreams, and upon which, in the earlier stages of judgment,
our denominative judgments are generally based, simply repeats an image
as a whole ; this involves no consciousness of the particular elements of
the idea, and, therefore, no consciousness of its identity is necessarily con-
nected with it, and it is in danger of being confused with others. To secure
its exactly identical repetition, it is necessary above all that the idea should
be decomposed into its particular elements, and this decomposition is
again the condition which enables us to distinguish a thing from all others.
It consists in going back to absolutely simple and perfectly definite char-
acteristics, and the condition most essential to this is that fluctuating
differences should be fixed ; e.g., differences of colour must be fixed by a
generally accepted denotation, of magnitude by a fixed standard.
The result of such an attempt is a description as it takes place in a con-
junctive judgment. I might describe the wafer before me by saying it is an
orbicular, circular thing, two centimetres in diameter, one millimetre thick,
red, light, and smooth; that is, I should describe it by enumerating all the
predicates perceived through the different senses, and consciously recom-
bining them into one whole ; the import of the synthesis is stated by the
category of the thing, and the nature of the characteristics red, smooth,
etc., determines their dependence upon the spatial characteristics. Any
one hearing such a description is called upon to carry out, step by step, the
synthesis which in intuition was involuntary and, until completed, uncon-
scious; it is supposed that the hearer thus obtains the same idea from the
description which I had myself, always assuming that he thinks each
characteristic in just the same way.
But it is obvious that when I describe something in this way the result is
not what I intended; it is seldom that the description is equivalent to the
particular image, and it cannot replace intuition itself. The words “an
orbicular, circular, smooth thing" constitute a formula in general expres-
sions; to the hearer it is like a riddle to be guessed, a problem for his
imagination; how may he form an image of a thing which shall satisfy the
conditions of the problem? It is true that every additional characteristic
THE CONCEPT
267
distinguishes my idea from others which share the remaining characteristics,
but by the nature of the predicates it is left open to each individual to
form the idea in different ways. Predicates such as red, light, smooth, etc.,
even when accurately limited in meaning (e.g. light defined as of less
specific gravity than water), admit of many degrees of difference, amongst
which the hearer must choose before he can form his intuitable image.
The description gives us a sketch which fits not only an indefinite number
of things which are exactly alike, but also many distinguishable things;
it is, therefore, a formula having a generality which is not merely numerical,
but also generic.
We see further that this generality does not result merely from the
breadth of meaning of particular determinations, such as red, etc., it
frequently happens that the enumerated characteristics do not exhaust all
the attributes either directly perceived or inferable of my object. As the
above formula does not state the material nor the attributes dependent upon
it, it would apply just as well to a round piece of cardboard or a red
counter. In this case the incompleteness of the description is easily
corrected ; but the same deficiency may occur where differences are present
which are unrevealed to our knowledge, or such as we cannot recognise.
The most exact description of the germinal cell of a mammal would apply
without further modification to those of many other animals, although we
are bound to assume that there are hidden differences which manifest them-
selves in the course of development. Nor again can the description of
any real thing claim to be so exhaustive that it may not possibly apply in
every respect to some other thing, which nevertheless differs in some way
not known.
In a formula thus reduced to characteristics we have, then, not the full
expression of a thing, but what is in the first place a subjective creation,
expressing the idea we have formed from the intuition of a thing so far as
we can retain it in characteristics which every one determines in the same
way. It is a rule for the formation of the idea which we must observe, but
may observe in various ways. Its generality is due partly to the wide
meaning of the particular characteristics, partly to the possibility of adding
new characteristics to those already given. It matters little for the present
whether or not ordinary language has a special term for such an idea; if it
were worth while, one could be made,
1 We shall speak in Part III. of the necessity to which this gives rise of employing in
our determination of concepts characteristics based upon relations.
268
LOGIC
1
If our description were less complete—if, for instance, it omitted to state
the size—a difference would be neglected which distinguishes this object
from others which are larger and smaller ; the formula would be applicable
to many other objects, inasmuch as we could complete it by supplying any
possible magnitude. If it were more definite, if, e.g., rose-red were sub-
stituted for red, then a number of distinguishable objects which were
previously comprehended would now be excluded. We should, however,
still have a formula expressing a synthesis of characteristics to which others
may be added—a formula which the hearer can supplement in many ways.
3. It may thus happen that even the analysis of the idea of a single
object may give rise to a series of formulæ, including successively more and
more characteristics. As each characteristic is added the idea to be formed
becomes more definite, and by each additional characteristic objects are
excluded to which the previous ones by themselves applied. From each
of these formulæ we may obtain the preceding one by omitting, the subse-
quent one by adding, a characteristic. The fewer the characteristics com-
prehended, the greater the number of different objects of which the formula
can be predicated if we assume the possible differences to be actual, and
vice versa. The formulæ are related to each other as more and less general
concepts. Even the most specialized is still general in so far as its
characteristics admit of a certain width of interpretation ; only if all the
characteristics were perfectly definite would the generality of the concept
be merely numerical (0.8, “a cube of pure gold having sides measuring one
centimetre” is a perfectly definite concept).
This process is expressed by saying that we ascend from a given concept
to one more general by abstraction, i.e., by omission of characteristics; and
that we descend to one more special by determination, i.e., by the addition
of characteristics. Abstraction diminishes the intension, but widens the ex-
tension ; determination increases the intension, but narrows the extension.
Intension and extension stand in inverse relation. The more general
concept is called the higher or wider; the more special the lower or
narrower; the relation between them is that of subordination.
We should reach the same result if we were to start, not from one single
object, but from several; the problem being to state what characteristics
are common to various objects. The greater the number of different
objects to be comprehended, the fewer will be the characteristics they have
in common, and the smaller the intension of the concept; the fewer the
objects, the greater the intension.
THE CONCEFT
269
4. These propositions, simple and obvious as they appear, nevertheless
conceal several questions and difficulties which do not generally receive
sufficient attention. These refer partly to the processes of abstraction and
determination, partly to the relation between intension and extension.
In the first place, the omission and addition of characteristics is by no
means so much a matter of choice as would appear from these propositions.
Amongst the characteristics there is always one which determines the
nature of the synthesis by giving the category; should this be omitted, the
remaining characteristics would lose their common support, and the mean-
ing of their synthesis would be uncertain. It is only concepts within the
same category which can be subordinated to each other; and to speak of
such a concept as red as super-ordinate to rose, or reasonable as the super-
ordinate concept to man, or intentional as the super-ordinate concept to
murder, is only confusing.
Moreover, the characteristics are not all independent of one another; to
some extent they presuppose each other. It would be useless to omit the
characteristic extended and retain red; the latter presupposes the former.
Thus the course of generalizing abstraction is prescribed to it within certain
limits.
It is the same with determination. In the first place, it is a matter of
course that incompatible characteristics cannot be added without giving
rise to contradiction. But by what is the determination to be guided ? A
twofold ground for the determination here presents itself. If the given
concept-formula contains characteristics which naturally admit of a further.
series of distinctions—as red admits of a series of shades, circular of all
possible magnitudes of the diameter, etc.—then the addition of one of these
distinctions naturally presents itself as the next step in determination, and
finds its justification in the given concept itself. But even here we must
take care that other characteristics do not exclude some of these possible
characteristics and thus limit the determination. The concept of a plane
figure bounded by three straight lines contains nothing about the magnitude
of the figure, nor about the magnitude of the straight lines and their relation
to each other. Some magnitude of the straight lines is necessarily implied
in the concept, but it is left for the determination to settle which. I can-
not, however, fix upon any determination I like for each straight line; my
choice is limited by the law that any two sides taken together must be
greater than the third, this law being prescribed by the remaining character-
istics and the nature of the synthesis demanded. Thus determination
270
LOGIC
cannot proceed from one characteristic alone, but only from the whole
complex.
But determination of this kind is accompanied by another, which adds
new and independent characteristics having no special connection with
anything in the given concept. Matter, for instance, may be determined
as extended and heavy substance; but at our present stage of knowledge
we cannot regard the specific attributes of particular materials as in any
way modifications of extension and weight. In such cases, however, we
find that determination is guided by our purely empirical knowledge of
objects which fall under the concept of matter; we add those characteristics
which, in our experience, we find combined with the more general ones.
Only if we had full insight into the nature of things could this determina-
tion be guided by the contents of our ideas.
5. Because there are these two modes of determination it is uncertain
what we are to understand by the extension of a concept. The logical
point of view, where the first demand is for conceptually determined
predicates, is concerned only with the ideas with which we approach actual
things. Hence the relation of subordination can never be found except
between concepts, and the generality of the concept consists in its being
contained in the thought of a number of ideas distinguished conceptually,
i.e., by different characteristics according to their intension. The mere
numerical generality, through which the same idea is found in an indefi-
nite number of particular intuited things, has nothing to do with the
nature of the concept; it is one and the same concept which is thought
in all the instances, and whether it can be predicated of one or of a
hundred things, its nature is the same.
Hence the extension of a concept can never be measured by the
empirical number of similar things which fall under it, if, in opposition
to the principium identitatis indiscernibilium, we recognise the possibility
of objects which for our knowledge are not distinguished by their attri-
butes, but only by difference in time or space.
On the contrary, it must be laid down that a concept which does not
admit of further determination has no longer any extension ; it represents
the final limitation of extension, the point, even though that which cor-
responds to it may be empirically forthcoming in millions of instances.
Assuming all cast-iron to be the same, then a cast-iron ball having a
diameter of 10 centimetres is such a concept.
There are certain characteristics which can be conceptually determined
THE CONCEPT
271
only by fixing limits within a continuum of imperceptibly small differences.
In connection with these alone is it true that even the lowest conceptually
determined formula still has an extension, which, however, cannot be
further broken up into discrete concepts.
The question of singular concepts partakes of this difficulty. A concept
can never be called singular because there happens to be only one thing
corresponding to it in empirical reality; any more than the logical nature
of the concept would be affected if there were no object whatever cor-
responding to it. Only concepts whose characteristics involve the unique-
ness of the corresponding object can be called singular; in this sense the
centre of the material universe is a singular concept. The question, on
the other hand, as to whether all individuals which actually fall under a
given concept are distinguished otherwise than spatially and temporally,
and whether only one, or whether several, particular things can be com-
prehended in a concept of the smallest extension, has nothing to do with
logic, but belongs to the science of reality.
For this reason also it is purely a matter of chance when the same
number of things fall under two concepts of different intension. Hence
as concepts they must not be called equivalent or interchangeable ideas,
but only in so far as, when used as names, they denote things which are
the same within the range of our knowledge. They are really different,
and logically considered they have a different extension. Two-footed un-
feathered animal is a different concept from that of man; only when used
as names do they denote the same beings. We must, then, distinguish
between the logical extension of the concept and the empirical extension of
the name.
At most there is room for doubt as to whether such concepts as
“equilateral triangle ” and “equiangular triangle” are identical or dif-
ferent. They differ in the formula ; but as the characteristic equilateral,
taken together with those comprehended by the word triangle, necessarily
contains the characteristic equiangular, and vice versâ, they are absolutely
equivalent. Only by insisting upon the verbal expression can we main-
tain that they are different; and in that case we must also say that an
equilateral rectangle and a rectangular rhombus are different concepts.
Again, it is only the extensions of subordinated concepts which are
directly comparable. We cannot compare the extensions of concepts which
are independent of each other, except in so far as every concept which
admits of many additional determinations may be generally called wider,
272
while those which admit of few may be called narrower. There can, how-
ever, be no definite and universal standard of measurement for the exten-
There is a further distinction between the logical and the empirical
extension of a concept. The logical extension consists in all the concepts
which are gained by the further determination of its characteristics when
this determination is involved in the characteristics themselves. But we
may be guided in our task merely by our knowledge of actually existing
things, and thus fail to work out any series of determinations or com-
binations of characteristics because no empirical occasion presents itself
for so doing. When this is the case, because we do not see any necessity
for selecting these, and only these determinations, we can only speak of
an empirical extension. No one could infer from the concept of metal
that there are just so many and no more different metals, nor could we
even discover the number by attempting all the possible combinations of
characteristics; for us the extension of the concept metal consists in the
concepts of the metals we know. Just for this reason, however, the
6. The expressions Genus and Species are often used with reference to
the relation of subordination between ideas ; each concept is genus to a
lower, species to a higher concept. Of these terms it is again true that
they have no fixed meaning except within the same category. Red is not
the generic concept of rose, but only of the various shades of red. The
highest genera, the apãra yévn, are therefore the categories; and their
common element is again nothing but the relation which consists in being
objects of thought. Unless we accept this limitation, there would be as
many highest genera as there are independent characteristics of any
kind.
We must of course distinguish between the generic concept and the
genus in its concrete sense as the sum-total of all the things falling under
å generic concept, between the generic concept “human being” and the
human race or genus.
7. When a concept contains different characteristics which are inde-
pendent of each other, the higher concepts to which we may pass are
various. From the concept of the square we may ascend to that of the
equilateral quadrangle, or the equiangular quadrangle or the regular figure,
according as we omit one or the other of the independent characteristics
equiangular, equilateral, four-sided. All these higher concepts are equally
THE CONCEPT
273
related as generic concepts to that of the square. In like manner the
determination may take place in different order, according as one or the
other of a number of independent characteristics is first to be added. We
may proceed from the concept plane figure bounded by straight lines in
the order figura plana rectilinea quadrilatera—figura plana rectilinea
quadrilatera æquilatera--figura plana rectilinea quadrilatera, æquilatera,
æquiangula ; but we may also proceed in this order : figura plana
rectilinea æquiangula—figura plana rectilinea æquiangula, æquilatera—
figura plana rectilinea æquiangula, æquilatera, quadrilatera, etc. Thus
every concept containing characteristics independent of each other may
find a place in different series of subordinated concepts, and to exhaust
all possible variations would need an arithmetical calculation of combina-
tions.
There is therefore no order of succession in the subordination neces-
sarily given by the nature of the concepts; there is no settled order of
precedence according to which all concepts which have a logical possibility
and justification may be arranged in one way. Just because concepts, as
we understand them, are subjective creations, formulæ whose chief pur-
pose is merely to fix our ideas and mould them into commonly accepted
and unambiguous predicates, they are capable of unlimited variation by the
many ways in which they may be combined. 1
8. As the primary function of concepts is to serve as predicates in our
manifold judgments, we cannot regard it as an imperfection that, generally
speaking, they are poorer in determinations than the concrete and fully
determined subjects of which they are predicated, and that they are more
or less deficient when compared with the intuitable reality of particular
things and events. The fact that no one can eat "fruit" in general, but
only apples, pears, etc., each, moreover, of an absolutely definite kind, with
its own individual size and shape, in no way diminishes the value of the
concept “fruit.” Nor is the value of the concept "clock” any the less
because no one can have a clock in general, but only a clock with a pen-
1 The idea of an arrangement of concepts such that the more specialized concepts
branch off in increasing numbers from one point, the concept of the őv or something, is
thoroughly vicious. It presupposes that there must be a much smaller number of higher
generic concepts than of the more specialized ; but if we regard concepts as being com-
binations of a limited number of characteristics it depends entirely upon their inter-
relations whether combinations of greater or less generality are the most numerous. The
necessity of any fixed order, and hence this imaginary pyramid of concepts, can be
grounded only upon the metaphysical view which regards the higher concept as the real
S. L.
274
LOGIC
.
dulum, or a clock with a spring. It is a necessary part of the purpose and
function of the concept that it should thus differ from the real thing. For
this reason, when logical theory aims at supplying a supposed deficiency
by making the statement or condition that the concept of a thing should
contain its essential characteristics, it fails to understand the most impor-
tant and universal purpose of the formation of concepts. Moreover, ac-
cording to this theory, that which is left undetermined by the concept is
represented as unessential, as accidental. Now, apart from the fact that
a complete knowledge of the whole universe would be necessary before we
could know what are the essential characteristics of a thing and what not,
this view, when taken in connection with the subordination of concepts,
would lead to the pantheistic conclusion that there is only one essential
nature of all things, and that all differences are merely accidental, having
their ultimate ground only in the subjective view of things. There is no
absolute and fixed line to be drawn between differences which must be
neglected in our determination of concepts, unless these are to be multi-
mulated in concepts. Hence there is as much reason for saying that the
differences between the last species are accidental in respect to the genus
as for saying that the merely individual differences of a thing which falls
under a lowest concept are accidental; and, finally, since a higher genus is
always related to its species in the same way as the most specialized idea is
related to distinguishable individuals, the essential nature, properly speak-
ing, can only be expressed by the highest concept. This is, in fact, the
origin of Spinoza's doctrine, that there is only one substance, and that all
differences are merely modifications of this.
The distinction between essential and unessential characteristics first
When we desire something actual as means to an end, these means are
generally so constituted as to possess also a number of attributes which are
not desired, and therefore not determined by the end ; with reference to it
they are accidental. The necessity of guarding against the cold gives rise
to the concept of a covering which will prevent the loss of heat; and
this necessitates that the material which is to serve the purpose shall be
flexible and a bad conductor of heat. But any available material has
many other attributes besides those of being flexible and a bad conductor
of heat, and these other attributes contribute nothing towards the purpose.
With reference to the concept of clothing, they are accidental. In the
THE CONCEPT
275
same way the concept of a clock is originally a concept of purpose—the
concept of an apparatus which measures time by spatial changes. So far
as concerns the concept of the clock, the mode of its construction is
accidental so long as it fulfils its purpose. Here then the subjective
concept with its characteristics does actually precede the reality. It
follows from the nature of the things which must be used as means that
we cannot realize those determinations alone which are included in the
concept ; its species are determined by the variety of the means. Only
when nature itself is placed under the concept of purpose, and regarded as
aiming at the realization of certain ideas or forms which, like human
purposes, take the shape of indeterminate and varying thoughts, is there
any meaning in distinguishing between the essential and unessential
characteristics in the idea of an existing thing. If nature is concerned
merely with creating the form, structure, and organization of a horse, and
if colour has nothing to do with her purpose, then it is an unessential
characteristic which is only present because the horse must have some
colour. The fact that such characteristics vary in individuals otherwise
similar is then taken as a sign that they are immaterial. Nevertheless,
from the scientific point of view the colour of the white or of the black
horse follows as necessarily from the constitution of the particular indi-
vidual as the structure of its skeleton and muscles.
Thus the distinction of essential and unessential is always found when
we compare an idea with a previously given concept in which it is con-
tained, and try to find in it the realization of the concept. The penal law
sets forth certain concepts of crimes, and the judge endeavours to find in
particular concrete actions the characteristics determined by the law; for
the subsumption of the crime, and the meting out of punishment, these
are essential, while the special circumstances of the deed which are un-
provided for are unessential. If one man has killed another, it is essential
to know whether he did it intentionally or unintentionally, with or without
deliberation; it is unessential whether he did it with a round or a conical
bullet.
The distinction recurs again when the problem before us is to give con-
ceptual determination to the meaning of some word in ordinary use; here
the unessential characteristics are those which belong, not to the general
meaning, but only to the particular things included by it, or to the more
specialized ideas. In this sense it is unessential to the concept of the
house whether it is roofed with tiles or straw, but it is essential that it
276
LOGIC
should have some roof. The actual meaning of the word “house”
includes the characteristic of having a roof, but does not specify the
material.
9. This logical treatment of the difference between the essential and
unessential characteristics of a thing must be carefully distinguished from
the question as to what belongs to the real nature of a thing, what is essen-
tial to it or not (cf. $ 33, 4, p. 198). We may be called upon to form our
concepts of things in such a way that they shall express the essential
nature of things, i.e. those determinations which belong to them indepen-
dently of all other things, and proceed entirely from their own nature.
Then the characteristics of the concept must include the essential deter-
minations of the things, and all things having the same essential nature
must fall under the same concept. But it is clear that unless we are to
fall in with the pantheistic tendency, this condition can only be fulfilled
by the infimæ species ; it is inapplicable to any higher concept. In the
same way it is clear that these essential concepts, if attainable at all, can
form but a small part of the concepts of which we have need. Knowledge
is concerned not only with the essential nature of things, which always
remains one and the same, but also with the many manifestations, pheno-
mena and effects due to this nature; and for this also judgments are
needed which have concepts for their predicates.
From one point of view there is certainly a difference between the per-
manent and lasting states or attributes of a thing and those which change
and vary, the difference which Descartes meant to denote by his dis-
tinction between attributa and modi. As the concept must be a constant
idea, and the concept of a thing means something enduring in time, only
that which belongs permanently to the thing can be contained in the
concept of it. Thus its changing aspects are unessential with respect to
the thing, but only because they cannot be included in the concept, not
as having no reference to the real nature of the thing. For it is just in
these changes that the real nature unfolds itself, and if we wish to express
the real nature of a thing, we must include in the concept the permanent
ground of its changeable aspects, under some such name as faculty, or
.
power.
10. The distinction between essential and unessential characteristics,
which in reference to the concept as such is meaningless, must not be
confused with the distinction between fundamental and derivative charac-
teristics. When from a combination of elementary characteristics other
THE CONCEPT
277
predicates necessarily follow, then the former are called fundamental, the
latter derivative. It is a fundamental attribute of the rectangle to have
parallel sides and right angles, it is a derivative attribute to have equal
diagonals. It is a fundamental characteristic of an odd number that when
divided by two there is a remainder one ; derivative, that it is not divisible
by even numbers, and so on. But here again we must guard against
confusing the logical and the metaphysical. We must not look upon the
fundamental characteristics as constituting the real essence of a thing; in
many cases nothing is known about this. All we can say is, that accord-
ing to the way in which we consider the attributes to be dependent upon
each other, these fundamental characteristics constitute the concept as a
fully determined idea.
11. It follows from our doctrine of the negation that negative deter-
minations can never be original elements in the idea, and therefore that
they cannot be characteristics in the proper sense. Every negative deter-
mination presupposes a negative judgment, and the subject of this judg-
ment must be capable of being distinctly thought before the negation which
is founded upon it. How far negative determinations may nevertheless be
necessary to enable us to arrange our concepts will appear from what
follows.
§ 43.
We must not confuse the distinction of simple characteristics and the
resulting distinction of composite concepts with the difference of the
objects in which the concept is contained. Different concepts which are
contained in, and can be predicated of, the same object, are called com-
patible; they are generally cross concepts. Different concepts which are
incompatible cannot be contained in the same things; their extensions are
mutually exclusive.
The determination of a generic concept by incompatible characteristics
gives rise to its differentiation into disjunct co-ordinate concepts, and a
complete enumeration of disjunct co-ordinate concepts constitutes a DIVI-
SION.
Division may proceed either by a development of characteristics already
1 Derivative are not the same as dependent characteristics. A characteristic is depen-
dent when we cannot think of it without presupposing another, as colour presupposes
extension; it is derivative when it is also the necessary consequence of other
characteristics.
278
LOGIC
given in the concept, or by the addition of new ones ; in the latter case
sometimes by negative determinations. In division we are justified in in-
cluding negative characteristics of the form non-B in a concept, but not in
regarding non-B itself as an independent concept.
The distinction between so-called contradictory and contrary opposi-
tion, when rightly understood, coincides with the distinction between a
division having two terms and one which has more than two.
The members of a division may be complete either in a merely empirical,
or in a logical sense.
I. The distinction between the various characteristics must find its
expression in the negation, which tells us that A is not B, not C, etc.
(S 21, I ; $ 22, 6). Conceptual determination can only be complete so
long as this negation remains obvious and indisputable, and is not made
uncertain by the indefiniteness of ordinary language when dealing with
gradual transitions.
The same is true of all composite concepts, which are not absolutely
identical, i.e., equivalent syntheses of the same characteristics. They neces-
sarily differ in their contents, according to the difference of their character-
istics, and this difference is again expressed by the negation of identity,
which tells us that A is not the same as B. The only object of the nega-
tion is to confirm the fixed and immutable rule according to which differ-
ent words signify different things, and which, if we are concerned merely
with the contents of concepts denoted by different words, holds good even
when the predicate denotes a concept to which the subject is subordinated :
square is not parallelogram.
The attempt has been made to express a maximum of difference by
speaking of disparate or incomparable concepts, which have no character-
istic whatever in common (such are understanding and table, and the
various simple characteristics themselves, red and sweet, etc.). These are
distinguished from concepts which are comparable, which have one or
more characteristics in common (hence, according to the ordinary doctrine,
are included in the same higher concept) and differ only in the remaining
characteristics. But this distinction is only relative. Nothing whatever is
absolutely incomparable, to the extent at least that the formal logical
determinations apply to everything which enters into thought. But if we
disregard this fact then the most fundamental difference to be found
amongst concepts is that which causes their characteristics to be synthe-
sized in a different way, the difference of their categories. To this extent
THE CONCEPT
279
it is correct to speak of concepts which belong to different categories as
fundamentally different (e.g. man and virtue, man and movement); of those
which stand within the same category as relatively different. But funda-
mentally different ideas may still have many characteristics in, common,
though they have them in a different way, as with iron and metallic, man
and living, and yet not fall under the same higher concept in the ordinary
sense, since subordination has no meaning except within the same category.
2. We must be careful to distinguish between the difference of concepts
themselves according to their content, and difference of the objects in
which they are contained, and of which they can therefore be predicated.
Composite concepts would be impossible unless we could think of different
characteristics as determinations of one and the same idea, whatever the
form of their synthesis may be; and our ability to form ideas of the incal-
culable number of different things is especially dependent upon the pos-
sibility of combining different attributes as determinations of the same
thing. Every concept which admits of further determination by different
characteristics is included by the addition of these in various other con-
cepts; while on the other hand many higher concepts may be included in
one and the same lower concept.
Characteristics which can be combined in one concept, and concepts
which can be thought as parts of one concept, are called compatible.
When one species is comprehended under different generic concepts, these
are called cross concepts, inasmuch as they have at least a part of their
extensions in common; when they are represented figuratively (say, as
circles) the boundaries of their extensions intersect and include a portion
which is common to all. Thus in the square, quadrangle and regular figure
overlap. It is clear that the concept in which two higher concepts overlap
arises from the combination of characteristics in which these two differ, and
which thus appear as mutual determinations. The two concepts abc and
abg overlap in the concept abcg, and this may be regarded as the deter-
mination of a b c by &, or of a bg by c.
3. Opposed to compatible characteristics are those which are irrecon-
cilable or incompatible (cf. § 22, 8-13, p. 131 sq.). These cannot be
thought together in the same concept, but are mutually exclusive as deter-
minations of the same thing. There is no characteristic which would be
incompatible with all others; all must at least be compatible with the
formal logical determinations. But incompatibility itself, when logical, is
involved in the nature of our ideas (cf. § 22, 8, p. 131 sq.).
280
LOGIC
4. Upon the fact that characteristics which are incompatible among
themselves may yet be all compatible with another, is based the differ-
entiation of concepts, and their complete development 1 (Division).
When a concept A is determined by two incompatible characteristics b
and c, these are called specific differences, and the resulting concepts are
themselves incompatible; i.e., they cannot both be thought as parts of the
same lower concept, nor both be predicated of it (no Ab is Ac, no Acis Ab).
Hence their extensions are absolutely distinct, and all the more specialized
concepts which are developed out of them are also incompatible, each of
these extensions, meanwhile, forming a part of the extension of the higher
concept (right-angled and acute-angled quadrangle, red and yellow rose,
etc.). Such concepts are called disjunct, and when their relation of subor-
dination to a higher concept is the same, disjunct-co-ordinate concepts.
When a concept A admits of only a limited number of mutually exclu-
sive determinations b c d, there arises a series of disjunct concepts, whose
extension covers the extension of the concept A, so that when A is deve-
loped into all the differences possible to it, each lower concept must
possess one or the other of these determinations. The concept A is said
to be divided into the concepts Ab, Ac, Ad, and these are called the
members of the division.
The division itself is represented by a divisive judgment : A is partly
Ab, partly Ac, partly Ad. Of every particular thing which falls under A
the disjunctive judgment is true that it is either Ab or Ac or Ad. (See
$ 37, 6, 7.)
5. Every differentiation presupposes that a concept is still undeter-
mined in one or more of its characteristics and admits of additional and
mutually exclusive differences; or that the synthesis of its characteristics
is incomplete and leaves room for more characteristics. Every division
presupposes that the total number of possible determinations is limited and
1 The prevailing logical terminology is inconvenient in that it employs the same ex-
pressions to denote two processes so different as the analysis of a concept into its cha-
racteristics and the development of opposed concepts from one higher concept ; these
expressions being derived from the act of dividing and signifying sometimes the division
of the content into its elements, at others the division of its extension into mutually ex-
clusive extensions. To this is due the paradox that by dividing a concept we do not
get parts of the concept, but concepts which each contain the whole divided concept as a
part. If we keep consistently to the content of the concept we are concerned with nothing
but a development of the characteristics contained in it. The term division (Aristotelian
dialpeous) is more applicable to the sum of the particular objects which fall under the con-
cept; this sum is regarded as a whole to be broken up into different groups.
THE CONCEPT
281
completely known. The concept of the rectilineal plane figure is undeter-
mined in several points, both as to the number of the sides and their
magnitude, and as to their relative as well as their absolute magnitude ;
and again as to the relative magnitudes of the angles (the absolute magni-
tude of these is not a completely independent characteristic, but depends
within certain limits upon the number of sides). According as determina-
tions are added on one or the other of such points, the concept is
developed in different directions into its differences. In the same way the
concept of fluidity is as yet undetermined with respect to its transparency
or capacity of reflecting light, with respect to its smell, taste, etc. Smell,
taste, and colour are not differences in one of the characteristics forming
the concept of fluidity; but they can be added to the other characteristics
because their general possibility is involved in the characteristics of the
concept fluidity.
Strictly speaking, only the first form of differentiation can be called
development or explication. If we call that characteristic which is differ-
entiated the ground of division (fundamentum divisionis), then the ground
of division here is in the given concept itself, and consists in the fact that
a characteristic admits of mutually exclusive determinations. Thus the
concept of the line is developed into the concepts of straight and curved
lines. The idea of the line involves movement, and this cannot be thought
without direction; direction which remains the same forms the straight line,
direction which is constantly changing the curved. The concept of the
curved line develops into the concepts of those which return into them-
selves and are thus closed, and those which may be continued to infinity,
for constant change of direction includes both possibilities.
The second form of differentiation adds determinations from without.
The ground of division is in the first place nothing but the indefinite
possibility of a further characteristic which is independent of those already
present, or the possibility of various irreconcilable characteristics ; the
question is asked whether there are any more characteristics which are recon-
cilable with Ab, and such determination might be called synthetic. The
concept of fluidity contains no characteristics but those which are founded
upon sensations of sight and touch, only the mere possibility of taste and of
differences of taste are given with it; they must be added as new elements.
It is here then that there arises the possibility of negative distinguishing
characteristics, which express mere privation. We divide the concept of
organic being into feeling and not feeling, of flowers into scented and
282
LOGIC
scentless, of fluids into colourless and coloured; the absence of a character-
istic which is compatible with the remaining characteristics, but is not
necessarily connected with them, forms here a specific difference. In
such cases the negative formula loses its indefiniteness; it has for its
content the possibility of the positive characteristic which is included in
the general concept and realized in one of its species. Its function is
not the independent expression of some content; it serves merely to mark
a distinction and to fix the order of the concepts.
We must carefully distinguish between these privative characteristics as
means of differentiation, and those in which the negative expression of
characteristics is only an indirect statement of the positive differences con-
tained in the same general characteristic. When I divide lines into
straight and not straight, or men into white and not white, the negative
expression has a definite positive meaning ; it signifies those character-
istics which are excluded from the negated difference on the ground of the
same fundamentum divisionis. The negation of the possible determination
is limited to a definite area and thus states something positive; it is
grounded upon a disjunction (straight or crooked, white or coloured, and
again white or yellow or red or brown or black). The negation of one
member of the disjunction contains the assertion of the others.
This negative formula finds a double application. In the first place it
serves to comprehend a number of co-ordinate disjunct members into one
expression, because they are alike in some other respect in which they
differ from the concept excluded by the formula. The meaning of divid-
ing men into white and coloured (i.l., not white) lies in the fact that in all
coloured people the capacity for higher culture possessed by the white is
wanting. Otherwise, if colour alone were taken into consideration, the
difference between black and red, or red and yellow, is as great as that
between yellow and white; there would be no ground for expressing this
series of equivalent differences by the negation of one alone.
The second application is where one amongst an infinite series of
possible differences can be conceptually determined, this being impossible
or less easy with the others because of their endless number; they can be
conceptually determined only by limiting them with reference to the one.
This is the case with regular and irregular figures. Each of the latter has
itself a definite relation between sides and angles, but opposed to the
simple characteristic of having equal sides and equal angles there is an
endless number of other relations, none of which can be reduced to so
THE CONCEPT
283
(D
simple an expression, and which it is absolutely impossible to determine
one by one.
6. Here, then, in connection with the division of concepts, we find the
value and significance of negative expressions, to which we were obliged
($ 22, 11, P. 134 sq.) to deny any justification when put forward as in-
dependent symbols of ideas, by themselves and without reference to the
question before us. We can see now also in what sense the distinction
between the so-called contrary and contradictory oppositions is justified.
If we limit the expression “opposition ” to the relation between disjunct
co-ordinate concepts, then we find contradictory opposition between the
disjunct members of a division having two members, contrary opposition
between the disjunct members of a division having more than two. In
the former case, one member can always be quite definitely and unam-
biguously denoted by the negation of the determination which consti-
tutes the other member ; not so in the latter case. In the former case,
if Ab and Ac are the disjunct members, Hb is the same as A non-c, and
Ac is the same as A non-b; in the latter case, if Ab, Ac, Ad are the
members, Ac is indeed included in the formula A non-b, but as this
formula comprehends both Ac and Ad, it should be expressed as
A non-b, c.
7. When the number of differences is by nature unlimited, we cannot
speak of a division in the proper sense ; but only of the development of
a higher concept into an infinite series of disjunct lower concepts. Thus
the concept of the polygon may be developed into the species triangle,
quadrangle, pentagon, and so on in infinitum.
8. Our attention is drawn by this example to another point. When
a characteristic taken by itself implies a series of disjunct differences, -
as the characteristic plurality implies numbers, and colour the particular
colours,—then it depends upon the nature of the remaining characteristics
whether any of these different determinations can be combined with the
concept, or only certain of them. All numbers occur as disjunct charac-
teristics of the concept of the spherical polygon ; but the characteristics
of the rectilineal plane figure exclude the number 2, and those of a
body bounded by plane surfaces exclude the numbers 2 and 3.
This choice amongst the various determinations of a characteristic
becomes of special importance when the process of division does not
take place by the development of the contents of a given concept, thus
circumscribing its logical extension, but starts from its empirical extension.
1
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Then the problem arises of dividing a concept in such a manner that all
the different determinations may be empirically forthcoming. The fact
that the human body is not transparent involves its having some colour ;
and if we were to develop the concept from this characteristic alone, we
should have to introduce all the colours as members of the division.
Starting from this characteristic and leaving other considerations out of
the question, we are as much bound to assume a species of blue or green
men as of black or white. In reality many of the colours are wanting,
and when we divide the concept man on the ground of colour, we
enumerate only those colours which are actually forthcoming, regarding
the division as complete when it includes all these actual variations. .
But there is no doubt that in this limitation we generally confuse two
quite distinct problems: there is the problem of classifying a given
number of particular beings, and this we shall afterwards examine more
closely, and there is the problem of presenting a system of concepts to
serve for our knowledge of the particular by means of Predicates which
have a perfect logical determination. If it were merely a matter of
chance that only some colours are actually found within the range of our
experience as the colour of the human skin, then the so-called division
of men would be no division of the concept, but merely a classification
of actually given men; we could never say that we had in this way
exhaustively divided the concept. It would be a mere enumeration of
disjunct species; just as in chemistry we enumerate the metals without
meaning to say that no more new kinds can be discovered.
If, indeed, we can regard the fact that no other complexions are forth-
coming as a sign that a blue or green complexion is excluded by the other
characteristics of the human being, then, and then only, would it be
possible to accept the empirical classification of men as an exhaustive
division of the concept man. That a mere classification of what is given
in experience is frequently substituted for the division of the concept,
the logical extension being thus confused with the empirical—is quite in
accordance with the habit of neglecting to consider the concept according
to its intension, and with the more popular and intuitable method of
always starting from the empirical extension. In consideration of this it
must always be remembered that logical completeness of division is never
guaranteed by the fact that the extensions of certain members of a division
are together equal to the empirical extension of the concept divided.
9. When the division has been carried out, it brings to light a dis-
THE CONCEPT
285
tinction amongst the characteristics which has not yet been noticed ; the
distinction between the nota communes and the notæ propriæ. Some of
the characteristics, that is, may be common to a great number of concepts
which are otherwise different; while others presuppose a definite com-
bination of other characteristics, and thus distinguish a given concept
from all its higher or co-ordinate concepts. Thus the characteristic
“possessing only plane right angles” can occur only in the quadrangle;
it is a nota propria of the right-angled quadrangle. But such a nota
propria may also belong to a generic concept, hence characteristics which
belong only to an infima species are called specific notæ propriæ. Where
such characteristics are found they distinguish one concept from all others,
and they are then called distinguishing characteristics.
10. The same concept may be divided according to different grounds,
and because the resulting concepts generally overlap, these are called cross
divisions. Thus the division of parallelograms into rectangular and
oblique-angled crosses their division into equilateral and unequilateral ;
the division of plants into phanerogams and cryptogams crosses their
division into land and water plants. Such a combination of grounds is a
means of breaking up a concept into a number of others which are not
immediately subordinated. The number of members resulting from
several independent divisions, each of which by itself would yield a, b, c,
etc., members, is equal to the product of these numbers.
II. We can imagine a logical system containing all the most simple
combinations of characteristics which can be thought as independent and
isolated concepts, in which these combinations should again be developed
by division on all sides and according to all grounds into the most specific
concepts possible. We should then have a systematic synopsis of all the
concepts we could possibly construct; both their relations of subordination
and their differences would be fully determined, and we should be able to
see at once how any given idea was subordinated and opposed to all
others. The logical ideal of a perfect analysis of our ideas would then be
attained, and we should have moreover a system of Predicates appropriate
to all particular objects, and a means of classifying them in the most
varied ways. For though every object would then fall under only one
lowest concept, so that it would be distinguished from all other objects
which did not agree with it in every characteristic, still its various
There is no ground for any special treatment of what is called sub-division, for the
process is exactly the same whether we divide a higher or a lower generic concept.
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LOGIC
aspects would enable us to subsume it under different series of higher
concepts.
§ 44.
A DEFINITION is a judgment which states the meaning of a term denot-
ing a concept. This it may do, either by an expression which exhibits the
concept broken up into its characteristics, and gives a complete account of
its content, or by stating the genus next above it, and the specific differ-
ence, thus indicating its position in the ordered system of concepts.
All logical definitions are nominal definitions. The demand for a real
definition arises from the confusion between metaphysical and logical
problems.
Definitions are analytical or explicative when they refer to a concept
which is already formed and denoted by a recognised term; they are
synthetical or determinative when by synthesizing determinate characteristics
they present us with a new concept, and introduce a term for it.
We must distinguish between definition proper and the attempt to dis-
cover the concepts upon which our ordinary use of language is grounded.
1. Suppose our logical ideal to be attained, and every concept to have,
moreover, its established and unambiguous denotation in language: then
the problem of stating the contents of a concept would be solved by the
mere repetition of the analysis and synthesis through which it first became
a concept, and we should only have to make sure that we could at any
moment realize the meaning of such a word by unfolding the elementary
characteristics contained in the concept denoted by it, and that we could
recognise its position as subordinate and disjunct. The first is done by a
formula stating the particular characteristics, from the synthesis of which
the concept arises; the second by a formula naming the genus proximum
and the differentia specifica, i.e., exhibiting the concept as member of a
division. (Since the same concept may have different genera, and the
order of determination may vary, there may be different formulæ for the
second answer. The square is a quadrilateral regular figure, an equilateral
rectangle, etc.; such formulæ differ only apparently, and cease to differ
when the analysis is continued, and these higher concepts are also resolved
into their characteristics.)
We may call the statement of all the characteristics of a concept, or of
its genus proximum and differentia specifica, definition, and it is evident that
in such definition we cannot be concerned with the explanation of a con-
THE CONCEPT
287
(
cept, but that, so far as there is any explanation, it is that of a term. An
idea is not a concept unless it is clear, i.l., unless we are fully conscious of
what is contained in our thought of it ; thus the definition is the concept
itself, not something different. It is only the term, which in comparison
with the concept is external and fortuitous, which secretes the wealth of a
thought in one sound, and which, indeed, is frequently used like x and y
in algebra, as a mere symbol of which we fail to realize the meaning at
every step ; it is the word which, because its external form fails to show
its relation to the words which stand for higher or lower concepts, as a
chemical formula shows composition from elements, needs to be explained
and to have its content constantly brought to mind. Such explanation
is especially needed when the word is taken from popular language with
its fluctuating boundaries, and when we have formed, or wish to form, a
constant and unambiguous symbol, from one which was uncertain and
ambiguous. If we were to carry out Leibniz' ideal of a characteristica
universalis, then the symbol indissolubly connected in thought with every
concept would also be its definition, and would enable us to see its rela-
tion to all others.
Definition in this sense, then, can never be anything more than nominal
definition, stating the meaning of the word; it can be a real definition ?
1 To insist that a definition should be real in any other sense is to confuse different
problems. We cannot say whether any actual object corresponds to a concept of com-
plete logical definition until we have our concept and can subsume under it the objects
given. We cannot say whether the characteristics of a concept represent the essential
nature of the things which fall under it, or whether they include the real causes of these
things, until we have a perfect knowledge of the objects ; but this knowledge itself
cannot be called a definition. This applies also to the example given by Lotze (Logik,
2nd ed., p. 202): “When we call the soul the subject of consciousness, of ideation, of
feeling and will, this may be appropriately called a nominal definition. The real defini-
tion of the soul could be established only by proving either that the subject of conscious-
ness and its manifold phenomena could be nothing but a supersensuous and indivisible
being, or that it could be nothing but a complete system of material elements." The
knowledge of the nature of the being which we have first determined in our concept of
the subject of consciousness is no definition, it merely establishes the dependence of the
characteristics first thought of upon others which are not yet included in the concept.
By the knowledge of this dependence the concept is enriched ; we now understand by
"soul” an immaterial, indivisible being, which is the subject of consciousness. But
this definition is nominal in the same sense that the first was, and in the same sense that
the first was it is also real; here again we "name the conditions which any thing real
must fulfil, if it is to claim the name of soul” ; the only difference is that we name them
more fully. The two concepts merely denote two stages on our way towards the goal of
knowledge ; further investigation will teach us how the beings which fall under this
enriched concept must, by their nature, be related to other beings, and from such in-
creased knowledge will result still richer definitions. Knowledge always presupposes
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LOGIC
only in the sense that it must analyse the contents of the concept in
thought, and distinguish them from the contents of other concepts.
Merely verbal explanations, such as “logic is the science of thought,"
“ democracy is the rule of the people,” or explanations of verbal abbrevia-
tions, such as “a perpendicular is a perpendicular straight line," cannot be
called definitions at all (cf. § 5, 3, p. 27).
Thus a definition is a judgment, in which the meaning of a word
representing a concept is equated to the meaning of a composite expres-
sion; and this expression states the particular characteristics of the con-
cept, and the manner in which they are synthesized, by means of the
particular words forming the expression, and the way in which they are
grammatically connected. We have an equation between two symbols of
the same concept, and the symbols may therefore be substituted for each
other. It follows, as a matter of course, that anything which is covered
by the one word is also covered by the expression, i.e., that the extensions
of subject and predicate are absolutely the same. The existence or
material possibility of something corresponding to the concept may indeed
be presupposed by the definition, but can never be stated by it; the
definition is an explicative judgment, such as we dealt with in $ 16.
From this it follows directly that the definition (definiens) must not repeat
the word to be defined (the definiendum). We must not define idem per idem,
for in so doing we fail to fulfil the condition that analysis must always
break up the thought, which, when it appears in one word, is a unit, into
elements which are necessarily denoted by different words. This is the
source also of the objection to repeating in the definiens even a word of
the same derivation (e.., freedom is the ability to act freely), an objection
which is justified only when the etymological relation of the two words is
unequivocal, and both are used in exactly the same sense (e.g., redness is
the quality of being red). The explanation of freedom given above may
serve as it stands for a definition, because the meaning of “free” is limited
a definition of the word which it employs, to give clear determination to its object; the
characteristics which are thus established may be found to be necessarily connected with
others, and then these are taken into the definition and the same process repeated with
the concept thus enriched. The demand for a real deninition, containing the essential
characteristics, is a return to the Aristotelian demand, that the concept should state the
essence of the thing, according to his metaphysical theory. Now that we have left the
Aristotelian metaphysics far behind, and confess our ignorance in most departments of
knowledge of the ti cotl, in the Aristotelian sense, it would be well also if logic were to
relinquish the concept of the real definition. It has ceased to have any meaning in
logic, and represents only a one-sided ideal of knowledge.
THE CONCEPT
289
by the expression, “to act freely," and not every instance of being free,
e.g., free from pain, is to be called freedom. In such cases it is the mean-
ing of the derivative syllable which is the chief object of the definition ;
and there is as much justification for this as for explaining only one
portion of a composite term (e.g., vital force is the inner ground of
vitality).
It follows further from the nature of the analysis demanded that in
defining we must go back to simpler elements, and that a correct definition
must not move in a circle, so as to reintroduce the definiendum itself in its
enumeration of characteristics.
On the other hand, the rule “ definitio ne fiat per negationem” does not
hold good under all circumstances. It is true that the statement of what
a thing is not does not tell us what it is; but as a concept is often dis-
tinguished from co-ordinate concepts only by the privation of a char-
acteristic, and as this task of distinguishing is included in definition, we
cannot always avoid negative determinations.
That an enumeration of the species of a concept cannot be a definition
is evident from the fact that the species contain the concept, and their
enumeration would involve a circle.
The rule that definitions must be precise prohibits the statement of
characteristics, which are already contained in, or necessarily connected
with others (derivative characteristics), e.g., to include in the definition of
a parallelogram the statement that the opposite sides are equal as well
as parallel. Still, a so-called “superfluity in definition” is not positively
wrong, and is even preferable where there is not absolute certainty as to
the connection between the characteristics.
For the names of ultimate elements there is no definition ; we must
assume that every one attaches the same meaning to these. They can
be named, but not explained. Where they are not yet known they can
only be shown by bringing about the conditions under which the idea will
be aroused. This is possible in the case of colours, smells, and tastes, if
we assume that different people are similarly constituted. The only case
in which we find something analogous to definition is with a series of
concepts bearing a common name, the statement of which recalls the
various members of the series-1.9., when we say “red is a colour.” Here
we can give something which corresponds to the genus proximum, but we
cannot give the differentia specifica; this could be replaced at best only
negatively, by denial of all other varieties.
S. L.
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LOGIC
If, then, in constructing our concepts we are obliged to fall back upon
the laws of our simple mental functions and the forms of their synthesis, a
perfect definition becomes one which enables us to build up the idea of
the object from its elements ; this alone can be called a genetic definition.
3. Unless we may assume a complete and accepted analysis of our
ideas into elements which are perfectly definite in their determination,
and denoted by all in the same way, there can be no concepts in the
logical sense, and this would make it generally impossible to solve any
problem of definition-as impossible as from an equation of which every
term is an unknown quantity to determine any one of them. Every defini-
tion presupposes a scientific terminology.
When such a terminology is not forthcoming we can form a good de-
finition only in so far as it may be possible to find expressions in ordinary
language which are unambiguous, and which may serve, at any rate in
practice, for the unerring subsumption of actual objects. Such, for instance,
is the case with jurisprudence in its application to the relations of daily life.
4. It may happen that although the elements of certain concepts are
familiar to us, we have not ourselves as yet formed all the concepts which
might be formed from them, nor completely learned the meaning of their
denotations. Then the definition, when heard, serves both as a guide
to the formation of our concepts and as an interpretation of a word we
do not understand.
Moreover, since all that is included in the logical ideal is that all the
elements and forms of combination should be conceptually established,
the formation of composite concepts may be continually progressive.
This is the more true because of the impracticability of attempting all the
combinations of concepts possible in the sphere of reality, until we can dis-
cern the grounds of the real compatibility or incompatibility of particular
characteristics, and of their combinations, or until the occasion for forming
some definite combination presents itself. Hence the necessity of forming
new concepts, and of coining new words for them, to which we must give
conceptually determined meanings.
The definitions first mentioned set forth analytical equations, in which
the import of a word is expressed by means of an equivalent formula.
The equations, by means of which we first get definite expressions for new
concepts, are determinative equations; they give import to a symbol by
equating it with an expression consisting of familiar elements. When we
first form the mathematical concept of a function, we give a meaning to
THE CONCEFT
291
the word by means of a formula, which has an external resemblance to a
nominal definition, but which is really different. Definitions of words
which stand for concepts already formed have been called analytical ;
those which introduce the term for a new concept, synthetical.1
5. We must further distinguish between these two kinds of definitions
and those explanations of words which merely serve to establish the
way in which language is actually used. In their original purpose these
are merely atternpts to justify this actual use of language, and to give a
reason for it by showing that it is grounded in each instance upon a
definite concept, which is contained in the thought of all the objects
named by the word and in no others, and they thus indicate the point of view
from which language ranges many objects under the same name ($ 40, 5,
note). When these attempts are successful, they narrate the meaning,
which, as a matter of fact, always belongs to a certain word. It is only to
explanations of this sort that the warning against making a definition too
narrow or too wide originally applied, i.e., its characteristics must exclude
no objects which language continues to name by the word, and include
none which language names by another word. But it is evident, first,
that a definition is only possible when we presuppose characteristics which
are conceptually determined, and then that many words do not admit of
any definition in this sense. This is sometimes because their denotations
have become arbitrarily extended, thus making it necessary to distinguish
between their different meanings, sometimes because they are used only
to denote certain individual phenomena, and their extension to others,
even when they agree in possessing the common characteristics, is not
authorized by the use of language. The greatest acuteness can find no
simple definition of the word people, when we try to give the usual
meaning of the word. Words such as church, theocracy, feudalism, are
not symbols of concepts; they merely denote certain historical phenomena
by their prominent features, and are thus names of single things. The
dispute as to the concept belonging to them may continue for ever. .
Here also, when the problem from which we start is that of discovering
a concept from the objects to which ordinary language has given the same
name, there is a meaning in the rule that the essential characteristics
Drobisch, § 117 sqq., rightly notices that in a synthetical definition the definiendum
really occupies the place of the predicate, this predicate being nothing more than the
word as a name. In the case of the definitions at the beginning of Spinoza's Ethics the
formula employed - Per substantiam intelligo id quod, etc.— shows them to be definitions
of the second kind ; that is, they introduce simple verbal denominations for definite ideas.
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LOGIC
:
should be united in the concept (cf. § 42, 8). For here, no doubt, what
we have to do is to determine the concept in such a way that it may con-
tain the ground upon which the name was given, and that only those
characteristics may be included by which we were guided in giving the
name, and upon which it depends whether or not new things will be
called by the same name. Starting from the empirical extension of the
name “man," we should be obliged by the laws of abstraction to include
in the concept the characteristic “without a tail,” for this is a character-
istic common to all known men. When, however, we have determined
that, assuming complete similarity in all other respects, we should not be
deterred by the external appearance of the rudiments of a tail, which are
present in human beings, from continuing to call the bearers of this limb
a man, then the characteristic “ without a tail” is no longer a part of the
concept “man”; it must not be included in the definition, because it is
not taken into account in subsuming the particular under this concept.
But it depends entirely upon the point of view taken in classifying objects
by means of language what is in this sense essential, and what is imma-
terial. A characteristic may be immaterial in one aspect, while in another
it is essential.
From this problem of determining the actual meaning of a word from
the way in which it is used as a matter of fact, we must distinguish that
of stating the meaning in which certain words ought to be used in defi-
nite scientific statements or laws, as opposed to the uncertainty of their
ordinary use. Assuming the general concept under which they fall to be
given and known, any determination may serve for this purpose which
marks the limits within which the word is to be applied with certainty,
and without ambiguity, even though the distinguishing marks employed
may be only derivative and accidental. As an extreme instance, we may
take section 1 of the German Penal Code, which distinguishes between
crimes, misdemeanours, and transgressions, according to the measure of
punishment attached to the actions. Taken as a definition in the ordinary
sense, this would be a logical monstrosity; as merely marking the limits
within which certain terms are meant to be employed, when it is assumed
that the general meaning of these terms as a punishable violation of the
law is known, it is justifiable.1 We find a similar instance in the statement
that the warm zone is that which lies between the tropics.
1 Cf. what G. Rümelin has to say on this point in his Juristische Begriffsbildung, 1878,
p. 22 sq.
THE CONCEPT
293
6. It may be that our only aim is to denote certain objects in such a
way that we may be able to distinguish them confidently from all other
similar objects. Then it is not necessary to state the whole contents of
the concept; a formula which states its distinguishing attributes, and which
may be called a diagnostic definition, is sufficient. Chemical reactions -
which are peculiar to certain substances are instances of such characteris-
tics; they make it superfluous to state the complete contents of the
concept when the only object is to subsume given phenomena correctly,
and to distinguish them from others. The property of colouring starch
blue is characteristic of iodine; hence the manifestation of this property
is sufficient to prove the presence of iodine, and is a means by which to
distinguish iodine from all other similar elements. But only in this con-
nection can this characteristic be substituted for the whole concept; its
significance lies in the fact that its presence proves the presence of the
remaining characteristics which constitute the concept of iodine. We find
similar distinguishing attributes of a derivative kind in the spectral lines of
the particular substances.
From one point of view it is impossible, as Kant has shown, to give
any exhaustive definitions of natural products. We must be content to
include in our formulæ a selection of characteristics which may state the
most easily recognisable attributes so far as to enable us to distinguish the
objects with confidence. For this reason, all definitions of such objects
are diagnostic, inasmuch as they cannot enumerate all the characteristics
which belong to the object, nor even all which are contained in our
knowledge of it.1 Nevertheless, there still remains a difference between
S
1 In such definitions we see a particular aspect of the nature of concepts in their rela-
tion to concrete existence. So far we have not expressly considered a difficulty which has
been lately revived by Volkelt (Erfahrung und Denken, p. 342 sq.) with penetration
and acuteness, the question, that is, as to whether the general idea as such is in any
way conceivable; can we form any actual idea which is general, or must we not rather
agree with Berkeley that we have only particular intuitions, and that generality is to be
found in the word alone? Referring to Lotze (Logik, edn. 2, p. 40 sq.), Volkelt says
that generality cannot be obtained by simply omitting the distinguishing characteristics.
“ Must we not say that the thought of a triangle which is neither equilateral nor
irregular, neither acute-angled, right-angled, nor obtuse-angled, is no thought at all ? "
Generality, therefore, can be conceived only with reference to the indeterminate totality
of the particular; in the concept is implied the thought that the general idea is a con-
ceivable something only when accompanied by distinguishing characteristics, only in the
particular or as the particular. Hence it follows that the ideal expressed by the concept
could only be realized in a consciousness which should combine with the general idea its
appropriate intuition in one indivisible act, and should do so, moreover, as infinite,
absolute timeless thought. These propositions are no doubt true in so far as an all-
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LOGIC
those formulæ which are only intended to afford the greatest possible
facilities for diagnosis, and those which are also meant to represent the
contents of a concept. The latter will give some at least of the funda-
mental determinations, and will achieve this by a statement of the genus
proximum ; to them applies the rule definitio ne fiat per accidens. For the
former, casual and superficial distinguishing marks will suffice ; they are
not intended to be characteristics of concepts, but only of the objects
which are to be subsumed under given concepts.
embracing consciousness of this kind is the ideal of our thought; a consciousness which
should include the whole system of concepts with all its specifications, as well as its
realization in concrete phenomena. At the same time, that view of concepts which
solves the difficulty, and from which, moreover, general concepts as such derive their
importance for actual thought, has been lost sight of, the view, that is, that logical con-
cepts are meant primarily to serve as predicates, and not to represent the existent as
such, for this must naturally always be particular, concrete, and determinate. The
thought of “a triangle” which is neither equilateral nor irregular, neither right-angled
nor oblique-angled, is indeed nonsense ; if I am to think of triangle as a particular thing
given in intuition, I must carry out the determinations, and not negate them. But then,
am I not to be able to affirm merely that a figure is a triangle, without concerning my.
self about its magnitude or more exact shape ? All judgment, as well as all our con-
struction of concepts, depends upon our power of analysis, and of thus making promi-
nent one aspect of a thing. If I have a clear idea of what an angle is, and of what the
number three is, then “triangle" is assuredly a predicate which is completely deter-
mined and comprehensible by itself. Again, have I really no subjective correlative to
this general word “angle”? Certainly not, if I begin to think of complete intuitions,
but I may find such a correlative in the process by which I intuit an angle, in the sudden
change of direction which—whether great or small—is a matter of immediate feeling as
I move my eyes. Could I have no idea of the number three unless I also thought of
definite objects? Is it not sufficient to be conscious of the process of counting three, a
process which I can apply to whatever I may choose? It is not the part of conceptual
formulæ to take the place of intuitions of the particular; they merely enable us to make
a logical analysis of such intuitions. They are based on the fact that every particular
thing can be expressed by general predicates.
CHAPTER II.
THE TRUTH OF IMMEDIATE JUDGMENTS.
IMMEDIATE JUDGMENTS are those which we can state with a consciousness
of their objective validity, without anything being presupposed beyond the
ideas of subject and predicate which are connected in them ($ 18, 1).
The most obvious of these are (1) the merely explicative judgments, which
only state in the predicate what is thought in the idea denoted by the
subject word, and (2) judgments concerning the particular which rest upon
immediate intuition, and which state what predicate belongs to a given
particular idea. Amongst the latter we may distinguish between (a)
statements concerning ourselves, and (6) judgments of perception con-
cerning the external world.
§ 45.
For the truth of judgments which merely státe something about the
relations of our established concepts we find a ground in the Principle of
Agreement, and in so far as the relations of concepts include the incom-
patibility of certain characteristics and concepts, in the Principle of
Contradiction.
1. We have seen that we cannot speak in an unambiguous sense of the
truth or falsehood of judgment unless the ideas presupposed in it are
completely determined. Explicative judgments (S 16) deal only with ideas
which are assumed to be already possessed by every one. When those
ideas are concepts in the logical sense, such judgments merely state the
relations between concepts which are already fully determined; they are a
repetition of the process of unification and differentiation which took place
when the concept was formed.
2. Positive judgments containing definitions, judgments which predicate
its characteristics of a concept, and judgments which predicate a higher
concept of a lower one, all derive their necessary truth from the given
295
296
LOGIC
contents of subject and predicate. The fact which they presuppose (s 39,
3) is that the concepts standing as subject or predicate should be actually
always and by every one. But the law according to which the judgment is
necessary when this is presupposed is none other than the law of agree-
ment (S 14). Now, for the first time, when the invariability of our ideas
is assured not merely for the moment of judging ($ 14, 4, p. 82), but for
the whole duration of consciousness, can this principle be applied not only
as a natural law but as a normal law of thought; and because the con-
cepts are the same for all, it becomes also a guarantee for the universal
validity of the judgments.
Thus it does not depend upon anything in the nature of the Principle
of Agreement whether it is to be regarded as a natural or a normal law,
but upon the data to which it is applied. In the first case, it is applied to
that which happens to be present to consciousness at the moment; in the
second, to an ideal state in which all the ordered contents of the ideas are
present without change for one consciousness, an ideal which can never be
completely attained empirically. This ideal constancy alone can appear
as the principle of identity in a normative sense, which demands that A
should = A, i.e., that in every act of thought the conceptual elements
should be always the same, and should be known as the same (in praxi
that we should always connect exactly the same meaning with a word).
To satisfy this demand is possible only for a consciousness which is
absolutely certain of an invariability in its ideas independent of all
temporal change; a consciousness, therefore, which can think as if the
whole world of concepts stood in unchanging clearness before a timeless
intuition. But the principle of identity in this sense is not the principle
of our judgment; for this unifies not that which is the same, but that
which differs.
3. It might be asked upon what the validity of the Principle of Agree-
ment itself depends; and in answer, we can only fall back upon our
consciousness that the unification of elements which agree is something
absolutely self-evident. When we reflect upon our action in judgment, we
are conscious of it as always the same, just as it is possible for us to be
assured of the identity of our ego through all temporally different acts,
past as well as future, and to represent in one act of thought the unvarying
repetition of the same “ I am” through an unlimited series of moments;
and just as it is possible for us to retain the same ideas in the mind, and
THE TRUTH OF IMMEDIATE JUDGMENTS
297
to be conscious that they are the same, so also it is possible for us to be
assured that in our judgment we shall always proceed in the same way as
certainly as we are ourselves the same. All consciousness of necessity
depends finally upon our immediate certainty that our action is invariable.
For this reason it may be urged that, after all, it is only an inner experi-
ence which yields us this certainty, and to this there is no answer. But
then we must distinguish between the experience of the particular acts of
our varying ideation and the experience which in each particular act is
accompanied by the certainty that it is not dependent upon the momen-
tary and changing conditions of the particular act, but will continue the
same throughout all changing moments. It is this immediate certainty
which gives us the immediate and unanalysable intuition of necessity, and
though this is indeed the object of experience, i.e., of an immediate
consciousness taking place at a given point of time, yet it is not merely the
result of a number of experiences.1
4. The establishment of definite relations amongst concepts leads also,
and as directly, to the necessity of all negative judgments which distin-
guish between different concepts as wholes, and, according to the Principle
of Contradiction (S 23, p. 139), of negative judgments which deny
irreconcilable characteristics or concepts of a concept. To put the same
thing in another way, it involves the necessary falsity of judgments which
attempt to attribute a predicate to a concept contradicted by it (contra-
dictio in adjecto). The establishment of conceptual relations involves the
incompatibility of certain characteristics as an invariable relation ; that is,
it involves the necessity of denying b when a is affirmed. Thus to
ascribe b to a concept containing a, is to say that the same thing is a and
is not a.
5. The Principle of Contradiction as a normal law has just the same
meaning as when it appears as a natural law, merely determining the
meaning of the negation ; but while as a natural law it states only the im-
possibility of consciously affirming at any moment both that A is b and
that A is not b, as a normal law it is definitely applied to the whole range
1 For this reason I cannot altogether agree with the view taken by Baumann
(Philosophie als Orientierung über die Welt, p. 296 sq.) concerning mathematical
necessity. The experience that when repeating our ideas we always form them in the
same way cannot of itself yield necessity; the fact that anything actually happens cannot
exclude the thought that it might possibly be otherwise, only the consciousness that the
fact will always actually be as it now actually is—.l., the consciousness of its necessity-
can do this.
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LOGIC
of invariable concepts covered by the comprehending unity of conscious-
ness. It is in this application that it becomes the ground for what is
generally known as the principium contradictionis, a principle which then
ceases to be co-ordinate with the principle of identity (in the sense of the
formula A is A) and presupposes it as already satisfied by the absolute
invariability of our concepts. And here again the absolute validity of the
Principle of Contradiction, and consequently of those propositions which
deny a contradictio in adjecto, rests upon the immediate consciousness
that, so surely as we ourselves remain the same, our action in denial always
is and always will be the same.1
6. To the establishment of conceptual relations is also due the validity
of judgments of possibility, which attribute to a concept as yet unde-
termined the possibility of receiving compatible determinations (8 34, 5,
p. 207), and of disjunctions which are based upon division.
A concept may cover a number of species, or be applicable to many
particular things, and may therefore be predicated of different subjects.
To the extent to which this is the case the hypothetical necessity of at-
tributing the predicate of the concept to that which falls under it also
follows immediately from the relations of concepts. If the statement “ A
is B” is true of the concepts, then the statement "if anything is A it is
B,” or “all A's are B's,” is true also. Such judgments have always been
rightly regarded as analytical, and as owing their certainty to the principle
of agreement. It is the same with negative judgments; if the statement
“B is incompatible with A” is true of the concepts, then the statement
“ if anything is A it is not B” is also true.
7. In all these judgments, if we assume our concepts to be established,
we have only to read off what we have ourselves put into them; we are
dealing only with fixed ideas, and no one who has exactly the same ideas
can possibly doubt the judgments. For this reason they are independent
of time and unconditionally valid ; according to Leibnitz they are eternal
and necessary truths. But just for this reason they never make the direct
1 J. S. Mill (Logic, Bk. ii. fin.) treats the principle of contradiction as one of our
earliest and most familiar generalizations from experience, and takes it to mean that
belief and unbelief are two different mental states which exclude each other; a fact which
we learn from the simplest observation of our own minds. To some extent I agree with
him, but then the puzzle is : how do we know that they are not merely different but
mutually exclusive? If the certainty that they are mutually exclusive is to follow from a
slight observation, still the necessity of this mutual exclusion must be a matter of im-
mediate consciousness.
THE TRUTH OF IMMEDIATE JUDGMENTS
299
statement that anything is; neither do they refer to definite, particular
things, nor to existing objects. An existential judgment can never be
analytical in the Kantian sense ; for in an existential judgment the question
is—as Kant has irrefutably shown—whether anything exists which corre-
sponds to the concept. We first think of the subject of the existential
judgment as without existence, then we go on to say that it also exists just
as it is thought. Thus the ground for affirming that something exists
conceptual thought. If there is any such ground, it must be a something
present to consciousness which is distinct from conceptual thought.
8. But while it is easy to discern the truth of conceptual judgments
when we assume a completed system of concepts, we are far from having
exhausted the proper function of concepts. Conceptual judgments are
valuable as constantly reanimating our concepts and keeping them before
our minds, and as developing the abbreviation of the word into its fuller
meaning. Nevertheless the whole value and significance of a system of
concepts lies in its application, and in the assistance it gives, when used
for predication, towards a knowledge of that which is not yet contained in
the system as such. It is the organon of all knowledge, but it is not
knowledge itself; the apparatus with which we work, but not the product.
If all our thought were but a monotonous recurrence of what we already
know, and all our judgments but repetitions of those by which we formed
our concepts—as is tacitly implied in the school logic—then the human
mind would be condemned to everlasting sterility. Its progress consists
in constantly combining new elements with established concepts, or with
new concepts formed from these. Nor does the ideal perfection of a
universally accepted system of concepts complete the problem of know-
ledge, any more than a lexicon is the literature of a nation. The
progress of thought and investigation gives rise to new intuitions and
ideas, and our chief task is to become aware of the laws according to
which our judgment in its constant progress has a claim to truth and
universal validity.
9. This progress in thought and knowledge has its origin in the par-
ticular individuals who form judgments, and spread them abroad by
communicating them to others. Since the predicate must always be
assumed to have been previously given, the condition upon which these
judgments will be formed is that new ideas shall arise to serve as subjects.
When these are only new conceptual creations brought about by deter-
300
LOGIC
minative definitions (8 48, 2) the question of their validity is covered by
the laws given above. They serve only to effect a new abbreviation and
to introduce a term ; any judgment concerning them is again nothing
more than the explication of a concept.
It is different when the new subjects are ideas of particular objects. We
must assume for the present that the distinction between the idea of a
particular thing and the thought of the contents of a concept is accepted
and known to every one (S 7, p. 40 sq.); if we express it by the distinction
between intuition and concept, we must still assume that it is immediately
comprehensible. The most we can do is to determine it by derivative
and external characteristics, to say that what we think in the form of a
concept is purely mental, can be repeated at pleasure and without altera-
tion, and is dependent upon nothing but our own mental activity ; while,
on the other hand, that which is intuited is presented to us at a given
moment, and our thinking of it depends upon conditions placing it in a
relation to us which is independent of our own mental activity, and com-
pels us to locate in a particular object contents which might be expressed
in a general form.
It may happen that when a particular thing is given to me in intuition I
am nevertheless aware that it is peculiar to me as an individual, and that
if it is presented to others also it is so only by chance. Such is the case
with a dream, or a vision appearing to me alone, or the mental production
of creative imagination which for the moment appears as a particular ob-
ject independent of voluntary thought. Then, according to the Principle
of Agreement, I must, in so far as I consciously retain the idea of the object,
describe it correctly, i.e. in a manner corresponding to its contents; but
beyond this we can have no motive in seeking a ground for such judg-
ments, inasmuch as they are absolutely individual and incommunicable,
and can be believed by any one to whom the object is not presented upon
authority alone.
But the ideas may be such as can be produced in every one alike, and,
indeed, under certain conditions, must be produced in all alike, so that
they are naturally capable of being shared in by every one; and then we
have a motive for making our judgments concerning them in such a way
that they may be recognised as universally valid. This, for instance, is the
case with geometrical figures, 1 inasmuch as we suppose the idea of space to
i Geometrical constructions occupy a peculiar position, in so far as in them the distinc-
tion between the particular image and the concept disappears from one point of view. So
THE TRUTH OF IMMEDIATE JUDGMENTS
301
be the same for all, and the elementary data of geometry to be given as
intuitions. But more especially is it the case with all which we regard as
existing. When we affirm that anything exists, we think of it as a par-
ticular thing, or as the determination of a particular thing. It is further im-
plied in the concept of being, that the existent is independent of individual
thought, and the same for all. But if it exists, not through, but before
thought, it may conceivably stand in different relations to different
thinkers; the idea of it may be present to one person, and not to another;
it may be complete in one person, incomplete in another. Inasmuch as
the ground for affirming is not to be found in the conceptual thought
which is common to every one, it may lie in data of consciousness which
differ with the individual. On the other hand, a judgment concerning the
existent can only be true when all agree to it, since the existent is the
same for all who know it. It is this which makes us want to ascertain the
ground upon which the necessity rests of our judgments concerning the
existent.
When it is affirmed or assumed that something exists, we may generally
distinguish between the idea of the particular thing as subject, and the
judgment that it is,1 whether the latter be only tacitly understood (as
is generally the case), or expressly stated in an existential judgment.
$ 46.
Those judgments in which we give utterance to that immediate con-
sciousness of our own action which is present in every moment of our
waking life take the first place amongst immediate judgments concerning
the existent. Their certainty cannot be analysed any further. They in-
far as we regard them merely as mental images, due to our constructive activity alone,
images which are indeed particular intuitions at the moment, but which can be repeated
at will in such a manner that their identity is purely an identity of the ideal content-
such constructions possess the generality of the idea and of the concept ; the particular
as such is general. While, on the other hand, inasmuch as it is presupposed that the
elements of such constructions are presented to all in the same way, and that they can be
forced upon every one by external perception, they are allied by the fact that they are
the same for all to the intuitable existent, and we can speak, in a certain sense, of their
objective being. To avoid repetition, we will reserve a more careful investigation of the
judgments arising out of them for Part III.
1 Being in general cannot be regarded as the true generic concept to the particular
things which are ; conceptually regarded it is only a common name. For, inasmuch as
“Being” is for us a relational predicate, it cannot be a common characteristic ; we
should have to show that this predicate had its origin in a determination common to all
existing things.
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LOGIC
clude not only the certainty of the judgment "I am," but also the
certainty of the reality of the unity between substance and action.
In so far as they are subject to time, these judgments presuppose a
universal necessity to think of our particular actions as occurring in a
temporal series, and universal laws as assigning to each particular its
position in this temporal series.
1. Judgments such as “I feel pain,” “ I see light," "I wish this or that,"
are so absolutely certain, and so obviously valid, that they seem to leave
no room for a logical investigation as to their justification and the ground
of their necessity. Nor, indeed, can any one doubt their immediate truth
if we presuppose clearness of consciousness, and distinctness and complete
development of the concepts which serve as predicates. Assuming that
a person speaks the truth, no one can take upon himself the right of doubt-
ing his statements, and questioning whether or not he is to be believed
in what he says about himself. It would seem then that at present we
have only to determine what is the difference between these and con-
ceptual judgments.
2. This difference is fundamental. Conceptual judgments have subjects
which are assumed to be thought by every one in the same way. The
judgment, “I see,” has a subject which can be present to no one as it is
to me. The conceptual judgment unfolds the contents of its subject, these
contents being always contained in it in the same way; the contents of that
which is denoted by “I” can never be exhaustively stated; it is given to
us in a manner which is absolutely incomparable with all other objects of
thought. The conceptual judgment says, “ If I think of A, I must think
of it as having the determination B”; in the judgment of self-conscious-
ness there is no if. The subject is simply thought whenever anything is
thought, and the fact that it is thought is the absolute presupposition of all
other thought. The conceptual judgment tells us nothing as to the
existence of its objects, but the judgment, “I see,” always includes the
judgment, “I am.” We can always ask whether that which is contained
in a concept exists; I can never ask whether I exist. The charac-
teristics of the concept are unvarying; the predicates of the ego, with the
exception of the ego itself, change from moment to moment, and yet
every judgment as it is formed possesses an immediate certainty of truth,
which can only be acknowledged, and never proved. The Principle of
Agreement does indeed guarantee that the general concept of the predicate
shall agree with the action immediately intuited, but it cannot guarantee
S
THE TRUTH OF IMMEDIATE JUDGMENTS
303
N
2
either the statement that the subject is just performing this action, or the
statement involved in this, that the subject exists.1
3. If we are thus obliged to acknowledge that the utterances of every
self-consciousness possess a certainty which cannot be referred to some-
thing else upon which it is dependent, then all that remains for us to do is
to ascertain how much is involved in this acknowledgment.
In the first place, we find that with reference to this subject it is im-
possible to separate the mere thought of it from its being. Thus the judg-
ment, “I am,” differs from all other existential judgments, in that its sub-
ject is not the mere idea of an ego to which being is ascribed ; subject
and predicate are inseparably connected.
Further, the immediate certainty of self-consciousness involves, at any
rate upon this point, the reality of the synthesis between substance and ac-
tion ; and so far as actions may be referred to attributes, the reality also of
the synthesis between substance and attribute.
Finally, we find that the most fundamental certainty with respect to
being attaches to a judgment which cannot be repeated in the same way
by any one else, and which depends upon a purely individual act. For the
idea which some one else has of me is different from that which I have of
myself; it refers to the same subject, but not in the same way. Thus the
affirmation of being in its most original form is an act peculiar to the
individual, and dependent upon conditions peculiar to the individual.
Any judgment concerning another ego is necessarily mediated, whether it
is the acknowledgment of his being or belief in his utterances.
4. This immediate certainty, however, belongs only to the self-con-
sciousness of the moment; to the judgment which states what is present at
the moment. Thus the judgment is true only for a given point of time.
The way in which we are conscious of our particular states involves the
idea of time, for we are never conscious of a particular act without a
recollection of the act which preceded it in time, and our self-conscious-
ness always includes the consciousness of a self which is identical in time.
Now, in so far as every moment brings with it the thought of our being at
a previous time, and thereby of our continuous existence, we find im-
? Kant's doctrine, that statements of the inner sense refer only to phenomena, because
of the subjectivity of time, does not affect the logical character of such judgments; it
merely affects the metaphysical import, and the meaning of the statement about reality,
which they involve. Their immediate certainty as judgments is as unassailable under the
Kantian hypothesis as under any other.
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LOGIC
mediate certainty here also ; the “I am " involves an “I was before,”
which is as unquestionable as itself. But, strictly speaking, the certainty
extends no further. It is true that, when we are dealing with the
particulars of memory, the statement, that “I believe I once did so and
so,” cannot be questioned, but the belief itself cannot lay claim to the same
certainty. The inference of the reality of an actual previous event, from
the reality of a present recollection, could only be justified if there were
an absolutely necessary law, according to which I must, under all circum-
stances, retain the conviction of having at one time acted as I now believe
myself to have acted ; if, that is, there were no such thing as the discovery
of an error in our recollection. Now it is true that we regard some of
our recollections as absolutely certain, particularly those of more recent
events. But it is just as certain that, occasionally at least, our memory
deceives us, and that there is no sure criterion by which to distinguish
between perfect and imperfect recollections; in the last instance our only
warrant for the truth and trustworthiness of our recollections is our ability
to place them in a conscious connection, which is continuous and con-
sistent in all aspects. Thus the judgment that I have actually performed
a given action, because I believe that I remember doing so, cannot be
regarded as immediately certain. It is a mediated judgment in so far as
it infers from a present idea the reality of a previous action corresponding
to it, and for judgment such as this there is no rule which is immediately
certain and absolutely reliable.1
i Compare W. Windelband's excellent pamphlet, Ueber die Gewissheit der Erkenntniss,
a work which agrees in so many points with the position here laid down, that, with the
exception of a few passages, I could subscribe to it almost word for word. With refer-
ence to the above question as to the source of our certainty that an idea is a recollection,
he says (p. 87 sq.) that in the last instance it is nothing more than a distinct feeling
accompanying the idea, which tells us that it has been presented before ; this feeling,
however, is again due to the fact that with the idea there is associated the subconscious
idea of its connection with, and reference to, the ego, which is excited together with it,
and manifests itself in consciousness as a feeling of recollection. In this way he explains
how it is that we are able to have ideas for the second time, without knowing them to be
recollections, for this happens when we have not been clearly conscious of their connection
with the thinking ego. This explanation is correct to the extent that there is a peculiar
feeling by which we generally distinguish the known from the unknown. But this feel-
ing can yield no certainty unless it enable us to recall some accompaniment of the
particular idea, other than that in which it now appears, and thus to connect the past
with the present. I may, on seeing some person, experience most strongly the feeling
which generally distinguishes the known from the unknown, but I shall not have perfect
certainty until I recollect the circumstances under which I previously saw him, and thus
fit him into the complex of ideas, which constitutes my self-consciousness, and is always
THE TRUTH OF IMMEDIATE JUDGMENTS
305
D
Here, again, we are met by the psychological difficulty which we find in
being certain that our concepts are invariable, and hence in being certain
that the logical ideal is attained. For since our thought takes place in
temporally differentiated acts, the uncertainty of memory affects also my
consciousness that what I now think is what I thought before. For this
reason the logical ideal can only be approximately reached, and needs
not only unremitting practice, but also external aids. Amongst these
writing takes the highest place, and so great is its importance that it is safe
to say that without writing science is impossible.
5. On the other hand, we must note that every judgment concerning a
present action, in so far as it places this action in a temporal series, also
determines a particular point of time for its own validity ; this "now" is
an essential part of the judgment, because, if referred to another point of
time, the validity of this judgment would be annulled by others. If, then,
a judgment which thus includes the time of its validity is to be objectively
valid, it is not sufficient to assume that there is a universal necessity for
the particular moments of consciousness to appear to every one alike as
moving in a temporal series. It is not sufficient, that is, that there should
be a time which is the same for all. When such a judgment lays claim to
universal validity, there must also be universal laws making it necessary to
assign a definite time to the truth of every judgment. If, then, my judg-
ment is to be valid and universally acknowledged, I must be able to de-
termine the time for which it is valid in a universally valid way.
Thus the Kantian teaching that time in general is a necessary idea is
not sufficient. We need also the determination in an objective time of a
point of time which shall be the same for all; and we need a common
measure of time according to which every particular fact of consciousness
has its place assigned to it.
The question as to how these laws may be discovered cannot be
answered by reference to any immediate certainty, for it depends upon a
comparison between that which is immediately certain to me and the
temporal ideas of others. Its investigation forms a problem to be dealt
with in our third part.
present. In this consists that reference to the ego, rightly emphasized by Windelband.
It is not a reference to the abstract unity of self-consciousness, but to the empirical ego,
and knowledge in the sphere of recollection is nothing but the continual review and con-
sistent combination of a number of acts of my past life.
S. L.
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LOGIC
§ 47.
Immediate judgments concerning external existence are JUDGMENTS OF
PERCEPTION. As ordinarily used, they include the statement that their
subject exists. The perception is in the first place subjectively certain
(§ 46) in so far as it implies the statement that I have at the moment the
idea of a definite existing thing; the condition upon which a judgment
of perception becomes objectively valid is that there should be a necessity
to refer this subjective fact to some existing thing, according to which we
are compelled to interpret the contents of a perception as the real predi-
cate of an existing thing. Especially must there be laws according to
which my spatial intuitions may be translated into the spatial determina-
tions of objects, my reference of attributes or changes to a thing into the
real attributes and activities of substances, and my idea of its relations into
real relations.
1. To ordinary consciousness the judgments of perception, in which
we make statements concerning that which is immediately present and
external, appear as immediately certain as the statements of immediate
self-consciousness.
These judgments of perception include first of all the consciousness
that an idea of a particular thing is at the moment present to me, and has
the peculiar and indescribable character whereby perception is distin-
guished from memory and from merely inward ideation. Our possession
of fixed concepts and a denotation for them next enables us to express
the contents of what is thus presented in a universally valid form. This
is done partly by subsuming 1 it as a whole under a generic concept (a
process corresponding to the denominative judgment), partly by analysing
it into its particular elements, and stating the predicates which correspond
to these. When these predicates are simple the judgment continues to be
immediate; one element of the perception is recognised as agreeing with
a conceptually determined characteristic (what I see is red). But the
process may be one of subsumption under composite concepts; and then,
instead of an immediate naming which unifies a whole with a whole, we
? Concerning the term subsumption, cf. § 8, 6, note.
2 To the extent in which there is a difficulty in maintaining the conceptual limits of
distinctions which melt into each other in the merely internal reproduction of concepts,
the objective validity of such a judgment may no doubt depend upon other processes
(measurement, etc.).
THE TRUTH OF IMMEDIATE JUDGMENTS
307
1
have the necessity of a comparison between the particular characteristics
of the perception and the characteristics of the concept. The judgment
then becomes mediate, in that it is the result of a number of particular
judgments (cf. § 56 on the inference of subsumption).
2. If no more were meant by a judgment of perception than that my
present sensation is of redness or sweetness, the Principle of Agreement
would suffice here again to guarantee that the judgment is necessary, and
such that every one having the same idea must affirm it.
But such a judgment does not compare mere ideas. It refers an idea
to a particular object which is thought of as existing, and it states a predi-
cate as objectively belonging to this definite thing. If the judgment is to
be true, it is not sufficient that there should be a ground for the agreement
of the particular idea with the general. The confident assumption of
ordinary judgment that this particular idea refers to a definite existing
object, and that this object possesses the predicates which I attribute to
it, must also be well grounded. This is possible only if there is some law
according to which the subjective affections and ideas of the individual
are referred to objective things with unfailing and universally valid neces-
sity. Now the universality of the conviction that real objects correspond
to our sensations does indeed prove that we are under a psychological
obligation to affirm the reality of what is felt. But it is also proved by the
fact that our senses often, as it is said, deceive us, and by the conflicting
statements of different observers of the same object, that this universal
obligation is no guarantee of complete unanimity in each particular case.
So that here again we may find, and often do find, that we have to distin-
guish between that which actually occurs according to psychological laws,
and that which is universally valid, and we cannot speak of a sufficient
foundation for such judgments unless all subjective differences can be
eliminated. This, however, is only possible if we can bring to light
universal laws according to which we necessarily refer the subjective
sensation to an objective reality, and can test every case by them. Then
only can we pass from the judgment, “I am sure that I saw and perceived
this or that,” to the judgment, “ this or that is there, has happened.”
3. Once it is recognised that in perception we have at first only sub-
jective occurrences, and that only the presence of the idea is immediately
given, its reference to an external thing being a subsequent, though
generally unconscious, step, then for every judgment concerning external
existence we need a law, according to which the idea must always-at least
308
LOGIC
under certain conditions-be necessarily referred to some external existing
object. Scepticism denies that there is any such necessity, or, at any rate,
that it can be known to us. Subjective idealism affirms the necessity,
but only in the sense that we necessarily think of what is perceived as a
real external object. To it this affirmation of an external existence is a
mere act of Thought, and though the necessity thus leads to a second
stage in our ideas, it does not lead to an existence independent of our-
selves. The reality which we affirm is only a reality of appearances, not
of independent things.
We are not concerned here to settle this disputed question. It is
sufficient to show that the immediate certainty of our judgments of per-
ception does not rest upon any absolute necessity, until some general law
has been shown according to which the fact of perception necessitates the
recognition of the existence of an external object.
From a logical point of view it is, moreover, quite indifferent whether
this law is represented as assuring us of the actual existence of external
things—that is, in the realistic sense ; or in the idealistic sense as only
necessitating that the idea of real objects should follow upon perception.
The logical character of the resulting judgments, their necessity and
universal validity, would be the same in either case; the only difference
would be in the meaning of the predicate “to be” (in the empirical sense).
Only the sceptical view that it is impossible to attain to necessary judg-
ments would exclude them from logical treatment.
Now, the universal law for which we are seeking cannot be to the effect
that whenever I perceive anything there exists something, which corre-
sponds to the particular idea developed according to psychological laws
from my perception. On the contrary, it has been shown over and over
again, and from wholly different points of view, that it is possible even to
doubt the existence of the whole external world, and it has been main-
tained that no logical necessity invalidating that doubt corresponds to the
psychological necessity of assuming such a world. If, then, there are,
nevertheless, ways and means of attaining to a conviction of external
y reality, they are not to be found in the simple facts of perception, but in
the particular nature of our perceptions.
4. But even if we allow that there are principles which necessitate the
reference of our perceptions to something really existing, we have still to
* Cf. Baumann's treatment of these propositions in the first chapters of his Philosophie
als Orientierung über die Welt.
THE TRUTH OF IMMEDIATE JUDGMENTS
309
consider the conditions under which these principles are applicable.
The question is, what are the presuppositions necessary in order that the
subjective fact of perception may warrant an objectively valid judgment ?
The extent to which judgments of perception may vary with different indi-
viduals sufficiently shows that such judgments cannot under all circum-
stances be universally valid, since they lead to contradictions.
Generally speaking, there are two grounds, to either of which these
divergencies amongst individual percipients may be due. The difference
may lie in the very beginning of the process, in the empirical data from
which the formation of the subject idea and the judgment about it starts ;
in the affections of our organs of sense, or, more exactly speaking, in the
manner in which we become aware of such affections. Or it may lie in
the subsequent processes which in ordinary thought take place uncon-
sciously, but which nevertheless do take place, and may be shown-
principally by means of the so-called deceptions of the senses-to be ana-
logous to inferences.
5. With reference to the first of these grounds, the certainty with which
we ascribe to objects our sensations of colour, temperature, etc., as their
attributes, depends upon the conviction that there is an invariable con-
nection between the assumed object and ourselves, a connection such that
the same attribute in the object always and invariably corresponds to the
same sensation in every subject. Even Bacon, in his firm belief that cel-
lars are colder in summer than in winter, assumed that his sensation of
temperature was an unvarying and infallible test of the state of the object :
whatever feels cold, is cold, and just as cold as it feels. The contradiction
to which this assumption leads, by forcing us to affirm and deny the same
thing, brought such judgments of the senses into discredit in very early
times. From the very beginning of Greek philosophy sense-perception
was, to some extent at least, excluded from the sphere of true knowledge,
because of its subjective variability and the extent to which it differed in
different individuals. Only since the time of Bacon have men bethought
themselves that after all this is the basis upon which the greater part of
our knowledge rests, and that all we have to do is to learn the art of using
the instrument correctly. But the Logic which followed Plato and Aris-
totle has perpetuated to the present day the neglect of the conditions
upon which these judgments are valid. The concept was thought to be
a more than sufficient substitute for an untrustworthy perception, until
Kant showed clearly that in mere conceptual knowledge we merely retrace
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LOGIC
our steps, and never advance any nearer to the object. But any logic is
incomplete which fails to inquire into the conditions of the validity of
these judgments, for it is these which both guide us in our formation of
concepts and justify its importance. .
6. A judgment of perception, then, can lay claim to universal validity
only when the sense-affection upon which it depends is the expression of
an invariable relation between the assumed object and the subject, when
the sensation is the infallible sign of an objective quality. And it can
claim this validity only to the extent in which we can assure ourselves that
it is invariable, hence that every one has an exactly similar organization
and sensibility, or else that variations can be accurately corrected. In our
third part we shall have to investigate the means by which we may suc-
ceed in finding a basis for our judgments which shall satisfy—at least
practically—this necessity for such an absolute similarity or reducibility in
our affections as will enable them to be substituted for each other.
7. The idea of the spatial nature of that which is perceived is indis-
solubly connected with the perceptions of sight and touch; we think of
what we see and touch as spatially extended and as having a definite form
and size, and we assign to it a definite position in space. Here, again,
what we first have is a subjective idea, and the position assigned to things
is determined in the first instance by reference to our own bodies as the
centres from which our local determinations proceed. It may be ques-
tioned how many of our spatial ideas are given from the very first, and are
inseparably combined with the sensation itself; that some of our spatial
ideas, such as the idea of the corporeal form of objects and their distance
from us and from each other, are not originally presented with the sensa-
tion, but are the result of combinations which for the most part take
place unconsciously, can be indisputably proved.
In the first place, it is clear that if there is to be an objectively valid
judgment, not about my idea, but about something which exists in space
and has a definite extension and form, there must be absolute certainty
that the idea of space is the same for all, and that the spatial interpreta-
tions which we give to our sensations are necessarily determined in a
given way. Only when this is the case can the judgment concerning ob-
jective extension and spatial relations which results from my sensation be
objectively necessary, and the spatial object be the same for all. One
condition, therefore, of objectively valid judgments of perception is that
the idea of space shall be the same for every one, not arbitrary or other-
:
THE TRUTH OF IMMEDIATE JUDGMENTS
311
wise liable to variations, but completely determined, and that every one
shall think of space in the same way; and such judgments cannot attain
to certainty unless we recognise these laws which govern the representa-
tion of space. It is not merely with the possibility of pure geometry as a
science that we are concerned here. In geometry every one has his own
space, and different spaces are only congruent, or at least similar; it makes
no difference whereabouts in such a space we draw our lines or construct
our figures. Geometrical figures have no position in space. It is different
when we assert that something exists in the objective space which is the
same for all. When I judge that “this is here,” or “that is there,” I
state something which is to be valid for every one and which determines
the position of an object in such a way that the place where it is to be
found may be generally known, and its spatial relations be the same for
all. Constant practice generally enables us to determine such relations in
our immediate surroundings without special discipline; but this does not
make it any the less necessary in strict theory to investigate the conditions.
and normal laws for an objectively valid determination of the form and
place of particular objects. In astronomy we have a proof of how many
presuppositions are involved in judgments concerning the position of
heavenly bodies which lay claim to objective validity, and how such judg-
ments are really valid only when the presuppositions are acknowledged to
be absolutely certain and necessary. But these presuppositions include
not merely the universal propositions of geometry, they include also pro-
positions concerning the reference of sensations to a definite place, and
these in their turn depend upon optical laws, e.g. that the rays of light
·move in straight lines throughout the same medium, but are refracted
upon entering into another. We are not concerned here with the way in
which we arrive at our knowledge of these presuppositions ; only so much
is clear, that they must ultimately depend upon something which is imme-
diately certain, and which does not derive its necessity from elsewhere, if
the particular judgment is to be objectively valid.
8. It is the same with motion. The immediate perception of motion
cannot lead to a valid judgment unless we presuppose a local determina-
tion which has taken place according to necessary laws. But this is not
sufficient. All movement, so far as we can perceive it, is only relative;
that is, a mutual change of position amongst visible objects. But our
judgments are meant to bear the objective significance that A moves to-
wards B, and hence we have need of universal laws according to which
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LOGIC
we may interpret relative change of position into actual movement, into
change of position in space, and by which we may judge what is to be re-
garded as in motion and what as at rest. Here again the history of as-
tronomy proves to us that we cannot arrive at objectively valid judgments
concerning motion unless we presuppose universal principles according to
which the subjective perception of motion is referred to actual motion,
and the subjective phenomenon interpreted into an objective event. The
difficulty of clearly distinguishing between the concepts of relative and
absolute motion is sufficient proof of the labour involved in discovering
these ultimate principles.
9. Still more important is the reference of our sensations to definite
things. It is true that the form in which we refer the material given by
sensation to permanent things is part of the unalterable nature of our
thought; and we could not throw off this psychological constraint even if
we would. But just because the thought of a thing is not already included
in the affection itself, we can conceive of a difference in the process. This
difference, indeed, is hardly apparent when we have to do with motionless
and permanent phenomena ; anything which, for our apprehension, is un-
changing, which keeps the same position in space, and has fixed limits, is
unhesitatingly looked upon as one and the same thing. In the same way it
is so universally assumed that two things cannot occupy the same position
in space that all our references are founded upon this presupposition ; not
even spatial movement, if it is observed as continuous, is by itself suffi-
cient to make us uncertain in our reference.
But wherever we find change of form, magnitude, or sensuous qualities,
it becomes a problem as to how the successive stages in the change should
be referred to the assumed substance. The necessity appears of generally
accepted principles according to which the individual must guide his judg-
ment, if he wishes not merely to state his views, but to make objectively
valid propositions. When a column of quicksilver expands or contracts,
we describe the succession in our perceptions by the proposition " this
grows smaller,” or “this grows larger.” We use the same words to describe
the growth of a crystal or the diminution of a piece of ice in the air ; such
propositions seem to imply that in both cases it is a definite thing, and,
moreover, the same thing, which changes its volume. But for the physicist
the two propositions have a different meaning. In the first case, he does
really consider that it is the same subject which occupies now more, now
less, room; in the second case, the increased crystal or the half-melted ice
THE TRUTH OF IMMEDIATE JUDGMENTS
313
is no longer the same thing as before ; something has been added to the
original thing or a part has been taken away. For the child water
vanishes when it evaporates, and wood when it burns; for the physicist the
same thing remains, it is only in another form. The proposition “this
water evaporates” has a quite different meaning as apprehended by the
one or the other. Kant has included the principle of the permanence of
substance amongst the a priori principles of the understanding. This it
is not, if we mean that in all our references of sensations to objects this
principle guides us by a natural necessity of the understanding; if it were
so, words signifying beginning and ceasing, growth and diminution, could
never have arisen and been applied to things in any language. It is only
as a condition of consistent experience that a principle is necessary which
regulates the manner in which we add substance to accident in thought;
but the principle, as Kant understands it, is impossible until it has been
established that weight is to be the measure of the quantity of substance,
and this is one of the later results of science. The only truth in Kant's
teaching on this point is, that we can have no consistent and necessary
judgment concerning the particular unless there is such a principle; in this
sense alone is it originally necessary, it is necessary if there is to be any
science of experience. Whether we are to accept it as necessary because
a priori in the ordinary sense of being independent of all experience and
self-evident, or because our experience can only be made thoroughly con-
sistent by means of this principle, is another question.
10. The difficulty of establishing the real identity of the same thing
upon the ground of temporally disconnected perceptions is only a special
case of the difficulty of applying the concept of the thing as that which is
identical with itself in time to particular instances. Here again we need
definite rules upon which to base the assertion.
II. Our analysis has already shown that the conditions upon which the
validity of any judgment concerning the particular depends are different
from, and much more complicated than, those of the validity of merely
analytical judgments, based upon a generally accepted system of concepts.
It has further shown that the demand for perfectly valid judgments puts an
end to the natural immediateness of narrative judgments, and necessitates
their mediation in order that they may be true, and that we may be certain
of their truth.
Thus from the point of view of the conditions of science, as distinguished
from that of the psychological genesis of judgments, Kant was right, after
314
LOGIC
all, in regarding only conceptual judgments as analytical, all others as
synthetical, and in inquiring into the principles of their synthesis a priori
as the conditions of their objective validity.
12. The necessity of guiding principles is still more evident in judg.
ments of causality than in the inference from phenomenon to substance.
We are so accustomed in our ordinary judgment to apply the idea of
efficiency, and we make use of it in simple, every-day matters so entirely
without reflection, that judgments which state that a blow has broken a
window-pane and that drinking quenches the thirst are formed as if they
were immediate; in employing transitive verbs we unconsciously appro-
priate the idea of efficacy which they contain. The given relation between
events is unhesitatingly expressed by verbs and adjectives containing the
thought of efficacy, and we therefore believe that we apprehend this
efficacy as directly as we do change or movement. But let us reduce the
particular verbs which express an effectuation to definite concepts. We
shall find that they contain some elements which are of a nature to be
intuitively perceived—a movement of the one thing and a subsequent
change of the other. But in addition to these, there is an element which
is not intuitable, that is, the causal-relation itself, which implies that the
subsequent change is really produced by the other, that it does not proceed
from the subject in which it takes place, but is forced upon it by the
cause. The objective validity of our apprehension of events which we can
perceive is to be estimated according to principles already laid down.
For the statement that a part of them is caused by something else we need
a further fundamental principle, according to which a perceptible event
may be known, with an objectively valid and necessary knowledge, to be
an instance of causality. Only in this way can a causal judgment con-
cerning the particular attain to objective validity. For here, even more
than with the concept of substance, it is obvious that while it is a necessary
result of human nature and of the laws according to which our thought
develops, that events are causally connected by us, and that we cannot get
rid of the need to regard the one as the consequence of the other; yet
this does not exclude widely different applications of the same general
principle, and wide differences in our way of referring the particular to
causal connections. It was the natural desire for causality which drove
men to seek the causes of events in the power of spirits or in the position
of the stars; but no such proposition has objective validity unless there is
a fixed and necessary rule, according to which we may refer events to
1
THE TRUTH OF IMMEDIATE JUDGMENTS
315
causes, and discover what is the cause of a given event; indeed, it is only
on this condition that any causal connection amongst particular events can
be asserted with validity. It was such a rule as this that Kant sought in
his a priori principle. He looked for a condition of scientific experience
and of objectively valid causal judgments which should necessitate a.
particular manner of connecting the subjectively given manifold, and a
particular interpretation of that which is empirically co-presented, thus
transforming (to use Kant's distinction) a judgment of perception into a
judgment of experience. Here again he believes that in the synthetical
principle a priori that everything which happens presupposes something
upon which it follows according to rule, he has set forth this ultimate con-
dition of objective judgments, and that by showing it to be a priori he has
given the ground of its necessity. But here again it may be asked
whether the fundamental principle in this form is really to be acknowledged.
as necessary and a priori, or whether it is merely accepted as necessary
because it is the only hypothesis which enables us to shape our experience
consistently. Moreover, it may even be questioned whether in this form.
it is sufficient, or, indeed, at all fitted, to serve as a basis for the objec-
tivity of our causal judgments. So much, however, is certain, that only in
proportion as our reference of perceptions to causal relations takes place
in accordance with fixed rules can we assert in any particular instance that
a phenomenon, B, is the effect of another, A, and from this it follows that
every particular causal judgment must have its ground in a reference to the
general principle; that is, it must be inferred and synthetical. If we con-
sider how difficult it often is to decide what is the cause of a given event,
we shall be the more ready to agree with the statement that there is.
absolutely no causal judgment, the necessity of which is immediately
certain.
$ 48.
The final and highest general rules—besides the Principle of Agreement
-upon which all other propositions are grounded, are either axioms of
1 His well-known example (Prol., § 20) is the judgment " when the sun shines on the
stone it becomes warm.” This is a mere judgment of perception, and however often I
may have perceived it or others may have perceived it, it contains no necessity ; it merely
happens that the perceptions are generally connected in this way. But when I say "the
sun warms the stone,” the concept of cause has been added from the understanding to
the perception, and this establishes a necessary connection between the concept of sun-
shine and that of warmth ; the synthetical judgment becomes necessarily and universally
valid, hence it is objective, and passes from perception to experience.
316
LOGIC
the formation of concepts, or postulates concerning the existent. The
assumptions made upon the ground of these postulates are ultimately
regulated by the law of contradiction.
1. From what has been said it will at least be evident that the purely
empirical view, which regards the particular facts of experience taken as
objective statements as that which is immediately certain and upon which
all other propositions are founded, can never be the ground for a science
consisting of universally valid propositions. Since the facts of perception
belong to the individual, each man's statements about them are originally
valid for him alone. Nor could we get further than this subjective
validity unless there were rules according to which a universally valid
proposition may be inferred from the subjective fact. Any view which
maintains that the facts of perception, as ordinarily understood, are the
final certainty, must either lead to the scepticism of Hume, which will not
allow us to pass from subjective impressions to any statement concerning
“ being”; or else—if we are allowed to proceed so far as to state that
something is-- to the proposition of Protagoras, that what appears to any
one is for him. In either case there is no possibility of a truth which is
valid for all. It is true that particular empirical theories, such as that of
Mill, do aim at erecting a science upon this foundation. But such theories
always surreptitiously assume propositions having universal validity; some-
times assuming as a matter of course that judgments of perception are the
same for every one, and state objective being as well as guarantee real
knowledge ; sometimes setting forth our inferences from these judgments
of perception as self-evident, although without some universally valid
assumption there is no manner of justification for them.1
2. In opposition to this view, I hope that I have shown that perception
cannot be a ground for necessary and universally-valid judgment concern-
ing the existent, unless the necessity of our particular judgments is based
upon universal principles. Ultimately these principles must somehow be
immediately certain ; and they cannot derive their certainty from an ex-
perience which, in the form of true judgments, is impossible without them.
Thus the question arises whether there are any immediately certain pro-
positions of this nature. Such propositions would state the necessity of
the processes by which, from the fundamental subjective facts of immediate
sensation, we obtain the idea of a world of particular things existing in
1 We reserve a detailed examination of Mill's theory until we come to investigate the
process of induction.
THE TRUTH OF IMMEDIATE JUDGMENTS
317
space and time, and the reality of their attributes and actions as of their
manifold relations. Their general formula would be: given the condi-
tions of individual perception, to obtain necessary statements concerning
the existence of objects, and given statements concerning the existence of
these objects to obtain from them other necessary statements.
If, from the fact that I have definite spatial intuitions, it could be in-
ferred in accordance with these principles that a space, such as I imagine
it, exists objectively; if it followed that, because I have a sensation of
light at a particular point of this space, there exists a bright object at this
point, according to the principle that any felt quality requires a substance
in which it is inherent; if, from the fact that a thing is or changes, it could
be inferred that another thing is or changes, the necessity of such proposi-
tions being as obvious as the principle of contradiction--then there would
be no difficulty in finding a ground even for judgments of perception. For
the subjective fact that I have this or that idea must be recognised as im-
mediately certain, and this would be the empirical datum from which our
judgments concerning the existent would necessarily follow in accordance
with such laws.
These propositions would have to be certain a priori, in the sense that
they would be merely the conscious expression of an invariable and in-
evitable function of our thought, and accompanied by the conviction that so
surely as we are ourselves we are obliged to judge in such a way. They
would not proceed from the contents of the object of thought as expressed
in the concept, but would ascribe to these contents a predicate, derived
not from themselves, but from the particular manner in which they happen
to be presented, from the specific character of the perception. To this
extent synthetical judgments might be grounded upon them.
Here we may see how from this point of view also the Kantian ques-
tion, “How are synthetical judgments a priori possible ?” is of funda-
mental importance. For it is evident that upon the answer to this
question depends the possibility of passing from individual thought as it
constantly recurs to universally valid propositions, and from the subjec-
tive formation of ideas to judgments concerning the existent.
3. That there are such propositions is recognised whenever it is taught
that there are AXIOMS upon which our knowledge of the existent depends.
In accordance with Aristotle's teaching, axioms have been distinguished
1 Treating of those elements of our knowledge for which no further ground can be
given, Aristotle distinguishes in the Anal. post., i. 2 and 10, between åčiwua (åpxn nv åváykn
318
LOGIC
from definitions and the analytical judgments following from these, on the
one hand, and from postulates on the other. When thus distinguished
they are looked upon as propositions having a truth and certainty which is
immediately evident. Hence their contradictory cannot possibly be
thought, and as they are not mere explications of concepts they form the
ultimate presuppositions upon which all knowledge must be grounded.
Moreover, the name Axiom is not given to particular judgments of im-
mediate certainty-for instance, to the utterances of immediate self-
consciousness--but only to universal propositions which express a necessity
of extensive application. Aristotle, for instance, in addition to the ab-
solutely first and most universal axiom--the principle of contradiction-
recognised special axioms for each department of knowledge, e.g. mathe-
matical axioms. Postulates, on the other hand, are propositions which
neither admit of further proof or derivation, nor can be accepted as
immediately and necessarily certain ; their certainty however is assumed,
not upon the ground of logical necessity, but upon psychological reasons
of a more general kind.
An inquiry as to whether all the propositions which have at various
times been employed as axioms have really merited this title could only
be carried out by an investigation into the special departments of know-
ledge which is beyond the scope of general logic. Nevertheless our
previous investigations are a sufficient ground upon which to base an
important distinction with reference to the import of such propositions,
one which has not generally been recognised, though it was indicated by
Kant. We mean the distinction between axioms referring to the for-
έχειν τον ότιoύν μαθησόμενον--και ανάγκη είναι δι' αυτό και δοκείν ανάγκη), and θέσις (ήν μή έστι
deitat, undáváykn Š XELV TÖv Malnobuevóv tl). He again divides the Oéols into ÚT 6060ls,
which states that something is or is not, and oplo uds, which gives the "what "only, not the
“that.” While a 'mbOeots which contradicts the presuppositions of the learner is alrnua.
The last term has never attained to any fixed meaning. The modern use of the term
postulate has been determined—though again not absolutely~ by Kant, when in the
Kritik d. r. V. he refers to the mathematical use of the term : “the practical
proposition which contains nothing but the synthesis whereby an object is presented to
us, and its concept created, is a postulate.” Accordingly he calls the principles of modality
postulates because they point out the manner in which the concept of things is connected
with our faculty of knowledge. But in the Kritik der practischen Vernunfl a postulate is
a theoretical proposition-though it is not demonstrable as such—inasmuch as it is in-
separably dependent upon an a priori practical law of unconditional validity. We find
the same discrepancy in Kant's Logic. I have given a wider meaning to the second
definition in the text.
1 In his distinction between the mathematical and dynamical use of the synthesis of
the pure concepts of the understanding.
THE TRUTH OF IMMEDIATE JUDGMENTS
319
mation of concepts, and axioms referring to the knowledge of a particular
existing thing.
We have laid it down that the possibility of a logically perfect formation
of our concepts depends upon our being able to state necessary laws
according to which all our ideas are formed. It is certain that logically
perfect concepts are no natural product, but have to be obtained by a
conscious synthesis ; and it is as certain that this synthesis must be
governed by rules which are obviously necessary, but which constitute
primarily a ground only for the form of our concepts and the mutual
reference of their elements, not for the assertion that a particular thing
exists. Thus the proposition that we cannot think of any attribute as
real without presupposing a thing to which it attaches is a rule which
determines the construction of our ideas and the relation between their
elements.
All propositions, again, concerning the incompatibility of certain char-
acteristics are axioms for the construction of concepts. It is fixed by the
nature of our thought itself that certain determinations cannot be com-
bined in one idea, and this impossibility can be certain for us only in the
same way as the principle of agreement is certain. (Essentially different
from these are propositions concerning incompatibility which are only
empirically inferred; as, for instance, that a gaseous state is incompatible
with great specific weight.)
Mathematical axioms are to be classed with these axioms for the con-
struction of concepts (when, that is, they are not merely analytical
propositions, such as the principle that two magnitudes which are both
equal to a third are equal to one another, which follows analytically from
the concept of equality). For inasmuch as all geometrical figures pre-
suppose space and are governed by the nature of our idea of space, such
axioms express nothing but the manner of synthesis which is necessitated
by our idea of space. It is upon the inevitable rules of this idea that the
axiom “two straight lines cannot enclose a space” is based.
From one point of view all these axioms may be treated as analytical
propositions ; when, that is, we look to the fact that though not derived
from the concepts of the grammatical subjects, they are involved in the
nature of the ideas presupposed in these subjects ($ 18, 5, P. 110 sq.). That
they appear to be synthetical is due only to their being relational judg-
ments, which must have been preceded by a synthesis in the ideas without
which there would have been no relation. They are based upon the
1)
320
LOGIC
fact that the different elements of our ideas are not independent of one
another.
Such axioms there are also in reference to all we think of as existent; they
hold good, however, only when it is the concept of being which is in ques-
tion, and not with reference to any assertion that this or that particular
thing is. Spinoza's axion-omnia quæ sunt, vel in se vel in alio sunt—is
one of these : and it refers to the fact that nothing but substance with
accident can be thought of as existing.
But these axioms are not meant to serve as grounds for the judgment
that this or that particular thing is. The one last quoted, for instance,
leaves it quite undetermined to what we are to apply the concept of being
in itself, and being in something else (independent and dependent being).
Other axioms, however, are needed for our judgments concerning the
particular existent; axioms upon which we may base the assertion that a
certain particular thing must be thought to exist because we form an idea of
it in a certain way, or because another particular thing either is or has been.
And it is just this which constitutes their characteristic difference from
the former axioms. The axiom of causality, for instance, as formulated in
the law of inertia, says nothing about the necessary idea of motion ; what it
says is that if a given body actually moves at one moment, it will continue
to move in the next in the same direction and with the same velocity, and
that if it changes its motion another body is there which has influenced it.
Thus the general formula of such axioms is sometimes “if I perceive a
particular thing under given conditions, it exists”; sometimes “if some
particular thing is, then some other is also.” In this way they regulate
the process, by which my ideas of the particular are interpreted as reality.
We need only attend to what always takes place in the formation of our
ideas to become conscious of the necessity of the former axioms. The
necessity of the latter, just because they refer to the existent, cannot be
derived from the necessity of thought so simply, except in so far as we
assume as our highest axiom that thought and being correspond.
4. The history of science proves irresistibly how vain is the belief that
we can ground the statement that a given thing is, and is this or that, upon
simple and immediate axiorns, or that the universe of the particular can be
derived from them as necessary consequence. Neither the principle “non
datur vacuum” nor the axiom that “a thing can only take effect where it
is,” neither the assertion that “like only effects like,” nor the statement
that “the effect does not continue without the cause,” have been of any
THE TRUTH OF IMMEDIATE JUDGMENTS 321
avail, and the criterion of inability to think otherwise has been constantly
misconstrued as the psychological impossibility due to habit, instead of
logical necessity.1
Even Kant's splendid attempt to exhibit the synthetical judgments a
priori, which are the ground of all experience, has really only resulted in
shewing that such synthetical judgments a priori must hold good if experi-
ence is to be possible as science. He starts by assuming that there is a
science of experience, and working back from this he seeks the conditions
of it, guided by the principle that all cognitions must admit of being united
in one consciousness. But neither his derivation of the categories from
the forms of judgment given in the traditional Logic and supplemented by
himself, nor yet the synthetical principles obtained from this basis and
their proofs, have succeeded in convincing his readers that they have here
propositions which are absolutely necessary and self-evident, whose contra-
dictory cannot possibly be thought, and which are contained a priori in
our understanding. On the other hand, again, the proof that our sensa-
tions as they occur must necessarily submit themselves to the categories
and a priori principles leaves much room for question.
Schopenhauer abandoned the extensive fortress of the twelve categories
in order that he might maintain more strongly the citadel of causality ;
but although his simplification of Kant is very instructive, it cannot take
the place of the Kantian pure forms of the understanding and synthetical
principles a priori. Even if he aimed at nothing more than psychological
explanation of the process by which every one is forced to objectify his
spatial intuitions and think of them as external, the principle of causality is
insufficient. We may, indeed, infer from it that I must assume something
other than myself as the cause of my sense affections, since I am not con-
scious of having produced them myself. But it does not follow either that
this cause is necessarily in space, nor that it consists in the object of intui-
tion itself considered as an existing thing. No doubt scientific reflection
upon our sense perceptions, which begins by assuming that they are
occasioned by external objects, finds itself confirmed in this assumption by
the fact that it is thus enabled to explain our sensations, and it is for this
reason that Schopenhauer's theory has been approved by Helmholtz. But
it is after all convincing only after we have already tacitly presupposed the
existence of objects, the assumption of which it was intended to explain,
When once it is evident that the general principle of causality contains no
" Cf. Mill's Logic, bk. 2, ch. 7, and bk. 5, ch. 3.
S. L.
322
LOGIC
information as to the nature of the cause of a given effect, we see the im-
possibility of inferring from it the existence of any definite cause.
There are still more serious defects in this principle when regarded as a
principle of objective truth. Even if we allow that it holds good as a uni-
versal and self-evident axiom, it cannot be the ground of our inference of
external objects unless the proposition “I am not aware of having myself
caused my affections,” is a proof that I am really not their cause. Thus
its application involves the axiom that I am not the cause of anything
which I do not produce consciously; an axiom which no one will assert to
be valid a priori. Nor could it be a principle of objective truth unless it
were to guarantee that everything thus objectified by the individual were
eo facto valid. It may be a natural law of our thought; but the conditions
under which it may become a normal law are still to be discovered. 1
Thus the principle of causality also fails to enable us to assert that this
or that particular thing necessarily corresponds to my perception, and is
like my idea of it; for by itself it tells us nothing of the nature of the
cause.
It cannot be allowed, then, that the general propositions which guarantee
the objective validity of our judgments of perception, are obvious as simple,
self-evident truths; nor that we find them in a form which, by itself, makes
the reference of our perceptions to an existing thing, and of certain per-
ceptions to a certain thing, a priori certain. But it still remains open to
us to acknowledge the existence of an external world which is the same for
all, as a postulate of our search for science and knowledge which we can-
not avoid believing, although we recognise that it is not self-evident.”
1 I agree with Windelband (p. 76 loc. cit.) that it is a first principle of knowledge
--more accurately of our attainment of knowledge—which makes us seek a cause for
every phenomenon ; but then this law is not sufficient to show the sufficient ground for
every phenomenon. Such a law, however, would be necessary as a ground for our judg-
ments of perception. Cf. the criticism of this theory of causality in the work of Spir,
Denken und Wirklichkeit, p. 121 sq.
2 Baumann's proof of realism (Philosophie als Orientierung über die Welt, p. 248 sq.)
comes to much the same as this, so far as I can see.
Zeller's investigation “über die Gründe unseres Glaubens an die Realität der Aussen-
welt” (Vorträge und Abhandlungen, dritte Sammlung, p. 225 sq.), which is a model of
clearness and caution, leads to practically the same result, although he attempts to dispose
of the argument that I myself am the only real being which exists by a refutation to which
he attributes the importance of a proof. The proof, however, is only derived by him from
the fact that such an assumption would render the contents of consciousness inexplicable,
and thus it presupposes the necessity not only of explanation but of causal explanation.
But this necessity is in the first instance subjective, a necessity imposed by our desire to
know. That the conviction of the reality of an external world is justified by the necessity
THE TRUTH OF IMMEDIATE JUDGMENTS 323
This postulate being granted, the question arises : What are the universal
conditions required by the nature of our perceptions, if they are to be
referred to an external existence, and if the judgments resulting from them
are to be made thoroughly consistent ? To discover these presuppositions
is, then, the aim, and not the starting point of science. Nevertheless for
our guiding clue in this discovery we must fall back upon a principle whose
likeness to the principle of contradiction may impose upon us, but which
is really only a particular application of that principle ; i.e. it is impossible
that the same thing should both be and not be, that it should both be A
and not be A. The principle of contradiction as a natural law of our
thought states that it is impossible that we should consciously both affirm
and deny the same proposition. If we assume that there is a defi-
nitely fixed conceptual system which is present without variation to an
ideal consciousness, and the same for all thinking beings, then all concep-
tual judgments are established by the principle of agreement. Hence it
follows also from the principle of contradiction that all judgments contra-
dicting these are false, whether they are direct negations, or judgments
predicating incompatible characteristics. When this is the sense in which
“the same cannot be both B and not B," we mean by the same, the same
concept, the definite contents of my idea.
But when we are forming judgments about the existent, this principle
prohibits us in the first place from thinking that the same thing both
is and is not. If then we can infer from the assumptions we have made
about the existent one conclusion, that a particular object of thought is,
and another conclusion that the same particular object of thought is not,
the two propositions cannot both be true, and there must be something
false in our assumptions. And in the same way it is impossible to think
that the same particular A both is B and is not B.
Since it is part of the concept of being, that it is the same for all who
think, so that true judgments about the same thing must agree, whoever
of explanation and understanding is true only as a postulate. We cannot accept it as an
axiom that nothing incomprehensible can exist ; indeed a complete understanding of all
that is presented to us can never be more than a problem set before us which we shall
never completely solve. Though, therefore, I completely agree with him that the theory
which regards our ideas as only the products of the conscious subject is untenable, still
I regard the final presupposition upon which is based our conviction of the reality of an
external world as nothing more than a postulate. This however is quite sufficient to en-
able me to accept the statement of the problem as formulated on p. 263: the causes of
those phenomena of consciousness which we call perceptions must be determined in a
way which will correspond to the facts.
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LOGIC
forms them, it follows that contradictory judgments, even when inferred by
different people on the ground of their perceptions, cannot be true of one
and the same existing thing. It is true that this argument is ultimately
based upon our concept of being, and that we cannot go beyond this.
But there is no other scientific knowledge than the knowledge which tells
us that if we would think of anything as existing, we must necessarily think
of it in a given way. If we could suppose it possible for contradiction to
be repugnant to our thought only, and to be admissible in the existent, all
our efforts to know the existent would be rendered fruitless.
In the third part, I hope to show how the nature of the problems to be
solved, and the conditions under which we attain our knowledge, have
necessarily given rise to that process in our experiential knowledge which
is exhibited by the history of the actual development of science. I shall
show, that is, that the whole task has consisted in affirming an existent
in accordance with the postulate that something is, and upon the ground
of our perception, and in making our hypotheses about it in such a way that
our statements concerning it may be free from contradiction. The history
of science shows us a continual process of re-construction and correction
in our ideas of the existent, a process which enters upon a new stage
whenever our hypotheses lead to contradictions. There is no other confir-
mation of our belief that any given thing is, than the complete con-
sistency of all our judgments with reference to the existent; the return of
the circle into itself. All the general propositions which we accept with
respect to the existent must finally be such that the immediately certain,
the subjective fact of perception, which was the starting point of the whole
process, may in its turn be a necessary consequence of them. In this way
the immediate assumption from which we always set out, that sensible
qualities are immediate attributes of the existent, has been rectified; by
accepting it we were led to contradictory conclusions. In this way the
axioms of physics, the principle of the permanence of substance, etc., have
been discovered. Kant, in his Antinomies, chose this same way to show
that space and time are only subjective forms of intuition, and that every-
thing therein is only phenomenal; to assume that they are real in the
ordinary sense leads in his opinion to contradiction.
The principle of causality, at any rate in the form in which alone it can be
applied, enters into this process of building up knowledge from experience.
It enters, that is, as the postulate that the existent is knowable as necessary,
i.e. determined according to universally valid laws. For not even the
THE TRUTH OF IMMEDIATE JUDGMENTS
325
firmest conviction that everything has its cause could enable us to assert
confidently the existence of a particular thing, if causes worked by
chance.1
1 In order to avoid repetition I postpone a complete exposition of the principle of
causality to Part III.
CHAPTER III.
THE RULES OF INFERENCE AS THE GROUND FOR MEDIATED
JUDGMENTS.
It has been shown in the previous section that judgments which we were
obliged to regard as immediate from the point of view of natural thought,
must nevertheless admit of being presented as necessary consequences of
a general law when we have to ask for the ground of their certainty.
Analytical judgments must be shown to follow from the principle of agree-
ment ; judgments of perception from the laws, according to which we de-
rive from our subjective affections the conviction that there are material
things. And since these general laws can be known only in the form of
judgments, the contents of the previous chapter are to a large extent dealt
with under this one; only the highest and ultimate laws, together with the
immediate utterances of self-consciousness, are excluded, as incapable of
being reduced to more remote principles. 1
§ 49.
The most general formula according to which we derive one judgment
from another is the HYPOTHETICAL SYLLOGISM. This may be either the sim-
ple application of the proposition that the affirmation of the ground involves
that of the consequence, the denial of the consequence that of the ground
(in which case it is called the Mixed Hypothetical Syllogism); or (as the so-
called Pure Hypothetical Syllogism) it may be based upon the principle that
the consequence of the consequence, is the consequence of the ground.
1. The process of drawing a conclusion or inference takes place psycho-
logically whenever we are led to believe in the truth of a judgment by our
belief in the truth of one or more other judgments, and not immediately by
the ideas of the subject and predicate connected in it. There are many
ways in which this belief may be brought about psychologically (8 19, 3-4,
P. 114 sq.); and it often happens that we are not even clearly conscious of
1 For some appropriate remarks on the relation between judgment and inference, cf.
Schuppe's Erk. Logik, p. 124 sq.
326
THE RULES OF INFERENCE.
327
the process of mediation by which we derive the certainty of one judgment
from that of another. This mediation depends frequently upon habits of
association and combination which are governed, as a matter of fact, by
fixed rules of which we are not expressly conscious. Every expectation of a
future event is based upon an inference which extends beyond what is given ;
but the ground of our expectation, which is to be found in previous experi-
ences, is not expressly present in consciousness in the form of a universal
proposition every time we expect that an unsupported body will fall to the
ground, that eating will satisfy hunger, or that what we say will be under-
stood of those who hear. We pass without conscious mediation from the
certainty of the given event to the certainty that a future one will also take
place.
But logical theory has to enquire as to what are the conditions under
which inference is valid. That is to say, since every inference involves the
belief that one judgment (the conclusion or inferred proposition) is true,
because one or more other judgments (the premises) are true, we have to
investigate the logical necessity of this belief that the premises are a
sufficient ground for the conclusion.
2. The question as to how one judgment may be grounded upon
another, may be regarded from two points of view. We may either start
from a given judgment which is accepted as valid, and ask what further
judgment can be grounded upon this ; or we may start from a question, from
the tentative suggestion of a mediated judgment, and ask “how can this
judgment be grounded, and under what conditions ? What must be certain
in order that it may be valid ?”
3. It is evident that, given a valid judgment A, another and a different
judgment X cannot be safely grounded upon it unless there is an uncon-
ditional and universally valid proposition “If A is true, X is true.” All
that is expressed by this hypothetical judgment is, that X is the necessary
consequence of A, and that any one who accepts A must also accept X.
Without such a rule there would be no logical justification for an inference ;
if A might be true without X being true, the certainty of the former would
be no ground for the certainty of the latter. Thus the objective validity of
an inference from A to X must always be dependent upon the validity of
this hypothetical rule.
Hence the most general, logical scheme for all inference is the so-called
mixed hypothetical syllogism : 1
1 Cf. Kant's Logik (Hartenst., 1, p. 453 8 57): “The general principle upon which
328
LOGIC
A is true.
If  is true, then X is true;
Therefore X is true.
If A is true, then X is true.
A is true;
Therefore X is true.
The order of the premises depends upon what the movement of thought
happens to be. If the validity of the judgment A represents the matter-of-
fact element in the ground, the datum from which the inference is made,
while the hypothetical judgment is the law which contains the necessity, the
rule according to which the inference is made, then either the one or the
other may come first in the actual course of thought. But in logical ter-
minology the rule according to which we infer is always called the major
premise (G. Obersatz), the datum from which we infer the minor premise
(G. Untersatz) or assumption.
4. If A presents itself first, the question arises “is there a judgment
which tells us that if A is true X is also true?” But if, on the contrary, it is
the rule which is first present, the question is whether we can apply the
rule : “Is A true, and X because of A ?”
In the latter case the rule is capable of a two-fold application. It may
be applied if A is true, i.e., is recognised as certain ; but it may also be
applied if X is not true, according to the law that the denial of the con-
sequence involves the denial of the ground.
In this way there arises the inference :
If A is true, X is true:
X is not true;
Therefore A is not true.
5. All the ways in which we can make an inference of a simple
statement must admit of being reduced to one of these two forms, which
are generally known as the modus ponens and modus tollens of the mixed
hypothetical syllogism, since by inference in this sense we cannot under-
stand anything else but that one judgment necessarily follows from the
other.
We may, then, lay it down as certain that the validity of a judgment can
depends the validity of all inference made by reason may be definitely expressed in the
following formula : that which falls under the condition of a rule falls under the rule
itself.” This proposition contains just that view of the nature of inference which is given
in what follows.
1 The so-called modus tollens may itself be reduced to the modus ponens, for we can
always infer from the judgment “if A is true, then X is true," the other judgment “ if X
is not true, A is not true."
THE RULES OF INFERENCE :
329
never be inferred from one single judgment, but that two premises at least
are always essential.
One judgment can be inferred from others only upon condition that one
of the premises is an unconditionally valid judgment, the expression of a
necessary connection.
It is this premise which really carries us from one certainty to the other,
and the ground for our progress is the law that the affirmation of the (hypo-
thetical) ground involves that of the consequence, the denial of the conse-
quence that of the ground.1
6. The hypothetical judgment which mediates a conclusion, may itself
be mediated and inferred : indeed the proposition that X is a necessary
consequence of A is known to be necessary if X is a consequence of a
consequence of A. If then it is true that
If A is true, M is true;
If M is true, X is true; then it follows that
If A is true, X is true.
The principle upon which this syllogism is grounded follows from the
concept of consequence; it may be formulated “the consequence of the
consequence is the consequence of the ground.” 2
1 Another proof that this form of hypothetical inference is the natural and general for-
mula for all inference is its universal appearance in the phrases which we generally em-
ploy to state our conclusions. Such conjunctive forms as “since—because—hence-for,”
etc., are nothing more than verbal abbreviations of the schema, for these particles have a
double import ; they express the validity of both propositions, antecedent as well as con-
sequent, and they also express the necessity of the connection between them, thus pointing
to a hypothetical judgment.
2 The principle that denial of the consequence involves denial of the ground may be
applied in two ways :
I. If A is true, B is true.
If C is true, B is not true.
therefore If A is true, C is not true.
and If C is true, A is not true.
i.e. if two premises have contradictory consequences, each involves the denial of the
other.
II. If A is true, B is true.
If A is not true, C is true.
therefore If C is not true, B is true.
and If B is not true, C is true.
i.e. the consequence of an affirmation and the consequence of its denial are mutually ex-
clusive. Both these formulæ, however, may be reduced to the two given above. Instead
of the minor premise in I, we may substitute :
If B is true, C is not true ;
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LOGIC
This is the so-called pure hypothetical syllogism ; here again we see the
necessity of having at least two premises. But what we have said of two
members holds good of an unlimited number: the affirmation of the ground
involves that of every consequence of its consequence, and thus we are en-
abled to obtain a complete series of inferences connecting the first ground
with the last consequence. This is the hypothetical sorites, and its premises
may be arranged in two ways :
I. If A is true, B is true.
If B is true, C is true.
If C is true, D is true,
If A is true, D is true.
II. If C is true, D is true.
If B is true, C is true.
If A is true, B is true.
If A is true, D is true.
In the first case the premises proceed from one consequence to another
still further removed from the original ground (epi-syllogistically); in the
second case they proceed backwards to anterior grounds (prosyllogistically).
$ 50.
In the mixed hypothetical syllogism the hypothetical rule only enables
us to derive one given judgment from one other given judgment. But if
the consequence follows merely from the attribution of a given predicate to
any subject, then the hypothetical rule may be applied to an indefinite
number of judgments. In this case the minor premise serves for the intro-
duction (póolnys) of a definite subject, and so leads to the conclusion.
1. The logical theory of inference would be now complete if our only
object were to express in a general formula the essential conditions to be
fulfilled by all inference in deriving the validity of one judgment from the
validity of another.
But this formula of the hypothetical syllogism is deficient in a way
which seriously impairs its value. If we could make no inferences except
in accordance with it, we should need a special rule every time we de-
and then we get,
If A is true, B is true.
If B is true, C is not true.
If A is true, C is not true.
that is a simple progress from consequence to consequence.
may substitute for our major premise :
If B is not true, A is not true.
If A is not true, C is true.
If B is not true, C is true.
In the same way in II. we
THE RULES OF INFERENCE.
331
rived one simple judgment from another; so that we should have as many
rules as we had instances of their application, while for the derivation of
a hypothetical judgment two others would be necessary. Moreover,
before any inference could be made, everything which enables us to pro-
ceed from one judgment to another must have been already fully thought
out; so that any real progress, any truly synthetical judgment, would be
impossible. Progress to new judgments—which alone in the process of
thought is of any value—is always presupposed as having already taken
place by the hypothetical syllogism in its simplest form as given above.
For the knowledge we seek is just this necessary dependence of one
judgment upon another.
2. Any further development of the theory of inference must then start
from the question “upon what is this necessity of connexion between A
and X based ? ” and from the further question as to whether there is no
other means of attaining to a hypothetical judgment than by way of the
pure hypothetical syllogism, which always presupposes other hypothetical
judgments; whether, that is, we may regard all particular connexions of
this sort as ultimate and unanalysable, or whether it is possible to derive
the necessity from a smaller number of laws.
In many cases, no doubt, a connexion of this kind, which obtains be-
tween a definite antecedent and a definite consequent, and is expressed by
a hypothetical judgment is ultimate; and the necessary sequence is given
immediately. Whenever I resolve upon a definite course of action in the
event of certain circumstances, or make a promise under certain conditions,
or enter into some contract, I give rise to a hypothetical judgment which
owes its validity to my will; and the fulfilment of the intention, promise,
or contract depends upon the simple, hypothetical syllogism “if A is, B*
ought to be, A is, therefore B ought to be. The connexion is established
by my will, and owes its validity to my actual volition. The necessity
grounded thereon admits of no further analysis; the dependence of the
one judgment upon the other is determined directly (cf. Appendix B, p. 383).
3. But the law according to which X follows from A is not necessarily
the judgment“ if A is true, X is true.” Spinoza makes the following in-
ference (Eth., 1, 11): if anything exists, then there also exists an abso-
lutely infinite Being ; now I certainly exist, therefore an absolutely infinite
Being“-i.e. God-exists. Expressed in a general form: the judgment
C is D (God exists), follows from the judgment A is B (I exist) not only
when we know that if A is B, C is D, but also when we know that if any-
332
LOGIC
thing is B, C is D. That is, the inference holds good if the inferred
judgment necessarily follows whenever the predicate belongs to any sub-
ject; when it is the consequence not merely of predication concerning a
given subject, but of predication concerning any subject whatever with
this predicate.
4. Such a law by virtue of its generality covers an unlimited number
of particular cases, and it owes its generality to the fact that the conse-
quence depends only upon the predicate, not upon the particular subject
to which this predicate may be ascribed.
Thus besides the inference expressed by the hypothetical syllogism we
find here a definite subject introduced in place of the indefinite substra-
tum of the predicate, the process called by the Aristotelians mpóolnyes.1
Because the same predicate may be assigned to an indefinite number of
particular subjects, the consequence holds good for every particular judg-
ment in which this assignment actually takes place. And as we have
:seen (S 31, 8, p. 187, and $ 33, 2, p. 197), this is the only form in which the
necessity is recognisable as such.
5. The hypothetical judgment may be one which makes one predicate
depend upon another predicate of the same subject : if anything is A, the
:same thing is also B. Then it would not only be applicable to a plurality
of data having the same consequence, but would also include a number of
.consequences; the introduction of the definite subject would take place
both in the antecedent and in the consequent.
If anything is A, it is B
C is A
Therefore C is B
Here we have no longer a simple, hypothetical syllogism. It is medi-
ated by the fact that in the minor premise a definite subject is named to
which the predication applies, while at first only the general possibility of
a subject was assumed. The hypothetical judgment includes in its for-
mula the several judgments : if C is A, then C is B; if D is A, then D is
B, etc., thus necessitating an indefinite number of particular consequences.
1 In the inference :
καθ' ου το Β κατά τούτου το Α
Β κατά του Γ
Α κατά του Γ
the minor premise is the poolmyrs. Cf. Prantl, 1, 376 sq., and my Programm, p. 8.
THE RULES OF INFERENCE
333
There is added to the necessity expressed by the major proposition the
property of being universally applicable : the rule has become a law.
6. The same is true of hypothetical judgments which attach conse-
quences not to simple predications, but to connections between relations,
and thus become more complicated in their expression. The proposition
that if two magnitudes are equal to a third they are equal to one another,
states a connexion between relations which holds good for any objects
whatever which come under these relations. When I infer therefrom that
because A=B and C=B, therefore A=C, I have again introduced into
the general formula the definite magnitudes A, B, C, to which the rela-
tional-predicate of equality applies. The minor premise does not say that
any two magnitudes are equal to a third, but that these definite magni-
tudes A and C are equal to the third B. In this case the introduction
must take place by means of a number of particular judgments, which
must be taken together to allow of the application of the antecedent.
7. The proposition that one of the premises must state a necessary
connexion seems to be contradicted by many instances from ordinary, and
even from scientific, practice. I infer, A is the father of B, B the father
of C, therefore A is the grandfather of C; that Breslau is in Silesia, Silesia
in Prussia, therefore Breslau is in Prussia; that A=B, B=C, therefore
A=C; that A>B, B>C, therefore A>C; that A is to the right of B,
B to the right of C, therefore A is to the right of C, and so on. But
though these premises seen by themselves to be a sufficient ground for
the conclusion, and there appears to be no universal major premise, it is
not really so. No doubt we make our inferences in such cases with the
greatest confidence, without being conscious of a universal major premise,
or without expressly formulating it; in the last example it would be the
proposition, “when A is to the right of B, and B to the right of C, then
A is necessarily to the right of C.” But would the syllogism be valid
unless either this proposition were true, or the still more general one that
whatever lies to the right of a second thing which is to the right of a
third, lies also to the right of this third ? It is true that because the rela-
tions of space or of magnitudes are so immediately intuitable, and because
they are so incessantly present to thought, we are saved the necessity of
always formulating in words the laws by which they are governed. Never-
theless nothing but the validity of the necessary connexion between the
1 Cf. F. H. Bradley, in his Principles of Logic, London, 1883, p. 227; a work which
is eminently original and very instructive in its frequently excellent criticisms.
334
LOGIC
various relations can support the conclusion ; in mathematics, indeed, the
fundamental principle that two magnitudes which are equal to a third are
equal to each other, is expressly put before everything else. Logical in-
vestigation is not concerned with that which is expressly thought and
consciously emphasized in the actual process of inference; but only with
that which must be true if a syllogism is to be valid, if the conclusion is
to be a necessary consequence of the premises. The propositions A=B,
B=C, do not really constitute the only premises of the syllogism; they
merely contain the assumtio, which here consists of two propositions. We
cannot pass from them to the conclusion A=C unless we can see that if
A=B, and B=C, it is necessary also that A=C.
But these examples show the importance of that class of connexions
which we have just noticed (6), and the frequency of inferences from
major premises which state that the two relations in which one object
stands to two others necessitate a third between these two others. Many
of the propositions upon which all inference is ultimately based will for
this reason take the form of hypothetical judgments with antecedents
which have two members because they contain a twofold relation. To
this class of inference belongs also the principle according to which we
infer identity. Identity itself is nothing but a relation between objects
of thought. The premises A is identical with B, B is identical with C,
yield the conclusion A is identical with C only because the third identity
follows from the two first by virtue of the concept of identity; because,
therefore, the law holds good that two objects of thought which are
identical with a third are identical with each other.
In the same way when we substitute an equivalent expression for the
subject or predicate in any judgment—whether it be a different manner
of denoting one and the same individual, or a different expression for a
concept—we are only justified in so doing by our knowledge that the
same predicate must be affirmed or denied of the same subjects.1
8. The psychical operation actually taking place in such a process of
inference presents different aspects, which have led to different views of
the syllogism. On the one hand, it is pointed out that what really takes
place in inference is a synthesis of different elements, and that the con-
1 In such examples as : Aristotle was the philosopher of Stagira.
Aristotle was the tutor of Alexander, therefore, etc.,
we have directly but the substitution of one expression for another ; only when there
is some indirect implication can such inferences as this be significant and rise above the
level of mere verbal trivialities.
THE RULES OF INFERENCE.
335
clusion is an immediate judgment, inasmuch as it only analyses this
synthesis. When I infer that because A is to the left of B, and B to the
left of C, therefore A is to the left of C, the combination of the two
premises suffices to give me the three points A, B, C, in this particular
position, and from this it is immediately evident that A is to the left of C.
Thus the essential part of the syllogistic process is the combination of
different elements in one whole, a construction which yields complete all
that is expressed in the conclusion. In the same way suppose we have an
individual S, possessing a complex M of tangible and visible attributes,
and in this complex a perceptible attribute P; S and M and P form, as it
were, the image of a single thing. Our knowledge that Pappertains
to S is certain, as evidently, and on the same ground, as that M belongs to
it or that P belongs to M. The premises effect a combination, and the
intuition of this gives us an immediate knowledge of the fact that the
elements connected in the conclusion belong together.? According to the
opposite view, inference, consists in comparing the two premises and
recognising the necessity of attributing a predicate P to the subject S;
only a discernment of this necessity can be the ground for actually think-
ing the unity SP. According to this view, the person making the inference
stands in the same position as some one hearing the judgment SP spoken;
he first receives the ideas apart from one another in the two premises, and
is then called upon to unify them. In other words, according to the first
view, the real inference takes place before the formulation of the conclu-
sion, this being only an analytical expression of knowledge already
acquired; while, according to the second view, the inference first creates
the conviction that the predicate P must be attributed to the subject S,
thus giving rise synthetically to the thought of the unity SP. This latter
view is more emphasized in ordinary accounts of the syllogism, in propor-
tion as they aim at making inference mechanical by the rules and figures
of the syllogism, and at turning it into a species of calculation. In an
algebraical calculation I work only with symbols; not until I have finished
do I interpret the equation I have obtained, and then I realize again what
I have denoted by symbols ; I get my result not before the conclusion, but
by means of the conclusion. But even when the process of inference is
not one which is at first carried on merely in words or symbols, the result
being afterwards realized, it still depends upon the nature of premises and
Cf. Bradley, Principles of Logic, p. 235.
2 Schuppe, Erk. Logik, p. 260.
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LOGIC
conclusion whether or not the former will at once blend into one whole,
which can then only be expressed analytically. When we have to do with
a negative premise, such a synthesis is prohibited by the nature of the
negation. But even with positive premises Bradley's theory breaks down
as soon as we come to deal with relations which are less immediately and
obviously intuitable than the simple spatial relations from which he starts,
or with predicates which do not belong to those contents of the concept
denoted by the middle term which are invariably present to thought.
But in any case this distinction in the syllogistic operation applies
only to the psychological process; the question as to whether or not the
conclusion follows necessarily from the premises is not affected by it.
For when the synthesis actually takes place in such a way that it finds
only analytical expression in the conclusion, it is not necessary and un-
ambiguous unless there is some law which prescribes this synthesis and
prohibits any other. The synthesis A-B-C, results from the premises A to
the left of B, B to the left of C, only because it is prescribed by the law of
spatial relations. The truth of the conclusion depends upon the truth of
the premises, and it makes no difference to this dependence whether in
any particular instance there is unconscious obedience to the law in the
synthesis, or whether it forms a conscious ground by which the synthesis is
guided.
$ 51.
The general hypothetical rule according to which an inference is made
is of a synthetical nature when it is not already included in the judgment
which is taken as a ground, or in its elements, but is added to it from other
sources. Such rules may be either axioms, which serve to connect
relations, or general propositions, gained by induction from experience, or
laws which state some connection established by the will.
Other hypothetical rules are given with the judgment itself from which
the inference is made, and may be analytically developed from it. They
may be derived from the form of the judgment, in so far as the act of
judgment is governed by universal logical laws, or from the contents of
the concepts of which it is composed in so far as these concepts contain
universal judgments.
1. Hypothetical propositions which state a universal connection as
explained in the preceding paragraph may be derived from very different
sources.
THE RULES OF INFERENCE
337
In the first place, there are the universal propositions which are the
expression of an immediately obvious necessity to be found in the relations
of certain objects of thought (synthetical judgments a priori in Kant's
sense). The most important of these are the mathematical axioms which
state how the relations of number, space and time are connected.
A constant experience without any exception may be the ground of our
belief in other universal connections. We shall have to enquire in Part III.
how it is possible to pass from particular perceptions to judgments having
a universal and unconditional validity; here we may be content with the
universal conviction that many necessary connections may be inferred from
experience. That a body expands when it is heated, that white light is
broken up when passed through a refracting medium, are instances of
such laws. If the condition is at any time present, we confidently infer
that the result mentioned in the law will also appear, and our confidence is
ultimately based upon simple facts of perception which have shown us
the one event connected with the other.
We find a wide field, again, for our inferences in the application of
general laws which have their origin in our will and are meant to regulate
that will. In laying down a general rule of conduct, our will determines
that there shall be a universally valid connection between certain conditions
and certain modes of action. If we will the general law, it is logically
necessary that we should will the particular actions prescribed by the law,
if our will is to be constant and consistent, and valid for every one who
agrees in willing the general law. All penal codes in imposing a penalty
of imprisonment for theft, of capital punishment for murder, lay down a
series of hypothetical judgments which establish a universal connection
between committing the crime and incurring the penalty. These judg-
ments, moreover, may also be regarded as theoretical propositions in so far
as they express the general obligation of the judge to give sentence in
accordance with the law.
In analytical geometry an equation such as y2 = px determines the con-
struction of a curve ; by means of it to every value of the abscissa is
assigned the appropriate value of the ordinate. This relation between
x and y has the force of a hypothetical judgment, and may be selected at
will to enable us to construct freely any spatial image, and to this
extent such a formula is comparable with the positive establishment of a
law.
In cases like these we add to the judgment A, which is the ground of
S. L.
338
LOGIC
our inference, a general law which is not thought with the judgment, nor
analytically contained in it.
2. The case would be different with connections involved in the fact
that a certain judgment was uttered or thought; rules, that is, which could
be derived from the judgment itself, and which would tell us upon the
ground of universally valid laws, that if this judgment be true, some other
must also be true ; rules which could be adduced without applying to any
external source.
How can the fact that the judgment A is B is true yield any further
knowledge? It may do so in two ways. It may be that the particular
form of synthesis between the two elements in the judgment A is B,
renders it possible and necessary to apply other forms of connection (in
judgments) quite apart from the meaning of A and B ; that is, there are
laws by which all judgment is governed, and according to which any judg-
ment whatever will yield other judgments containing the same elements.
But it may also be that the predication of B of the subject A involves other
judgments by reason of the particular meaning attaching to A and B in this
judgment. In the former case the rules will be formal, in the latter,
material.
$ 52.
The so-called IMMEDIATE INFERENCES, which are only formal variations
of the same judgment, are based upon the universal nature of the judg-
ment, which is the same, however the matter varies. Amongst these we
generally find enumerated the inferences of OPPOSITION, OF CHANGE OF RELA-
TION, of ÆQUIPOLLENCE, of SUBALTERNATION, of MODAL CONSEQUENCE, of
CONVERSION, and of CONTRAPOSITION.
1. The most obvious inferences of all, and those which can be derived
entirely from the meaning of judgment itself, are generally quite omitted.
The judgment “ A is B” involves the judgments “it is true that A is B,”
and “it is necessary to state that A is B”; also that "A and B are com-
patible.”
2. This leads to the INFERENCE OF OPPOSITION,—inference, that is, from
the truth of one judgment to the falsity of its contradictory opposite, and,
vice versâ, from the falsity of one judgment to the truth of its contradictory
opposite. This kind of inference is based upon the principle of contradic-
tion and of twofold negation, which simply tells us that the two judgments
“ A is not B,” and “it is false that A is B," and the two judgments “ A is
THE RULES OF INFERENCE
339
B” and “it is false that A is not B,” have just the same meaning. It is
the same with respect to hypothetical judgments. The denial of the judg-
ment “if A is true, B is true,” is equivalent to the judgment "even if A is
true, it is not necessary that B should be true”; if the latter judgment is
false, the former is true.
3. When we change the unconditionally universal judgment “all A's are
B’s” into the hypothetical judgment “if anything is A, it is B,” we take for
our predicate that necessity which, in the unconditionally universal judg.
ment formed the ground of its universality ; and the unconditionally uni-
versal judgment, when substituted for the hypothetical, expresses univers-
ality as the consequence of necessity. In the same way, when a disjunctive
judgment is broken up into hypothetical judgments, or when several hypo-
theticals (if A is not B, it is C; if A is not C, it is B) are combined in one
disjunctive (A is either B or C), the meaning of the verbal forms finds a
different expression.
4. Other forms generally given are :
(a) INFERENCES OF ÆQUIPOLLENCE. From the judgment A is B we may
infer that A is not non-B, an inference which the indefiniteness of non-B
makes worthless. (The inference that snow is white and therefore not red
cannot be regarded as purely formal; it presupposes a judgment concerning
the matter of the predicate, the judgment that anything white is not red.)
(6) INFERENCE BY SUBALTERNATION. Here it is inferred from the judg-
ment all A's are B (or not B) that some A's are B (or not B), and from the
falsity of the judgment some A's are B (not B) the falsity of the judgment
all A's are B (not B). But the true predicate in the universal judgment is
"all,” and hence this inference is dependent upon the contents of the
predicate, and is only a particular instance of the rule that the smaller
number is contained in the greater. The same rule enables us to conclude
that where there are three there must be two, etc; so that the inference
here is not a formal transposition authorised by the nature of the act of
judgment; it is merely a conclusion drawn from the meaning of the pre-
dicate. We should have as much justification for saying that the inference
that the part must be where the whole is, is immediate.
(c) In inference by what is called MODAL CONSEQUENCE we are said to
derive actuality and possibility from necessity, and possibility from actu-
ality; further the negation of actuality and necessity follows from the nega-
tion of possibility, the negation of necessity from that of actuality. So far
as concerns the act of judgment itself, there is no distinction between
340
LOGIC
necessity, possibility, and actuality; if, on the other hand, these terms are
used as predicates, having reference to reality, then the inference depends
upon their contents, and has no place here.
5. Since the time of Aristotle the CONVERSION of judgments has played
the most important part in the doctrine of immediate inferences. By
means of this process it is said that from the judgment A is B we may
obtain another having B for its subject and A for its predicate. We are
taught that by conversion :
The universal affirmative judgment, all A's are B, will give us some B's
are A (conversio per accidens, the quantity being changed).
The universal negative, no A is B, gives us no B is A (conversio simplex
the quantity being unchanged).
The particular affirmative some A's are B gives us some B's are A
(conv. simplex).
While the particular negative some A's are not B admits of no conver-
sion.
Taking first the affirmative judgments, we may point out that, if their
conversion is to have any meaning, they must be judgments in which the
predicate is the generic idea to the subject, both belonging to the same
category, so that the predicate may become subject in the same sense as
the original subject. They must be, moreover, judgments concerning in-
dividual subjects, so that it is no strain to their meaning to interpret them
by saying that the subjects named may be included amongst the objects
denoted by the predicate-term. They must, that is, be such judgments as
“all firs are trees,” “no larches are firs," etc. ; where the correctness of
the conversion may be proved by enumeration.
Where these conditions are not complied with, the conversion has a
forced sound, and the meaning of the judgment is altered. The judginent
“all planets move in ellipses” is based upon the category of action ;
change it into “some things moving in ellipses are planets,” and instead of
taking the predicate for subject we have introduced a new subject; we
have connected the concept of thing with the predicate, and, since it
is absurd to determine a concept of substance by a temporal process our
concept is an unnatural creation. Instead of a judgment of action we
have obtained a judgment of subsumption. In passing, therefore, from
one judgment to another, we are not really independent of the meaning of
the terms employed.
The true significance of such conversion is first to tell us that the predi-
THE RULES OF INFERENCE
341
cate is compatible with the subject, and next to supplement the universal
judgment by showing that though it may be necessary to think of A as B
it does not follow that B belongs exclusively to A. It is this warning
which is the most important part of the meaning of the conversion, and
it coincides with the rule that we may not infer the ground from the con-
sequence. Applied to the hypothetical judgment, it prohibits us from
simply transposing the judgment if A is true, then B is true, and inferring
that if B is true, then A is true. All that we can infer is that if B is true,
A may be true, which corresponds to the particularity of the converted
categorical judgment.
The case is different with the conversion of the universal negative judg-
ment. This expresses the fact that exclusion between two concepts is
always mutual; that if a subject A excludes a predicate B, it certainly
cannot be true that anything possessing B can be A. Or we may avoid
the awkwardness of changing adjectival and verbal predicates into sub-
stantives by making use of the hypothetical formula, and then, from the
judgment
If anything is A it is not B, it follows that
If anything is B, it is not A.
Where the consequence, the negation of B, is denied of any object, there
we can no longer use the subject-concept as a name for it.
6. Besides conversion we have also CONTRAPOSITION. Here a new judg-
ment is formed from A is B by taking the so-called contradictory opposite
of the predicate as subject, and the original subject as predicate, and
altering the quality of the judgment; that is, changing affirmation into
negation and vice versâ. By this means we may obtain
from all A's are B,
no non-B is A,
from no A is B,
some non-B is A,
from some A is B,
nothing,
from some A is not B,
some non-B is A.
We may leave the reader either to prove these inferences himself or to
find the proofs elsewhere. We need not point out that this form is nothing
but an artificial perversion, which conceals the good sense really contained
in these propositions by introducing the unmanageable non-B, and by
arbitrarily constraining the predicate-concepts to take the form of substan-
tives. The results of this process are propositions such as "nothing not
having equal diagonals is a rectangle.”
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LOGIC
The whole meaning of contraposition is clear at once when we use the
hypothetical form and retain the predicate as predicate. Instead of all
A's are B we then have
If anything is A, it is B, and from this it follows that
If anything is not B it is not A.
Contraposition in this form is parallel with the conversion of negative
judgments, which from the judgment
If anything is A, it is not B, infers that
If anything is B; it is not A.
Both these instances of what is called simple conversion and contraposition
have a meaning and are useful; they express the complete meaning of the
statement that a predicate must either belong, or not belong, to a subject.
The remaining cases yield only particular judgments; that is, we cannot
obtain any definite conclusion, but only the denial that certain concepts
are incompatible or necessarily connected.
No A is B, i.e.,
If anything is A it is not B,
but this does not necessitate the inference that because something is not B
it is A, although it may be A.
7. The doctrine of immediate inferences may be still further extended
to apply to the disjunctive judgment. If A is either B or C, it is false
that it is both B and C, and false that it is neither B nor C. If it is false
that A is either B or C, then A may be both B and C, or A may be
neither B nor C, or A may be either B or C or D. Here again the con-
pendently of the particular elements of the judgment.
8. Finally, by extending the concept of immediate inference beyond
its customary sphere, we may also include all those operations by means
of which we combine a plurality of particular judgments, and thus form
conjunctive or copulative judgments. From A is B and A is C it follows
that A is both B and C; from A is not B and A is not C it follows that
A is neither B nor C. The conjunctive judgment is only the verbal ex-
pression of the fact which is involved in our consciousness of the validity
of both judgments; it tells us nothing new as to the matter, and merely
serves to make us expressly aware of a connection which was already there.
These operations are of great importance to thought, in its arrangement
THE RULES OF INFERENCE
343
and combination of particular items of knowledge, and for this reason they
are worthy of being mentioned here.
9. The value of this doctrine of the so-called immediate inferences
consists, as Mill rightly said, in enabling us to recognise the same judg-
ment in different forms and expressions. The judgments thus inferred
from each other may be simple transpositions of a given statement, which
enable it to be reduced to a form more convenient for the context to
which it refers; or they may serve to make prominent special aspects of
the statement which are not emphasized by the verbal expression; or,
finally, they may serve as precautionary rules, teaching us not to confuse
one judgment with another like it, or to find more in it than it really
contains.
§ 53.
Given a simple judgment, we may derive from it others having their
ground in the contents of its elements. In so doing we must be guided
by rules which may be obtained either from an analysis of the predicate-
concept, or by reference to the extension of the subject-concept.
I. If it is true that A is B, then it is evident that in affirming B of A
we affirm of A everything which we think of as connoted by B. In the
same way by affirming B of A we exclude from A everything excluded by
the connotation of B.
Suppose that B contains the conceptual characteristics c, d, e, or the
derivative determinations f, &, h, and that it excludes the characteristics
m, n, o, and the concepts P, Q, R, etc. Then, because we affirm B of A,
we must also affirm c, d, e, f, g, h, and deny m, n, o, P, Q, R.
These conceptual relations find their simple expression in the judgments :
If anything is B, it is c, d, e, etc.
If anything is B, it is not m, not n, not P, etc.
In this way, by analysing the concept B, and by enumerating the
characteristics incompatible with it, we obtain the rule by which to pass
from A is B to another judgment in accordance with the principle Nota
notæ est nota rei, repugnans notæ repugnat rei. Thus we get the following
forms of inference:
1. If anything is B, then it is c, d, e
A is B
Therefore A is c, d, e
·
LOGIC
344
2. If anything is B, then it is not P, Q, R
A is B
Therefore A is not P, Q, R
It is clear that these inferences are valid, whatever A may be—a par-
ticular thing or a concept-and whatever the sense in which B is attributed
to A. Everything contained in the thought of the concept B is predi-
cated by it; everything excluded by it is denied when it is predicated;
the new judgments are necessary consequences of predicating B of A.
It is clear also that if A is a definite particular subject, there is no other
way of passing beyond the judgment A is B without having recourse to
other propositions.
2. The judgment A is B may be explicative or unconditionally univer-
sal—one, that is, in which the denotation of the subject is not used as the
name of a certain particular thing, but as the symbol of a concept, so that
the judgment A is B has itself the significance “if anything is A, it is B."
In this case there is another way in which we may pass from the judgment
A is B to a different one; we may attribute B to everything of which A
is predicated, or which is contained in the sphere of A. Our judgment
then reverts to the particular kinds of A, or to the individuals compre-
hended in A, and A is B serves as major premise.
If anything is A it is B
X, Y, Z are A
Therefore X, Y, Z are B
In the former kind of inference the content of the original predicate was
unfolded, and we proceeded from it to particular determinations or deriva-
tive predicates. In the latter kind the extension of the original subject is
specified, and the predicate is attributed to the subjects comprehended by the
original concept; and in so doing we are guided by the rule known as the
Dictum de omni, Quidquid valet de omnibus, valet etiam de singulis. This
rule has reference to the fact that the formula “If anything is A, it is B”
generally appears as the so-called universal proposition, “All A's are B.” 1
1 In his essay, von der faischen Spitzfindigkeit der vier syllog. Figuren, Kant has
shown briefly and clearly that what is called the Dictum de omni follows from the prin-
ciple “ nota notæ est nota rei.” That is, the particular thing falls under a concept only
because this concept is to be found in it as its characteristic. This does not make the
two formulæ equivalent, as B. Erdmann maintains (Philos. Aufsätze zu E. Zeller's
Jubiläum, p. 202); the first as being original and primary is distinguished from the
second, which is derivative and secondary.
THE RULES OF INFERENCE
345
Here again the treatment of the negation runs parallel with that of the
affirmation. If in place of the affirmative judgment we have the negation
A is not N-meaning anything which is A is not N—then the same
negation applies to everything which is A.
That which is A is not N
X, Y, Z are A
X, Y, Z are not N
(Dictum de nullo.)
3. A comparison between these two cases, the analysis of the predicate
and the specialization of the subject, shows that notwithstanding the differ-
ence between them, they both lead to the same formula.
If anything is A, it is B (it is not W)
Sis A
Sis B (S is not W)
The difference is only in the significance of the predication, and more
especially of the minor premise. When this serves to subsume a subject
under its genus, the predicate being thus fitted to take its place as subject-
concept without changing its meaning, then the function of the inference
is to specialise the extension, in the other case the inference serves to
unfold the contents. In the first case it is natural to express the major
premise (the rule) as a general proposition, but not in the second ; and
while it is the major premise which stands first in the former, in the
latter it is the minor premise.
In the inference: All men are mortal ; Caius is a man, therefore Caius
is mortal, I pass from my original proposition to the extension of the
subject-concept. In the inference:
Caius has fever;
Any one having fever is ill,
Therefore Caius is ill,
I pass from my original predicate “having fever” to the further determi-
nation “ill” connoted by it. But “having fever" is not a generic idea
to particular individuals. We may take a universal proposition of the
ordinary form for our major premise :
All people having fever are ill,
Caius is a person having fever,
Therefore he is ill,
346
LOGIC
and this inference seems to have the same contents as the one preceding.
But the way in which the major premise is expressed is forced, and the
minor premise seems to be intended to state a subsumption under a
generic concept, while it really denotes a temporal condition.
4. It is evident that the more complicated relational-judgments may be
treated in just the same way by this explication of intension and specializa-
tion of extension, when they contain analogous predicates or subjects, and
this is true even though the respective terms may not appear verbally as
the grammatical subject or predicate.
The inference “Gravitation imparts the same velocity to all bodies,
therefore a piece of lead and a feather (in a vacuum) fall at the same rate,”
may be resolved into two inferences. On the one hand, it is a develop-
ment of the predicate into its consequences; on the other, a specialization
of the term “all bodies," which, though not the grammatical subject, really
denotes that concerning which the statement is made. It would be super-
fluous to begin by making this term the grammatical subject by means of
a forced transposition. We are as much justified in substituting species
for genus as if the major premise were “All A's are B,” and there is there-
fore no need for a special principle of substitution in addition to the
dictum de omni by which to justify such inferences. They differ from
others only in the grammatical form of their propositions.
5. When we start from a negative judgment it does not hold good that
everything which is necessarily contained in the thought of the negated
predicate is also negated. When I deny that this figure is a square, I do
not deny that it is rectangular or quadrangular; I only deny that all the
attributes are present. Hence no inference is possible by merely analys-
ing the negated predicate. We cannot say:
If anything is B it is c, d
A is not B
1
Therefore it is not c, d
Nor does it hold good that anything excluded from the negated predicate
may be affirmed; it does not follow that because something is not red it
is black. Hence it is no valid inference to say:
If anything is B, it is not C
A is not B
Therefore it is C
THE RULES OF INFERENCE
347
The invalidity of this inference follows obviously from the rule that the
negation of the ground does not necessitate the negation of the conse-
quence.
It is the same when we turn to the extension. Here again it does not
follow that because A is not B, therefore that which is not A is B; we are
unable for the same reason to infer
If anything is A, it is not B
C is not A
Therefore it is B
But when the judgments are such as express conditions having the
negated predicate for consequence, or judgments which specialise the ex-
tension of the predicate, then we get the following inferences :
A is not B
A is not B
If anything is C, it is B
C, D, E is B
Therefore A is not C
Therefore A is not C, D, E
These may be shown to be applications of the rule that the denial of the
consequence involves that of the ground :
That which is A is B
is not N
C is not B
C is N
C is not A
C is not A
6. These are the only ways possible in which we can pass from a simple
judgment to another definite judgment by means of the conceptual rela-
tions present. In all of them we are led by two principles. The one is
that all which is contained in the connotation of a concept must be
affirmed of everything of which the concept is affirmed, hence of all the
species of the concept and of all the individuals which fall under it. The
other, that whatever is excluded from a concept is excluded from every-
thing in the thought of which this concept is contained; hence from its
whole extension. We have moreover shown how the modus ponens and
modus tollens of the hypothetical inference reappears in these forms.
7. We obtain the same result if we start differently from the other point
($ 49, 2), and ask whether or not there are any grounds for some synthesis
A is B. This question may be solved at once if we can recognise B as
contained in A, the judgment thus proving to be analytical. But if not,
some mediation is needed to assure us that A is B, and unless we are to
348
LOGIC
adduce propositions from elsewhere, this mediation can consist only in
discovering in A a predicate X from which B necessarily follows. If the
two propositions, “If anything is X, it is B,” and “A is X,” are both
valid, then we can infer that A is B. It makes no essential difference to
this process whether X is the generic idea to A, and B belongs to it, or
whether it is another predicative determination of which В forms part of
the connotation; all that is affected is the meaning of the minor premise
In the same way, if we can discover in A a determination Y, of which it
is true that if anything is Y, it is not B, the question can be decided in
the negative. The inference then is :
If anything is Y, it is not B
A is Y
Therefore A is not B
These two forms represent the shortest and simplest way of arriving at
some decision as to a suggested synthesis, and they represent the only way
if we assume beforehand that all necessary connections must be derived
from the relations which already exist between concepts, hence that they
must be ultimately reduced to analytical judgments. It is this which
makes the middle concept important in inference as being both predi-
cate of A and subject of a universal affirmative or negative judgment having
the predicate B; it mediates the attribution or negation of the predicate B
to the subject A.1
The negation of the hypothesis A is B may also be brought about in a
less direct manner when the judgment, if anything is Y it is not B, is not
immediately obtainable. Then the judgment “ A is Y” may be supple-
mented by a second, " that which is B is not Y; or else we may know that
anything which is B is Z, and A is not Z. Then we get-
That which is B is not Y
A is Y
That which is B is 2
A is not Z
Therefore A is not B
Therefore A is not B.
The first of these formulæ is really reducible to the preceding negative
formula ; for from the major premise it follows that that which is Y is
not B.
1 Cf. Kant, von der falschen Spitsfindigkeit der vier syllogist. Figuren, $ 1.
THE RULES OF INFERENCE
349
This kind of mediation is based upon the principle that when a predi-
cate is affirmed of one subject and denied of another, these two subjects
cannot be compatible. It is naturally substituted for the preceding method
when A is a substantival concept, Y and Z being predicate determinations
such as are ill adapted to become subjects. Suppose, e.g., that the ques-
tion arises whether this stone is a diamond, I know that diamonds do not
possess double refraction, and I argue :
That which is a diamond does not possess double refraction.
This stone possesses double refraction ;
Therefore it is not a diamond.
This is more natural than to say, Everything possessing double refraction
is not a diamond.
Thus our investigation of the different kinds of mediation by means of
which any given question may be decided leads to exactly the same result
in all cases. If our inference is to be based upon simple analytical rela-
tions and opposition of concepts, then the modus ponens and modus tollens
in their different applications, prove to be the only forms of inference of
which we can make use.
$ 54.
The ordinary doctrine of the CATEGORICAL SYLLOGISM, which has grown
out of the Aristotelian theory, is based upon the presupposition of the pre-
ceding section ; i.e., that our inferences are grounded upon established rela-
tions between concepts. The distinction of figures and moods was justified
from the point of view of the Aristotelian doctrine ; but, from the point of
view of the traditional doctrine, they are superfluous specializations, which
may be resolved into the more general formulæ of the preceding paragraph.
1. Both the Aristotelian doctrine of the syllogism and the ordinary
teaching which has grown out of it presuppose established relations
amongst concepts. Aristotle himself assumes an objective system of
concepts which realizes itself in the material world in such a way that the
concept manifests itself everywhere as constituting the essence of things
and as the cause of their particular determination. Thus all judgments
containing true knowledge are for him the expression of necessary relations,
and the function of the syllogism is to reveal the whole force and bearing
of each particular concept in our knowledge by combining particular
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LOGIC
judgments and making them mutually dependent through their concep-
tual unity. The verbal expression of these conceptual relations is due
to the fact that they always appear as the essence of particular things,
which are, therefore, when conceptually determined, the real subject of
judgment; in this way the relations between concepts manifest themselves
in universal or particular, affirmative or negative, judgments. Ordinary
logic, on the contrary, is based upon a subjective system of concepts,
which is not sought for in the process of knowledge, but is assumed as a
preliminary datum.
2. Now the fundamental relation is that of the subordination of con-
cepts. The natural predicate to every concept is the concept next above
it; thus if A, B, C are three concepts, which are subordinated to each
other, their relation is expressed in the two propositions; A kard Tavtos
Toû B, B katà Tavtòs Toll T; and from these we obtain, by means of the
syllogism, A katà mavròs toll T. It is from this relation of subordination
that the terminology is derived, according to which B is called the uéros
όρος (terminus medius), A and Γ, the two άκρα-A being the μείζον άκρον
(terminus major), T the ělattov åkpov (terminus minor). For this reason
also the first proposition, which predicates the highest concept (the predi-
cate of the conclusion) of the middle concept, has been called the major
proposition; the second, which predicates the middle concept of the lowest
(the subject of the conclusion), the minor proposition; the result of the
syllogism is the conclusion.
Taking the usual symbols, P for the highest concept, M for the middle
concept, and S for the lowest, then the form in which the nature of the
syllogism is most directly and immediately obvious is the familiar-
Omne M est Pi
Omne S est M
Ergo omne S est P.
3. Aristotle next proceeds to introduce the distinction between negative
and affirmative judgments, and he shows that if the major proposition is
negative, it is still possible to have an inference with a negative conclusion.
No M is P
All S is M
Therefore no S is P.
THE RULES OF INFERENCE
351
If, on the other hand, the major proposition were affirmative, and the
minor negative, no inference could be drawn, “ for nothing would follow as
necessary from the validity of the premises.” When P is true of all M,
while M is not true of any S, then P may be true of all S, or it may not
(living being-man-horse ; living being-man--stone). Nor can any-
thing be inferred when both premises are negative.
When the distinction between universal and particular judgments is
introduced, it follows for similar reasons that the major premise cannot
be particular, though the minor premise may be a particular affirmative
judgment.
We may then infer—
All M is P
Some S is M
Therefore some S is P.
No M is P
Some Sis M
Some S is not P
These are the four spórou or modi of the syllogism, which result from
two premises, in the first of which the middle concept is subject, while
in the second it is predicate. They are the four perfect syllogisms
(ovlloyio puoi TÉ ELOL), and in them the four kinds of judgment are deduced
from premises which contain the middle concept in the way we have
stated.
4. But it may also be that the middle concept is predicate in both
premises, or subject in both premises. In the former case we have the
second figure, in the latter the third (δεύτερον and τρίτον σχημα). In these
figures the syllogisms possible are-
In the second figure :
Mood 1.
No Pis M
All S is M
Mood 2.
All P is M
No Sis M
No Sis P
No Sis P
Mood 3.
No Pis M
Some S is M
Some S is not P
Mood 4.
All P is M
Some S is not M
Some S not is P
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LOGIC
In the third figure :
Mood 1.
All M is P
All M is s
Mood 2.
No M is P
All M is S
Some S is not P
Mood 3.
Some Mis P
All M is s
Some Sis P
Some S is P
Mood 4.
All M is P
Some M is s
Mood 5.
Some M is not P
All M is s
Mood 6.
No M is P
Some M is s
Some S is not P
Some S is P
The syllogisms of these two figures are not recognised by Aristotle as
perfect, and he reduces them to the first figure either by conversion of the
judgments or by indirect proof. He then proceeds to investigate in a
similar manner the various inferences from premises which are judgments
of necessity and possibility.
5. Notwithstanding many attacks, this Aristotelian doctrine has always
reasserted itself as the essential part of all scholastic logic, although its
original meaning and the significance which Aristotle attached to it has
in most cases been lost sight of. This misunderstanding is obvious from
the introduction of the so-called fourth figure ;1 and more particularly from
the fact that instead of recognising the necessity of conceptual relations to
be at the root of all inference, it became customary to look upon the
premises as mere statements as to how concepts are related in their exten-
1 It was discovered, that is, that Aristotle had overlooked one way of arranging the
middle concept, that in which it is predicate of the major premise and subject of the
minor. By introducing this it was found that ſive additional moods were possible :
I.
All P's are M
All M's are s
Some S's are P
2.
All P's are M
No Miss
No Sis P
3.
Some P is M
All M is s
Some Sis P
5
No Pis M
No Pis M
All Miss
Some Miss
Some S is not P
Some S is not P
It is evident that any one forcing the concepts into this unnatural position must have for.
gotten all the fundamental presuppositions of the Aristotelian theory; the need of sup.
plementing the Aristotelian doctrine could only have been felt in a treatment which
dealt with the external form alone.
THE RULES OF INFERENCE
353
sions. It was for this reason that the cogency of the premises as proof
was in the first instance based upon the relations between numerical
expressions, as if the object of inference were to find one or more par-
ticular things in a given number, and its problem to think of the objects
falling under a concept all at once, and then to find out what is included
amongst them and what is not. The same misunderstanding has led to
the favourite method of proving the particular figures of the syllogism by
1
concepts; as if the function of all judgments were to place the subject
within the sphere of the predicate concept, and to exhibit it as a part of a
greater number of objects bearing the same name, and not rather to state
what it is and what it does. This mistake is in a large measure due to
the irrational manner in which the particular judgment is usually treated.
Thus the doctrine of the syllogism degenerated into a sort of calculating
machine, by means of which any one who would take the trouble to re-
member the 19 moods by aid of the versus memoriales, and to practise
them upon meaningless examples, could learn everything from the external
forms of judgment, from the position of subject and predicate, without
need of further reflection.
6. Leaving the presuppositions of the doctrine for the present un-
touched, what strikes us first is that in the fig. I the distinction between
the third and first, and between the fourth and second, moods, is quite un-
important. No change whatever is made in the course of thought because
the minor proposition is particular in the third and fourth moods. Since
the “some S” of the minor proposition and of the conclusion must always
mean the same S, and since the predicate is attributed to them because of
a conceptual determination which is common to both, the meaning of the
inference is exactly the same as when the subject is universal. It is the
value of the result with respect to the determination of the concept S
which differs, not the operation of inference; and it was in reference to
this difference of value that Aristotle, who always kept the conclusion in
view as the principal object, made his distinction. So far as concerns
the form of deduction we have, strictly speaking, only two kinds of
inference :
All M's are P
No M is P
(All, some, one) S are M (All, some, one) S are M
(All, some, one) S are P (All, some, one) S are not P
A A
S. L.
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LOGIC
In the first case the middle concept adds a predicate to its subject; in
the second case it excludes one.
In the same way the moods of the fig. 2 may be reduced to two kinds
of inference; when a predicate M, which is excluded from another concept
P, is contained in any subject S, then P is itself excluded from the
subject; and when a concept M, which comprehends another concept P,
is excluded from a subject, then Pis excluded from the subject; it makes
no difference whether the S is expressed as universal or as particular.
Thus we have:
No P is M
All Pis M
(All, some, one) S are M (All, some, one) S are not M
(All, some, one) S are not P (All, some, one) S are not P
Now, the indispensable rule according to which we infer, when reduced
to its most appropriate expression, runs for the first figure as follows :
If anything is B, it is A (moods 1 and 3).
If anything is B, it is not X (moods 2 and 4).
In both cases the assumption takes the form :
Certain subjects C are B,
and it follows :
Therefore they are A, therefore they are not X.
But the second figure must also be based upon these same rules, for
there is no other method of inference from simple conceptual relations.
In the second figure, however, we infer from the fact that the consequence
is wanting ; that is, we infer from the invalidity of the consequence to the
invalidity of the ground.
If anything is B it is A ;
Now C (all C, some C) is not A,
Therefore it is not B (moods 2 and 4).
If anything is B it is not X;
Now C (all C, some C) is X,
Thus both the connexion between the first and second figures, and
their difference become evident when we see that in the first figure we
infer from the validity of the ground to the validity of an affirmative or
negative consequence, while in the second we infer from the invalidity of
THE RULES 355
C
OF INFERENCE
the affirmative or negative consequence to the invalidity of the ground.1
The first two of the Aristotelian figures, therefore, coincide exactly with the
results of 8 53.
All the moods of the first and second figures can thus be exhibited in a
single formula in such a way as to show both the grounds of inference
and how they differ.
Major premise :
If anything is B, it is A—it is not X.
Minor premise and conclusion of fig. 1 :
C (all, some, one C) is B,
Therefore C (all, some, one C) is A-is not X.
Minor premise and conclusion of fig. 2.
C (all, some, one C) is not A-is X,
Therefore C (all, some, one C) is not B.
7. The particular judgments of fig. 3. differ essentially in meaning
from the particular judgments of figs. I. and 2. In the latter the
term which is particular stands from the first as subject, and the fact
that it is particular is unimportant, may indeed be due merely to the
verbal expression; the subjects of the minor premise and of the conclusion
are the same. But in the third figure the particular term is subject only
in the conclusion, and possesses therefore all the indefiniteness of the
particular. It is equivalent to a mere judgment of possibility, and in the
third figure there can be no such thing as a necessary consequence in the
ordinary sense. In the first, third and fourth moods alike, the essential
point is that two predicates belong to the same subject, for in the third
and fourth the burden of inference rests only upon that part of all M
which is identical with some M. But all that follows from this is that
the two predicates are compatible, i.e., do not exclude each other. In
the same way the common characteristic of the second, fifth and sixth
moods is, that one predicate P is absent from a subject to which the
other predicate belongs, and from this it follows that they are not
1 This gives us also a solution for such difficulties as that two negative premises may
yield a conclusion notwithstanding Aristotle's rule ; e.g., that which is not M is not P, S
is not M, whence it follows that S is not P.
The conclusion is doubtless true, but it is false that it follows from two negative
premises in the Aristotelian sense. The proposition “that which is not M is not P,” is
negative merely in form ; really it is equivalent to all P's are M; and the connexion
between the negatives is based upon the positive relation between the predicates. Ob-
jections such as these arise only where the method of treatment is quite superficial.
356
LOGIC
necessarily connected. Strictly speaking, then, the rule according to
which the inference takes place, and upon which the deduction of the
conclusion from the premises is based, finds no expression in the premises.
The major premise suppressed in the affirmative moods is : “If two
predicates belong to the same subject, they are compatible, they do not
necessarily exclude each other”; the two premises taken together form
the minor for this suppressed major premise. In the moods with
negative conclusions, again, the major premise is : “If one of two predi-
cates belongs to a subject, but not the other, then they are not necessarily
connected”; here again the two premises together represent the minor
to the above-stated rule.
That which is inferred, then, in this figure is the definite denial of a
necessity, either of a necessary exclusion or of a necessary connexion.
The weakness of the third figure is that it cannot prove necessity, but can
only deny it, and this weakness finds its expression in the fact that the
conclusion is particular.
From this point of view, as Lotze shows (p. 113), two negative premises
may yield a similar conclusion as to the negation of a necessity. If M is
not P and M is not S, it follows that the negation of P does not neces-
sarily involve the affirmation of S, nor the negation of S the affirmation
of P; that which is not P is not necessarily S, and vice versa. That
which is denied is therefore the connexion which would be expressed by
the disjunctive judgment “M is either P or S.” The two premises may
be combined in the judgment: “M is neither P nor S,” which is the
negation of the disjunction “ M is either P or S.” Aristotle's exclusion
of these inferences may be explained by the fact that their results cannot
be expressed by any of the kinds of judgment which he had in view; for
if we follow the ordinary formula, the conclusion must run “some not
S is not P.” But this tells us nothing about the relation between the
concepts S and P, neither whether they exclude each other wholly or
partially, nor whether they wholly or partially coincide. Thus the rule
ex mere negativis nihil sequitur in its original signification is not affected,
although the proposition that everything must be either X or Y may be
refuted by an instance in which Z is neither X nor 7.1
1 On Schuppe's attempt further to extend the number of inferences which can be
drawn from the combinations of premises rejected by Aristotle, see Appendix C.
THE RULES OF INFERENCE
357
§ 55.
Where the categorical syllogism presupposes an analytical judgment
concerning concepts as its major premise, it cannot serve as a basis for
thought in its perpetual progress to fresh knowledge. Its sole function is
to keep before us the established relations between our concepts in every
application of them. The categorical syllogisms gain a higher significance
only when we make them subservient to the formation of our concepts,
as was done by Aristotle; or when their major premises are not merely
judgments concerning concepts, but synthetical propositions in the Kan-
tian sense.
1. The whole syllogistic process becomes of doubtful value if, instead
of regarding it as a means to the construction of concepts by a Socratic
Taywy), we look upon it in the light of the scholastic logic. If, that is,
we accept it as based upon a finished system of concepts incapable of
further growth, and upon the analytical judgments yielded by such a
system.
That is to say, if the normal syllogism consist of three concepts,
S, M, P, in simple subordination to each other, then the presupposed
relations of these concepts involve the conclusion S is P as directly as
they involve the minor premise S is M, or the major premise M is P; P
forms a part of the intension of the concept S just as much as any other
of its characteristics or combinations of characteristics. But if S represent
a particular thing, we cannot be certain of its subordination to M until we
have enumerated all its characteristics ($ 47, 1, p. 306), thus including
those which constitute P; indeed, we must know that S is P before we
can say that it is M. In the proposition “the square is a quadrangular
figure,” the predicate is certainly not more remote than in the proposition
“the square is a parallelogram," and to infer that “the square is a
parallelogram and therefore a quadrangular figure ” is quite superfluous.
The proposition “this figure is a parallelogram” presupposes that “this
figure is quadrangular”; a particular figure cannot be recognised as a
parallelogram until it is known to be quadrangular; hence to infer" it is a
parallelogram and therefore quadrangular” is not merely superfluous but
perverse. Again, what do we gain by this process of continuous ascent
to higher concepts ? If our object is to extend our knowledge by means
of judgments, we are moving in the wrong direction; our predicates
become poorer and less significant, we learn less about our subjects, and
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LOGIC
lose instead of gaining by our progress. If I know that a square is a
parallelogram, I know much more than I can learn by erecting a ladder of
inferences which end by teaching me that it is spatial or divisible, or that
it is a being of some kind. To this last predicate all inferences must
finally attain which mount the conceptual pyramid by successive steps
(from species to genus).
2. The nature of the syllogistic process, as represented in the scholastic
logic, appears most clearly from the success achieved by the theory that
syllogistic inference is really only concerned with the substitution of one
term for another. Benekel tells us that in syllogistic inference we replace
one of the elements of a given judgment by another, being led to do so
by a second judgment, which tells us of a relation between the first term
and the new one. The substitution may take place whenever the new
element in no way surpasses the old (keeps within the limits of the old).
Either the substituted element may be the same expressed differently,
or it may be a part of that for which it is substituted. In the in-
ference “some quadrangular figures are not parallelograms; all rhombs
are parallelograms, therefore some quadrangular figures are not rhombs,”
I have substituted rhombs for parallelograms, the part for the whole.
In the inference “some parallelograms are oblique-angled ; all parallelo-
grams are quadrangles, therefore some quadrangles are oblique-angled,”
I have substituted another expression (some quadrangles), for the same
subject (some parallelograms). In the first instance the new element
(rhombs) is a part of the extension of the old (parallelogram); in the
second instance the substituted element (quadrangle) is a part of the
intension of the old (parallelogram), and enables us to think of the same
thing under another expression.
From this theory Beneke derived all possible kinds of inference, and the
conclusion he then came to was that such inferences in no way extend or
enrich our thought. The part must always be contained in the whole,
and in substituting the former for the latter I lose rather than gain in the
ideas which form the material for thought.
It is only in inferences with a negative conclusion that any progress is
made ; for when we think of a concept, we do not think of everything
1 System der Logik, I, p. 217. Cf. Ueberweg, Logik, ſ 120. This substitution
differs from that which we have mentioned above ($ 50) as Introduction of the Minor
(arpboanys). There the process is one which supplies a definite subject where one was
wanting, here we substitute one definite concept for another in which it is contained.
THE RULES OF INFERENCE
359
which it is not, and the syllogism thus serves to introduce new differentia-
tions. But every concept as such belongs to us only in so far as it is
member of a system and disjunct from its co-ordinate members. Hence
the proximate and most important negations are certainly included in the
thought of the concept itself, and nothing is to be gained by adducing
others which are remoter and less relevant. If I know that man is an
animal, that is sufficient to distinguish him from other existing things which
are most nearly allied ; I need no syllogism to assure me that he is not a
metal nor a geometrical figure.
From this point of view, then, the syllogism can at most serve to warn
us, when we connect no definite concepts with our words, of all that is
involved in a statement by reminding us of what is really said by our
predicate. By recalling all that is involved in our statements, it would
lead us to analyse them; it would thus interpret a proposition when we
failed to understand it, but would not help us forward when we did under-
stand. It would be an aid in teaching, or a polemical weapon, but not an
organon of knowledge. To demand, therefore, that the syllogism should
proceed entirely according to the so-called principle of identity, as, for
instance, Leibnitz emphatically did, is to render the syllogism worthless.
3. The importance of the syllogism, or more exactly of the form in
which the syllogism is ordinarily presented, was attacked from another
point of view by J. S. Mill.1 In the inference-
All men are mortal;
Socrates is a man,
Therefore Socrates is mortal,
the conclusion seems to be drawn from the major premise. But in reality
the major premise presupposes the conclusion, for before I can know that
all men are mortal I must know already that Socrates is mortal; as long
as there is any uncertainty about this proposition, the proposition “all
men are mortal” is not yet certain. Every such inference, therefore, con-
tains a petitin principii, it presupposes what it is meant to prove. It is no
1 Logic, book ii., ch. 3, § 2.
2 In the same way the minor premise also presupposes the conclusion, as Lotze (Logik,
2. ed., p. 122) has shown most completely with reference to conceptual judgments of
subsumption. Where would be the truth of the minor premise, “Socrates is a man,” if
it were doubtful whether or not the attribute mortality belonged to him as well as the
other attributes of men, for the major premise adduces mortality as a general characteristic
common to all men.
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LOGIC
solution of the difficulty to say that the conclusion is not stated explicitly
and directly in the premises. We are not, of course, called upon, when-
ever we state a universal proposition, to think of all the particular instances
to which it applies ; nevertheless our statement involves the validity of the
proposition for all particular instances, and it is a statement for which we
have no ground unless we are already certain of all particular instances.
Must we then say that the syllogism is absolutely useless and without
significance ? Mill endeavours to avoid this conclusion by means of a
distinction. The real ground for my statement that any man now living
is mortal cannot be the general proposition “all men are mortal"; this
presupposes, if valid, that I have some means of knowing that those who
are now living are mortal. But we may find the ground in our previous
experience of a number of particular cases. Because a number of men
have died we infer that those who are now living will also die. Thus we
really infer from particular cases to other particular cases. It would seem
that the general proposition is quite superfluous, and that we go out of
our way in passing through it.
Nevertheless it has a meaning. It is evident that the particular
instances known to us cannot enable us to infer a new instance with confi-
dence, unless they provided a sufficient ground for the general proposi-
tion also. This general proposition is an abbreviated formula for all that
we hold ourselves justified in inferring upon the testimony of experience ;
in it is contained the only real inference, and what follows is merely a
“deciphering our notes” which we have made to remind us that experience
justifies us in passing to further instances. We may have forgotten these
particular instances, and remember only that the general proposition was
grounded upon them. We then turn to the general proposition and
interpret it; we do not infer from this abbreviation of the results of our
experience, but according to it. In the same way the application of a law
or of a general rule accepted on some authority is an interpretation; we
interpret that which the legislator or authority meant to say.
Thus, though we do not naturally pass through the general proposition
in inference, we add greatly to the security of our process by so doing.
For the experience which justifies the inference to one case must be
such as is sufficient to support the general proposition ; and a conscious-
ness of the general proposition is most valuable in enabling us to avoid
hasty and ill-grounded inference. It obliges us to consider more care-
fully the adequacy of our experience ; and if there happen to have been
THE RULES OF INFERENCE
361
any contradictory experiences, our attempt to frame a universal judgment
recalls them to mind.
These criticisms of Mill's are most instructive, for while disclosing a
weak point in the syllogism, they, nevertheless, are an involuntary confirma-
tion of its true and fundamental importance. The weak point disclosed
lies in the meaning ordinarily attached to the proposition “All A’s are
B,” which is taken to be a mere summation of particular judgments in an
abbreviated expression, an enumeration of particular instances. If this
were so, then, of course, the certainty of the judgment with regard to the
sum-total would depend upon its certainty in regard to the particular items.
But the universal major premise should not be understood as the statement
of this numerical generality; it is the statement of the necessity of connect-
ing the predicate with the subject. This necessity cannot be attained,
even by a complete enumeration ; indeed it can never be known at all
in a directly empirical manner. To investigate the conditions under which
we may infer from particular experiences to a necessary law upon which
they rest, is the main object of a theory of induction; and we hope to show
that such an inference can never be possible unless we assume that some
unconditionally valid principles are to be found. Mill's position is justified
to the extent that the universal major premise is drawn ultimately from
particular data, which are the real proof for those judgments which have
reference to the empirical ; but it is false that the major premise might be
dispensed with in inference. Only by proving necessity can the particular
data be proof of any particular case. His argument rests upon a confusion
between the two processes of describing the psychological process of
inference and laying down logical laws for it. There is no doubt that we
frequently infer from one particular case to another, but the question is
whether we are justified in so doing. This question is decided by the
validity of the general proposition, which does not merely—as Mill repre-
sents—yield a collateral security, but is the one thing which makes the
inference legitimate. Mill himself allows that the inference from particular
cases to a new instance is not justified unless the general proposition may
be inferred; and in reality the truth of the universal major premise is the
condition of the truth of the conclusion. Thus the conclusion does, after
all, depend upon the major premise, and cannot be proved without it.
But all that is maintained by the Aristotelian doctrine of the syllogism is
nothing more than this : that a satisfactory and scientifically valid inference
is possible only in the syllogistic forms, and on condition of a universal
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LOGIC
major premise. Aristotle himself teaches that we arrive at universal major
premises by means of induction. But then his induction is certainly not
based upon the purely empirical ground of a collection of instances, which,
as it can yield no necessity, would make logic impossible ; but upon the
presupposition that particular phenomena are governed by conceptual
necessity, which must therefore be knowable from particular instances.
Thus the attack fails to touch the absolute validity of the syllogistic
rules wherever a reliable inference is to be made from one judgment to
another. It is only when the attempt is made to base the syllogism
entirely upon the so-called principle of identity-when therefore the
premises are purely analytical propositions—that the syllogistic process
seems to be without value.
-4. So far is this from being Aristotle's view that he regards the syllo-
gism as the preliminary means of attaining that which is presupposed in
the scholastic logic—definition. His premises are mainly empirical judg-
ments concerning that which is given in intuition, and the syllogism is the
means by which he arranges these items of knowledge in such a way as to
exhibit their mutual dependence. In this way the material dependence
of the conceptual determinations realized in being, the true causal relation
is exhibited; and thus an exhaustive definition is framed, which expresses
a dependence of the special determinations upon the general correspond-
ing to these conceptual relations. It is for this reason that the middle
concept is said to correspond to the cause, and that the premises are
selected and arranged in such a way as to represent the real dependence
amongst things.
Although the syllogism as thus applied is most closely connected with
the Aristotelian metaphysics, yet the logical laws are not limited to this
special application ; the end in view merely determines the particular way
in which they are formulated. The traditional logic has forgotten the end,
but has retained the formulation to which it led, and which is apparent in
the exclusively categorical treatment, and more especially in the coordina-
tion of the particular with the universal judgment. It is no wonder that
the formulæ of logic no longer correspond to the altered problems of
science.
5. Mathematics, which throughout makes use of the syllogism and owes
its scientific certainty to this form, is often cited as an answer to all attacks
upon the theory of the syllogism. This is quite justifiable so far as show-
ing that all mathematical propositions, with the exception of axioms and
THE RULES OF INFERENCE
363
definitions, are proved by syllogisms, or at any rate on the principles by
which the syllogistic forms are determined. But to overlook the wide
difference between mathematical propositions and the examples of the
scholastic logic, with their analytical judgments, is a great mistake. Do we
find such inferences as “the square is a parallelogram, therefore it is a
quadrangular figure," " the circle is a curve of the second degree, therefore
it is a conic section,” in geometry ? does it ever concern itself with such
trifling subsumptions ? This is all included in the definition of the par-
ticular object, and the syllogism is not there for the purpose of repeating
this definition ; the real task of geometry is to develop the laws of the
relations which certain conditions bring about between particular objects,
such as lines and angles, the relations, that is, of equality, inequality, etc.
From the point of view of the concept these relations are predicates which
are added to it from without; they are not contained in the definition, and
cannot be learned from it; indeed they do not exist until the particular
objects enter into spatial relations. In the concept of the triangle-that
is, in its definition, we find absolutely nothing about the fact that its angles
are equal to two right angles, the idea of two right angles is not contained
in the idea of the triangle. The judgment is based firstly upon the addi-
tion of the angles, and secondly upon their comparison with two adjacent
angles, that is, it is based upon relations which have to be created. It
forms no part of the concept of the right-angled triangle that the square of
the hypotenuse is equal to the sum of the squares of the two remaining
sides; for in the concept of the triangle I think of nothing more nor less
than a plane surface, bounded by three intersecting straight lines, and in
this there is nothing to oblige me to construct squares upon the sides and
then compare them. It is not until I have done so by means of inventive
construction that I can investigate the relations in which these squares
stand to each other.
Geometry, then, always goes beyond mere conceptual judgments in
seeking its propositions, and by combining necessary relations taken from
some other source with that which is given in the definition, it obtains pre-
dicates which are not contained in the definition. But just for this reason
we cannot, as a rule, regard its major premises as judgments of subsump-
tion, and though its syllogisms may appear to be framed in the scholastic
form Barbara, they are not so in reality. Ueberweg, for instance, gives
1 System der Logik, edn. 3, p. 304 ; edn. 5, p. 360. We find a similar example in Wundt,
Logik, 1, p. 297. Cf. my “ Logische Fragen,” Vierteljahrschr. f. wiss. Phil., iv. p. 478
364
LOGIC
as an example of this figure : All triangles with proportional sides are tri-
angles with respectively equal angles-all triangles with respectively equal
angles are similar figures—therefore all triangles with proportional sides
are similar figures; and this inference is to all appearance the same as :
All negroes are men, all men are mortal, therefore all negroes are mortal.
In reality, however, the difference is very wide. There is no specific con-
cept formed from the concept of triangle by means of the differentia “ pro-
portional sides," nor any general concept “similar figure" to which the
specific concept might be subordinated by means of the middle concept
"triangle with respectively equal angles.” The inference does not proceed
by means of such subordination at all, but solely by means of relations
which form no part of the concept triangle. Where two or more triangles
are given having proportional sides, it follows that the other relation-
equality of angles—will also be present; and because equality of angles in-
volves the similarity of the triangles it follows that the relation of similarity
is given together with the relation of proportionality of sides. It is only by
a crude inaccuracy of expression that these propositions can take the form
of a proposition concerning “all triangles” of a particular construction, as
if the predicate might be true of each particular triangle in itself. The
inference, correctly expressed, would run :
If two or more triangles have proportional sides, they have equal angles.
If two or more triangles have equal angles, they are similar. Therefore,
if two or more triangles have proportional sides, they are similar.
It is evident that from the nature of the case the propositions must be
expressed hypothetically, if what they mean is that one relation between
different things necessitates another.
It is significant that the guiding principle of mathematical inferences is
the proposition that two magnitudes which are equal to a third are equal
to each other; that is, it is a proposition concerning necessary connection
between relations. Equally significant is it that mathematical reasoning
frequently proceeds by substituting one magnitude for another to which it
is equal. Processes such as these find no place in the ordinary forms of
the syllogism, though by means of these general laws they can always be
exhibited as strictly syllogistic.
6. What we have said of geometry applies also to other branches of
science. What we have to establish by inferences are elements not yet
contained in the concept, not given analytically; and these are, on the one
hand, relations, on the other everything which depends upon varying and
THE RULES OF INFERENCE
365
TTT
changeable events, more especially therefore all causal relations. The
inference of the judge does not proceed by subordinating particular
offences. When once the case before him is subsumed and recognised as
murder he does not infer analytically “ therefore it is a crime, and therefore
an infringement of the law," but he proceeds at once to the conclusion
commanded by the synthetical rule of the law—“ therefore it is to be
punished by death.” Capital punishment is not analytically contained in
the concept of murder, it is synthetically connected by the will of the legis-
lator with that particular crime. The physician who has diagnosed an ill-
ness as typhus does not go on to infer that it is therefore an infectious
disease, but he infers that therefore the treatment must be this or that; the
remedies which counteract typhus are not analytically contained in its
concept, but are synthetically demanded by the rules of experience. When
the physicist knows that a body has fallen for four seconds it would avail
him nothing to analyse the concept of the fall; but if he introduces the
particular value into the formula S=jgt? he knows that the distance of
the fall is 15 x 16 feet.
Here again Kant's teaching becomes important. His question "How
are synthetical judgments a priori, i.e. unconditionally and universally valid
synthetical judgments, possible ? is for the syllogism also the vital question,
without which it is but a barren process.
7. From what has been said we may understand how important for
inference are all those general principles which have reference to necessary
connections between relations, and by means of which we obtain relational
judgments. Such are the principles that two concepts or objects which
are identical with a third are identical with each other; that two magni-
tudes which are equal to a third are equal to one another ; that if equals
are added to equals the results will be equal; as well as those principles
which govern spatial relations. It is, after all, a question of secondary im-
portance whether these principles are themselves looked upon as analytical
because derived from the concepts of identity, equality, etc. ; or whether
they are accepted as synthetical judgments a priori. The important point
is that because they refer to relations they enable us to pass beyond the
merely analytical judgments which alone are treated of by the ordinary
logic.
8. For this reason the scholastic categorical syllogisms are much too
narrow, and ill-adapted to serve as general formulæ of easy application.
For judgments of subsumption, and judgments which state simple predi-
366
LOGIC
cates of a subject, they are the natural expression; so soon as we have to do
with more complicated relations, such as the dependence of a predicate
upon several conditions, they become inapplicable. Here the hypothetical
form with its consequent mpóolnyus becomes the natural expression; as
comprehending all universal categorical judgments, it is the formula which
naturally presents itself for use, more especially because in it necessity and
not generality appears as the true basis of inference. We need but glance at
any mathematical or physical textbook to assure ourselves that by far the
greater number of propositions which are used as major premises do not
take the form of universal categorical judgments, but are hypothetical in
expression or at any rate in nature. Propositions such as “two circles
which intersect have no common centre,” are hypothetical in nature; the
relative proposition states the condition upon which the predicate is denied.
And in the same way the first axioms are of the nature of hypothetical
judgments. The proposition “two straight lines cannot enclose a space”
means “no matter where or how I draw two straight lines, the two together
will not include a space”; it says nothing about two straight lines in the
sense of stating an attribute which is common to both. The proposition,
"everything which happens has a cause" presupposes by the predicate of
the first clause that something actually happens; it does not develop the
concept of happening, but states the connection of every particular event
with something else which exists. It is the same with the formulæ of
analytical mechanics; these and others of the same description are hypo-
thetical judgments, and inferences are made in accordance with them by
substituting definite values for the general symbols.1
Some writers-e.. Wundt. (Logik, 1, p. 291)-include amongst the forms of inference
a special“ inference of identity,” and even of “ equation " ; but I consider this superfluous.
We might as well give a special place and name to the inference a), b)c, therefore a).
The peculiarity of these forms does not lie in the manner of inference itself, but in the
particular principle upon which they are based, though this, no doubt, is frequently not
expressly formulated because it is taken for granted. A the same as B, B the same as C,
therefore A the same as C, is nothing more than an application of a principle referring
to the particular predicate of identity. The only possible reason for laying special em-
phasis upon this inference is that in inaccurate language the judgment A is B frequently
means identity without expressly saying so.
On the whole it seems to me that there is little to be gained by specializing the doctrine
of inference any further. On the contrary, I prefer to emphasize the common element in
all kinds of inference instead of multiplying distinctions of form which in fact consist
merely in the different contents of the premises which determine the conclusion; to ex-
haust these would be impossible. It is true that Wundt attempts to give a general for-
mula for all inference. “When different judgments are related to each other by concepts
which are common to both, then the other concepts in the judgments which are not com-
THE 77 T
367
RULES OF INFERENCE
TTT
$ 56.
The syllogism which has a CONJUNCTIVE JUDGMENT for its major
premise serves to subsume the particular under established concepts by
means of their definitions.
I. The syllogism finds a special function in subsuming the particular
under established concepts, and in so doing it falls into certain forms
adapted to this purpose.
There is no other way of finding out whether any thing A falls under a
concept B than by showing that it contains all the characteristics of B; if
these are to be found in it without exception, then it falls under the concept
B. Here, then, the middle concept is not a single predicate, but a series
of predicates which are combined in a conjunctive judgment, but which
assume the function of a single concept just because they belong together.
One characteristic alone is sufficient to show that a thing A does not fall
under a concept B if it belong to A and is excluded from B; the subsump-
tion is then rejected by a syllogism of the second figure ; i.e., modo tollente.
Thus we get the forms having for major premise a definition : Pis a, b,
6, or the reverse
That which is a, b, c is P;
Sis a, b, c,
Therefore S is P.
The form of exclusion is :
Pis a, b, c ;
S is not a;
S is not P.
and this coincides with the syllogisms of the second figure modo tollente.
mon to both are also related, and this relation finds its expression in a new judgment.
But even if we disregard the vagueness of this formula, the proposition is false, because
too wide; how are the concepts S and P related when S is not M and M is P? Lotze
again, remarks that the most important inferences would be such as would not merely
predicate a general P of S through the mediation of M, but would show how the par-
ticular modifications of the M which belonged to the S necessitated a particular form of
P. This is quite true so far as it goes, but it involves no special mode of inference; it
merely involves principles different from those which are ordinarily noticed in the
categorical syllogism-principles which state the law according to which every modi.
fication of M brings with it a modification of P, but from which our conclusions must
always be drawn according to the simple rules of hypothetical inference. Let S be a
figure, M an ellipse, and P eccentric. Then E= a2-62 : a states the law according
to which every modification of the relation of the axes involves a modification of the
eccentricity; but the equation is by nature a hypothetical judgment, from which we may
draw conclusions by substituting definite values.
368
LOGIC
§ 57.
Inference from a DIVISIVE JUDGMENT, which some logicians have called
inductive inference, cannot lead to an unconditionally universal judgment
when the division is only empirical. If it is logical, the inference is super-
fluous, unless, indeed, it is introduced incidentally, say, as a link in a chain
of inferences.
1. An attempt has been made to add to the syllogistic forms the so-
called inductive syllogism, which resembles the inference from definition,
in that the middle concept is not simple in form. When, that is, we have a
complete division of a concept A into the species M, N, O, or a complete
enumeration of the individuals which fall under it, and a common predicate
belonging to all the species or individuals, then we get the syllogism :
A is partly M, partly N, and partly 0;
M and N and O are all P,
Therefore A is P.
2. But in this formula there lurks an ambiguity, which may be cleared
away by our distinction between empirical and logical extension.
Let us begin by considering an example, that, for instance, given by
Apelt : 1
Major premise: The solar system consists of the sun, and the planets
Mercury, Venus, Earth, Mars, etc.
Minor premises : Mercury moves round the sun from west to east, Venus
moves round the sun from west to east, etc.
Conclusion : All planets move round the sun from west to east.
Here the major premise states the extension of the concept planet ; the
conclusion affirms of all planets a predicate which, according to the minor
premises, belongs to each one by itself.
But what is gained by this ? Not an unconditionally universal judgment,
attributing to the concept planet the necessity of moving from west to èast;
but merely an empirically universal judgment which combines the particular
subjects of the minor premises under one name, after it has been estab-
lished by the major premise that those mentioned are all the planets—of
course, only so far as we know at present. The word planet does not serve
as the symbol of a definite concept, but only as the common name of a
definite number of particular things. Hence the inference in which one
iudgment is grounded upon others, refers only to our right to substitute a
1 Theorie der Induction, p. 17.
THE RULES OF INFERENCE
369
common denotation for the proper names, and the expression “all” for the
sum of the particular planets. It is, however, in no way proved that
everything which is a planet must necessarily move from west to east. The
judgment which merely contains an empirical enumeration of the planets
cannot tell us whether they owe their proper movement to the attributes on
account of which they fall under the concept of planet, or to some other
cause, which, so far as concerns the concept in question, is accidental. If
it could, then it must also follow that because all the kings of Prussia have
been called Frederick and William, therefore all kings of Prussia must of
necessity be so called.
3. It is just the same when, instead of naming the individuals, we name
the empirically known species of a genus. At one time, when none but the
older metals were known, it was a valid inference to say:
The metals are gold, silver, iron, etc.,
Gold, silver, iron, etc., are heavier than water
Therefore all metals are heavier than water.
By "all metals” is meant those which were known and were so called
because of their common properties. But it does not follow that these
common properties necessitate a specific weight greater than that of water,
and this conclusion has been refuted by the discovery of kalium.
To call such an inference inductive is a fundamental error, since the
essence of inductive inference consists in passing from empirical data to
an unconditionally universal judgment. For such an inference it is neces-
sary to show that those attributes upon which the common denotation is
grounded necessitate also the new predicate.
4. If again the judgment should rest upon a logical division such as
S
1 Given in full the premises would be:.
Mercury, Venus, Earth, etc., move round the sun from west to east.
Mercury, Venus, Earth, etc., are planets.
Therefore so many planets move round the sun from west to east.
The number of these planets is equal to the number of all the planets.
Therefore all the planets move from west to east round the sun.
The nature of the inference is just the same as when I infer from the premises :
MAM, Mz have attribute P
M1 M2 M3 are three M s,
that therefore three M's have attribute P.
Thus the inference by which we obtain a judgment of empirical universality is based
upon counting, upon the expression of a given plurality by a definite numerical concept;
my right to substitute “three M's” for M, M, Mz is based upon the identity of the num-
ber. Cf. above $ 52, 4.
S. L.
BB
370
LOGIC
would guarantee the absolute completeness of all members of the division,
the inference would be a superfluous circumlocution. For if one predicate
necessarily belongs to all the species of a genus, this predicate must have
a ground in something common to them all; i.e., in their generic concept,
from which it may be inferred :
Parallelograms are squares, oblongs, rhombs or rhomboids.
Squares, oblongs, rhombs and rhomboids have diagonals which bisect
each other.
Therefore all parallelograms have diagonals which bisect each other.
Such an inference as this is an instance of unnecessary circumlocution,
for the predicate might have been derived directly from the determinations
which constitute the concept of the parallelogram.
There are cases, however, in which we naturally pass through a complete
enumeration of particular cases on our way to the universal proposition.
The proof that the angle at the centre of the circle is double the angle
at the circumference on the same arc, begins by showing that the apex
of the angle at the circumference falls either upon one side produced of
the angle at the centre, or upon a chord falling within or without the
angle at the centre. In any one of these three cases it may be shown that
the angle at the centre is double the angle at the circumference; therefore
it is universally true that when an angle at the centre of a circle and an
angle at the circumference stand upon the same arc the former is double
the latter. Here again the proof is drawn from conditions which are
common to each case; but in each case the conditions are subsumed under
different major premises, and we arrive at the truth of the minor premises
in different ways. It is, however, clear that this can happen only when
the minor premises are inferred, never when they are immediately certain.
5. In the second figure such a division seems to give rise to an in-
ference in a somewhat different way. If it is true that,
A is B, C or D,
S is neither B nor C nor D,
then it follows that S is not A.
That which falls under none of the species of a genus cannot fall under
the genus itself. But here again we may say that if the division is em-
pirical, the inference is invalid, for the empirical extension is no guarantee
that the generic attributes are not to be found outside of the known
species. If, on the other hand, the division is logical, then the charac-
THE RULES OF INFERENCE
371
genus, and it is unnecessary to go through the division.
§ 58.
The so-called DISJUNCTIVE SYLLOGISM has no special principle of its
own; it ought not therefore to be given as a particular kind of syllogism.
I. In addition to the hypothetical and categorical syllogisms ordinary
logic gives also disjunctive syllogisms. These have a disjunctive judgment
for their major premise, and it is upon the relation of terms expressed in
the disjunction that the inference depends. If, for instance, the disjunc-
tion is of two terms, and A is either B or C, then by attributing one
predicate we exclude the other, while the denial of one predicate necessi-
tates the affirmation of the other.
I. Modus ponendo tollens :
A is either B or C;
But A is B (or C),
Therefore A is not C (not B).
II. Modus tollendo ponens :
A is either B or C;
But A is not B (not C),
Therefore A is C (or B).
Where the disjunction contains more terms the first modus leads to a
conjunctive negative judgment; the second gives a simple affirmative
only when the minor proposition is a conjunctive judgment denying all
the terms but one; where this is not the case the conclusion only limits the
disjunction to fewer terms.
I. A is either B or C or D;
A is B,
Therefore it is neither C nor D.
II. (a) A is either B or Cor D;
A is neither B nor C,
Therefore A is D.
(6) A is either B or C or D;
A is not B,
Therefore it is either C or D.
The major premise as here formulated, however, does not yield the most
372
LOGIC
general formula of the disjunctive syllogism, it is only a special instance
of the major premise:
Either the judgment B is true, or the judgment C;
B is true, therefore C is not,
B is not true, therefore C is, etc.
2. There is no ground here for a special syllogistic form, with a prin-
ciple of its own. All that the disjunctive judgment tells us is, in the first
place, that its terms are mutually exclusive, hence that the affirmation of
one involves the exclusion of the other; that is, the modus ponendo
tollens is an inference from the hypothetical judgment contained in the
disjunction “if A is B, it is not C (neither C nor D)”; in the second
place, that the negation of all the terms but one necessitates the affirma-
tion of this one; that is, the modus tollendo ponens is an inference from
the hypothetical judgment “if A is not B, it is C (when the disjunction
has more terms-if A is neither B nor D).” Thus the principle of the
inference differs in no way from that of the hypothetical syllogism. The
disjunctive judgment owes its importance to the fact that it expresses this
twofold necessity, but the distinction between the disjunctive and hypo-
thetical syllogisms is based upon the grammatical form alone.
3. In the actual use of disjunctive inference the major premises are
requently—in meaning, at least-hypothetical judgments having a dis-
junctive consequent; and from these the inference is drawn by means of
a apóolnuis:
If anything is A, it is either B or C;
Sis A, and also B,
Therefore it is not C.
S is A, but not B,
Therefore it is C.
Such inferences serve for the progressive subsumption of an object under
more and more definite concepts.
4. Further, the inference which, from the denial of all the terms of
a disjunction, infers the denial of the antecedent presupposition common
to all is akin to the form of inference given in $ 57, 4.
If A is true, then either B or C is true;
But neither B nor C is true,
Therefore A is not true.
Or by making use of a πρόσληψης :
THE RULES OF INFERENCE
373
If anything is P, it is either M or W;
S is neither M nor W,
Therefore S is not P.
In the categorical form:
A is either B or C;
S is neither B nor C,
Therefore S is not A.
Here we have the so-called dilemma, trilemma, etc. Here again the
inference is based upon the general principle that the denial of the con-
sequence involves the denial of the ground; the only difference is that
here the consequence is not simple, but consists of a number of mutually
exclusive possibilities.
$ 59.
The rules of the syllogism apply in just the same way even when the
premises are not stated as valid judgments, but only as assumed hypo-
theses. They then give rise to a hypothetical judgment, which exhibits
the conclusion as the necessary consequence of the premises.
In this way the principles that the ground involves the consequence,
and the denial of the consequence the denial of the ground, are applied to
the relation between the truth of the conclusion and the truth of the
premises, as well as the propositions that the negation of the ground does
not necessitate that of the consequence, nor the affirmation of the conse-
quence that of the ground.
I. There would be no object in a detailed investigation of the different
combinations which may be added to the list of inferences by means of
verbal abbreviations, or the introduction of copulative, conjunctive and
disjunctive propositions. The inference is always brought about by the
same means; its fundamental condition is a major premise which in some
form or another includes a necessary consequence, and constrains us to
affirm a proposition in case another proposition is true. To this is added
the minor premise which indicates an instance to which the major premise
is applicable. This may be done either directly, as in the mixed hypo-
thetical syllogism, or by applying a general rule to a special case included
in it by means of a judgment which shows that the general rule of the
major premise is applicable to a certain subject. For this reason we shall
not here investigate the sorites, which are nothing more than repeated appli-
cations of the rules of the syllogism, expressed in an abbreviated form.
374
LOGIC
2. In every syllogism it is asserted that the validity of the conclusion
follows from the validity of the premises ; and where the rules of the
syllogism are observed this is true even when the premises are only hypo-
thetically assumed. The simple hypothetical syllogism then reduces itself
to its major premise. Others, which contain more than the simple assump-
tion of the hypothesis, may be exhibited in hypothetical judgments of the
form “if A is true and B is true, then C is true” (if all men are mortal,
and Caius is a man, then Caius is mortal); judgments which emphasize
only the relation of consequence, apart from the validity of the premises.
Most hypothetical judgments are really based upon syllogistic relations
such as these; when one premise is taken for granted and not expressly
stated, they then appear as hypothetical judgments with a simple ante-
cedent.1
3. From this it follows that the principles concerning the relation
between ground and consequence may be applied to the relation between
conclusion and premises when these are regarded as nothing more than
hypotheses.
Not only, then, may we say that if the premises are true the conclusion
is necessarily true, but also that if the conclusion is false then the ground
from which it necessarily follows must be false. But since this ground
consists of two premises, we can infer from the falsity of the conclusion
only the falsity of one at least of the premises—either of major or minor
premise.
But it does not follow that if the premises are false, the conclusion must
also be false; nor does it follow that if the conclusion is true the premises
must also be true. Indeed it may happen that a true conclusion follows
with syllogistic necessity from false premises.
More especially, therefore, it does not follow that if one premise and the
conclusion are true, the other premise must also be true. Hence, the fact
that a proposition known to be true can be represented as the syllogistic
consequence of two premises, one of which is also known to be true, does
not enable us to infer that the other premise is also true.
1 Cf. my Programm, p. 40, and the examples there given. The necessity expressed
in the hypothetical judgment "if Caius is a man, he is mortal” is grounded upon the
suppressed proposition that all men are mortal. The judgment “if the earth moves round
the sun, the fixed stars have an annual parallax” presupposes a whole series of inferences
in which the premises are geometrical propositions of absolute certainty, and in no
way partaking of the hypothetical nature. But besides these hypothetical judgments
there are others of which the necessity is immediately known.
APPENDICES
APPENDIX A.
This view of the negation, and of its relation to the positive statement that
a predicate P belongs to a subject S, is at variance—though in different
ways-with the view of Lotze, Brentano, Bergmann, Windelband (in the
Strassburger Abhandlungen, 1884, p. 167 sq.). These writers all agree in
co-ordinating affirmation and negation ; they teach that the thought which
predicates P of S is at first undecided, and that according to the attitude
of mind with which we approach this thought we state it either as valid or
as invalid. But Lotze (edn. 2, p. 61) regards the thought of the relation
between P and S as the essential part of the judgment, and represents the
affirmation and negation of this thought as two opposed minor judgments
which predicate validity or invalidity of it; while the other logicians take
the opposite course, and consider the essence of the judgment to lie in this
decision as to validity or invalidity; the subject of the decision, they say, is
not a judgment, but a combination of ideas, or-like Bergmann-simply
an idea.
They have been led to this sharp distinction between the act of affirma-
tion or negation, and the subject which is affirmed or denied, by the fact
that in the former a psychical function becomes active which differs
essentially from the mere formation of ideas, or of combinations of ideas,
a function more nearly akin to practical action than to ideation.
Brentano (Psychologie, 1, p. 266 sq.) was the first to give a decided state-
ment to this distinction, and he was followed by Bergmann (Reine Logik,
I, p. 46), who calls judgment a critical attitude with respect to an idea,
a reflection upon its validity. He adds: “decision as to the validity of
an idea—that which judgment adds to mere ideation--is something more
than a merely theoretical relation ; it is not only a function of the intelli-
gence as opposed to the will, it is a manifestation of the spirit, in which
its practical nature, the faculty of willing, participates.”
Windelband takes the same view, and since his treatment of the subject
is the most thorough and the most carefully reasoned, it will suffice to ex-
377
378
APPENDICES
amine his arguments. As regards Bergmann and Brentano, I may refer to
the Vierteljahrschr. f. wiss. Phil., v. 97 sq., and my Impersonalien, p. 58.
Windelband distinguishes (Präludien, p. 28 sq.) between judgments simply
(Urtheile) and (Beurtheilungen) critical judgments. The former express
that two ideal contents belong together, the latter the attitude of the
critical consciousness towards the object thought of. In a judgment we
always state that a certain idea (the subject of the judgment) is added in
thought to another idea (the predicate of the judgment), the relation be-
tween them differing according to the different forms of the judgment. In
a criticism, on the other hand, the critical predicate is attributed to some-
thing which is assumed to be completely known, or of which we have a
complete idea (the subject of the critical proposition). This predicate in
no way extends our knowledge of its subject, but expresses the feeling
of approbation or disapprobation with which the critical consciousness
regards the object in thought (a thing is white-a thing is pleasant or un-
pleasant, an idea is true or false, an action is good or bad, a landscape is
beautiful or unpleasing, etc.). Moreover, none of these critical predica-
tions have any meaning except in so far as the object thought of corre-
sponds or not to an ideal with reference to which it is estimated by the
critical consciousness. Critical predicates contain a reference to a con-
sciousness which sets before itself certain ideals.
A particular application of this theory is to be found in reference to our
desire for knowledge. In so far as our thought aims at knowledge—i.e.
at truth-all our judgments are subject to criticism, which expresses either
the validity or the invalidity of the combination of ideas which has taken
place in the judgment. The purely theoretical judgment is to be found
only in the so-called problematical judgment, which combines certain
ideas but says nothing as to the truth of the combination. Whenever a
judgment is affirmed or denied, there is added to the theoretical function
that of a criticism as to its truth . . . All the propositions of knowledge
are combinations of ideas whose value for truth has been decided by
affirmation or negation.
Every critical judgment (he continues, p. 34) is the reaction of a
willing and feeling individual against a certain ideal content. ... But
the point of view from which the criticism is made, is expressed by the
contradictories pleasant and unpleasant, true and false, good and bad,
beautiful and ugly. The first pair is peculiar to the individual, the
others all contain a claim to universal validity. The same view is to be
unde
APPENDICES
379
found in the “Beiträge zur Lehre vom negativen Urtheil” (Strassburger
Abhn., p. 170), where it is said that the negation is a practical judg-
ment, a criticism, that it expresses not merely a relation between ideas,
but a disapproving attitude of consciousness towards the attempt to relate
them; it is in this that the rejection consists. For this reason Windelband
will not follow Brentano in placing judgment, as a special class of psychical
activity, between the theoretical formation of ideas and the practical
activities of love and hatred. He prefers to rank the logical estimation of
ideas on the practical side of psychical life, and holds that value from the
point of view of truth must be co-ordinated with other values.
I cannot completely agree with these views, much as there is of truth in
them. I have myself (Introdn., SS 1-4) laid stress upon the fact that logic
as such—as a critical and normative science—starts from an ideal, the ideal
of truth; that it presupposes the desire to think truly, and estimates every
actual judgment by this final ideal ; and that it seeks to distinguish between
the mental operations which are conducive to this aim and those which
thwart it. The logical treatment of these operations, as distinguished from
the psychological, is based entirely upon the consciousness of the ideal,
and I agree also with the further argument of the Präludien (p. 43) that
logic starts from the ideal of a normal consciousness (cf. 32, 7 and vol.
ii. SS 61, 62). But not even the logician can infer from this that in par-
ticular instances of affirming or denying he assumes a practical attitude
towards the judgment because he estimates the particular combination of
ideas by the universal ideal of truth; or that his activity is a reaction of
feeling or will, and not theoretical at all. When I make it my aim to keep
myself in good health, no doubt I do so by means of my will and by
reason of some feeling; and if on this account I give up some bad habit or
refuse the temptation to excess, there is no doubt that my will is active in
giving up the habit or rejecting the temptation ; it determines my be-
haviour with a view to my aim, and my No is a practical “I will not.”
But after all this will is based upon the purely theoretical knowledge that
the habit is injurious, the temptation fraught with danger. My will and
feeling have no direct share in this knowledge as to what is conducive to
my health or the reverse, for this depends upon our experience of the nature
of things, not upon willing or feeling. Nor does it follow that because I
desire to know the truth, therefore my critical judgment of a proposition
is an act of will. The distinction between a purely objective judgment,
and “criticism” with reference to some aim is important enough so far as
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APPENDICES
regards their contents; but after all such criticisms are all of them judg-
ments, which may be true or false, and differ only in that they are
judgments about the relation of the object to me and to my aim, not
judgments about the object by itself. This relation, moreover, simply
exists and is recognised; it is not approved or disapproved. “Sunshine
is pleasant” is a criticism of sunshine in relation to my feeling; but the
criticism itself, which the proposition expresses, is neither feeling nor will-
ing, but the simple recognition of the fact that sunshine excites a certain
feeling in me. The reaction of man as feeling is his enjoyment of warmth ;
the proposition in which he gives expression to this enjoyment is a function
of his thought. He has formed the general ideas of pleasant and un-
pleasant from his experience of contrary feelings, and by means of these
ideas—which are not themselves feelings—he expresses the relation which
actually exists between himself and certain things. It is the same with
good and bad, beautiful and ugly. The judgments in which these are
predicated differ from others only in the nature of the predicates, not in the
function of judgment itself; and these predicates express a relation be-
tween an object and myself, my will and feeling, which reappears in
particular instances.
But the predicates true and false contain not even such direct reference
to will and feeling, as is contained in the pairs which Windelband co-
ordinates with them. True and false as general ideas do not denote a
relation to the practical side of our life ; it depends neither upon our feel-
ing nor upon our will what is true or false, as it depends upon them what
is beautiful and what is good. For true and false are not predicates of
any objects of which I form an idea or about which I think; nor are they
-as Windelband somewhat inaccurately says-predicates of concepts.
They are predicates of judgments formed by us. As he says more accu-
rately elsewhere, they refer to combinations of ideas, not, that is, to ideas
already combined, to completed combinations, as if it should be said that
green tree or black horse were true or false ; it is the act itself of combin-
ing the ideas, the act through which the consciousness of unity arises, to
which the antithesis applies. Thus it is not ideas of any sort of objects
which we criticise by the predicates true and false, but the judging activity
itself.
Now it is perfectly true that where we actually find these predicates,
where the question arises as to the truth or falsehood of a judgment either
tentative or completed, there is in the background an ideal which, if not
APPENDICES
381
distinctly conceived, is at least vaguely striven after ; this is the ideal of
arbitrary fiction, and merely trifling with thoughts. It is this ideal which
affords us a standard by which to estimate the statements which suggest
themselves to us or the assertions of other people; we regard some as con-
forming to the ideal, others as contradictory to it. In one sense we may
indeed say that this involves an approval and disapproval; for in propor-
tion as the ideal is clearly conceived and earnestly striven after, the agree-
ment of a given judgment with it is certain to arouse a feeling of pleasure,
its disagreement a feeling of pain (though in the narrower and stricter
sense approval and disapproval could extend only to actions regarded as
voluntary; we disapprove of error when it is a fault, such as the conse-
quence of inattention). Nevertheless, it is presupposed by this approval
and disapproval that the relation of a tentative or completed judgment to
the ideal of truth should have been recognised as completely objective.
We disapprove of the false because it is false, but it is not false because
we disapprove of it. Our feeling must be grounded upon the theoretical
knowledge that a judgment is true or false, just as we must know that the
means will lead to our end before we choose them.
But from the logical point of view, where we estimate every judgment
negations as well as affirmations. We say of negations also that they are
true and false, and this alone is sufficient reason for denying that the
antithesis of approval and disapproval is to be unhesitatingly set down as
coinciding with that of affirmative and negative judgments; nor can we
find in it any ground for the co-ordination of affirmation and negation.
As a matter of fact both positive and negative judgments are estimated
according to a logical standard, and we must therefore distinguish be-
tween this logical treatment, which criticises, according to its ideal, the
movements of thought as they actually occur, and the psychological treat-
ment. The latter inquires as to what takes place in our actual thought,
how the negation arises in its course, and how it is possible that the uni-
versal ideal of truth, which is the ground of approval or disapproval,
should arise at all. Here I may briefly state my view of the question,
which in all essential points agrees with Windelband's. I start from the
simplest immediate acts of judgment which arise from intuition ; in these
we have the connection between the ideas and the consciousness of its
validity, given together without any reflection, nor can it be said that we
382
APPENDICES
1
are in any way conscious of an ideal. These are acts of judgment which
take place quite unintentionally and with all the confidence of a process
which is natural and necessary, such as the recognition of objects around
us, the judgments that this is here and that is there ; such judgments are
accompanied by the immediate certainty that they are evident. If we
were psychologically unable to combine ideas in any other ways than this,
we should never think of inquiring as to truth and falsehood. But our
thought does extend beyond that which is given. Mediated by recollec-
tions and associations, judgments arise which, when first formed, are also
regarded as expressions of that which actually is; when, for instance, we
expect to find a familiar object in its familiar place, or assume that a flower
must have a scent. But some of these conjectures prove to be at variance
with the immediately certain ; when we fail to find what we expected, we
become conscious of the distinction between the mere idea and the actual
thing; that of which we are immediately certain differs from what we had
anticipated in our judgment. Here the negation appears, and annuls the
conjecture by denying its validity. This introduces a new attitude of
mind in that the subjective combination is separated from the conscious-
ness of certainty; it is compared with a certainty and recognised as dif-
ferent. In this way there arises the conception of invalidity. But this
attitude of mind presupposes not only the subjective combination, but also
a tendency to maintain its validity. The negation--as Fichte says—is
conditioned in matter, and unconditioned in form only, just as the con-
ception of difference (the importance of which for the negation is rightly
emphasized by Schuppe) presupposes the idea of distinguishable objects,
but is not given with it, the general idea arising only after reflection upon
particular acts of distinction. Thus the negation is doubly dependent
upon the positive judgment. It presupposes as its object a thought which
was expected to be valid, and it rejects an attempted statement. The
ground of its rejection, again, is ultimately something positive, an object
given to intuition and recognised as different from my idea-verum sui
index et falsi. It is only through experience like this that the ideal of
truth becomes conscious; we cannot feel the value of truth until the un-
true has drawn our attention to it. We must have experienced both the
immediate and evident certainty of immediate judgments, and the differ-
ence between subjective combinations and immediate certainty, before we
can form the idea of truth.
The negation, then, is not co-ordinate with the positive judgment, but
APPENDICES
383
presupposes it both in the synthesis between subject and predicate and in
the certainty of this synthesis, and this relation finds a clear expression
in language. If the view that affirmation and negation are two co-ordinate
modes of regarding a problematical synthesis S P were correct, it would
be strange that while the negation finds special expression in language,
the affirmation, as a rule, has none (Bergmann and Windelband expressly
recognise this). Only when a statement is threatened with denial do we
find the in unv, indeed, verily, etc.
Windelband rightly points out (Strassb. Abh., p. 170) that if we carried
our reflexion further we might go on indefinitely with the predicates valid
and invalid. A is B—it is true that A is B—it is true that A is B is a
true proposition, etc. ; A is not B—it is true that A is not B—it is false
that A is not B is a false proposition—it is false that A is B is a true pro-
position, etc. But this is no difficulty for our view; on the contrary, it
confirms it by showing that the judgment “the proposition is true, the
proposition is false” differs in nothing but its predicate from any other
judgment. The same never-ending reflection takes place with respect to
our self-consciousness : qui scit, eo ipso scit se scire .. . et sic in infini-
tum (Spinoza, Eth., ii. 21)—though indeed it is an abstract possibility only.
In reality we always come to some point where there is a certainty which
reflection fails to separate from that to which it refers, and which is not
therefore specially emphasized. Thus the objection proves what it was
meant to refute ; it proves that there is no judgment which is not ulti-
mately based upon that immediate judgment in which we can no longer
separate the connection of ideas from “approbation” or “confirmation.”
APPENDIX B.
This view that the hypothetical judgment states the consequent as neces-
sary consequence of the antecedent seems contrary to the way in which
logic and grammar generally speak of the antecedent as presupposition or
condition of the consequent. For if we understand condition in its
ordinary sense as meaning the conditio sine quâ non, as that which must
be realized before something else happens or is valid, then it seems to
imply that the negation of the antecedent involves that of the consequent,
and that the consequent ceases to be valid when the antecedent is not
true. But this is just what necessary consequence does not involve; the
384
APPENDICES
consequence may be there even when the ground is wanting, unless,
indeed, it is the sole ground, and all agree that the invalidity of the
antecedent does not involve that of the consequent. The proposition
that if a triangle is equilateral it is acute angled does not state that the
attribute equilateral is a condition of the attribute acute angled in the
sense that no triangle which is not equilateral could be acute-angled. On
the other hand, that which is merely a condition of an event does not
of itself suffice to bring about that event; for even if we take condition
to mean an integral part of the whole cause, it is still only a part, while
in the hypothetical judgment the antecedent is not merely one of the
conditions of the consequent, it is in itself sufficient to make the con-
sequent necessary. The contradiction disappears if we distinguish between
the subjective conditions of the statement and the matter of the state-
ment. The subjective condition of the affirmation of the consequent is
its certainty, and the judgment states that in my present stage of thought
the certainty of the consequent is dependent upon that of the antecedent.
Only in so far as the antecedent is valid am I able or willing to affirm
anything about the subject of the consequent; unless the antecedent is
valid I will affirm nothing ; unless the condition is fulfilled I will not answer
for the result-e.g. if you run hard, you will catch him. But this does not
mean that objectively quick running is the conditio sine quâ non of
catching him, for he may stand still, etc. On the other hand, I cannot
guarantee that the consequent will be true when the condition contained
in the antecedent is fulfilled unless the former is the necessary conse-
quence of the latter."
Bergmann (Reine Logik, 1, § 19, p. 202 sq.) considers the essential
feature of the hypothetical judgment to be that it makes a decision about
the thesis depend upon a decision about the hypothesis. He dis-
tinguishes between two meanings of the hypothetical judgment according
as it indicates only a relative decision, a decision with a reservation (as
Wolff teaches), or is intended to emphasize the connection between the
validity of the hypothesis and that of the thesis. As examples of the first
• meaning, he gives the propositions : if it is fine, I will visit you to-morrow
-Rome was governed first by kings, if Livy is a reliable authority—a
completely general theory of equations will never be found if we may judge
from the results of past attempts.
There is no doubt that in such judgments we wish to lay special
emphasis on the point that the thesis is not unconditionally asserted, but
APPENDICES
385
only with the reservation that the hypothesis must be true. But does
this invalidate the proposition that every hypothetical judgment affirms the
necessary connection between the validity of hypothesis and the validity
of thesis, that by this alone does it deserve the name of judgment, and
that it is this connection which is expressed by the verbal form “if-
then”? (I have never said—as Bergmann asserts, pp. 204, 208—that in
framing the judgment we are concerned only with the connexion between
hypothesis and thesis, nor that the proposition “if A is true, B is true” is
an inadequate expression for “B is the necessary consequence of A”).
In the last two examples the statement of the connexion is at once
obvious: If Livy is a reliable authority, that which he tells us is true ; he
tells us that Rome was first ruled by kings, therefore Rome was really
first ruled by kings—the truth of the thesis follows with logical necessity
from the truth of the hypothesis. In the last example, again : If we are
justified in inferring from past results to future, then future failure must be
inferred from actual past failure ; here again there is logical necessity of
the consequent.
The first example contains an apparent exception : to morrow I shall
visit you if it is fine. This seems to be really no more than a conditional
statement in which necessary connexion is absent. How can fine weather
have the visit for its necessary consequent? But upon more careful
examination even this example proves to be no exception. What it ex-
presses is an intention, a resolution which is formed as well as a promise
which is given. This resolution, in itself and as such, is not conditional; I
am now bound by my promise, for it is just this dependence of an action
upon the appearance of a given fact which is contained in my will ; what
I will at this moment is that the consequence shall actually take place
together with the condition ; by my will I establish a connexion, and then
by virtue of this willed connexion I affirm that the resolution will
be carried out so soon as the condition is present. This statement
finds its ground in my will, which cannot be self-contradictory. It is the
same with all promises, threats, and contracts which are conditional upon
certain events; by my will I determine that a future action shall be the
unfailing consequence of the realized condition. Here again what I state
is the connexion between condition and consequence (cf. what is said in
the work by Enneccerus : Rechtsgeschäft, Bedingung und Anfangstermin,
1888, p. 16, 175 sq.), but this connexion, in that it is willed, differs from
a real connexion which exists independently of my will and which is
S. L.
CC
386
APPENDICES
expressed by a purely theoretical statement. As such a statement the
proposition “if it is fine, I will visit you to-morrow" is false, for there is no
objectively necessary connexion as in the proposition “if it is fine, these
buds will open to-morrow”; it is objectively valid only because it is
assumed that my will is able to realize the connexion willed, and that it
will remain constant, hence that I shall not be untrue to niy promise.
We still hold therefore that statements containing a conditional “if-
then” are judgments only in so far as they state a necessary connexion.
APPENDIX C.
0
The number of conclusions which can be drawn from those combinations
of premises which are rejected by Aristotle is extended much further by
Schuppe (Erkenntnissth. Logik, p. 128 sq.).
Even when the two premises a is not b, and b is not c, express mere
difference they yet tell us, he says, that a and c coincide in the one
point of not being b, and under certain circumstances this may be a most
important discovery forming the only connexion between a and c. Still
this discovery may be expressed by merely repeating the two premises
together in the proposition “neither a nor c are b”; so that Schuppe
acknowledges that in this case again it is true that ex mere negativis nihil
sequitur.
But he holds that in judgments of necessary connexion this principle
is obviously false. For his first proof of this he selects the instance ex-
plained on p. 456 of an inference having for its major premise the propo-
sition “ that which is not M is not P.”
From “no M is p" and "Sis not M” we infer that we can certainly
find no ground in M for denying P of S, “a result which may sometimes
be very important when we are contending with vague ideas which deny
P of S because of its similarity with M, though without any definite state-
ment, a result therefore which may lead us to recognise that S is P.”
Schuppe omits to illustrate his principles with examples ; we shall find it
easier to test them if we take one which corresponds to the above words.
“No fish has warm blood-the whale is not a fish." From this he would
say we can infer that we must not be led by the similarity of the whale
to fish to deny that it has warm blood. But do we really draw this con-
clusion from both premises ? If we are in danger of concluding that
APPENDICES
387
because the whale is like a fish it has cold blood, it will be the minor pre-
mise alone which will check us, not both together. That is, when we
have the premises-
That which is fish is not warm-blooded ;
The whale is not a fish,
it is the minor premise alone which prevents the possibility of subsump-
tion ; the possibility of any conclusion whatever is prohibited by the rule
that we cannot infer from the failure of the hypothesis to the failure of the
thesis. So that here again Schuppe merely tells us in other words that
from premises of this kind no conclusion can be drawn. For these pre-
mises give us absolutely no information as to whether P belongs to S or
not.
“From no P is M and S is not M” (I change the letters which
Schuppe has misplaced here) “we make the similar inference that P is not
to be denied of S because of a vague idea that S is M; therefore, that in
this respect at least the possibility of SP must be maintained.” Here
again the false conclusion which is feared is prevented by the minor
premise S not M alone. S is M would of course yield the conclusion
that S is not P; but from S not M we get nothing definite, neither that s
is P nor that S is not P. M is not P, but M is not S either, proves that
S and P may both be absent from the same subject (Lotze's inference
which we mentioned above).
He questions in the same way the rule ex mere particularibus nihil
sequitur. “Some only, but at least some, M's are P, and some only, but
at least some, S's are M, where we do not yet know what M's are P and
what S's are M, assures us of the possibility of at least one case in
which S is P.” But an assured possibility (in distinction from one which
is quite vague and grounded only upon complete ignorance) would seem
to be found only where it is known that S and P do not exclude each
other; can we then infer from "some men are blind and some seeing
creatures are men,” the assured possibility that in some particular case a
seeing creature may be blind? “Such premises,” he goes on to say,
“often lead to the valuable knowledge: (1) that P belongs to or is depen-
dent upon the specific or individual differences of M, though it is not
necessitated nor excluded by the conceptual content of M. (2) That M
belongs to the specific or individual differences of S, though it is neither
necessitated nor excluded by the conceptual content S. (3) that whether
388
APPENDICES
S appears with or without P this is in no way connected with the presence
or absence of M.” Propositions 1 and 2, however, are not inferred from
both premises together; they merely present an interpretation of one of
them. No doubt this one, as formulated above, “Some only, but at least
some, M's are p” consists—as Schuppe himself shows later on-in two
judgments, "Some M's are P, some M's are not P,” and it is only from
these two propositions taken together that we can infer that P is “neither
necessitated nor excluded by the concept M.” These two judgments form
the application of the major premise " that which is connected with the
predicate M at one time but not at another is neither necessitated nor
excluded by it”; according to this familiar rule we can neither say that
all M's are P nor that no M is P.
But the third of these propositions, the only one which can be inferred
from both premises, is false. Instead of some M's are P, and some S’s
are M, let us take, for example, "some regular figures are rectangular,
some quadrangles are regular figures.” We cannot say that whether the
quadrangle appears as rectangular or not this has nothing to do with the
absence or presence of the attribute regular; the regular quadrangle is of
necessity rectangular. Again, “ some crystals have double refraction, some
minerals are crystals” —must we infer from this that when we find a
mineral having double refraction this has nothing to do with the fact of its
being or not being a crystal ?
On p. 133 he continues : “It is certain that the propositions, some M's
are P, some M's are S, do not connect the predicates P and S with the
some M's because of the attribute M; if they did, then the predicates must
belong to all M's; they connect them with specific or individual differ-
ences which fall under the concept M, and thus we are assured of the
conclusion that in any particular M the attributes P and S are neither
necessitated nor excluded by the characteristic M.” But this is only true
if it is also true that some M's are not P, and some M's are not S. So
that what we do is first to infer—as above—from the first pair of premises
(MIP, MoP) that P is neither necessitated nor excluded by M, from the
second (MIS, MOS) that S is neither necessitated nor excluded by M,
and then to sum up the two judgments in one “ P and S are neither
necessitated nor excluded by the characteristic M.” But this process is
not one in which we gain a definite relation between S and P by eliminat-
ing M; no such relation can be determined in any way, not even nega-
tively, from these premises.
APPENDICES
389
“From all M's are P, no S is M, it follows that if S, or one s, is P,
it certainly is not so by virtue of M.” It is enough to know that S is
not M in order to know that S can have no other predicate by virtue
of M.
“The statement that in the form PM and SM both premises must not
be affirmative is fundamentally false ” (p. 137). Here, he holds, we may
safely infer partial identity—sometimes even affinity. The nature of M
may be such as to make this partial identity as valuable a result as the
partial difference which is also inferred in the second figure. We have
spoken on p. 85 of this term “partial identity”; if we let it pass, we find
in the long run that all things are partially identical, and the conclusion is
therefore without value. If, again, it depends upon the nature of M
whether or not it has any value, we must regard the judgment, Both P
and S are M, as a simple summation in which the middle concept is not
eliminated. That it may be useful to know this as a preliminary step
towards the operations of classification, I do not of course dispute; but
we must not call it an inference unless we are to call every combination
of two judgments into a conjunctive or copulative proposition an in-
ference.
We may make the same answer to Wundt when he brings forward an
“inference of comparison” (Logik, i. p. 324) which is, he says, sometimes
an inference of agreement, sometimes of difference. In the first case we
have “ A has the characteristic M, B has the characteristic M, therefore
A and B agree in one characteristic”; in the second “A has the charac-
teristic M, B has not the characteristic M, therefore A and B have a
distinguishing characteristic.” But what ground is there for the “there-
fore” of the first inference? Evidently it must be the major premise
that if two objects or concepts have the same characteristic they agree in
one characteristic—a mere tautology from which we can learn nothing
whatever as to any other relations between the objects or concepts com-
pared, nothing as to whether they are identical or opposed, or anything
else. In the second inference, again, the “ therefore ” presupposes, ac-
cording to Wundt's rendering, nothing more than the major premise, “if
one of two objects has a characteristic which the other has not, then they
have a distinguishing characteristic.” Here indeed very little would be
told us by the inference itself, for it would contain no more than the two
premises themselves tell us in another form. But from the fact that two
objects have a distinguishing characteristic we may further infer that they
}
390
APPENDICES .
differ as wholes, that they cannot be identical, and, when we are dealing
with concepts, that they cannot be predicated of each other in any sense.
We have therefore at least a negative determination of their relation,
and as the recognition of difference and opposition is one of the funda-
mental operations of our thought this result is certainly important. It is
not merely a question of “ partial difference,” as Schuppe represents it,
like that of “partial identity”; from partial identity nothing can be in-
ferred, but from“ partial difference " it follows (p. 138) that S and P are
not identical as wholes, that they cannot be predicated of the same thing
nor of each other. It is of course presupposed that one of the premises
contains a necessity, and that we do not compare merely casual states.
It certainly does not follow that because the stove in my room yesterday
was hot, while the stove in my room to-day is cold, therefore the second
stove is not the same as the first ; a conclusion can be drawn only when
the major premise tells us that a predicate must be necessarily affirmed or
denied of a subject, so that the absence or presence of this predicate in-
volves that of the subject itself.–From what we have said it would appear
therefore that Aristotle was perfectly right in recognising only a negative
result in the second figure, saying of two positive premises : oºk čotal
ovlloycouós.
I cannot therefore allow that this criticism of the traditional doctrine is
justified. Nevertheless Schuppe is right in emphasizing the view that in
drawing an inference from two premises we frequently obtain our con-
clusion, not from the premises by themselves, but from a major premise
which alone enables us to get any result from combining the contents of
one premise with the contents of the other. Here we must distinguish
between two cases : either one of the premises is itself a hypothetical
judgment, in which case we merely need the general principle that the
affirmation of the ground involves that of the consequence, the denial of
the consequence that of the ground; or else the two premises need a more
special principle of which they are the application, and by means of which
they yield the conclusion according to the general principle of inference.
Inferences of the first and second figure which presuppose a universal
major premise belong to the first class; inferences of the third figure to
the second.
B. Erdmann (Philos. Aufsätze zum Doctorjubiläum E. Zellers, p. 201)
maintains that by introducing definitions we may get universal affirmative
conclusions in the second and third figures ; e.g., all mammals have lacteal
APPENDICES
391
glands, all whales have lacteal glands, therefore all whales are mammals.
But he overlooks the fact that the major premise does not tell us that it is
a definition, and the conclusion does not follow from what it does tell us,
For the inference to be valid it must stand "only mammals have lacteal
glands”; i.l., that which has lacteal glands is a mammal; then, however,
our inference is in the first figure.
END OF VOL I.
Butler & Tanner, The Selwood Printing Works, Frome, and London.

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